阅读说明：本技术 测量方法、测量装置、测量系统以及存储介质 (Measuring method, measuring device, measuring system, and storage medium ) 是由 小林祥宏 于 2021-03-16 设计创作，主要内容包括：本发明提供测量方法、测量装置、测量系统以及存储介质。该测量方法包括：获取包含移动体的各部位通过第一观测点的时刻以及作为针对作用的响应的物理量的第一观测点信息的步骤；获取包含所述各部位通过第二观测点的时刻以及作为针对作用的响应的物理量的第二观测点信息的步骤；算出所述各部位引起的结构物的挠曲波形的步骤；将所述挠曲波形相加而算出移动体挠曲波形,并根据所述移动体挠曲波形算出所述路径的挠曲波形的步骤；对第三观测点的加速度进行二次积分而算出位移波形的步骤；以及根据所述路径的挠曲波形算出对积分误差进行近似的多项式的各系数的值,并根据各系数的值对所述位移波形进行校正的步骤。(The invention provides a measuring method, a measuring device, a measuring system and a storage medium. The measuring method comprises the following steps: acquiring first observation point information including a time at which each part of the moving body passes through the first observation point and a physical quantity that is a response to the action; acquiring second observation point information including a time at which each of the portions passes through a second observation point and a physical quantity that is a response to the action; calculating a deflection waveform of the structure caused by each of the portions; calculating a moving body deflection waveform by adding the deflection waveforms, and calculating a deflection waveform of the path from the moving body deflection waveform; calculating a displacement waveform by performing quadratic integration on the acceleration of the third observation point; and calculating the value of each coefficient of a polynomial approximating the integral error from the deflection waveform of the path, and correcting the displacement waveform from the value of each coefficient.)

1. A method of measurement, comprising:

a first observation point information acquisition step of acquiring first observation point information including a time when a plurality of parts of a moving body pass through a first observation point, respectively, and a physical quantity as a response to an action on the first observation point, respectively, with respect to the plurality of parts, from observation information of a first observation device observing the first observation point, which is arranged in a first direction in which the moving body moves on a path of a structure, of the first observation point, a second observation point, and a third observation point between the first observation point and the second observation point;

a second observation point information acquisition step of acquiring second observation point information including a time at which the plurality of sites respectively pass through the second observation point and a physical quantity as a response to an action of the plurality of sites on the second observation point, from observation information of a second observation device observing the second observation point;

a deflection waveform calculation step of calculating a deflection waveform of the structure caused by each of the plurality of portions, based on the first observation point information and the second observation point information, a predetermined coefficient, and an approximate expression of deflection of the structure;

a path deflection waveform calculating step of calculating a moving body deflection waveform which is a deflection waveform of the structure caused by the moving body by adding the deflection waveforms of the structures caused by the plurality of portions calculated in the deflection waveform calculating step, and calculating a deflection waveform of the path from the moving body deflection waveform;

a displacement waveform calculation step of acquiring an acceleration of a third observation point from observation information of a third observation device observing the third observation point, and performing quadratic integration on the acquired acceleration to calculate a displacement waveform of the third observation point; and

a displacement waveform correction step of calculating, from the deflection waveform of the path calculated in the path deflection waveform calculation step, values of respective coefficients of a polynomial that approximates an integration error when the acceleration is quadratic-integrated in the displacement waveform calculation step, and correcting the displacement waveform from the calculated values of the respective coefficients.

2. The measuring method according to claim 1,

in the displacement waveform correction step, the difference between the displacement waveform and the polynomial is set to be approximately proportional to the deflection waveform of the path, and the value of each coefficient of the polynomial is calculated.

3. The measurement method according to claim 2,

in the displacement waveform correction step, a value of the scaling coefficient and a value of each coefficient of the polynomial are calculated by a least square method so that a difference between a waveform obtained by multiplying the scaling coefficient by the deflection waveform of the path and a waveform obtained by subtracting the polynomial from the displacement waveform is minimized.

4. The measurement method according to claim 2,

the polynomial is a quadratic polynomial in which the values of the coefficients of the first-order term and the 0-order term are zero;

in the displacement waveform correction step, the value of the scaling factor and the value of the coefficient of the quadratic term of the polynomial are calculated by a least square method so that a difference between a waveform obtained by multiplying the scaling factor by the deflection waveform of the path and a waveform obtained by subtracting the polynomial from the displacement waveform is minimized.

5. The measurement method according to claim 2,

in the displacement waveform correcting step,

calculating a value of each coefficient of a first quadratic polynomial so as to minimize a waveform obtained by adding a first proportional coefficient and a deflection waveform of the path to the displacement waveform;

calculating a value of each coefficient of a second-order polynomial so as to minimize a waveform obtained by adding a second proportional coefficient and a second-order polynomial, which is a difference between a waveform obtained by multiplying a second proportional coefficient by a deflection waveform of the path and the displacement waveform, to the waveform;

calculating a first sum, which is a sum of values obtained by adding the first difference to the second order polynomial, over a period of the displacement waveform;

calculating a second sum which is a sum of the second difference and a second order polynomial quadratic term of the second quadratic polynomial over the period of the displacement waveform;

calculating a third scale coefficient whose sum is 0 from a relationship among the first scale coefficient, the second scale coefficient, the first sum, and the second sum, and calculating a value of each coefficient of a third quadratic polynomial, which is a difference between a waveform obtained by multiplying the third scale coefficient by a deflection waveform of the path and the displacement waveform, so as to minimize a waveform obtained by adding the third quadratic polynomial to the third quadratic polynomial;

and correcting the displacement waveform according to the value of each coefficient of the third quadratic polynomial.

6. The measurement method according to claim 2,

in the displacement waveform correcting step,

calculating a value of each coefficient of a first quadratic polynomial so as to minimize a waveform obtained by adding a first proportional coefficient and a deflection waveform of the path to the displacement waveform;

calculating a value of each coefficient of a second-order polynomial so as to minimize a waveform obtained by adding a second proportional coefficient and a second-order polynomial, which is a difference between a waveform obtained by multiplying a second proportional coefficient by a deflection waveform of the path and the displacement waveform, to the waveform;

calculating a first sum of values obtained by adding the first difference to the first quadratic polynomial, the first sum being in a period during which the amplitude of the deflection waveform of the path is not zero;

calculating a second sum of values obtained by adding the second difference to the second quadratic polynomial, the second sum being obtained during the period in which the amplitude of the deflection waveform of the path is not zero;

calculating a third scale coefficient whose sum is 0 from a relationship among the first scale coefficient, the second scale coefficient, the first sum, and the second sum, and calculating a value of each coefficient of a third quadratic polynomial, which is a difference between a waveform obtained by multiplying the third scale coefficient by a deflection waveform of the path and the displacement waveform, so as to minimize a waveform obtained by adding the third quadratic polynomial to the third quadratic polynomial;

and correcting the displacement waveform according to the value of each coefficient of the third quadratic polynomial.

7. The measuring method according to claim 1,

the polynomial is a quadratic polynomial;

in the displacement waveform correction step, the value of each coefficient of the polynomial is calculated so as to minimize the difference between the displacement waveform and the polynomial in a period in which the amplitude of the deflection waveform of the path is zero.

8. The measurement method according to any one of claims 1 to 7,

in the displacement waveform calculating step, the acceleration in a direction intersecting a plane of the structure in which the moving body moves is acquired.

9. The measurement method according to any one of claims 1 to 7,

the approximate expression for the deflection of the structure is an expression based on a structural model of the structure.

10. The measurement method according to claim 9,

the structural model is a simply supported beam with two supported ends.

11. The measurement method according to any one of claims 1 to 7,

the approximate expression of the deflection of the structure is an expression normalized with respect to the maximum amplitude of the deflection at the center position between the first observation point and the second observation point.

12. The measurement method according to any one of claims 1 to 7,

the approximate expression of the deflection of the structure is an expression of a waveform of half a wavelength of a sine wave.

13. The measurement method according to any one of claims 1 to 7,

the structure is a superstructure of a bridge;

the upper structure is a structure erected on any one of adjacent bridge seats and piers, two adjacent bridge seats or two adjacent piers;

the two end parts of the upper structure are positioned at the positions of the adjacent bridge seat and the adjacent pier, the positions of the two adjacent bridge seats or the positions of the two adjacent piers;

the bridge is a highway bridge or a railway bridge.

14. The measurement method according to any one of claims 1 to 7,

the first observation point is set at a first end of the structure;

the second observation point is set at a second end of the structure different from the first end.

15. The measurement method according to any one of claims 1 to 7,

the moving body is a railway vehicle, an automobile, a tram, a construction vehicle or a military vehicle;

the plurality of portions are axles or wheels, respectively.

16. The measurement method according to any one of claims 1 to 7,

the first observation device, the second observation device, and the third observation device are acceleration sensors.

17. The measurement method according to any one of claims 1 to 7,

the first observation device and the second observation device are impact sensors, microphones, strain gauges, or load cells.

18. The measurement method according to any one of claims 1 to 7,

the structure is a structure which can play a role in a dynamic bridge weighing system.

19. A measuring apparatus is characterized by comprising:

a first observation point information acquisition unit that acquires first observation point information including a time when a plurality of parts of a moving body pass through a first observation point, respectively, and a physical quantity that is a response to an action on the first observation point, respectively, with respect to the plurality of parts, from observation information of a first observation device that observes the first observation point, among a first observation point, a second observation point, and a third observation point between the first observation point and the second observation point, of a structure arranged in a first direction in which the moving body moves on a path of the structure;

a second observation point information acquisition unit that acquires second observation point information including a time at which each of the plurality of sites passes through the second observation point and a physical quantity that is a response to an action of each of the plurality of sites on the second observation point, from observation information of a second observation device that observes the second observation point;

a deflection waveform calculation unit that calculates a deflection waveform of the structure caused by each of the plurality of portions, based on the first observation point information and the second observation point information, a predetermined coefficient, and an approximate expression of deflection of the structure;

a path deflection waveform calculation unit that calculates a moving body deflection waveform that is a deflection waveform of the structure caused by the moving body by adding the deflection waveforms of the structure caused by the plurality of portions calculated by the deflection waveform calculation unit, and calculates a deflection waveform of the path from the moving body deflection waveform;

a displacement waveform calculation unit that acquires acceleration of a third observation point from observation information of a third observation device that observes the third observation point, and calculates a displacement waveform of the third observation point by performing quadratic integration on the acquired acceleration; and

and a displacement waveform correction unit that calculates, from the deflection waveform of the path calculated by the path deflection waveform calculation unit, values of coefficients of a polynomial that approximates an integration error when the displacement waveform calculation unit integrates the acceleration twice, and corrects the displacement waveform based on the calculated values of the coefficients.

20. A measurement system is characterized by comprising:

the measurement device of claim 19;

the first observation device;

the second observation device; and

the third observation device.

21. A storage medium storing a measurement program that causes a computer to execute:

a first observation point information acquisition step of acquiring first observation point information including a time when a plurality of parts of a moving body pass through a first observation point, respectively, and a physical quantity as a response to an action on the first observation point, respectively, with respect to the plurality of parts, from observation information of a first observation device observing the first observation point, which is arranged in a first direction in which the moving body moves on a path of a structure, of the first observation point, a second observation point, and a third observation point between the first observation point and the second observation point;

a second observation point information acquisition step of acquiring second observation point information including a time at which the plurality of sites respectively pass through the second observation point and a physical quantity as a response to an action of the plurality of sites on the second observation point, from observation information of a second observation device observing the second observation point;

a deflection waveform calculation step of calculating a deflection waveform of the structure caused by each of the plurality of portions, based on the first observation point information and the second observation point information, a predetermined coefficient, and an approximate expression of deflection of the structure;

a path deflection waveform calculating step of calculating a moving body deflection waveform which is a deflection waveform of the structure caused by the moving body by adding the deflection waveforms of the structures caused by the plurality of portions calculated in the deflection waveform calculating step, and calculating a deflection waveform of the path from the moving body deflection waveform;

a displacement waveform calculation step of acquiring an acceleration of a third observation point from observation information of a third observation device observing the third observation point, and performing quadratic integration on the acquired acceleration to calculate a displacement waveform of the third observation point; and

a displacement waveform correction step of calculating, from the deflection waveform of the path calculated in the path deflection waveform calculation step, values of respective coefficients of a polynomial that approximates an integration error when the acceleration is quadratic-integrated in the displacement waveform calculation step, and correcting the displacement waveform from the calculated values of the respective coefficients.

Technical Field

The invention relates to a measuring method, a measuring device, a measuring system and a storage medium.

Background

Patent document 1 proposes a method of continuously measuring a strain value when a vehicle passes by using a strain gauge provided In a main beam of a bridge and calculating a dynamic weighing of the axle Weight (Weight In Motion) In order to measure the axle Weight, In which the axle Weight of a large vehicle passing through the bridge is important information for predicting damage of the bridge In maintenance management of the bridge, and describes a bridge passing vehicle monitoring system for measuring the Weight of the vehicle passing through the bridge based on a strain waveform measured by the strain gauge disposed on the main beam of the bridge.

More specifically, the bridge transit monitoring system arranges strain gauges on a main beam portion for each driving lane, calculates an inter-axle ratio of the vehicle by detecting a transit timing of an axle from a strain waveform measured by the strain gauges, and determines an inter-axle distance, a vehicle speed, and a vehicle type of the vehicle by comparing the calculated inter-axle ratio with an inter-axle ratio calculated from inter-axle distances registered in an inter-axle distance database. The bridge-passing vehicle monitoring system generates a strain waveform in which a reference axle load strain waveform is arranged on a time axis in accordance with the passage timing of the axle, and compares the reference axle load strain waveform with the strain waveform measured by the strain gauge to calculate the axle load of each axle. The bridge passage vehicle monitoring system calculates the vehicle weight by summing the axle weights of the respective axles.

Patent document 1: japanese laid-open patent publication No. 2009-237805

In the system described in patent document 1, the weight of the vehicle can be measured by using the strain waveform and the inter-axle distance database, and there is no need to measure the displacement of the bridge. For example, by replacing the strain gauge with an accelerometer such as an acceleration sensor, reduction in system cost is expected. However, when the displacement of the bridge is calculated by twice integrating the acceleration value detected by the accelerometer, the calculated displacement includes a large integration error due to an offset error of the acceleration value or the like, and thus it is difficult to calculate the displacement with high accuracy.

Disclosure of Invention

One aspect of the measurement method according to the present invention includes:

a first observation point information acquisition step of acquiring first observation point information including a time when a plurality of parts of a moving body pass through a first observation point, respectively, and a physical quantity as a response to an action on the first observation point, respectively, with respect to the plurality of parts, from observation information of a first observation device observing the first observation point, which is arranged in a first direction in which the moving body moves on a path of a structure, of the first observation point, a second observation point, and a third observation point between the first observation point and the second observation point; a second observation point information acquisition step of acquiring second observation point information including a time at which the plurality of sites respectively pass through the second observation point and a physical quantity as a response to an action of the plurality of sites on the second observation point, from observation information of a second observation device observing the second observation point; a deflection waveform calculation step of calculating a deflection waveform of the structure caused by each of the plurality of portions, based on the first observation point information and the second observation point information, a predetermined coefficient, and an approximate expression of deflection of the structure; a path deflection waveform calculating step of calculating a moving body deflection waveform which is a deflection waveform of the structure caused by the moving body by adding the deflection waveforms of the structures caused by the plurality of portions calculated in the deflection waveform calculating step, and calculating a deflection waveform of the path from the moving body deflection waveform; a displacement waveform calculation step of acquiring an acceleration of a third observation point from observation information of a third observation device observing the third observation point, and performing quadratic integration on the acquired acceleration to calculate a displacement waveform of the third observation point; and a displacement waveform correction step of calculating, from the deflection waveform of the path calculated in the path deflection waveform calculation step, values of respective coefficients of a polynomial that approximates an integration error when the acceleration is quadratic-integrated in the displacement waveform calculation step, and correcting the displacement waveform based on the calculated values of the respective coefficients.

The measuring method may also be in a mode of:

in the displacement waveform correction step, the difference between the displacement waveform and the polynomial is set to be approximately proportional to the deflection waveform of the path, and the value of each coefficient of the polynomial is calculated.

The measuring method may also be in a mode of:

in the displacement waveform correction step, a value of the scaling coefficient and a value of each coefficient of the polynomial are calculated by a least square method so that a difference between a waveform obtained by multiplying the scaling coefficient by the deflection waveform of the path and a waveform obtained by subtracting the polynomial from the displacement waveform is minimized.

The measuring method may also be in a mode of:

the polynomial is a quadratic polynomial in which the values of the coefficients of the first-order term and the 0-order term are zero; in the displacement waveform correction step, the value of the scaling factor and the value of the coefficient of the quadratic term of the polynomial are calculated by a least square method so that a difference between a waveform obtained by multiplying the scaling factor by the deflection waveform of the path and a waveform obtained by subtracting the polynomial from the displacement waveform is minimized.

The measuring method may also be in a mode of:

in the displacement waveform correction step, a value of each coefficient of a first quadratic polynomial is calculated so as to minimize a waveform obtained by adding a first proportional coefficient and a deflection waveform of the path to the displacement waveform; calculating a value of each coefficient of a second-order polynomial so as to minimize a waveform obtained by adding a second proportional coefficient and a second-order polynomial, which is a difference between a waveform obtained by multiplying a second proportional coefficient by a deflection waveform of the path and the displacement waveform, to the waveform; calculating a first sum, which is a sum of values obtained by adding the first difference to the second order polynomial, over a period of the displacement waveform; calculating a second sum which is a sum of the second difference and a second order polynomial quadratic term of the second quadratic polynomial over the period of the displacement waveform; calculating a third scale coefficient whose sum is 0 from a relationship among the first scale coefficient, the second scale coefficient, the first sum, and the second sum, and calculating a value of each coefficient of a third quadratic polynomial, which is a difference between a waveform obtained by multiplying the third scale coefficient by a deflection waveform of the path and the displacement waveform, so as to minimize a waveform obtained by adding the third quadratic polynomial to the third quadratic polynomial; and correcting the displacement waveform according to the value of each coefficient of the third quadratic polynomial.

The measuring method may also be in a mode of:

in the displacement waveform correction step, a value of each coefficient of a first quadratic polynomial is calculated so as to minimize a waveform obtained by adding a first proportional coefficient and a deflection waveform of the path to the displacement waveform; calculating a value of each coefficient of a second-order polynomial so as to minimize a waveform obtained by adding a second proportional coefficient and a second-order polynomial, which is a difference between a waveform obtained by multiplying a second proportional coefficient by a deflection waveform of the path and the displacement waveform, to the waveform; calculating a first sum of values obtained by adding the first difference to the first quadratic polynomial, the first sum being in a period during which the amplitude of the deflection waveform of the path is not zero; calculating a second sum of values obtained by adding the second difference to the second quadratic polynomial, the second sum being obtained during the period in which the amplitude of the deflection waveform of the path is not zero; calculating a third scale coefficient whose sum is 0 from a relationship among the first scale coefficient, the second scale coefficient, the first sum, and the second sum, and calculating a value of each coefficient of a third quadratic polynomial, which is a difference between a waveform obtained by multiplying the third scale coefficient by a deflection waveform of the path and the displacement waveform, so as to minimize a waveform obtained by adding the third quadratic polynomial to the third quadratic polynomial; and correcting the displacement waveform according to the value of each coefficient of the third quadratic polynomial.

The measuring method may also be in a mode of:

the polynomial is a quadratic polynomial; in the displacement waveform correction step, the value of each coefficient of the polynomial is calculated so as to minimize the difference between the displacement waveform and the polynomial in a period in which the amplitude of the deflection waveform of the path is zero.

The measuring method may also be in a mode of:

in the displacement waveform calculating step, the acceleration in a direction intersecting a plane of the structure in which the moving body moves is acquired.

The measuring method may also be in a mode of:

the approximate expression for the deflection of the structure is an expression based on a structural model of the structure.

The measuring method may also be in a mode of:

the structural model is a simply supported beam with two supported ends.

The measuring method may also be in a mode of:

the approximate expression of the deflection of the structure is an expression normalized with respect to the maximum amplitude of the deflection at the center position between the first observation point and the second observation point.

The measuring method may also be in a mode of:

the approximate expression of the deflection of the structure is an expression of a waveform of half a wavelength of a sine wave.

The measuring method may also be in a mode of:

the structure is a superstructure of a bridge; the upper structure is a structure erected on any one of adjacent bridge seats and piers, two adjacent bridge seats or two adjacent piers; the two end parts of the upper structure are positioned at the positions of the adjacent bridge seat and the adjacent pier, the positions of the two adjacent bridge seats or the positions of the two adjacent piers; the bridge is a highway bridge or a railway bridge.

The measuring method may also be in a mode of:

the first observation point is set at a first end of the structure; the second observation point is set at a second end of the structure different from the first end.

The measuring method may also be in a mode of:

the moving body is a railway vehicle, an automobile, a tram, a construction vehicle or a military vehicle; the plurality of portions are axles or wheels, respectively.

The measuring method may also be in a mode of:

the first observation device, the second observation device, and the third observation device are acceleration sensors.

The measuring method may also be in a mode of:

the first observation device and the second observation device are impact sensors, microphones, strain gauges, or load cells.

The measuring method may also be in a mode of:

the structure is a structure which can play a function in a BWIM (Bridge weight in Motion) system.

An aspect of a measuring apparatus according to the present invention includes: a first observation point information acquisition unit that acquires first observation point information including a time when a plurality of parts of a moving body pass through a first observation point, respectively, and a physical quantity that is a response to an action on the first observation point, respectively, with respect to the plurality of parts, from observation information of a first observation device that observes the first observation point, among a first observation point, a second observation point, and a third observation point between the first observation point and the second observation point, of a structure arranged in a first direction in which the moving body moves on a path of the structure; a second observation point information acquisition unit that acquires second observation point information including a time at which each of the plurality of sites passes through the second observation point and a physical quantity that is a response to an action of each of the plurality of sites on the second observation point, from observation information of a second observation device that observes the second observation point; a deflection waveform calculation unit that calculates a deflection waveform of the structure caused by each of the plurality of portions, based on the first observation point information and the second observation point information, a predetermined coefficient, and an approximate expression of deflection of the structure; a path deflection waveform calculation unit that calculates a moving body deflection waveform that is a deflection waveform of the structure caused by the moving body by adding the deflection waveforms of the structure caused by the plurality of portions calculated by the deflection waveform calculation unit, and calculates a deflection waveform of the path from the moving body deflection waveform; a displacement waveform calculation unit that acquires acceleration of a third observation point from observation information of a third observation device that observes the third observation point, and calculates a displacement waveform of the third observation point by performing quadratic integration on the acquired acceleration; and a displacement waveform correction unit that calculates, from the deflection waveform of the path calculated by the path deflection waveform calculation unit, values of coefficients of a polynomial that approximates an integration error when the displacement waveform calculation unit integrates the acceleration twice, and corrects the displacement waveform based on the calculated values of the coefficients.

One aspect of the measurement system according to the present invention includes: a mode of the measuring device; the first observation device; the second observation device; and the third observation device.

The storage medium according to the present invention stores a measurement program for causing a computer to execute the steps of: a first observation point information acquisition step of acquiring first observation point information including a time when a plurality of parts of a moving body pass through a first observation point, respectively, and a physical quantity as a response to an action on the first observation point, respectively, with respect to the plurality of parts, from observation information of a first observation device observing the first observation point, which is arranged in a first direction in which the moving body moves on a path of a structure, of the first observation point, a second observation point, and a third observation point between the first observation point and the second observation point; a second observation point information acquisition step of acquiring second observation point information including a time at which the plurality of sites respectively pass through the second observation point and a physical quantity as a response to an action of the plurality of sites on the second observation point, from observation information of a second observation device observing the second observation point; a deflection waveform calculation step of calculating a deflection waveform of the structure caused by each of the plurality of portions, based on the first observation point information and the second observation point information, a predetermined coefficient, and an approximate expression of deflection of the structure; a path deflection waveform calculating step of calculating a moving body deflection waveform which is a deflection waveform of the structure caused by the moving body by adding the deflection waveforms of the structures caused by the plurality of portions calculated in the deflection waveform calculating step, and calculating a deflection waveform of the path from the moving body deflection waveform; a displacement waveform calculation step of acquiring an acceleration of a third observation point from observation information of a third observation device observing the third observation point, and performing quadratic integration on the acquired acceleration to calculate a displacement waveform of the third observation point; and a displacement waveform correction step of calculating, from the deflection waveform of the path calculated in the path deflection waveform calculation step, values of respective coefficients of a polynomial that approximates an integration error when the acceleration is quadratic-integrated in the displacement waveform calculation step, and correcting the displacement waveform based on the calculated values of the respective coefficients.

Drawings

Fig. 1 is a diagram showing an example of a configuration of a measurement system.

Fig. 2 is a diagram showing an example of arrangement of sensors and observation points.

Fig. 3 is a diagram showing an example of arrangement of sensors and observation points.

Fig. 4 is a diagram showing an example of arrangement of sensors and observation points.

Fig. 5 is an explanatory diagram of the acceleration detected by the acceleration sensor.

Fig. 6 is a diagram showing an example of the axle information.

Fig. 7 is a diagram showing an example of arrangement of sensors and observation points.

Fig. 8 is a diagram showing an example of arrangement of sensors and observation points.

Fig. 9 is a diagram showing an example of arrangement of the sensors and the observation points.

Fig. 10 is a diagram showing an example of the acceleration detected at the observation point.

Fig. 11 is a graph in which the acceleration amplitude at each time point in fig. 10 is converted into the acceleration intensity.

Fig. 12 is a graph in which the acceleration intensity of fig. 11 is binarized by a predetermined threshold value.

Fig. 13 is a diagram of the pattern at the exit timing slid with respect to fig. 12.

Fig. 14 is an explanatory diagram of a structural model of the superstructure of the bridge.

Fig. 15 is an explanatory diagram of a structural model of the superstructure of the bridge.

Fig. 16 is a diagram showing an example of a waveform of the normalized deflection amount.

Fig. 17 is a diagram showing an example of a normalized deflection model.

Fig. 18 is a diagram showing an example of a deflection waveform of the bridge by each axle.

Fig. 19 is a diagram showing an example of a vehicle deflection waveform.

Fig. 20 is a diagram showing an example of a displacement waveform.

Fig. 21 is a diagram showing an example of a displacement waveform after correction.

Fig. 22 is a flowchart showing an example of the procedure of the measurement method according to the first embodiment.

Fig. 23 is a flowchart showing an example of the procedure of the deflection waveform calculation step.

Fig. 24 is a flowchart showing an example of the procedure of the route deflection waveform calculation step.

Fig. 25 is a flowchart showing an example of the procedure of the displacement waveform correction step in the first embodiment.

Fig. 26 is a diagram showing a configuration example of the measuring apparatus according to the first embodiment.

Fig. 27 is a diagram showing an example of a displacement waveform corrected in the second embodiment.

Fig. 28 is a diagram showing another example of the displacement waveform corrected in the second embodiment.

Fig. 29 is a flowchart showing an example of the procedure of the displacement waveform correction step in the second embodiment.

Fig. 30 is a diagram showing an example of a correlation straight line between the scale coefficient and the sum of residuals in the third embodiment.

Fig. 31 is a diagram showing an example of a displacement waveform corrected in the second embodiment.

Fig. 32 is a flowchart illustrating an example of the procedure of the displacement waveform correction step in the third embodiment.

Fig. 33 is a diagram showing an example of a relationship between a path deflection waveform and a function in the fourth embodiment.

Fig. 34 is a flowchart showing an example of the procedure of the displacement waveform correction step in the fourth embodiment.

Fig. 35 is a diagram showing an example of a relationship between a path deflection waveform and a function in the fifth embodiment.

Fig. 36 is a diagram showing an example of a quadratic polynomial representing an approximate integration error in the fifth embodiment.

Fig. 37 is a diagram showing an example of a displacement waveform in the fifth embodiment.

Fig. 38 is a flowchart showing an example of the procedure of the displacement waveform correction step in the fifth embodiment.

Fig. 39 is a diagram showing an example of the relationship between the path deflection waveform and three times in the sixth embodiment.

Fig. 40 is a diagram showing an example of a displacement waveform corrected in the sixth embodiment.

Fig. 41 is a diagram showing another example of the displacement waveform corrected in the sixth embodiment.

Fig. 42 is a graph showing a correlation curve between the displacement waveform and the displacement model waveform shown in fig. 40.

Fig. 43 is a graph showing a correlation curve between the displacement waveform and the displacement model waveform shown in fig. 41.

Fig. 44 is a flowchart showing an example of the procedure of the displacement waveform correction step in the sixth embodiment.

Fig. 45 is a flowchart showing another example of the procedure of the displacement waveform correction step in the sixth embodiment.

Fig. 46 is a diagram showing an example of a waveform of the normalized deflection amount in the seventh embodiment.

Description of the reference numerals

1 … measuring device, 2 … server, 4 … communication network, 5 … bridge, 6 … vehicle, 7 … superstructure, 7a … bridge deck, 7b … support, G … girder, F … floor, 8 … substructure, 8a … pier, 8b … bridge seat, 10 … measuring system, 21 … sensor, 22 … sensor, 23 … sensor, 110 … control section, 111 … first observation point information acquisition section, 112 … second observation point information acquisition section, 113 … deflection waveform calculation section, 114 … path deflection waveform calculation section, 115 … displacement waveform calculation section, 116 … displacement waveform correction section, 117 … output processing section, 120 … first communication section, 130 … storage section, 131 … measuring program, 140 … second communication section, 150 … operation section.

Detailed Description

Hereinafter, preferred embodiments of the present invention will be described in detail with reference to the accompanying drawings. The embodiments described below are not intended to unduly limit the contents of the present invention recited in the claims. Not all of the configurations described below are essential components of the present invention.

1. First embodiment

1-1. measuring system

Hereinafter, a description will be given of a measurement system for implementing the measurement method of the present embodiment, taking as an example a case where the structure is an upper structure of a bridge and the moving body is a vehicle. The vehicle passing through the Bridge according to the present embodiment is a vehicle that has a large weight and can be measured by a Bridge dynamic weighing (BWIM) system, such as a railway vehicle, an automobile, a railroad car, a construction vehicle, or a military vehicle. BWIM is a technology for measuring the weight, the number of axles, and the like of a vehicle passing through a bridge by measuring the deformation of the bridge, considering the bridge as a "balance". The superstructure of the bridge, which can analyze the weight of passing vehicles from the responses of deformation, strain, etc., is a structure in which BWIM functions, and a BWIM system, which applies a physical process between the action on the superstructure of the bridge and the response, can measure the weight of passing vehicles.

Fig. 1 is a diagram showing an example of a measurement system according to the present embodiment. As shown in fig. 1, the measurement system 10 according to the present embodiment includes a measurement device 1, at least one sensor 21 provided on the superstructure 7 of the bridge 5, at least one sensor 22, and at least one sensor 23. In addition, the measurement system 10 may have the server 2.

The bridge 5 is composed of an upper structure 7 and a lower structure 8, and the upper structure 7 includes a deck 7a composed of a floor F, a girder G, a cross beam not shown, and the like, and a support 7 b. The substructure 8 includes piers 8a and bridge seats 8 b. The superstructure 7 is a structure that is bridged between the adjacent bridge abutment 8b and the pier 8a, between the adjacent two bridge abutments 8b, or between the adjacent two piers 8 a. Both end portions of the superstructure 7 are located at the positions of the adjacent bridge abutment 8b and the pier 8a, the positions of the adjacent two bridge abutments 8b, or the positions of the adjacent two piers 8 a.

The measuring apparatus 1 and the sensors 21, 22, and 23 are connected by a cable (not shown), for example, and communicate via a communication Network such as a CAN (Controller Area Network). Alternatively, the measurement device 1 and the sensors 21, 22, and 23 may communicate via a wireless network.

For example, each sensor 21 outputs data indicating an impact caused by the vehicle 6 as a moving body entering the superstructure 7, and each sensor 22 outputs data indicating an impact caused by the vehicle 6 exiting the superstructure 7. In addition, for example, each sensor 23 outputs data for calculating the displacement of the upper structure 7 caused by the movement of the vehicle 6 as a moving body. In the present embodiment, each of the sensors 21, 22, and 23 is an acceleration sensor, and may be a crystal acceleration sensor or an MEMS (Micro Electro Mechanical Systems) acceleration sensor, for example.

In the present embodiment, each sensor 21 is provided at a first end portion in the longitudinal direction of the upper structure 7, and each sensor 22 is provided at a second end portion different from the first end portion in the longitudinal direction of the upper structure 7.

Each sensor 21 detects the acceleration of the superstructure 7 generated when the vehicle 6 enters the superstructure 7, and each sensor 22 detects the acceleration of the superstructure 7 generated when the vehicle 6 exits the superstructure 7. That is, in the present embodiment, each sensor 21 is an acceleration sensor that detects that the vehicle 6 enters the upper structure 7, and each sensor 22 is an acceleration sensor that detects that the vehicle 6 exits the upper structure 7.

Each sensor 23 is provided at the center in the longitudinal direction of the upper structure 7. However, each sensor 23 may be provided at a position not limited to the center of the upper structure 7 as long as it can detect acceleration for calculating the displacement of the upper structure 7.

The floor F, the main beam G, and the like of the upper structure 7 deform and flex vertically downward by a load applied to the vehicle 6 traveling on the upper structure 7. Each sensor 23 detects acceleration of deflection of the floor F and the main beam G caused by a load of the vehicle 6 traveling on the upper structure 7.

The measurement device 1 calculates the displacement of the deflection of the upper structure 7 caused by the travel of the vehicle 6 based on the acceleration data output from the sensors 21, 22, 23.

The measurement device 1 and the server 2 can communicate with each other via a communication network 4 such as the internet or a wireless network of a mobile phone. The measurement device 1 transmits information such as the time when the vehicle 6 travels on the superstructure 7 and the displacement of the superstructure 7 caused by the travel of the vehicle 6 to the server 2. The server 2 may store the information in a storage device, not shown, and perform processing such as monitoring of an overloaded vehicle and determination of an abnormality of the upper structure 7 based on the information.

In the present embodiment, the bridge 5 is a road bridge, such as a steel bridge or a girder bridge, an RC (Reinforced Concrete) bridge, or the like.

Fig. 2, 3, and 4 are views showing examples of installation of the sensors 21, 22, and 23 on the upper structure 7. Fig. 2 is a view of the upper structure 7 as viewed from above, fig. 3 is a sectional view of fig. 2 taken along line a-a, and fig. 4 is a sectional view of fig. 2 taken along line B-B or line C-C.

As shown in fig. 2, 3, and 4, the upper structure 7 has N lanes L as first to N-th paths along which the vehicle 6 as a moving body can move₁～L_NAnd K main beams G₁～G_K. Here, N, K are each an integer of 1 or more. In the examples of fig. 2, 3, and 4, the main beam G₁～G_KEach position and lane L of₁～L_NN is K-1, but the main beam G is identical₁～G_KDoes not necessarily have to be in contact with the lane L₁～L_NThe positions of the boundaries (2) are identical, but N.noteq.K-1 may be used.

In the examples of fig. 2, 3, and 4, the first end EA1 in the longitudinal direction of the upper structure 7 is provided at the main beam G₁～G_K-1Are respectively provided with sensors 21, and are arranged at the second end EA2 in the length direction of the upper structure 7 and at the main beam G₁～G_K-1On which sensors 22 are respectively arranged.

Further, at the central portion CA in the longitudinal direction of the upper structure 7, at the main beam G₁～G_K-1Are provided with sensors 23, respectively. In the examples of fig. 2, 3 and 4, N-K-1, the main beam G_KThe sensors 21, 22 and 23 are not arranged on the main beam G, but the main beam G can be arranged on_KIs provided with sensors 21, 22, 23, and a main beam G₁～G_K-1None of the sensors 21, 22, 23 is provided. Alternatively, N ═ K may be provided in the main beam G₁～G_KAre provided with sensors 21, 22, 23, respectively.

Further, since the sensors 21, 22, and 23 are provided on the floor F of the superstructure 7 and may be damaged by the traveling vehicle and the measurement accuracy may be affected by local deformation of the deck 7a, the sensors 21, 22, and 23 are provided on the girder G of the superstructure 7 in the examples of fig. 2, 3, and 4₁～G_K-1The above.

In the present embodiment, N observation points P are provided corresponding to each of N sensors 21₁～P_N. Observation point P₁～P_NAre N observation points of the superstructure 7 arranged along a second direction intersecting the first direction in which the vehicle 6 moves on the superstructure 7. In the examples of fig. 2, 3, and 4, observation point P is observed for each integer j of 1 or more and N or less_jAt the first endThe part EAl is arranged on the main beam G_jThe surface position of the floor F vertically above the sensor 21 provided thereon.

I.e. in the main beam G_jThe upper sensor 21 is an observation point P_jThe observation device of (1). To observation point P_jThe sensor 21 for observation may be provided at the observation point P so long as it can detect the traveling of the vehicle 6_jThe position of the generated acceleration may be sufficient, but it is preferable to set the position close to observation point P_jAt the location of (a). Thus, observation point P₁～P_NIn a one-to-one correspondence with the N sensors 21.

In the present embodiment, N observation points Q are set corresponding to each of N sensors 22₁～Q_N. Observation point Q₁～Q_NAre N observation points of the superstructure 7 arranged along a third direction intersecting the first direction in which the vehicle 6 moves on the superstructure 7. In the examples of fig. 2, 3, and 4, observation point Q is observed for each integer j of 1 or more and N or less_jIs set at the second end EA2 and is positioned at the main beam G_jThe surface position of the floor F vertically above the sensor 22 provided thereon. I.e. in the main beam G_jThe upper sensor 22 is an observation point Q_jThe observation device of (1). To observation point Q_jSensor 22 for observation may be provided at observation point Q so as to be able to detect traveling of vehicle 6_jThe position of the generated acceleration may be sufficient, but it is preferable to set the position close to observation point Q_jAt the location of (a). Thus, observation point Q₁～Q_NIn a one-to-one correspondence with the N sensors 22.

In the present embodiment, N observation points R are set corresponding to each of N sensors 23₁～R_N. Observation point R₁～R_NAre N observation points of the superstructure 7 aligned along a fourth direction intersecting the first direction in which the vehicle 6 moves on the superstructure 7. In the examples of fig. 2, 3, and 4, observation point R is observed for each integer j of 1 or more and N or less_jSet at the center part CA to be positioned at the main beam G_jThe ground vertically above the sensor 23 provided thereonSurface position of plate F. I.e. in the main beam G_jThe upper sensor 23 is an observation point R_jThe observation device of (1). To observation point R_jSensor 23 for observation may be provided at observation point R so long as it can detect traveling of vehicle 6_jThe position of the generated acceleration may be sufficient, but it is preferable to set the position close to observation point R_jAt the location of (a). Thus, observation point R₁～R_NIn a one-to-one correspondence with the N sensors 23.

In the present embodiment, N observation points P₁～P_NRespectively with the lane L₁～L_NAnd (7) corresponding. Likewise, N observation points Q₁～Q_NRespectively with the lane L₁～L_NAnd (7) corresponding. Likewise, N observation points R₁～R_NRespectively with the lane L₁～L_NAnd (7) corresponding. Relative to each integer j of more than 1 and less than N and the lane L_jObservation point P set correspondingly_jAnd an observation point Q_jAnd observation point P_jAnd observation point Q_jObservation point R between_jAlong the lane L of the vehicle 6 at the superstructure 7_jArranged in a first direction of upward movement. In the examples of fig. 2, 3 and 4, the first direction is along the lane L of the superstructure 7₁～L_NI.e. the length direction of the superstructure 7. The second direction, the third direction, and the fourth direction are Y directions orthogonal to the X direction within the traveling plane of the upper structure 7 on which the vehicle 6 travels, that is, width directions of the upper structure 7. However, in lane L₁～L_NIn the case of curved shapes or the like, the second direction, the third direction, and the fourth direction may be different from each other. In addition, the second direction, the third direction, and the fourth direction may not be orthogonal to the first direction, and may be, for example, from an end portion of the superstructure 7 on the vehicle 6 entrance side to the observation point P₁～P_NFrom the end of the superstructure 7 on the vehicle 6 exit side to the observation point Q₁～Q_NMay also be different. In addition, for example, from one end of superstructure 7 to observation point R₁～R_NMay also be different. In addition, the integer of 1 to N is not less thanj, observation point P_jIs an example of a "first observation point", observation point Q_jIs an example of a "second observation point", observation point R_jThis is an example of the "third observation point".

The number and the installation position of the N sensors 21, 22, and 23 are not limited to the examples shown in fig. 2, 3, and 4, and various modifications can be made.

The measurement device 1 acquires acceleration in a fifth direction intersecting the X direction as the first direction and the Y direction as the second direction, the third direction, and the fourth direction, respectively, from the acceleration data output from the sensors 21, 22, and 23. Observation point P₁～P_N、Q₁～Q_NThe observation point R is displaced in the direction orthogonal to the X-direction and the Y-direction by the impact₁～R_NSince the floor panel is deflected in the direction orthogonal to the X direction and the Y direction, the measuring device 1 preferably acquires the acceleration in the fifth direction orthogonal to the X direction and the Y direction, that is, the normal direction of the floor panel F, in order to accurately calculate the magnitude of the impact and the magnitude of the deflected acceleration.

Fig. 5 is a diagram illustrating the acceleration detected by the sensors 21, 22, and 23. The sensors 21, 22, and 23 are acceleration sensors that detect acceleration generated in each of three axes orthogonal to each other.

Applied to observation point P in order to detect the entry of vehicle 6 into superstructure 7₁～P_NThe sensors 21 are arranged such that one of the three detection axes, i.e., the x-axis, the y-axis, and the z-axis, is in a direction intersecting the first direction and the second direction. Likewise, to detect the application to observation point Q due to vehicle 6 exiting superstructure 7₁～Q_NThe sensors 22 are arranged such that one of the three detection axes, i.e., the x-axis, the y-axis, and the z-axis, is in a direction intersecting the first direction and the third direction. In addition, in order to detect observation point R caused by traveling of vehicle 6₁～R_NThe sensors 23 are arranged such that one of the three detection axes, i.e., the x-axis, the y-axis, and the z-axis, is a direction intersecting the first direction and the fourth direction. In the examples of fig. 2, 3 and 4, the first direction is XSince the second direction, the third direction, and the fourth direction are Y directions, the sensors 21, 22, and 23 are arranged such that one axis intersects the X direction and the Y direction. Observation point P₁～P_N、Q₁～Q_NSince the sensor 21 and the sensor 22 are displaced in the direction orthogonal to the X direction and the Y direction by the impact, it is desirable that the sensors are provided so that one axis is aligned with the direction orthogonal to the X direction and the Y direction, that is, the normal direction of the floor F in order to accurately detect the magnitude of the impact. In addition, due to observation point R₁～R_NSince the sensor 23 deflects in the direction orthogonal to the X direction and the Y direction, it is preferable to provide each sensor 23 so that one axis is aligned with the direction orthogonal to the X direction and the Y direction, that is, the normal direction of the floor F, in order to accurately detect the acceleration of the deflection.

However, when the sensors 21, 22, and 23 are provided in the upper structure 7, the installation location may be inclined. Even if the measuring apparatus 1 is not installed with one of the three detection axes of the sensors 21, 22, and 23 aligned with the normal direction of the floor F, the error is small and negligible because the error is substantially oriented toward the normal direction. Even if the measuring apparatus 1 is not installed with one of the three detection axes of the sensors 21, 22, and 23 aligned with the normal direction of the floor F, the detection error caused by the inclination of the sensors 21, 22, and 23 can be corrected by the three-axis synthesized acceleration obtained by synthesizing the accelerations of the x-axis, the y-axis, and the z-axis. Each of the sensors 21, 22, and 23 may be a uniaxial acceleration sensor that detects acceleration occurring at least in a direction substantially parallel to the vertical direction or acceleration in the normal direction of the floor F.

The following describes in detail the measurement method of the present embodiment executed by the measurement device 1.

1-2. Generation of axle information

In the present embodiment, the measurement device 1 acquires, from acceleration data as observation information obtained by the N sensors 21 as observation devices, first observation point information including respective passage observations of a plurality of portions of the vehicle 6 as a moving bodyMeasuring point P_jAnd as observation points P for the respective plurality of parts_jThe physical quantity of the response of the effect of (c). Likewise, in the present embodiment, the measurement device 1 acquires second observation point information including the passage of each of the plurality of portions of the vehicle 6 through the observation point Q from the acceleration data as the observation information obtained by the N sensors 22 as the observation devices_jAnd as observation points Q for the respective plurality of parts_jThe physical quantity of the response of the effect of (c). Here, j is an integer of 1 to N.

In the present embodiment, it is considered that loads generated by a plurality of axles or wheels of vehicle 6 are applied to upper structure 7, and a plurality of portions to be targets of acquiring the first observation point information and the second observation point information are axles or wheels, respectively. Hereinafter, in the present embodiment, the plurality of portions are each an axle.

In the present embodiment, each sensor 21 as an acceleration sensor detects that a plurality of axles respectively face observation point P_jThe resulting acceleration. Similarly, each sensor 22 as an acceleration sensor detects that a plurality of axles respectively face the observation point Q_jThe resulting acceleration.

In the present embodiment, as shown in fig. 2, observation point P₁～P_NIs set at a first end EA1 and an observation point Q₁～Q_NIs set at the second end EA 2. Therefore, it is possible to pass each of the plurality of axles of vehicle 6 through observation point P_jIs regarded as the entry time of each axle into the superstructure 7, more specifically into the lane L_jThe entry time of (c). In addition, a plurality of axles of vehicle 6 may pass observation point Q, respectively_jIs regarded as the exit time of each axle from the superstructure 7, more specifically, the exit lane L_jThe exit time of (c).

Therefore, in the present embodiment, the first observation point information includes the entrance of each axle of the vehicle 6 into the lane L_jAnd as the entry into the lane L for each axle_jThe physical quantity of the response of the time-of-flight action is the acceleration intensity. In additionIn addition, the second observation point information includes each axle exit lane L of the vehicle 6_jAnd as the exit lane L for each axle_jThe physical quantity of the response of the time-of-flight action is the acceleration intensity.

Further, since the entry and exit of each axle of vehicle 6 correspond to each other, each vehicle and each axle can be classified based on the first observation point information and the second observation point information, and the first observation point information, the second observation point information, and the classification information thereof are referred to as axle information.

That is, the axle information includes the entry lane L for each axle in addition to the first observation point information and the second observation point information_jThe entry time of the vehicle 6, the acceleration intensity at the time of entry, the exit time of the vehicle from the lane Lj, and the correspondence information of the acceleration intensity at the time of exit for each axle, and the correspondence information of the correspondence information between the vehicle 6 and each axle. Therefore, based on the axle information, the lane L through which each axle passes is determined for each vehicle 6 that passes through the upper structure 7_jPassing through observation point P_j、Q_jThe time of day and the intensity of the acceleration as it passes.

Fig. 6 shows an example of the axle information. In the example of fig. 6, the information on the first to fourth rows is information relating to the vehicle 6 of the vehicle number 1. The information on the first row is information on the first axle with axle number 1, the information on the second row is information on the second axle with axle number 2, the information on the third row is information on the third axle with axle number 3, and the information on the fourth row is information on the fourth axle with axle number 4. For example, the correspondence information of the first row indicates that the first axle of the axle number 1 of the vehicle 6 of the vehicle number 1 enters the lane L₂The entry time of (1) is ti11, the acceleration intensity during entry is pai11, and the following lane L₂The exit timing of the exit was to11, and the acceleration intensity at the exit was pao 11.

The information on the fifth to sixth rows is information on the vehicle 6 of the vehicle number 2. Information of the fifth line is correspondence information relating to the first axle of axle number 1, and information of the sixth lineIs the correspondence information relating to the second axle of axle number 2. For example, the correspondence information of the fifth row indicates that the first axle of the axle number 1 of the vehicle 6 of the vehicle number 2 enters the lane L₁The entry time of (1) is ti21, the acceleration intensity during entry is pai21, and the following lane L₁The exit timing of the exit was to21, and the acceleration intensity at the exit was pao 21.

The information on the seventh to eighth rows is information on the vehicle 6 of the vehicle number 3. The information on the seventh row is correspondence information relating to the first axle of axle number 1, and the information on the eighth row is correspondence information relating to the second axle of axle number 2. For example, the correspondence information of the seventh row indicates that the first axle of the axle number 1 of the vehicle 6 of the vehicle number 3 enters the lane L₁The entry time of (1) is ti31, the acceleration intensity during entry is pai31, and the following lane L₁The exit timing of the exit was to31, and the acceleration intensity at the exit was pao 31.

As an example, fig. 7, 8, and 9 show sensors 21 and 22 and observation point P when N is 2₁、P₂、Q₁、Q₂The procedure of the arrangement example of (1) to generate the axle information in the arrangement examples shown in fig. 7, 8, and 9 will be described.

Fig. 7 is a view of the upper structure 7 as viewed from above, fig. 8 is a sectional view of fig. 7 taken along line a-a, and fig. 9 is a sectional view of fig. 7 taken along line B-B or line C-C. In the examples of fig. 7, 8 and 9, the two sensors 21 are respectively provided at the first end EA1 of the superstructure 7 on the main beam G₁、G₃In addition, two sensors 22 are respectively arranged on the main beam G at the second end EA2 of the superstructure 7₁、G₃The above. In addition, with the lane L₁Corresponding observation point P₁、Q₁Are respectively arranged on the main beam G₁The sensors 21 and 22 are provided on the floor F vertically above the floor, and the lane L₂Corresponding observation point P₂、Q₂Are respectively arranged on the main beam G₃The surface position of the floor F vertically above the sensors 21 and 22 provided thereonThe above. Arranged on the main beam G₁Upper sensor 21 to observation point P₁Observe and arrange in the main beam G₃Upper sensor 21 to observation point P₂And (6) carrying out observation. In addition, is arranged on the main beam G₁Upper sensor 22 to observation point Q₁Observe and arrange in the main beam G₃Upper sensor 22 to observation point Q₂And (6) carrying out observation. Further, two sensors 23 are provided at the center CA of the upper structure 7, respectively, on the main beam G₁、G₃The above. In addition, with the lane L₁Corresponding observation point R₁Is set at and positioned on the main beam G₁The sensor 23 is provided on the surface of the floor F vertically above the floor, and the lane L₂Corresponding observation point R₂Is set at and positioned on the main beam G₃The sensor 23 is provided at a position on the surface of the floor F vertically above the floor. Arranged on the main beam G₁Upper sensor 23 to observation point R₁Observe and arrange in the main beam G₃Upper sensor 23 to observation point R₂And (6) carrying out observation.

The measuring apparatus 1 converts the acceleration at each time detected by each sensor 21, 22 into an amplitude, and acquires the acceleration intensity to generate axle information. Further, the acceleration detected by the sensor 23 is not used to acquire the axle information.

FIG. 10 shows a four-axis vehicle 6 in lane L₂Relative to observation point P during middle travel₁、P₂、Q₁、Q₂An example of the detected acceleration is shown. Fig. 11 is a graph in which the acceleration amplitude at each time point in fig. 10 is converted into the acceleration intensity. In the example of fig. 10 and 11, the vehicle 6 is in the lane L₂In the middle travel, the four axles of the vehicle 6 pass through the observation points P₂、Q₂A greater acceleration intensity is obtained at the moment of time. At four axles passing through observation points P₂The acceleration intensity obtained at the time of (a) is included in the first observation point information. In addition, the four axles pass through the observation points Q respectively₂The acceleration intensity obtained at the time of (a) is included in the second observation point information.

Furthermore, the measuring device 1 depends from the first axleThe time when the obtained acceleration intensity exceeds the predetermined threshold is obtained as the passing observation point P of each axle₂、Q₂At the time when each axle enters the lane L₂The time of entry and the secondary lane L₂Exit time of exit.

Fig. 12 is a graph in which the acceleration intensity of fig. 11 is binarized by a predetermined threshold value. In the example of fig. 12, it is obtained that four axles enter the lane L, respectively₂The time of entry and the secondary lane L₂Exit time of exit. Four axles enter the lane L respectively₂Is included in the first observation point information.

In addition, four axles are respectively driven from the lane L₂The exit time of the exit is included in the second observation point information.

Further, the measuring apparatus 1 brings the four axles into the lanes L, respectively₂Pattern 1 at the time of entry of (a) and four axles are respectively driven from the lane L₂The patterns 2 at the exit timing of the exit are compared to determine whether or not the two patterns are generated by the passage of the same vehicle 6. Since the intervals of the four axles do not change, the patterns 1, 2 coincide when the speed at which the vehicle 6 travels in the superstructure 7 is fixed. For example, the measuring apparatus 1 determines that the patterns 1 and 2 are generated when the pattern 1 and 2 are passed by the same vehicle 6 when the timing of any one of the patterns 1 and 2 is slid so that the entry timing and the exit timing of the first axle coincide with each other and the difference between the entry timing and the exit timing of each of the second to fourth axles is equal to or less than a predetermined threshold value, and determines that the patterns 1 and 2 are generated when the difference is greater than the predetermined threshold value. In order to prevent the multiple axles of the preceding vehicle 6 and the multiple axles of the following vehicle 6 from being mistakenly recognized as the axle of one vehicle 6 when two vehicles 6 travel in succession in one lane at the same speed, the measuring device 1 may divide the entry time and the exit time of two consecutive axles into two vehicles 6 when the interval between the entry time and the exit time of the two axles is equal to or greater than a predetermined time difference.

FIG. 13 is a view of FIG. 12 with four axles extending from lane L₂Pattern 2 at the exit timing of the exit slides to make the first oneThe entry time and the exit time of the axle coincide with each other. Fig. 13 is enlarged in the horizontal axis direction with respect to fig. 12. In the example of fig. 13, four axles enter the lane L, respectively₂Pattern 1 at the time of entry of (a) and four axles are respectively driven from the lane L₂The patterns 2 at the exit timing of the exit are almost identical, and it is determined that the patterns 1 and 2 are generated when the same vehicle 6 passes.

Furthermore, the measuring device 1 makes the lane L shown in FIG. 12 accessible₂Four entry times of (2), observation point P shown in fig. 11₂Four peak values of the acceleration intensity of (2), the slave lane L shown in fig. 12₂Four exit timings for exiting and observation point Q shown in fig. 11₂The peak values of the four acceleration intensities of (a) and (b) sequentially correspond from the first to obtain correspondence information of the first axle, correspondence information of the second axle, correspondence information of the third axle, and correspondence information of the fourth axle. Further, the measuring apparatus 1 acquires the lane L₂The vehicle 6 running in the middle has correspondence information obtained by associating the correspondence information of the four axles. These pieces of information are included in the axle information together with the first observation point information and the second observation point information.

The measuring device 1 can be used for the lane L passing through the superstructure 7 according to the axle information_jAnd determines each axle entry observation point P of the vehicle 6_jTime of entry of (2) and observation point P caused by each axle_jAcceleration intensity of (1), each axle from observation point Q_jExit timing of exit and observation point Q by each axle_jThe acceleration intensity of (2).

1-3. Generation of Path deflection waveforms

In the present embodiment, in the superstructure 7 of the bridge 5, it is considered that the floor F and the girder G will be constructed of_l～G_KOne or a plurality of such bridge decks 7a are arranged in series, and the measuring device 1 calculates the displacement of one bridge deck 7a from the displacement at the center in the longitudinal direction. The load applied to the superstructure 7 moves from one end of the superstructure 7 to the other. At this time, the central portion of the upper structure 7 can be expressed using the position of the load on the upper structure 7 and the load amountThe amount of deflection. In the present embodiment, in order to express the deflection deformation of the vehicle 6 when the axle moves on the upper structure 7 as a trace of the deflection amount generated by the movement of the one-point load on the beam, the deflection amount at the center portion is calculated in consideration of the structural model shown in fig. 14. In fig. 14, P is a load. a is the load position from the end of the superstructure 7 on the vehicle 6 entry side. b is the load position from the end of the superstructure 7 on the vehicle 6 exit side. I is the distance between the two ends of the superstructure 7. The structural model shown in fig. 14 is a simple beam that supports both ends with both ends as fulcrums.

In the structural model shown in fig. 14, when the position of the end of the upper structure 7 on the vehicle 6 entrance side is set to zero and the observed position of the deflection is set to x, the bending moment M of the simply supported beam is expressed by equation (1).

[ mathematical formula 1 ]

In the formula (1), the function H_aIs defined as formula (2).

[ mathematical formula 2 ]

The formula (1) is modified to obtain the formula (3).

[ mathematical formula 3 ]

On the other hand, the bending moment M is represented by equation (4). In formula (4), θ is an angle, I is a quadratic moment, and E is a young's modulus.

[ mathematical formula 4 ]

Formula (5) is obtained by substituting formula (4) for formula (3).

[ math figure 5 ]

Equation (6) for integrating equation (5) with respect to the observed position x is calculated to obtain equation (7). In formula (7), C₁Is the integration constant.

[ mathematical formula 6 ]

[ mathematical formula 7 ]

Further, equation (8) integrating equation (7) with respect to the observed position x is calculated to obtain equation (9). In formula (9), C₂Is the integration constant.

[ mathematical formula 8 ]

[ mathematical formula 9 ]

In the formula (9), θ x represents a deflection amount, and the formula (10) is obtained by replacing θ x with the deflection amount w.

[ MATHEMATICAL FORMULATION 10 ]

According to fig. 14, since b is l-a, equation (10) is modified to equation (11).

[ mathematical formula 11 ]

Assuming that x is 0, the deflection w is 0, and H is obtained from x.ltoreq.a_a0, so x w H_aFormula (12) is obtained by substituting formula (11) with 0.

[ MATHEMATICAL FORMULATION 12 ]

C₂＝0…(12)

Further, assuming that the deflection w is 0 when x is l, H is obtained from x > a_a1, so, x ═ l, w ═ 0, and H_aFormula (13) is obtained by substituting formula (11) for 1.

[ mathematical formula 13 ]

Substitution of b ═ l-a for formula (13) affords formula (14).

[ CHEMICAL EQUATION 14 ]

Integrating constant C of equation (12)₁And integral constant C of equation (13)₂Substitution of formula (10) gives formula (15).

[ mathematical formula 15 ]

The expression (15) is modified, and the amount w of deflection at the observation position x when the load P is applied to the position a is expressed by expression (16).

[ mathematical formula 16 ]

Fig. 15 shows a state in which the load P moves from one end of the simply supported beam to the other end thereof under the condition that the observation position x of the deflection is fixed to the center position of the simply supported beam, that is, x is l/2.

When the load position a is located on the left side of the observation position x ═ l/2, H is obtained from x > a_a1, so, x is l/2, H_aSubstitution of formula (16) for 1 yields formula (17).

[ mathematical formula 17 ]

Substitution of l ═ a + b for formula (17) was performed to obtain formula (18).

[ 18 ] of the mathematical formula

When a + b is l, the formula (18) is substituted, and the position of the load P is located on the left side of the central observation position x by l/2, the amount w of deflection of the observation position x_LBecomes formula (19).

[ mathematical formula 19 ]

On the other hand, when the load position a is located on the right side of the observation position x ≦ l/2, H is obtained from x ≦ a_a0, so, x is equal to l/2, H_aSubstitution of formula (16) with 0 yields formula (20).

[ mathematical formula 20 ]

When l + a is substituted into formula (20), the position of the load P is located at the observation position more than the centerThe amount w of deflection of the observation position x when x is set to l/2 further to the right_RBecomes expression (21).

[ mathematical formula 21 ]

When the load position a is the same as the observation position x ≦ l/2, H is obtained from x ≦ a_a0, therefore, H_aFormula (16) is substituted with 0, a, b, l, and 2 to obtain formula (22).

[ mathematical formula 22 ]

When formula (22) is further substituted with "a" and "l/2", the amount w of deflection at the observation position x at which the position of the load P is the same as the center observation position is formula (23).

[ mathematical formula 23 ]

In the simply supported beam having the supporting points at both ends, since the maximum deflection displacement is obtained when the load P is positioned at the center, the maximum deflection w is obtained according to the equation (23)_maxRepresented by formula (24).

[ mathematical formula 24 ]

The amount w of deflection of the observation position x when the position of the load P is located on the left side of the center observation position x of l/2_LDivided by the maximum deflection w_maxAt maximum deflection w_maxWhen normalization is performed, expression (25) is obtained from expression (19) and expression (24).

[ mathematical formula 25 ]

In formula (25), when a/l is r, formula (26) is obtained.

[ 26 ] of the mathematical formula

On the other hand, when the position of the load P is located on the right side of the central observation position x by l/2, the amount w of deflection of the observation position x is_RDivided by the maximum deflection w_maxAt maximum deflection w_maxWhen normalization is performed, expression (27) is obtained from expression (21) and expression (24).

[ mathematical formula 27 ]

Since b ═ l × (1-r) is known from a/l ═ r and a + b ═ l, formula (28) is obtained by substituting b ═ l × (1-r) into formula (27).

[ mathematical formula 28 ]

The coupling formulas (25) and (27) are normalized by a normalized deflection w normalized by a maximum deflection observed at the center portion when the load P moves on the simply supported beam_stdRepresented by formula (29).

[ mathematical formula 29 ]

In equation (29), R is a/l, and 1-R is b/l, which represents the ratio of the position of the load P to the distance l between the fulcrums of the simply supported beam, and the variable R is defined as shown in equation (30).

[ mathematical formula 30 ]

Equation (29) is replaced with equation (31) using equation (30).

[ mathematical formula 31 ]

w_std＝3R-4R³…(31)

Equations (30) and (31) indicate that, when the observation position is located at the center of the simply supported beam, the load P is located on the right and left sides of the center, and the deflection amounts are symmetrical.

FIG. 16 shows the normalized deflection w at the observed position x ═ l/2_stdAn example of the waveform of (1).

In fig. 16, the horizontal axis represents the position of the load P, and the vertical axis represents the normalized deflection w_std. In the example of fig. 16, the distance l between the fulcrums of the simply supported beams is 1.

The axle information includes the entry lane L of each axle of the vehicle 6_jThe time of entry and the secondary lane L_jSince the exit time of the exit, that is, the time when the vehicle 6 passes through the positions of both ends of the upper structure 7, the positions of both ends of the upper structure 7 are made to correspond to the entry time and the exit time of the axle, and the load positions a and b are replaced with time. However, the speed of the vehicle 6 is substantially fixed and the position is substantially proportional to the time.

When the loading position of the left end of the superstructure 7 is brought to the entry time t_iCorrespondingly, the load position of the right end of the upper structure 7 and the withdrawal time t are set_oWhen the load position is changed from the left end to the entering time t_iElapsed time t_p. Past the time t_pRepresented by formula (32).

[ mathematical formula 32 ]

t_p＝t-t_i…(32)

In addition, the distance 1 between the fulcrums is replaced by the time t from the entry_iTo exit time t_oTime t to_s. Time t_sRepresented by formula (33).

[ mathematical formula 33 ]

t_s＝t_o-t_i…(33)

Since the speed of the vehicle 6 is fixed, the load position a is located at the time t in the middle of the superstructure 7_cRepresented by formula (34).

[ mathematical formula 34 ]

As described above, the position is replaced with time, and the position of the load P is as shown in equations (35) and (36).

[ mathematical formula 35 ]

[ CHEMICAL FORMULATION 36 ]

Substituting the formula (35) and the formula (36) for the formula (29) by the normalized deflection w of time_stdRepresented by formula (37).

[ mathematical formula 37 ]

Alternatively, the variable R is replaced with time according to the equations (30) and (31), and the normalized deflection w normalized by the maximum amplitude is used_stdRepresented by formula (38).

[ mathematical formula 38 ]

Considering that the correlation between the time lapse and the normalized deflection is treated as the observation data, the normalized deflection w is treated_stdIs replaced byNormalized deflection model w of observation position at center of beam caused by movement of single concentrated load on simply supported beam of two end fulcrums_std(t), the formula (38) is changed to the formula (39). Equation (39) is an approximate equation of the deflection of the upper structure 7 as a structure, and is an equation based on the structural model of the upper structure 7. Specifically, equation (39) is a lane L in which the vehicle 6 moves_jObservation point P in_jAnd observation point Q_jThe maximum amplitude of deflection at the central position of (a) is normalized, and the maximum value is an equation of 1.

[ mathematical formula 39 ]

The normalized deflection model w_stdThe time information required for (t) is obtained from the axle information. Normalized deflection model w_std(t) becomes the maximum deflection w at the central position of the upper structure 7_maxThus, formula (40) is obtained.

[ 40 ] of mathematical formula

The deflection w represented by the above formula (23) is a deflection where the observation position x where the position of the load P is the same as the center observation position is l/2, and a maximum deflection w_maxThis gave the formula (41).

[ mathematical formula 41 ]

FIG. 17 shows a normalized deflection model w_stdAn example of (t) is given below. In the example of fig. 17, time t is entered_iExit time t 4_oAt time t, 6_c＝(t_i+t_o) In 5/2, the normalized deflection model w_std(t) becomes maximum at the central position of the upper structure 7Deflection w_max＝1。

Assuming that the upper structure 7 as a structure functions as bwim (bridge weight in motion), it is considered that deformation similar to a simple beam with both ends as fulcrums is performed. Further, since the vehicle 6 as a moving body passes through the upper structure 7 from one end portion of the upper structure 7 to the other end portion at a substantially constant speed, the middle portion of the upper structure 7 and the end portion of the upper structure 7 receive the same load, and it is considered that the observed displacement of the upper structure 7 and the acceleration intensity a of the axle obtained from the axle information_pApproximately proportional.

The proportionality coefficient is defined as the acceleration intensity a of the axle obtained from the axle information_pThe product of the predetermined coefficient p and the deflection waveform h (t) of the upper structure 7 due to each axle is obtained by the equation (42). In addition, the acceleration intensity a_pThe acceleration intensity at the time of entry included in the axle information may be the acceleration intensity at the time of exit, or may be a statistical value such as an average value of the acceleration intensity at the time of entry and the acceleration intensity at the time of exit.

[ mathematical formula 42 ]

H(t)＝pa_pw_std(t)…(42)

Formula (39) is substituted for formula (42), and the deflection waveform h (t) is represented by formula (43).

[ mathematical formula 43 ]

Up to now, it has been assumed that a single load P is applied to the superstructure 7, but due to the lane L on which the vehicle 6 is travelling_jTo which a load generated by each axle of the vehicle 6 is applied, equation (43) is replaced with the deflection waveform H as equation (44)_jk(t) of (d). In equation (44), k is an integer representing an axle number, and j is an integer representing a lane number. As shown in equation (44), the deflection waveform H_jk(t) and a predetermined coefficient p and acceleration intensity a_pjkThe product of the two is proportional.

[ mathematical formula 44 ]

FIG. 18 shows in lane L_jAn example of the bending waveform of the upper structure 7 caused by each axle included in the traveling vehicle 6. In the example of fig. 18, the vehicle 6 is a four-axle vehicle, showing four deflection waveforms H_j1(t)、H_j2(t)、H_j3(t)、H_j4(t) of (d). In the example of fig. 18, the load generated by the first and second axle shafts is relatively small, and the load generated by the third and fourth axle shafts is relatively large, and therefore, the deflection waveform H_j1(t)、H_j2(t) has a relatively small maximum amplitude, the deflection waveform H_j3(t)、H_j4The maximum amplitude of (t) is relatively large.

As shown in equation (45), from the lane L_jVehicle deflection waveform CP, which is the deflection waveform of the superstructure 7 caused by the medium-speed vehicle 6_jm(t) bending waveform H of upper structure 7 caused by each axle_jk(t) are added. In equation (45), m is an integer representing a vehicle number, k is an integer representing an axle number, and j is an integer representing a lane number.

[ MATHEMATICAL FORMULATION 45 ]

In FIG. 19, four of the deflection waveforms H shown in FIG. 18 are shown_jl(t)、H_j2(t)、H_j3(t)、H_j4(t) vehicle deflection waveform CP obtained by adding_jm(t)。

Suppose that M vehicles 6 travel in the lane L in the integral section for calculating the displacement from the observation result_jFor medium travel, as shown in equation (46), the vehicle is deflected to have a waveform CP_j1(t)～CP_jMThe sum of (t) is set as a lane L_jIs the path deflection waveform CP_j(t) of (d). M is an integer of 1 or more.

[ NUMERICAL EQUATION 46 ]

1-4 correction of displacement

Will be aligned with the observation point R_iThe acceleration waveform obtained by low-pass filtering the acceleration detected by the sensor 23 for observation is a_j(t) of (d). As shown in equation (47), the acceleration waveform A_j(t) acceleration value α at time t_(t)Deviation error from acceleration a₀And (4) summing.

[ math figure 47 ]

A_j(t)＝α_(t)+α₀…(47)

Acceleration waveform A of Pair (47)_j(t) integration, velocity waveform V_j(t) is represented by formula (48). In formula (48), v_(t)Is the velocity value at time t, v₀Is the velocity offset error.

[ MATHEMATICAL FORMULATION 48 ]

V_j(t)＝∫^tA_j(t)dt＝∫α_(t)+α₀dt＝v_(t)+α₀t+v₀…(48)

Further, velocity waveform V of the pair formula (48)_j(t) integration, displacement waveform U_j(t) is represented by formula (49). In formula (49), u_(t)Is the displacement value at time t, u₀Is the displacement offset error.

[ mathematical formula 49 ]

The integration section in equation (49) is, for example, the lane L entered from the vehicle 6_jSince the time required for the exit is relatively short, it can be considered that the acceleration offset error α is₀Velocity offset error v₀Displacement offset error u₀Are all fixed values. Therefore, according to equation (49), the integral error is approximated by a quadratic polynomial to approximate the integral error u_ε(t) is represented by formula (50).

[ mathematical formula 50 ]

u_ε(t)＝at²+bt+c…(50)

When the values of the coefficients a, b, and c of the equation (50) are obtained, the displacement waveform U is derived as shown in the equation (51)_j(t) subtracting the approximate integral error u_ε(t) obtaining a displacement waveform U_j(t) corrected displacement waveform CU_j(t)。

[ mathematical formula 51 ]

CU_j(t)＝U_j(t)-u_ε(t)＝U_j(t)-(at²+bt+c)…(51)

The vehicle deflection waveform CP_jmSince (t) is calculated using the approximation formula (39) based on the deflection of the structural model of the upper structure 7, the integral error that increases with the passage of time is not included. Therefore, in the present embodiment, the measuring device 1 uses the vehicle deflection waveform CP_jm(t) the integral error is estimated, and the values of the coefficients a, b, and c of the quadratic polynomial (50) are calculated.

As shown in equation (52), at time t_kThe proportionality coefficient d and the path deflection waveform CP_j(t) multiplied waveform dCP_j(t) and the slave displacement waveform U_j(t) subtracting the value representing the approximate integral error u_εThe residual error of the waveform after the quadratic polynomial (50) of (t) is defined as e_k. In formula (52), k is each integer of 1 to n. Time t₁～t_nThe time when n pieces of acceleration data are obtained in the integration interval of equation (49). The proportionality coefficient d is for deflecting the path to the waveform CP_j(t) adjusting to the displacement waveform U_j(t) coefficients of equivalent scale.

[ math figure 52 ]

e_k＝dCP_j(t_k)-(U_j(t_k)-u_ε(t_k))＝dCP_j(t_k)-U_j(t_k)+at_k ²+bt_k+c…(52)

Using a least square method to obtain a residual e of equation (52)_kThe coefficients a, b, c, d are calculated to be the minimum. First of all, the first step is to,equation (53) is obtained by squaring both sides of equation (52).

[ mathematical formula 53 ]

e_k ²＝(dCP_j(t_k)-U_j(t_k)+at_k ²+bt_k+c)²…(53)

Equation (53) is partially differentiated by the coefficient a to obtain equation (54).

[ mathematical formula 54 ]

at_k ⁴+bt_k ³+dCP_j(t_k)t_k ²+ct_k ²＝t_k ²U_j(t_k)…(54)

Further, equation (53) is partially differentiated by coefficient b to obtain equation (55).

[ MATHEMATICAL FORMULATION 55 ]

at_k ³+bt_k ²+dCP_j(t_k)t_k+ct_k＝t_kU_j(t_k)…(55)

Further, equation (53) is partially differentiated by coefficient c to obtain equation (56).

[ MATHEMATICAL FORMULATION 56 ]

at_k ²+bt_k+dCP_j(t_k)+c＝U_j(t_k)…(56)

Equation (53) is partially differentiated by coefficient d to obtain equation (57).

[ MATHEMATICAL FORMULATION 57 ]

CP_j(t_k)at_k ²+CP_j(t_k)bt_k+CP_j(t_k)c+dCP_j(t_k)²＝CP_j(t_k)U_j(t_k)…(57)

Formula (58) is obtained by combining formulae (54) to (57).

[ NUMERICAL EQUATION 58 ]

Each element of expression (58) is replaced with the sum of the data of the integration interval to obtain expression (59).

[ mathematical formula 59 ]

The values of the coefficients a, b, c, and d are calculated as shown in formulas (61) to (64) by substituting the elements of formula (59) as shown in formula (60) and by a simple method.

[ MATHEMATICAL FORMULATION 60 ]

[ mathematical formula 61 ]

[ CHEMICAL FORM 62 ]

[ mathematical formula 63 ]

[ MATHEMATICAL FORMATION 64 ]

The measuring apparatus 1 calculates the values of the coefficients a, b, and c by equations (61) to (63), and calculates the displacement waveform U by substituting the values of the coefficients a, b, and c into equation (51)_j(t) corrected displacement waveform CU_j(t)。

Fig. 20 shows a displacement waveform U_jAn example of (t) is given below. In addition, fig. 21 shows the displacement waveform U of fig. 20 with a solid line_j(t) corrected displacement waveform CU_jAn example of (t) is given below. In fig. 20 and 21, the horizontal axis represents time, and the vertical axis represents displacement. In fig. 21, the path deflection waveform CP is also shown by a broken line_j(t) waveform dCP multiplied by scaling factor d_j(t) of (d). As shown in FIG. 20, the displacement waveform U_j(t) includes large integration errors approximated with quadratic polynomials, displacement divergence. In contrast, as shown in fig. 21, the displacement waveform U_j(t) corrected displacement waveform CU_j(t) almost eliminating integral error, and waveform dCP_j(t) approximation.

1-5. measuring method

Fig. 22 is a flowchart showing an example of the procedure of the measurement method according to the first embodiment. In the present embodiment, the measuring apparatus 1 executes the procedure shown in fig. 22.

As shown in fig. 22, first, the measurement device 1 measures each integer j of 1 to N from the observation point P_jObservation information of sensor 21 performing observation acquires first observation point information including passage point P of a plurality of axles of vehicle 6 (step S1)_jAnd as observation points P for each of the plurality of axles_jThe physical quantity of the response of the action of (1) is the acceleration intensity. As described above, with respect to observation point P_jThe sensor 21 for observation is an acceleration sensor, and the observation information of the sensor 21 is at the observation point P_jDetection information of the generated acceleration. The measurement device 1 acquires first observation point information from the acceleration detected by each sensor 21. Step S1 is a first observation point information acquisition step.

Then, the measuring apparatus 1 measures the observation point Q_jObservation information of observation sensor 22 acquires second observation point information including passage of a plurality of axles of vehicle 6 through observation point Q (step S2)_jAnd as observation points Q for each of the plurality of axles_jThe physical quantity of the response of the action of (1) is the acceleration intensity. As described above, for observation point Q_jMake an observationSensor 22 is an acceleration sensor, and the observation information of sensor 22 is at observation point Q_jDetection information of the generated acceleration. The measurement device 1 acquires second observation point information from the acceleration detected by each sensor 22. This step S2 is a second observation point information acquisition step.

Next, the measurement device 1 calculates the deflection waveform H of the upper structure 7 caused by each of the plurality of axles of the vehicle 6, based on the first observation point information obtained in step S1, the second observation point information obtained in step S2, the predetermined coefficient p, and the approximate expression of the deflection of the upper structure 7_jk(t) (step S3). Specifically, the measurement device 1 generates the axle information using the first observation point information and the second observation point information, and calculates the deflection waveform H of the upper structure 7 caused by each axle of the vehicle 6 by the equation (44) using the axle information and the predetermined coefficient p_jk(t) of (d). Step S3 is a deflection waveform calculation step.

Next, the measurement device 1 uses the above equation (45) to calculate the deflection waveform H of the upper structure 7 caused by each of the plurality of axles of the vehicle 6 calculated in step S3_jk(t) adding the values to calculate the vehicle deflection waveform CP_jm(t) and according to the vehicle deflection waveform CP_jm(t) calculating the lane L_jIs of a path deflection waveform CP_j(t) (step S4). Step S4 is a path deflection waveform calculation step.

Then, the measuring apparatus 1 looks at the observation point R_jObservation point R for acquiring observation information of sensor 23 performing observation_jThe obtained acceleration is subjected to quadratic integration to calculate an observation point R_jDisplacement waveform U of_j(t) (step S5). As described above, for observation point R_jThe sensor 23 for performing the observation is an acceleration sensor, and the observation information of the sensor 23 is at the observation point R_jDetection information of the generated acceleration. The measuring apparatus 1 obtains an acceleration obtained by low-pass filtering the acceleration detected by the sensor 23, and calculates a displacement waveform U by quadratic integration of the obtained acceleration_j(t) of (d). This step S5 is a displacement waveform calculation step.

Next, the measuring apparatus 1 proceeds according to step S4Calculated path deflection waveform CP_j(t) calculating the values of the coefficients of the polynomial approximating the integral error in the acceleration quadratic integration in step S5, and calculating the displacement waveform U from the calculated values of the coefficients_j(t) corrected displacement waveform CU_j(t) (step S6). Specifically, the measuring apparatus 1 makes the displacement waveform U_j(t) difference from polynomial approximating integration error and path deflection waveform CP_j(t) are approximately proportional, and the value of each coefficient of the polynomial is calculated. This step S6 is a displacement waveform correction step.

Next, the measuring apparatus 1 applies the displacement waveform CU calculated in step S6_j(t) is output to the server 2 (step S7). This step S7 is an output step.

The measurement apparatus 1 repeats the processing of steps S1 to S7 until the measurement is completed (no in step S8).

Fig. 23 is a flowchart showing an example of the procedure of the deflection waveform calculation step in step S3 in fig. 22.

As shown in fig. 23, first, the surveying device 1 sets the integer j to1 (step S30), and enters the lane L for each axle using the first observation point information and the second observation point information (step S30)_jPattern 1 at the time of entry and each axle driven lane L_jPattern 2 at the exit timing of the exit is compared (step S31).

When the difference between the entry time of each axle included in the pattern 1 and the exit time of each axle included in the pattern 2 is equal to or less than the threshold value (yes in step S32), the measuring apparatus 1 associates the entry time and the acceleration intensity of each axle included in the pattern 1 and the exit time and the acceleration intensity of each axle included in the pattern 2 with one vehicle 6 to generate axle information (step S33).

When the difference between the entry time of each axle included in pattern 1 and the exit time of each axle included in pattern 2 is greater than the threshold value (no in step S32), the measurement device 1 does not perform the processing of step S33.

When the integer j is not N (no in step S34), the measurement apparatus 1 adds 1 to the integer j (step S35), and repeats the processing of steps S31 to S33.

When the integer j becomes N (yes in step S34), the measurement device 1 sets the integer j to1 (step S36), and uses the axle information generated in step S33 and the predetermined coefficient p for the lane L_jEach vehicle 6 traveling in the middle of the vehicle calculates a deflection waveform H of the upper structure 7 due to each axle_jk(t) (step S37).

When the integer j is not N (no in step S38), the measurement apparatus 1 adds 1 to the integer j (step S39), and repeats the processing of step S37.

Then, when the integer j becomes N (yes in step S38), the measurement apparatus 1 ends the processing of the deflection waveform calculation step.

Fig. 24 is a flowchart showing an example of the procedure of step S4 of fig. 22, i.e., a route deflection waveform calculation step.

As shown in fig. 24, first, the measuring apparatus 1 sets an integer j to1 (step S41), and if there is a lane L_jWhen the vehicle 6 has moved (yes in step S42), the bending waveforms H of the upper structure 7 for the respective axles of the M vehicles 6 moving in the lane Lj are derived from the above equation (45)_jk(t) adding the values to calculate the vehicle deflection waveform CP_jm(t) (step S43).

Next, when M is 1 (yes in step S44), the measurement device 1 converts the vehicle deflection waveform CP to a vehicle deflection waveform CP_j1(t) is set as a lane L_jIs of a path deflection waveform CP_j(t) (step S45).

When M is not 1 (no in step S44), the measurement device 1 converts the vehicle deflection waveform CP by the above equation (46)_j1(t)～CP_jM(t) adding to calculate the lane L_jIs of a path deflection waveform CP_j(t) (step S46).

The measuring device 1 is not in the lane L_jWhen the vehicle 6 has moved (no in step S42), the processing of steps S43 to S46 is not performed.

When the integer j is not N (no in step S47), the measurement apparatus 1 adds 1 to the integer j (step S48), and repeats the processing of steps S42 to S46.

Then, when the integer j becomes N (yes in step S47), the measurement apparatus 1 ends the processing of the path flexural waveform calculation step.

Fig. 25 is a flowchart showing an example of the procedure of step S6 of fig. 22, i.e., a displacement waveform correction step.

As shown in fig. 25, first, the measuring apparatus 1 sets an integer j to1 (step S61), and applies a scaling factor d and a path deflection waveform CP_j(t) multiplied waveform dCP_j(t) and the slave displacement waveform U_j(t) the value of the proportionality coefficient d and the values of the coefficients a, b, and c of the polynomial are calculated by the least square method so that the difference between the waveforms obtained by subtracting the above equation (50) which is a polynomial approximating the integral error is the smallest (step S62). Specifically, the measuring apparatus 1 calculates the values of the coefficients a, b, c, and d by the above equations (61) to (64).

Next, the measuring apparatus 1 derives the displacement waveform U from the above equation (51)_j(t) the displacement waveform U is calculated by subtracting the equation (50) which is a polynomial approximating the integral error_j(t) corrected displacement waveform CU_j(t) (step S63).

When the integer j is not N (no in step S64), the measurement apparatus 1 adds 1 to the integer j (step S65), and repeats the processing of steps S62 and S63.

Then, when the integer j becomes N (yes in step S64), the measurement apparatus 1 ends the processing of the displacement waveform correction step.

1-6. constitution of measuring device

Fig. 26 is a diagram showing a configuration example of the measuring apparatus 1 according to the first embodiment. As shown in fig. 26, the measurement device 1 includes a control unit 110, a first communication unit 120, a storage unit 130, a second communication unit 140, and an operation unit 150.

The control unit 110 calculates the displacement of the upper structure 7 and the like based on acceleration data output from the sensors 21, 22, 23 provided on the bridge 5.

The first communication unit 120 receives acceleration data from the sensors 21, 22, and 23. The acceleration data output from each of the sensors 21 and 22 is, for example, a digital signal. The first communication unit 120 outputs the acceleration data received from the sensors 21, 22, and 23 to the control unit 110.

The storage unit 130 is a memory for storing programs, data, and the like for causing the control unit 110 to perform calculation processing and control processing. The storage unit 130 stores programs, data, and the like for causing the control unit 110 to realize predetermined application functions. The storage unit 130 is configured by, for example, various IC (Integrated Circuit) memories such as a ROM (Read Only Memory), a flash ROM (flash ROM), a RAM (Random Access Memory), and the like, a hard disk, a Memory card, and other recording media.

The storage unit 130 includes a nonvolatile information storage device as a computer-readable device or medium, and various programs, data, and the like may be stored in the information storage device. The information storage device may be an optical disk such as an optical disk DVD or CD, a hard disk drive, a card memory, various memories such as a ROM, or the like. The control unit 110 may receive various programs, data, and the like via the communication network 4 and store the programs, data, and the like in the storage unit 130.

The second communication unit 140 transmits information such as the calculation result of the control unit 110 to the server 2 via the communication network 4.

The operation unit 150 performs processing for acquiring operation data from a user and transmitting the operation data to the control unit 110.

The control unit 110 includes a first observation point information acquisition unit 111, a second observation point information acquisition unit 112, a deflection waveform calculation unit 113, a path deflection waveform calculation unit 114, a displacement waveform calculation unit 115, a displacement waveform correction unit 116, and an output processing unit 117.

First observation point information acquisition unit 111 performs the following processing: for each integer j of 1-N, according to observation point P_jThe observation information of the observing sensor 21 obtains first observation point information including the passage of the plurality of axles of the vehicle 6 through the observation point P_jAnd as observation points P for each of the plurality of axles_jThe physical quantity of the response of the action of (1) is the acceleration intensity. That is, first observation point information acquisition unit 111 performs the first observation point in fig. 22And processing in the information acquisition step. First observation point information acquired by first observation point information acquisition unit 111 is stored in storage unit 130.

Second observation point information acquisition unit 112 performs the following processing: according to the observation point Q_jThe observation information of the observing sensor 22 acquires second observation point information including a plurality of axles of the vehicle 6 passing through the observation point Q_jAnd acceleration intensity, which is a physical quantity in response to the action on observation point Qj with respect to each of the plurality of axles. That is, second observation point information acquisition unit 112 performs the processing of the second observation point information acquisition step in fig. 22. Second observation point information acquired by second observation point information acquisition unit 112 is stored in storage unit 130.

The deflection waveform calculation unit 113 performs the following processing: the deflection waveform H of the upper structure 7 caused by each of the plurality of axles of the vehicle 6 is calculated from the first observation point information obtained by the first observation point information obtaining unit 111 and the second observation point information obtained by the second observation point information obtaining unit 112, the predetermined coefficient p, and the approximate expression of the deflection of the upper structure 7 based on the structural model of the upper structure 7_jk(t) of (d). That is, the deflection waveform calculating unit 113 performs the processing of the deflection waveform calculating step in fig. 22. The deflection waveform H calculated by the deflection waveform calculating unit 113_jk(t) is stored in the storage unit 130. The predetermined coefficient p and the approximate expression of the deflection of the upper structure 7 are stored in the storage unit 130 in advance.

The path deflection waveform calculation unit 114 performs the following processing: the deflection waveform H of the upper structure 7 caused by each of the plurality of axles of the vehicle 6 calculated by the deflection waveform calculating unit 113_jk(t) adding the values to calculate the vehicle deflection waveform CP_jm(t) and according to the vehicle deflection waveform CP_jm(t) calculating the lane L_jIs of a path deflection waveform CP_j(t) of (d). That is, the route deflection waveform calculation unit 114 performs the process of the route deflection waveform calculation step in fig. 22. The path deflection waveform CP calculated by the path deflection waveform calculating unit 114_j(t) is stored in the storage unit 130.

The displacement waveform calculation unit 115 performs the following processing: according to the point of viewMeasuring point R_jObservation point R for acquiring observation information of sensor 23 performing observation_jAnd the obtained acceleration is subjected to quadratic integration to calculate an observation point R_jDisplacement waveform U of_j(t) of (d). That is, the displacement waveform calculating unit 115 performs the process of the displacement waveform calculating step in fig. 22. The displacement waveform U calculated by the displacement waveform calculating unit 115_j(t) is stored in the storage unit 130.

The displacement waveform correction unit 116 performs the following processing: the path deflection waveform CP calculated by the path deflection waveform calculating part 114_j(t) calculating the value of each coefficient of a polynomial approximating the integral error when the displacement waveform calculating unit 115 quadratic-integrates the acceleration, and correcting the displacement waveform U based on the calculated value of each coefficient_j(t) of (d). That is, the displacement waveform correcting unit 116 performs the process of the displacement waveform correcting step in fig. 22. The displacement waveform correction section 116 corrects the displacement waveform U_j(t) displacement waveform CU corrected for_j(t) is stored in the storage unit 130.

The output processing unit 117 performs the displacement waveform CU calculated by the displacement waveform correcting unit 116_j(t) processing to be output to the server 2 via the second communication unit 140. That is, the output processing unit 117 performs the processing of the output step in fig. 22.

In the present embodiment, control unit 110 is a processor that executes various programs stored in storage unit 130, and executes measurement program 131 stored in storage unit 130, thereby realizing the functions of first observation point information acquisition unit 111, second observation point information acquisition unit 112, deflection waveform calculation unit 113, path deflection waveform calculation unit 114, displacement waveform calculation unit 115, displacement waveform correction unit 116, and output processing unit 117. In other words, the measurement program 131 is a program for causing the measurement apparatus 1 as a computer to execute the respective procedures of the flowchart shown in fig. 22.

The processor may implement the functions of the respective units by separate hardware, or may implement the functions of the respective units by integrated hardware, for example. For example, the processor may include hardware including at least one of a circuit that processes digital signals and a circuit that processes analog signals. The Processor may be a CPU (Central Processing Unit), a GPU (Graphics Processing Unit), a DSP (Digital Signal Processor), or the like. However, the control unit 110 may be configured as a custom IC (Integrated Circuit) such as an ASIC (Application Specific Integrated Circuit) to realize the functions of each unit, or may be configured as a CPU and an ASIC to realize the functions of each unit.

1-7. Effect

In the measurement method of the first embodiment described above, the measurement device 1 measures the observation point P_jThe observation information of the sensor 21 for observation is acquired and included in the lane L_jEach axle passage observation point P of the medium-traveling vehicle 6_jTime of day and first observation point information of the acceleration intensity. In addition, the measuring device 1 is based on the observation point Q_jObservation information of sensor 22 for performing observation is acquired including each axle passing observation point Q of vehicle 6_jTime and acceleration intensity of the first observation point. Further, the measurement device 1 calculates a deflection waveform H of the upper structure 7 caused by each axle by an equation (44) based on the first observation point information and the second observation point information, the predetermined coefficient p, and an approximate equation (39) of the deflection of the upper structure 7 based on the structural model of the upper structure 7_jk(t) and bending the waveform H_jk(t) adding the values to calculate the vehicle deflection waveform CP_jm(t) from the vehicle deflection waveform CP_jm(t) calculating the lane L_jIs of a path deflection waveform CP_j(t) of (d). Further, the measuring apparatus 1 measures the observation point R_jObservation point R is obtained from observation information of observation sensor 23_jAnd the obtained acceleration is subjected to quadratic integration to calculate an observation point R_jDisplacement waveform U of_j(t) of (d). In addition, the measuring device 1 deflects the waveform CP according to the path_j(t) calculating the values of coefficients a, b, and c of a polynomial (50) approximating the integral error in the quadratic integration of the acceleration, and correcting the displacement waveform U based on the calculated values of the coefficients a, b, and c_j(t) of (d). Specifically, the apparatus 1 is measured so that the proportionality coefficient d and the path deflection waveform C are setP_j(t) multiplied by the slave displacement waveform U_j(t) the value of the proportionality coefficient d and the values of the coefficients a, b, and c of the polynomial (50) are calculated by the least square method so that the difference between the waveforms obtained by subtracting the polynomial (50) from the (t) is the smallest, and the displacement waveform U is calculated from the displacement waveform U by the equation (51)_jDisplacement waveform CU obtained by subtracting polynomial (50) from (t)_j(t) of (d). Therefore, according to the measurement method of the first embodiment, the measurement device 1 can estimate an integral error when integrating the acceleration acting on the upper structure 7 by the vehicle 6, and can calculate the displacement waveform CU of the upper structure 7 with high accuracy_j(t)。

In addition, according to the measurement method of the first embodiment, the measurement apparatus 1 uses the displacement waveform U in the integration section_j(t) and Path Flex waveform CP_jSince the values of the coefficients a, b, and c and the value of the scaling coefficient d of the polynomial (50) are calculated for all the data of (t) by the least square method, the influence of the observed displacement data on the noise-based correction is small although the amount of calculation is large, and thus a highly accurate displacement waveform CU can be obtained_j(t)。

In addition, according to the measurement method of the first embodiment, the measurement device 1 has a higher degree of freedom in installation than the displacement gauge and the strain gauge, and calculates the displacement waveform CU using the acceleration sensor that can be easily installed_j(t), therefore, cost reduction of the measurement system 10 can be achieved.

Further, according to the measurement method of the first embodiment, the measurement device 1 can calculate the displacement waveform, which is the deformation of the superstructure 7 caused by the axle weight of the vehicle 6 passing through the superstructure 7, and therefore, it is possible to provide sufficient information necessary for maintenance management of the bridge 5 for predicting damage to the superstructure 7.

2. Second embodiment

The processing of the displacement waveform correction step of the measurement method of the second embodiment is different from that of the measurement method of the first embodiment. Hereinafter, in the second embodiment, the same components as those in the first embodiment are denoted by the same reference numerals, and the description overlapping with the first embodiment is omitted or simplified, and the description will be mainly given of the differences from the first embodiment.

In the measurement method of the second embodiment, an approximate integral error u that is an approximation of an integral error when calculating a displacement from an acceleration_εIn the above equation (50) of the quadratic polynomial of (t), the coefficient b of the first order term and the coefficient c of the 0 th order term are sufficiently small to be regarded as zero with respect to the coefficient a of the second order term. Thereby, the quadratic polynomial (50) is replaced by a quadratic polynomial (65) in which the coefficient b of the first order term and the coefficient c of the 0 order term are zero.

[ MATHEMATICAL FORMULATION 65 ]

u_ε(t)＝at²…(65)

Since the above equation (50) is replaced with equation (65), the displacement waveform U is corrected_jThe above formula (51) of (t) is replaced with formula (66).

[ CHEMICAL FORM 66 ]

CU_j(t)＝U_j(t)-u_ε(t)＝U_j(t)-at²…(66)

Since the expression (51) is replaced with the expression (66), it indicates the residual error e_kThe above equation (52) is replaced with equation (67).

[ CHEMICAL FORM 67 ]

e_k＝dCP_j(t_k)-(U_j(t_k)-u_ε(t_k))＝dCP_j(t_k)-U_j(t_k)+at_k ²…(67)

Using a least square method to obtain a residual e of formula (67)_kThe coefficients a and d are calculated to be minimum. First, expression (68) is obtained by squaring both sides of expression (67).

[ mathematical formula 68 ]

e_k ²＝(dCP_j(t_k)-U_j(t_k)+at_k ²)²…(68)

Equation (68) is partially differentiated by the coefficient a to obtain equation (69).

[ math formula 69 ]

at_k ⁴+dCP_j(t_k)t_k ²＝t_k ²U_j(t_k)…(69)

Equation (68) is partially differentiated by coefficient d to obtain equation (70).

[ MATHEMATICAL FORMULATION 70 ]

CP_j(t_k)at_k ²+dCP_j(t_k)²＝CP_j(t_k)U_j(t_k)…(70)

Formula (71) is obtained by combining formula (69) and formula (70).

[ MATHEMATICAL FORMULATION 71 ]

Each element of expression (71) is replaced with the sum of the data of the integration interval to obtain expression (72).

[ CHEMICAL FORM 72 ]

The values of the coefficients a and d are calculated as shown in equations (74) and (75) by substituting the elements of equation (72) as shown in equation (73) and by a simple method.

[ math figure 73 ]

[ CHEMICAL FORM 74 ]

[ mathematical formula 75 ]

Through type measuring device 1(74) The value of the coefficient a is calculated, and the displacement waveform U is calculated by substituting the value of the coefficient a into an expression (66)_j(t) corrected displacement waveform CU_j(t)。

Fig. 27 shows a displacement waveform U in solid line_j(t) corrected displacement waveform CU_jAn example of (t) is given below. In fig. 28, the displacement waveform CU is shown by a solid line_jAn example of (t) is given below. In fig. 27 and 28, the horizontal axis represents time, and the vertical axis represents displacement. In fig. 27 and 28, observation point R is tentatively shown_jA strain gauge is provided, and a displacement waveform EU obtained by converting a waveform measured from the strain gauge is also shown by a dotted line_j(t) of (d). As shown in fig. 27 and 28, the displacement waveform CU_j(t) almost eliminating integral error and displacement waveform EU_j(t) approximation. That is, the approximate integral error u can be defined as shown in the formula (65) or obtained_ε(t) the result of a quadratic polynomial.

Fig. 29 is a flowchart showing an example of the procedure of step S6 of fig. 22, i.e., a displacement waveform correction step.

As shown in fig. 29, first, the measuring apparatus 1 sets an integer j to1 (step S161) and applies a scaling factor d and a path deflection waveform CP_j(t) multiplied waveform dCP_j(t) and the slave displacement waveform U_j(t) the value of the scaling coefficient d and the value of the coefficient a of the polynomial are calculated by the least square method so that the difference between the waveforms obtained by subtracting the above equation (65) which is a polynomial approximating the integral error is the smallest (step S162). Specifically, the measuring apparatus 1 calculates the values of the coefficients a and d by equations (74) and (75).

Next, the measuring apparatus 1 follows the displacement waveform U as shown in equation (66)_j(t) the displacement waveform U is calculated by subtracting an equation (65) which is a polynomial approximating the integral error_j(t) corrected displacement waveform CU_j(t) (step S163).

When the integer j is not N (no in step S164), the measurement apparatus 1 adds 1 to the integer j (step S165), and repeats the processing in steps S162 and S163.

Then, when the integer j becomes N (yes in step S164), the measurement apparatus 1 ends the processing of the displacement waveform correction step.

The configuration of the measuring apparatus 1 according to the second embodiment is the same as that of fig. 26, and therefore, illustration and description thereof are omitted.

In the measurement method of the second embodiment described above, the device 1 is measured such that the proportionality coefficient d and the path deflection waveform CP are set_j(t) multiplying the resulting waveform by the slave displacement waveform U_j(t) the value of the proportional coefficient d and the value of the coefficient a of the quadratic term (65) are calculated by the least square method so that the difference between the waveforms obtained by subtracting the value of the coefficient b of the first order term and the value of the quadratic term (65) of which the value of the coefficient c of the 0 order term is 0 from the waveform of displacement U is minimized, and the waveform of displacement U is calculated by the equation (66)_j(t) displacement waveform CU obtained by subtracting quadratic polynomial (65)_j(t) of (d). Therefore, according to the measurement method of the second embodiment, the measurement device 1 can estimate the integral error when integrating the acceleration acting on the upper structure 7 by the vehicle 6, and can calculate the displacement waveform CU of the upper structure 7 with high accuracy_j(t)。

In addition, according to the measurement method of the second embodiment, the measurement apparatus 1 uses the displacement waveform U in the integration section_j(t) and Path Flex waveform CP_jSince the value of the coefficient a and the value of the scaling coefficient d of the quadratic polynomial (65) are calculated by the least square method for all the data of (t), the correction accuracy is lower than that of the measurement method of the first embodiment in which the values of the coefficients a, b, and c and the value of the scaling coefficient d are calculated, but the calculation amount is small.

In addition, according to the measurement method of the second embodiment, the measurement device 1 has a higher degree of freedom in installation than the displacement gauge and the strain gauge, and calculates the displacement waveform CU using the acceleration sensor that can be easily installed_j(t), therefore, cost reduction of the measurement system 10 can be achieved.

3. Third embodiment

The processing of the displacement waveform correction step in the measurement method of the third embodiment is different from the measurement methods of the first and second embodiments. Hereinafter, in the third embodiment, the same components as those in the first embodiment or the second embodiment are denoted by the same reference numerals, and overlapping description with the first embodiment or the second embodiment is omitted or simplified, and the description will be mainly given of differences from the first embodiment and the second embodiment.

As shown in equation (76), at time t_kAn arbitrary first scaling factor d₁Sum path deflection waveform CP_j(t) multiplied waveform d₁CP_j(t) and the slave displacement waveform U_j(t) the residual of the waveform after subtracting the first quadratic polynomial is set as e_k1. In other words, the residual e_klIs to use the first scaling factor d₁Sum path deflection waveform CP_j(t) multiplied waveform d₁CP_j(t) and displacement waveform U_j(t) the first difference plus the first quadratic polynomial.

[ CHEMICAL FORM 76 ]

e_k1＝d₁CP_j(t_k)-{U_j(t_k)-(a₁t_k ²+b₁t_k+c₁)}＝d₁CP_j(t_k)-U_j(t_k)+a₁t_k ²+b₁t_k+c₁…(76)

Similarly, as shown in equation (77), at time t_kThe value is compared with an arbitrary first scaling factor d₁Different arbitrary second scaling factor d₂Sum path deflection waveform CP_j(t) waveform d obtained by multiplication₂CP_j(t) and the slave displacement waveform U_j(t) the residual of the waveform obtained by subtracting the second-order polynomial is set as e_k2. In other words, the residual e_k2Is to the second proportionality coefficient d₂Sum path deflection waveform CP_j(t) multiplied waveform d₂CP_j(t) and displacement waveform U_j(t) the second difference plus the second order polynomial.

[ CHEMICAL FORM 77 ]

e_k2＝d₂CP_j(t_k)-(U_j(t_k)-(a₂t_k ²+b₂t_k+c₂))＝d₂CP_j(t_k)-U_j(t_k)+a₂t_k ²+b₂t_k+c₂…(77)

In the formula (76), the waveform d₁CP_j(t_k) And displacement waveform U_j(t_k) Is set as u₁’(t_k) When the formula (76) is changed to the formula (78).

[ mathematical formula 78 ]

e_k1＝u₁′(t_k)+(a₁t_k ²+b₁t_k+c₁)…(78)

Similarly, in equation (77), the waveform d₂CP_j(t_k) And displacement waveform U_j(t_k) Is set as u₂’(t_k) When the formula (77) is the formula (79).

[ mathematical formula 79 ]

e_k2＝u₂′(t_k)+(a₂t_k ²+b₂t_k+c₂)…(79)

Residual error e of formula (78) by least squares_k1The coefficients a of the first quadratic polynomial are calculated in a minimum manner₁、b₁、c₁. First, expression (80) is obtained by squaring both sides of expression (78).

[ CHEMICAL FORM 80 ]

e_k1 ²＝{u₁′(t_k)+(a₁t_k ²+b₁t_k+c₁)}²…(80)

Using the coefficient a₁Partial differentiation of equation (80) gives equation (81).

[ mathematical formula 81 ]

a₁t_k ⁴+b₁t_k ³+c₁t_k ²＝-t_k ²u₁′(t_k)…(81)

In addition, the coefficient b is used₁To formula (80) is advancedPartial differentiation is performed to obtain equation (82).

[ mathematical formula 82 ]

a₁t_k ³+b₁t_k ²+c₁t_k＝-t_ku₁′(t_k)…(82)

In addition, the coefficient c is used₁Partial differentiation of equation (80) gives equation (83).

[ MATHEMATICAL FORMULATION 83 ]

a₁t_k ²+b₁t_k+c₁＝-u₁′(t_k)…(83)

Formula (84) is obtained by combining formulae (81) to (83).

[ mathematical formula 84 ]

Each element of equation (84) is replaced with the sum of the data of the integration interval to obtain equation (85).

[ math formula 85 ]

The respective elements of the formula (85) are replaced as shown in the formula (86), and the coefficient a is calculated as shown in the formulae (87) to (89) by a simple method₁、b₁、c₁The value of (c).

[ NUMERICAL EQUATION 86 ]

[ mathematical formula 87 ]

[ MATHEMATICAL FORMULATION 88 ]

[ MATHEMATICAL FORMATION 89 ]

Similarly, the residual e of equation (79) is calculated by the least square method_k2The coefficients a of the second quadratic polynomial are calculated in a minimum manner₂、b₂、c₂. First, expression (90) is obtained by squaring both sides of expression (79).

[ MATHEMATICAL FORMATION 90 ]

e_k2 ²＝{u₂′(t_k)+(a₂t_k ²+b₂t_k+c₂)}²…(90)

Using the coefficient a₂、b₂、c₂The partial differentiation of the equations (90) is performed, and the partial differentiation is combined to obtain the equation (91).

[ mathematical formula 91 ]

Each element of expression (91) is replaced with the sum of the data of the integration interval, and expression (92) is obtained.

[ mathematical formula 92 ]

The respective elements of the formula (92) are replaced as shown in the formula (93), and the coefficient a is calculated as shown in the formulas (94) to (96) by a line simplification method₂、b₂、c₂The value of (c).

[ mathematical formula 93 ]

[ mathematical formula 94 ]

[ MATHEMATICAL FORMATION 95 ]

[ MATHEMATICAL FORMULATION 96 ]

The residual e represented by the above equation (76)₁₁～e_n1Is set as a first sum E_n1. However, as shown in the formula (97), the coefficient b is set₁、c₁Calculating a first sum E of zero_n1. In other words, the first sum E_n1Is to calculate a second order term a of the first difference and the first second order polynomial₁t²Displacement waveform U of the added value_j(t) the sum of the periods of time, the first difference being a first scaling factor d₁Sum path deflection waveform CP_j(t) multiplied waveform d₁CP_j(t) and displacement waveform U_j(t) difference.

[ MATHEMATICAL FORMATION 97 ]

Similarly, the residual e represented by the above equation (77)₁₂～e_n2Is set as a second sum E_n2. However, as shown in the formula (98), the coefficient b is set to₂、c₂Calculating a second sum E of zero_n2. In other words, the second sum En2 is the second order term a calculated by summing the second difference with a second order polynomial₂t²Displacement waveform U of the added value_j(t) the sum of the periods of time, the second difference being a second scaling factor d₂Sum path deflection waveform CP_j(t) multiplied waveform d₂CP_j(t) and displacement waveform U_j(t) difference.

[ mathematical formula 98 ]

As can be seen from equations (97) and (98), the sum of the residuals linearly increases and decreases with respect to the increase and decrease of the scale factor. Therefore, the first scale coefficient d is used in the phasor coordinate whose scale coefficient is the x coordinate and whose residual is the y coordinate₁The second proportionality coefficient d₂First sum E_n1And a second sum E_n2The correlation between the scale factor and the sum of the residuals is expressed by equation (99).

[ mathematical formula 99 ]

A third scaling factor d in which the sum of the values of the x coordinates of the intersection of the straight line represented by equation (99) and y equal to 0, i.e., the residual is zero₀Calculated by equation (100).

[ mathematical formula 100 ]

Fig. 30 shows a correlation straight line between the sum of the scale factor represented by expression (99) and the residual and the third scale factor d calculated by expression (100)₀An example of the method.

Approximate integral error u approximating integral error_ε(t) is expressed as a third order polynomial (101).

[ mathematical formula 101 ]

u_ε(t)＝a₀t²+b₀t+c₀…(101)

At this time, as shown in equation (102), at time t_kA third scaling factor d₀Sum path deflection waveform CP_j(t) multiplied waveform d₀CP_j(t) and the slave displacement waveform U_j(t) subtracting the approximate integral error u represented by the third-order polynomial (101)_εThe residual error of the waveform after (t) is denoted as e_k0. In other words, the residual e_k0Is a waveform obtained by adding a third difference, which is a third scaling factor d, to a third second order polynomial (101)₀Sum path deflection waveform CP_j(t) multiplied waveform d₀CP_j(t) and displacement waveform U_j(t) difference between (t).

[ mathematical formula 102 ]

e_k0＝a₀CP_j(t_k)-(U_j(t_k)-u_ε(t_k))＝d₀CP_j(t_k)-U_j(t_k)+a₀t_k ²+b₀t_k+c₀…(102)

The waveform d is calculated by the above equation (100)₀CP_j(t_k) And displacement waveform U_j(t_k) And the second order term a of the third quadratic polynomial (101)₀t²Third sum E in integration interval of added values_n0A third proportionality coefficient d of zero₀. In the formula (102), the waveform d₀CP_j(t_k) And displacement waveform U_j(t_k) Is set as u₀’(t_k) When the formula (102) is expressed, the formula (103) is expressed.

[ mathematical formula 103 ]

e_k0＝u₀′(t_k)+(a₀t_k ²+b₀t_k+c₀)…(103)

Residual error e of formula (103) by least squares_k0Each coefficient a of formula (103) is calculated in a minimum manner₀、b₀、c₀. Firstly, the method comprises the following steps ofThe two sides are squared to obtain the formula (104).

[ CHEMICAL FORM 104 ]

e_k0 ²＝{u₀′(t_k)+(a₀t_k ²+b₀t_k+c₀)}²…(104)

Using the coefficient a₀、b₀、c₀The partial derivatives of the formulae (104) are respectively combined to obtain the formula (105).

[ MATHEMATICAL FORMULATION 105 ]

The elements of expression (105) are replaced with the sum of the data of the integration interval to obtain expression (106).

[ mathematical formula 106 ]

The respective elements of the formula (106) are replaced as shown in the formula (107), and the coefficient a is calculated as shown in the formulas (108) to (110) by a line reduction method₀、b₀、c₀The value of (c).

[ CHEMICAL EQUATION 107 ]

[ mathematical formula 108 ]

[ mathematical formula 109 ]

[ math formula 110 ]

As shown in equation (111), by shifting waveform U from_j(t) subtracting the value representing the approximate integral error u_ε(t) obtaining a displacement waveform U by a third quadratic polynomial_j(t) corrected displacement waveform CU_j(t)。

[ mathematical formula 111 ]

CU_j(t)＝U_j(t)-u_ε(t)＝U_j(t)-(a₀t²+b₀t+c₀)…(111)

The measuring apparatus 1 calculates the coefficient a by using the equations (108) to (110)₀、b₀、c₀By dividing the coefficient a by₀、b₀、c₀By substituting the value of (1) into the formula (111), the displacement waveform U is calculated_j(t) corrected displacement waveform CU_j(t)。

Fig. 31 shows a displacement waveform U with a solid line_j(t) corrected displacement waveform CU_jAn example of (t) is given below. In fig. 31, the horizontal axis represents time, and the vertical axis represents displacement. In fig. 31, the path deflection waveform CP is also shown by a broken line_j(t) multiplied by a scaling factor d₀The latter waveform d₀CP_j(t) of (d). In addition, in fig. 31, observation point R is tentatively observed_jThe strain gauge is provided, and the displacement waveform FU obtained by converting the waveform measured by the strain gauge is also shown by a one-dot chain line_j(t) of (d). As shown in fig. 31, the displacement waveform CU_j(t) almost removing the integral error, and waveform d₀CP_j(t) displacement waveform FU_j(t) approximation.

Fig. 32 is a flowchart showing an example of the procedure of step S6 of fig. 22, i.e., a displacement waveform correction step.

As shown in fig. 32, first, the measuring apparatus 1 sets an integer j to1 (step S261) and sets a first scaling factor d₁Sum path deflection waveform CP_j(t) multiplied waveform d₁CP_j(t) and displacement waveform U_j(t) first differential additionUpper first order polynomial a₁t²+b₁t+c₁And each coefficient a of the first quadratic polynomial is calculated so that the obtained waveform is minimized₁、b₁、c₁Is detected (step S262). Specifically, the measuring apparatus 1 calculates each coefficient a by equations (87) to (89)₁、b₁、c₁The value of (c).

Then, the device 1 is measured to determine the second scaling factor d₂Sum path deflection waveform CP_j(t) multiplied waveform d₂CP_j(t) and displacement waveform U_j(t) second difference plus second order polynomial a₂t²+b₂t+c₂And calculating each coefficient a of the second-order polynomial so that the obtained waveform is minimized₂、b₂、c₂Is detected (step S263). Specifically, the measuring apparatus 1 calculates each coefficient a by the equations (94) to (96)₂、b₂、c₂The value of (c).

The measuring device 1 then calculates a first sum E in the integration interval_n1(step S264), the integration interval is calculated by dividing the first difference by the second order a of the first quadratic polynomial₁t²Displacement waveform U of the added value_j(t) the calculated period. Specifically, the measuring apparatus 1 calculates the first sum E by the equation (97)_n1。

The measuring device 1 then calculates a second sum E in the integration interval_n2(step S265) the integration interval is calculated by dividing the second difference by the second quadratic term a of the second quadratic polynomial₂t²Displacement waveform U of the added value_j(t) period. Specifically, the measuring apparatus 1 calculates the second sum E by the equation (98)_n2。

The measuring device 1 is then operated according to a first scaling factor d₁A second proportionality coefficient d₂First sum E_n1And a second sum E_n2In the integration section, a third sum E in the integration section is calculated_n0A third proportionality coefficient d of zero₀(step S266), the integral interval is a third second degree polynomial (101) which is a polynomial for approximating the third difference and the integral error) Second order term of a₀t²Displacement waveform U of the added value_jDuring the period (t), the third difference is the third proportionality coefficient d₀Sum path deflection waveform CP_j(t) multiplied waveform d₀CP_j(t) and displacement waveform U_j(t) difference. Specifically, the measuring apparatus 1 calculates the third proportionality coefficient d by the equation (100)₀。

Then, the measurement device 1 calculates each coefficient a of the third-order polynomial (101) so that the waveform obtained by adding the third difference to the third-order polynomial (101) is minimized₀、b₀、c₀Value of (1) (step S267). Specifically, the measuring apparatus 1 calculates each coefficient a by equations (108) to (110)₀、b₀、c₀The value of (c).

Next, the measuring apparatus 1 follows the displacement waveform U as shown in equation (111)_j(t) subtracting a third-order polynomial (101) which is a polynomial approximating the integral error, thereby calculating a displacement waveform U_j(t) corrected displacement waveform CU_j(t) (step S268).

When the integer j is not N (no in step S269), the measurement apparatus 1 adds 1 to the integer j (step S270), and repeats the processing of steps S262 to S268.

Then, when the integer j becomes N (yes in step S269), the measurement apparatus 1 ends the processing of the displacement waveform correction step.

The configuration of the measuring apparatus 1 according to the third embodiment is the same as that of fig. 26, and therefore, illustration and description thereof are omitted.

In the measuring method of the third embodiment described above, the measuring apparatus 1 measures the first scale factor d₁And path deflection waveform CP_j(t) multiplied waveform d₁CP_j(t) and displacement waveform U_j(t) first difference plus first quadratic polynomial a₁t²+b₁t+c₁Calculating each coefficient a of the first quadratic polynomial in such a way that the waveform is minimized₁、b₁、c₁The value of (c). In addition, the device 1 is measured to determine the second proportionality coefficient d₂And path deflection waveform CP_j(t) multiplicationThe latter waveform d₂CP_j(t) and displacement waveform U_j(t) second difference plus second order polynomial a₂t²+b₂t+c₂Calculating each coefficient a of the second-order polynomial so that the waveform is minimized₂、b₂、c₂The value of (c). In addition, the measuring apparatus 1 calculates a second order a of the first difference and the first second order polynomial₁t²First sum E in integration interval of added values_n1. The measuring apparatus 1 calculates a second order term a of a second quadratic polynomial₂t²Second sum E in integration interval of added values_n2. In addition, the measuring device 1 is based on a first proportionality coefficient d₁A second proportionality coefficient d₂First sum E_n1And a second sum E_n2A second order polynomial a of a third second order polynomial 101 approximating the integration error and a third difference are calculated₀t²Third sum E in integration interval of added values_n0A third proportionality coefficient d of zero₀The third difference is a third scaling factor d₀And path deflection waveform CP_j(t) multiplied waveform d₀CP_j(t) and displacement waveform U_j(t) difference. The measurement device 1 calculates each coefficient a of the third-order polynomial (101) so that the waveform obtained by adding the third difference to the third-order polynomial (101) is minimized₀、b₀、c₀The value of (c). Then, the measuring apparatus 1 derives the displacement waveform U from the equation (111)_j(t) subtracting the third quadratic polynomial (101) to calculate a displacement waveform U_j(t) corrected displacement waveform CU_j(t) of (d). Therefore, according to the measurement method of the third embodiment, the measurement device 1 can estimate the integral error when integrating the acceleration acting on the upper structure 7 by the vehicle 6, and can calculate the displacement waveform CU of the upper structure 7 with high accuracy_j(t)。

In addition, according to the measurement method of the third embodiment, the measurement apparatus 1 calculates each coefficient a of the third-order polynomial (101)₀、b₀、c₀The calculation process of (a) is long, and the calculation amount is mediumTo a certain extent, but a displacement waveform CU with high accuracy can be obtained_j(t)。

In addition, according to the measurement method of the third embodiment, the measurement device 1 has a higher degree of freedom in installation than the displacement gauge and the strain gauge, and calculates the displacement waveform CU using the acceleration sensor that can be easily installed_j(t), therefore, cost reduction of the measurement system 10 can be achieved.

4. Fourth embodiment

The processing of the displacement waveform correction step in the measurement method of the fourth embodiment is different from the measurement methods of the first to third embodiments. Hereinafter, in the fourth embodiment, the same components as those in the first to third embodiments are denoted by the same reference numerals, and overlapping description with the first to third embodiments is omitted or simplified, and the description will be mainly given of differences from the first to third embodiments.

In the measuring method of the fourth embodiment, the measuring apparatus 1 calculates the first sum E_n1And a second sum E_n2The process of (1) is different from that of the third embodiment, and the other processes of the measuring apparatus 1 are the same as those of the third embodiment.

Specifically, the first sums E are calculated respectively_n1And a second sum E_n2The above-mentioned formula (97) and formula (98) are replaced with formula (112) and formula (113), respectively.

[ MATHEMATICAL FORMULATION 112 ]

[ CHEMICAL FORM 113 ]

In the equations (112) and (113), the function H_(Pk)Is defined by formula (114).

[ CHEMICAL FORMULATION 114 ]

The path deflection waveform CP is shown in FIG. 33_j(t) and function H_(Pk)An example of the relationship of (1). In fig. 33, the horizontal axis represents time, and the left vertical axis represents the path deflection waveform CP_j(t) amplitude, right vertical axis is function H_(Pk)The value of (c). As shown in fig. 33, the path deflection waveform CP in the integration section_j(t) period during which the amplitude is zero, function H_(Pk)Is 0, in the path deflection waveform CP_j(t) amplitude of non-zero period, function H_(Pk)Has a value of 1. Therefore, the first difference and the first quadratic polynomial a are calculated by the equation (112)₁t²+b₁t+c₁Path deflection waveform CP of the added value_j(t) first sum E in a period where amplitude is not zero_n1The first difference is a first scaling factor d₁Sum path deflection waveform CP_j(t) multiplied waveform and displacement waveform U_j(t) difference. Similarly, the second difference and the second-order polynomial a are calculated by the equation (113)₂t²+b₂t+c₂Path deflection waveform CP of the added value_j(t) second sum E in a period where the amplitude is not zero_n2The second difference is a second scaling factor d₂Sum path deflection waveform CP_j(t) multiplied waveform and displacement waveform U_j(t) difference.

Using a first scaling factor d₁A second proportionality coefficient d₂First sum E_n1And a second sum E_n2The third proportionality coefficient d is calculated by the above equation (100)₀. Specifically, the waveform d is calculated by the above equation (100)₀CP_j(t_k) And displacement waveform U_j(t_k) And a third second order polynomial a expressed by the above equation (101)₀t²+b₀t+c₀Path deflection waveform CP of the added value_j(t) third sum E in a period where amplitude is not zero_n0A third proportionality coefficient d of zero₀。

Then, the measuring apparatus 1 calculates the coefficient a by the above-described equations (108) to (110)₀、b₀、c₀And a coefficient a₀、b₀、c₀By substituting the value of (1) into the formula (111), the displacement waveform U is calculated_j(t) corrected displacement waveform CU_j(t)。

Fig. 34 is a flowchart showing an example of the procedure of step S6 of fig. 22, i.e., a displacement waveform correction step.

As shown in fig. 34, first, the measuring apparatus 1 sets the integer j to1 (step S361), and uses the first scale factor d₁Sum path deflection waveform CP_j(t) multiplied waveform d₁CP_j(t) and displacement waveform U_j(t) first difference plus first quadratic polynomial a₁t²+b₁t+c₁And each coefficient a of the first quadratic polynomial is calculated so that the obtained waveform is minimized₁、b₁、c₁Is detected (step S362). Specifically, the measuring apparatus 1 calculates each coefficient a by the above-described equations (87) to (89)₁、b₁、c₁The value of (c).

Then, the device 1 is measured to determine the second scaling factor d₂Sum path deflection waveform CP_j(t) multiplied waveform d₂CP_j(t) and displacement waveform U_j(t) second difference plus second order polynomial a₂t²+b₂t+c₂And calculating each coefficient a of the second-order polynomial so that the obtained waveform is minimized₂、b₂、c₂Value of (1) (step S363). Specifically, the measuring apparatus 1 calculates each coefficient a by the above-described equations (94) to (96)₂、b₂、c₂The value of (c).

The measuring device 1 then calculates a first quadratic polynomial a from the first difference₁t²+b₁t+c₁Path deflection waveform CP of the added value_j(t) a first sum E in a period other than zero_n1(step S364). Specifically, the measuring apparatus 1 calculates the first sum E by the equation (112)_n1。

Then, measureThe quantity means 1 calculates a second difference and a second quadratic polynomial a₂t²+b₂t+c₂Path deflection waveform CP of the added value_j(t) a second sum E in a period other than zero_n2(step S365). Specifically, the measuring apparatus 1 calculates the second sum E by the equation (113)_n2。

The measuring device 1 is then operated according to a first scaling factor d₁A second proportionality coefficient d₂First sum E_n1And a second sum E_n2A third quadratic polynomial a which is a polynomial approximating the integration error and a third difference₀t²+b₀t+c₀Path deflection waveform CP of the added value_j(t) a third sum E in a period other than zero_n0A third proportionality coefficient d of zero₀(step S366), the third difference is the third proportionality coefficient d₀Sum path deflection waveform CP_j(t) amplitude multiplied waveform d₀CP_j(t) and displacement waveform U_j(t) difference. Specifically, the measuring apparatus 1 calculates the third proportionality coefficient d by the above equation (100)₀。

The measuring apparatus 1 then uses a third difference with a third-order polynomial a₀t²+b₀t+c₀Calculating each coefficient a of the third-order polynomial so that the added waveform is minimized₀、b₀、c₀Value of (1) (step S367). Specifically, the measuring apparatus 1 calculates each coefficient a by the above-described equations (108) to (110)₀、b₀、c₀The value of (c).

Next, the measuring apparatus 1 follows the displacement waveform U as shown in the above equation (111)_j(t) subtracting a third-order polynomial a as a polynomial approximating the integral error₀t²+b₀t+c₀Thereby calculating a displacement waveform U_j(t) corrected displacement waveform CU_j(t) (step S368).

When the integer j is not N (no in step S369), the measurement apparatus 1 adds 1 to the integer j (step S370), and repeats the processing of steps S362 to S368.

Then, when the integer j becomes N (yes in step S369), the measurement apparatus 1 ends the processing of the displacement waveform correction step.

The configuration of the measuring apparatus 1 according to the fourth embodiment is the same as that of fig. 26, and therefore, illustration and description thereof are omitted.

In the measuring method of the fourth embodiment described above, the measuring apparatus 1 measures the first scale factor d₁Sum path deflection waveform CP_j(t) multiplied waveform d₁CP_j(t) and displacement waveform U_j(t) first difference plus first quadratic polynomial a₁t²+b₁t+c₁Calculating each coefficient a of the first quadratic polynomial in such a way that the waveform is minimized₁、b₁、c₁The value of (c). In addition, the device 1 is measured to determine the second proportionality coefficient d₂Sum path deflection waveform CP_j(t) multiplied waveform d₂CP_j(t) and displacement waveform U_j(t) second difference plus second order polynomial a₂t²+b₂t+c₂Calculating each coefficient a of the second-order polynomial so that the waveform is minimized₂、b₂、c₂The value of (c). In addition, the measuring apparatus 1 calculates a second order a of the first difference and the first second order polynomial₁t²Path deflection waveform CP of the added value_j(t) first sum E in a period where amplitude is not zero_n1. The measuring apparatus 1 calculates a second order term a of a second quadratic polynomial₂t²Path deflection waveform CP of the added value_j(t) second sum E in a period where the amplitude is not zero_n2. In addition, the measuring device 1 is based on a first proportionality coefficient d₁A second proportionality coefficient d₂First sum E_n1And a second sum E_n2A second order polynomial a of a third second order polynomial 101 approximating the integration error and a third difference are calculated₀t²Path deflection waveform CP of the added value_j(t) third sum E in a period where amplitude is not zero_n0A third proportionality coefficient d of zero₀The third difference is a third scaling factor d₀And path deflection waveform CP_j(t) multiplied waveform d₀CP_j(t) and displacement waveform U_j(t) difference. The measurement device 1 calculates each coefficient a of the third-order polynomial (101) so that the waveform obtained by adding the third difference to the third-order polynomial (101) is minimized₀、b₀、c₀The value of (c). Then, the measuring apparatus 1 derives the displacement waveform U from the equation (111)_j(t) subtracting the third quadratic polynomial (101) to calculate a displacement waveform U_j(t) corrected displacement waveform CU_j(t) of (d). Therefore, according to the measurement method of the fourth embodiment, the measurement device 1 can estimate the integral error when integrating the acceleration acting on the upper structure 7 by the vehicle 6, and can calculate the displacement waveform CU of the upper structure 7 with high accuracy_j(t)。

In addition, according to the measurement method of the fourth embodiment, the measurement device 1 calculates the path deflection waveform CP_j(t) first sum E in a period where amplitude is not zero_n1And a second sum E_n2Therefore, the first sum E in the integration interval is calculated_n1And a second sum E_n2The amount of calculation is small compared to the measurement method of the first embodiment.

In addition, according to the measurement method of the fourth embodiment, the measurement device 1 has a higher degree of freedom in installation than the displacement gauge and the strain gauge, and calculates the displacement waveform CU using the acceleration sensor that can be easily installed_j(t), therefore, cost reduction of the measurement system 10 can be achieved.

5. Fifth embodiment

The processing of the displacement waveform correction step in the measurement method of the fifth embodiment is different from the measurement methods of the first to fourth embodiments. Hereinafter, in the fifth embodiment, the same components as those in the first to fourth embodiments are denoted by the same reference numerals, and overlapping description with the first to fourth embodiments is omitted or simplified, and the description will be mainly given of differences from the first to fourth embodiments.

Considering that the vehicle 6 is not in the lane L_jPeriod of medium travelInterval observation point R_jIf the displacement does not occur, the displacement waveform U in the period can be regarded as_j(t) represents an integral error caused by acceleration not related to the running of the vehicle 6. Moreover, the vehicle 6 is not in the lane L_jThe period of travel corresponds to the path deflection waveform CP_j(t) a period during which the amplitude is zero. Therefore, in the measuring method of the fifth embodiment, the measuring device 1 deflects the waveform CP in the path_j(t) displacement waveform U during a period in which the amplitude is zero_j(t) calculating the value of each coefficient of the polynomial so that the difference between (t) and the polynomial approximating the integral error is minimized.

The path deflection waveform CP is selected_j(t) displacement waveform U during a period in which the amplitude is zero_j(t) Displacement waveform U'_j(t) is defined as formula (115). In the formula (115), the function H_inv(Pk)Is defined by formula (116).

[ MATHEMATICAL FORMULATION 115 ]

[ CHEMICAL FORM 116 ]

The path deflection waveform CP is shown in FIG. 35_j(t) and function H_inv(Pk)An example of the relationship of (1). In fig. 35, the horizontal axis represents time, and the left vertical axis represents the path deflection waveform CP_j(t) amplitude, right vertical axis is function H_inv(Pk)The value of (c). As shown in FIG. 35, the path deflection waveform CP in the integration interval_j(t) amplitude of non-zero period, function H_inv(Pk)Is 0, in the path deflection waveform CP_j(t) period during which the amplitude is zero, function H_inv(Pk)Has a value of 1.

In the present embodiment, the integral error is also approximated by a quadratic polynomial to approximate the integral error u_ε(t) is represented by the above formula (50). As shown in equation (117), at time t_kWill shift waveform U'_j(t) and the approximate integral error u_εThe residual error of (t) is denoted as e_k. In formula (117), k is each integer of 1 to n.

[ mathematical formula 117 ]

e_k＝U′_j(t_k)-u_ε(t_k)＝U′_j(t_k)-(at_k ²+bt_k+c)…(117)

Residual error e of equation (117) by least squares_kThe coefficients a, b, and c are calculated to be minimum. First, expression (118) is obtained by squaring both sides of expression (117).

[ MATHEMATICAL FORMULATION 118 ]

e_k ²＝{U′_j(t_k)-(at_k ²+bt_k+c)}²…(118)

The coefficients a, b, and c are used to partially differentiate equation (118), and the coefficients are combined to obtain equation (119).

[ MATHEMATICAL FORMULATION 119 ]

The elements of equation (119) are replaced with the path deflection waveform CP_jThe sum of the data in the period in which the amplitude of (t) is zero is obtained as expression (120).

[ MATHEMATICAL FORMULATION 120 ]

The values of the coefficients a, b, and c are calculated by substituting the elements of the formula (120) as shown in the formula (121) and by performing a reduction method as shown in the formulas (122) to (124).

[ MATHEMATICAL FORMULATION 121 ]

[ MATHEMATICAL FORMULATION 122 ]

[ mathematical formula 123 ]

[ MATHEMATICAL FORMULATION 124 ]

The dotted line in FIG. 36 shows the approximate integral error u_ε(t) second degree polynomial at²An example of + bt + c. In fig. 36, the horizontal axis represents time, and the vertical axis represents displacement. Further, the function H is shown by a solid line in fig. 36_inv(Pk)Displacement waveform U of interval of 1_j(t), function H is shown in dotted lines_inv(Pk)Displacement waveform U of interval of 0_j(t) of (d). Displacement waveform U_jThe solid line portion of (t) is used to calculate the values of the coefficients a, b, and c.

Then, the measurement device 1 calculates the displacement waveform U by substituting the values of the coefficients a, b, and c into the above equation (51)_j(t) corrected displacement waveform CU_j(t)。

Fig. 37 shows a displacement waveform CU by a solid line_jAn example of (t) is given below. In fig. 37, the horizontal axis represents time, and the vertical axis represents displacement. In addition, in fig. 37, observation point R is tentatively observed_jA strain gauge is provided, and a displacement waveform EU converted from a waveform measured by the strain gauge is also shown by a dotted line_j(t) of (d). As shown in fig. 37, the displacement waveform CU_j(t) almost eliminating integral error and displacement waveform EU_j(t) approximation.

Fig. 38 is a flowchart showing an example of the procedure of step S6 of fig. 22, i.e., a displacement waveform correction step.

As shown in fig. 38, first, the measuring apparatus 1 sets an integer j to1 (step S461), and uses the path deflection waveform CP_j(t) displacement waveform U during a period in which the amplitude is zero_j(t) and a quadratic polynomial at as a polynomial approximating the integral error²The values of the coefficients a, b, and c of the quadratic polynomial are calculated so that the difference between + bt + c is the smallest (step S462). Specifically, the measuring apparatus 1 calculates the values of the coefficients a, b, and c by equations (122) to (124).

Next, the measuring apparatus 1 derives the displacement waveform U from the above equation (51)_j(t) subtracting a quadratic polynomial at as a polynomial approximating the integral error²+ bt + c, thereby calculating the displacement waveform U_j(t) corrected displacement waveform CU_j(t) (step S463).

When the integer j is not N (no in step S464), the measurement apparatus 1 adds 1 to the integer j (step S465), and repeats the processing in steps S462 and S463.

Then, when the integer j becomes N (yes in step S464), the measurement apparatus 1 ends the processing of the displacement waveform correction step.

The configuration of the measuring apparatus 1 according to the fifth embodiment is the same as that of fig. 26, and therefore, illustration and description thereof are omitted.

In the measurement method of the fifth embodiment described above, the measurement device 1 deflects the path with the waveform CP_j(t) displacement waveform U during a period in which the amplitude is zero_j(t) and a quadratic polynomial at approximating the integral error²The values of the coefficients a, b, and c of the quadratic polynomial are calculated so that the difference between + bt + c is the smallest. Then, the measuring apparatus 1 derives the displacement waveform U from the equation (51)_j(t) subtracting a quadratic polynomial at²+ bt + c, thereby calculating the displacement waveform U_j(t) corrected displacement waveform CU_j(t) of (d). Therefore, according to the measurement method of the fifth embodiment, the measurement device 1 can estimate an integral error when integrating the acceleration acting on the upper structure 7 by the vehicle 6, and can calculate the displacement waveform CU of the upper structure 7 with high accuracy_j(t)。

In addition, according to the measuring method of the fifth embodiment, the measuring apparatus 1 uses the path deflection waveform CP_j(t) is zero, that is, the vehicle 6 is not runningDisplacement waveform U during traveling_jSince the integral error is estimated from the value of (t), the displacement waveform U can be corrected with high accuracy in an environment where the amount of calculation is small and the influence of noise is small_j(t)。

In addition, according to the measurement method of the fifth embodiment, the measurement device 1 has a higher degree of freedom in installation than the displacement gauge and the strain gauge, and calculates the displacement waveform CU using the acceleration sensor that can be easily installed_j(t), therefore, cost reduction of the measurement system 10 can be achieved.

6. Sixth embodiment

The processing of the displacement waveform correction step in the measurement method of the sixth embodiment is different from the measurement methods of the first to fifth embodiments. Hereinafter, in the sixth embodiment, the same components as those in the first to fifth embodiments are denoted by the same reference numerals, and overlapping description with the first to fifth embodiments is omitted or simplified, and the description will be mainly given of differences from the first to fifth embodiments.

In the present embodiment, the integral error is also approximated by a quadratic polynomial to approximate the integral error u_ε(t) is represented by the above formula (50). In the present embodiment, the measuring apparatus 1 uses the vehicle 6 not in the lane L_jThree different times t in the period of upper running₁、t₂、t₃Displacement waveform U of_jThe value of (t) is used to estimate the integration error. The vehicle 6 is not in the lane L_jThe middle travel period corresponds to the path deflection waveform CP_j(t) has a period of zero amplitude, and thus the path deflection waveform CP is selected_j(t) three times t at which the amplitude of t is zero₁、t₂、t₃。

The path deflection waveform CP is shown in FIG. 39_j(t) and time t₁、t₂、t₃An example of the relationship of (1). In the example of fig. 39, time t near the start time of the integration interval is selected₁Path deflection waveform CP_jImmediately before the start and immediately after the end of the period in which the amplitude of (t) is not zero₂And time t₃。

As shown in equation (125), at time t_kWill displace the waveform U_j(t) and the approximate integral error u_εThe residual error of (t) is denoted as e_k. In the formula (125), k is an integer of 1 to 3.

[ MATHEMATICAL FORMULATION 125 ]

e_k＝U_j(t_k)-u_ε(t_k)＝U_j(t_k)-(at_k ²+bt_k+c)…(125)

Residual error e of equation (125) by least squares_kThe coefficients a, b, and c are calculated to be minimum. First, expression (126) is obtained by squaring both sides of expression (125).

[ math formula 126 ]

e_k ²＝{U_j(t_k)-(at_k ²+bt_k+c)}²…(126)

Equation (126) is partially differentiated by coefficients a, b, and c, respectively, and combined to obtain equation (127).

[ math figure 127 ]

Each element of equation (127) is replaced with time t₁、t₂、t₃To obtain the formula (128).

[ math formula 128 ]

The values of the coefficients a, b, and c are calculated by substituting the elements of the formula (128) as shown in the formula (129) and by performing a reduction method as shown in the formulas (130) to (132).

[ math formula 129 ]

[ mathematical formula 130 ]

[ mathematical formula 131 ]

[ MATHEMATICAL FORMULATION 132 ]

Then, the measurement device 1 calculates the displacement waveform U by substituting the values of the coefficients a, b, and c into the above equation (51)_j(t) corrected displacement waveform CU_j(t)。

In the present embodiment, the measuring device 1 measures the displacement waveform CU_j(t) and Path Flex waveform CP_j(t) comparing, thereby comparing the displacement waveform CU_j(t) the accuracy was evaluated.

Will shift waveform CU_j(t) maximum amplitude value and Path flexural waveform CP_j(t) the ratio of the maximum amplitude value is set as the amplitude ratio r_jObtaining a displacement model waveform UCP by the formula (133)_j(t) the displacement model waveform UCP_j(t) is the path deflection waveform CP_j(t) amplitude is adjusted to be equal to displacement waveform CU_j(t) waveform with the maximum amplitude being identical.

[ MATHEMATICAL FORMULATION 133 ]

UCP_j(t)＝r_jCP_j(t)…(133)

Measuring device 1 pair displacement waveform CU_j(t) and displacement model waveform UCP_j(t) comparing the displacement waveform CU, and judging that the displacement waveform CU is the displacement waveform CU when the error is within the allowable range_j(t) normal, and when the error is not within the allowable range, the displacement waveform CU is judged to be the displacement waveform CU_j(t) abnormality.

Alternatively, the measuring apparatus 1 may reselect the three times t when the error is not within the allowable range₁、t₂、t₃The values of the coefficients a, b, and c are calculated again. Then, the measuring device 1 aligns the displacement waveform CU_j(t) and displacement model waveform UCP_j(t) comparing the displacement waveform CU, and judging that the displacement waveform CU is the displacement waveform CU when the error is within the allowable range_j(t) normal, and when the error is not within the allowable range, the displacement waveform CU is judged to be the displacement waveform CU_j(t) abnormality.

The displacement waveform U is shown in solid line in fig. 40_j(t) corrected displacement waveform CU_jAn example of (t) is given below. In addition, fig. 41 shows a displacement waveform U by a solid line_j(t) corrected displacement waveform CU_j(t) Another example. In fig. 40 and 41, the horizontal axis represents time, and the vertical axis represents displacement. In fig. 40 and 41, the displacement model waveform UCP is also shown by a broken line_j(t) displacement waveform U is shown by a one-dot chain line_j(t)。

In fig. 42, the displacement waveform CU shown in fig. 40 is shown by a solid line_j(t) and displacement model waveform UCP_j(t) correlation curve. In fig. 43, the displacement waveform CU shown in fig. 41 is shown by a solid line_j(t) and displacement model waveform UCP_j(t) correlation curve. In fig. 42 and 43, the horizontal axis represents the displacement waveform CU_j(t) displacement, vertical axis is displacement model waveform UCP_j(t) displacement. In fig. 42 and 43, ideal correlation straight lines are also shown by dashed-dotted lines. For example, the measurement device 1 may determine that the displacement waveform CU is a displacement waveform CU when the maximum value of the difference between the correlation curve and the ideal correlation straight line is equal to or less than a predetermined threshold value in the integration interval_j(t) normal, and when the maximum value of the difference is larger than a predetermined threshold value, it is determined that the displacement waveform CU is a displacement waveform CU_j(t) abnormality.

Fig. 44 is a flowchart showing an example of the procedure of step S6 of fig. 22, i.e., a displacement waveform correction step.

As shown in fig. 44, first, the measuring apparatus 1 sets an integer j to1 (step S561), and selects the path deflection waveform CP_j(t) three times t during which the amplitude of (t) is zero₁、t₂、t₃(step S562). The measuring apparatus 1 selects, for example, a time t close to the start time of the integration interval₁And select the path deflection waveform CP_jImmediately before the start and immediately after the end of the period in which the amplitude of (t) is not zero₂And time t₃。

Then, the device 1 is measured at time t₁、t₂、t₃Displacement waveform U_j(t) and a quadratic polynomial at approximating the integral error²The values of the coefficients a, b, and c of the quadratic polynomial are calculated so that the difference between + bt + c is the smallest (step S563). Specifically, the measuring apparatus 1 calculates the values of the coefficients a, b, and c by equations (130) to (132).

Next, the measuring apparatus 1 derives the displacement waveform U from the above equation (51)_j(t) subtracting a quadratic polynomial at as a polynomial approximating the integral error²+ bt + c, thereby calculating the displacement waveform U_j(t) corrected displacement waveform CU_j(t) (step S564).

Next, the measuring apparatus 1 calculates a displacement waveform CU in the integration section_j(t) maximum amplitude value and Path flexural waveform CP_j(t) amplitude ratio r of maximum amplitude value_j(step S565).

Subsequently, the measuring device 1 aligns the displacement waveform CU_j(t) and Path deflection waveform CP_j(t) multiplying by amplitude ratio r_jPost-displacement model waveform UCP_j(t) comparison is performed (step S566).

Then, the measuring device 1 is in the displacement waveform CU_j(t) relative to the displacement model waveform UCP_jIf the error of (t) is not within the allowable range (no in step S567), a displacement waveform CU is generated_j(t) information of abnormality (step S568).

When the error is within the allowable range (yes in step S567), the surveying instrument 1 does not perform the process of step S568.

When integer j is not N (no in step S569), measuring apparatus 1 adds 1 to integer j (step S570), and repeats the processing of steps S562 to S568.

Then, when the integer j becomes N (yes in step S569), the measurement apparatus 1 ends the processing of the displacement waveform correction step.

Fig. 45 is a flowchart showing another example of the procedure of step S6 of fig. 22, i.e., the shift waveform correction step.

As shown in fig. 45, first, the measurement apparatus 1 sets the integer j to1 (step S661), and performs the processing of steps S662 to S666 similar to steps S562 to S566 in fig. 44.

Then, when the displacement waveform CU_j(t) relative to the displacement model waveform UCP_jIf the error (t) is not within the allowable range (no in step S667) and the reselection is possible (yes in step S668), the measurement apparatus 1 reselects the time t₁、t₂、t₃(step S669), and the processing of and after step S663 is performed again. For example, the measurement device 1 may select the time t close to the start time of the integration interval in step S662₁Select path deflection waveform CP_jImmediately before the start and immediately after the end of the period in which the amplitude of (t) is not zero₂And time t₃At step S669, time t is not changed₁Will be at time t₂Change to the previous time, change the time t₃Change to the latter instant, thereby reselecting instant t₁、t₂、t₃。

In addition, if time t cannot be reselected₁、t₂、t₃(NO in step S668), the measurement device 1 generates a waveform CU indicating the displacement_j(t) information of abnormality (step S670).

When the error is within the allowable range (yes in step S667), the measurement apparatus 1 does not perform the processing of steps S668 to S670.

When the integer j is not N (no in step S671), the measurement apparatus 1 adds 1 to the integer j (step S672), and repeats the processing of steps S662 to S670.

Then, when the integer j becomes N (yes in step S671), the measurement device 1 ends the processing of the displacement waveform correction step.

The configuration of the measuring apparatus 1 according to the sixth embodiment is the same as that of fig. 26, and therefore, illustration and description thereof are omitted.

In the measurement method of the sixth embodiment described above, the measurement device 1 is configured to deflect the waveform CP in the path_j(t) three times t during which the amplitude of (t) is zero₁、t₂、t₃Displacement waveform U_j(t) and a quadratic polynomial at²The values of the coefficients a, b, and c of the quadratic polynomial are calculated so that the difference between + bt + c is the smallest. Then, the measuring apparatus 1 derives the displacement waveform U from the equation (51)_j(t) subtracting a quadratic polynomial at²+ bt + c, thereby calculating the displacement waveform U_j(t) corrected displacement waveform CU_j(t) of (d). Therefore, according to the measurement method of the sixth embodiment, the measurement device 1 can estimate the integral error when integrating the acceleration acting on the upper structure 7 by the vehicle 6, and can calculate the displacement waveform CU of the upper structure 7 with high accuracy_j(t)。

In the measurement method according to the sixth embodiment, the measurement device 1 calculates the displacement waveform CU in the integration section_j(t) maximum amplitude value and Path flexural waveform CP_j(t) amplitude ratio r of maximum amplitude value_jAnd for the displacement waveform CU_j(t) and displacement model waveform UCP_j(t) comparing the displacement waveform CU and generating a displacement waveform CU when the error is not within the allowable range_j(t) information of abnormality. Therefore, according to the measurement method of the sixth embodiment, for example, the displacement waveform CU calculated by the measurement device 1 is received_j(t) the server 2 can determine the displacement waveform CU_j(t) is normal.

In addition, according to the measurement method of the sixth embodiment, the measurement apparatus 1 uses the path deflection waveform CP_j(t) has zero amplitude, that is, three times t during the period in which the vehicle 6 is not running₁、t₂、t₃Displacement waveform U of_jSince the integral error is estimated from the value of (t), the displacement waveform U can be corrected with high accuracy in an environment where the amount of calculation is small and the influence of noise is small_j(t)。

In addition, according to the measuring method of the sixth embodiment, the measuring device 1 is provided from the outside as compared with the displacement gauge and the strain gaugeHigh degree of freedom, and calculation of displacement waveform CU using easily settable acceleration sensor_j(t), therefore, cost reduction of the measurement system 10 can be achieved.

7. Seventh embodiment

In the measurement methods of the first to sixth embodiments, the approximate expression of the deflection of the upper structure 7 is set as an expression based on the structural model of the upper structure 7, and therefore, the deflection amount w is normalized as shown in the above expression (29)_stdThe expression differs between a section where the load position a is smaller than l/2 and a section where the load position a is larger than l/2. In contrast, in the measurement method according to the seventh embodiment, the approximation formula of the deflection of the upper structure 7 is approximated by the formula of the waveform of the half wavelength of the sine wave so that the formula in the section where the load position a is smaller than l/2 is the same as the formula in the section where the load position a is larger than l/2. Hereinafter, in the seventh embodiment, the same components as those in the first to sixth embodiments are denoted by the same reference numerals, and overlapping description with the first to sixth embodiments is omitted or simplified, and the description will be mainly given of differences from the first to sixth embodiments.

In the present embodiment, the normalized deflection amount w_stdRepresented by formula (134).

[ mathematical formula 134 ]

In the formula (134), since the load position a is 0. ltoreq. a.ltoreq.l, the deflection w is normalized by the formula (134)_stdApproximately a sinusoidal half wave.

Fig. 46 shows the normalized deflection w calculated by the equation (134) when the observed position x is l/2 by a solid line_stdAn example of the waveform of (1). In fig. 46, the horizontal axis represents the position of the load P, and the vertical axis represents the normalized deflection w_std. In the example of fig. 46, the distance l between the fulcrums of the simply supported beams is 10. FIG. 46 shows the normalized deflection w calculated by the above equation (29) by a broken line_stdThe waveform of (2).

As shown in fig. 46Normalized deflection w calculated by the equation (134)_stdAnd the normalized deflection w calculated by the equation (29)_stdBy approximation of the waveform of (a), equation (29) can be replaced with equation (134). By this substitution, the above equation (39) is substituted with equation (135). The expression (135) is a normalized expression whose maximum value is 1. Equation (135) is an approximate equation of the deflection of the upper structure 7 as a structure, and is an equation of a waveform of half a wavelength of a sine wave.

[ MATHEMATICAL FORMULATION 135 ]

The formula (44) is replaced with the formula (136) according to the formula (135).

[ math formula 136 ]

The deflection waveform calculating unit 113 calculates the lane L by the equation (136)_jDeflection waveform H of upper structure 7 by each axle of running vehicle 6_jk(t)。

The path deflection waveform calculation unit 114 uses the above equation (45) to calculate the deflection waveform H calculated by the deflection waveform calculation unit 113_jk(t) adding the values to calculate the vehicle deflection waveform CP_jm(t) and according to the vehicle deflection waveform CP_jm(t) calculating the lane L_jIs of a path deflection waveform CP_j(t)。

The displacement waveform correction unit 116 corrects the path deflection waveform CP calculated by the path deflection waveform calculation unit 114_j(t) to correct the displacement waveform U_j(t)。

According to the measurement method of the seventh embodiment described above, as in the first to sixth embodiments, the measurement device 1 can estimate the integral error when integrating the acceleration acting on the upper structure 7 by the vehicle 6, and can calculate the displacement waveform CU of the upper structure 7 with high accuracy_j(t)。

8. Modification example

The present invention is not limited to the embodiment, and various modifications can be made within the scope of the present invention.

In each of the above embodiments, the polynomial for approximating the integration error is a quadratic polynomial, but may be a polynomial other than quadratic. For example, in order to improve the approximation accuracy of the integral error, the polynomial for approximating the integral error may be a polynomial of three or more times.

In each of the above embodiments, the measuring apparatus 1 calculates the displacement waveform CU by the formula (51), the formula (66), or the formula (111)_j(t), however, the displacement waveform CU may be obtained by a predetermined correlation equation_j(t) conversion to a load waveform. For example, observation point R_jLoad waveform CW of_j(t) and displacement x_jThe relation of (t) is shown in the formula (137). First order coefficient Sc of formula (137)_jAnd 0 th order coefficient Ic_jObtained by a load test using a plurality of vehicles.

[ MATHEMATICAL FORMULATION 137 ]

CW_j(t)＝Sc_j·x_j(t)+Ic_j…(137)

In formula (137), if Ic is provided_jIf it is sufficiently small, the formula (138) is obtained.

[ CHEMICAL FORM 138 ]

CW_j(t)＝Sc_j·x_j(t)…(138)

In the formula (138), the displacement x_j(t) replacement by displacement waveform CU_j(t) load waveform CW_j(t) and displacement waveform CU_jThe correlation formula of (t) is represented by formula (139). The measurement device 1 can convert the displacement waveform CU by the correlation equation (139)_j(t) conversion to load waveform CW_j(t)。

[ math formula 139 ]

CW_j(t)＝Sc_j·CU_j(t)…(139)

In each of the above embodiments, observation point P is pointed out₁～P_NObservation device for performing observation and observation point Q₁～Q_NThe observation devices for observation areThe acceleration sensor is not limited to this, and may be, for example, an impact sensor, a microphone, a strain gauge, or a load cell. The observation point P may be observed by one observation device without the observation device and the observation point corresponding to each other one to one₁～P_N、Q₁～Q_NA part or all of.

The impact sensor detects an impact acceleration as an observation point P for each axle of the vehicle 6₁～P_N、Q₁～Q_NThe response of the action of (c). The measuring device 1 is based on relative observation point P₁～P_NObtaining first observation point information according to the impact acceleration relative to the observation point Q₁～Q_NThe second observation point information is obtained from the impact acceleration. The microphone detects a sound as each axle pair observation point P for the vehicle 6₁～P_N、Q₁～Q_NThe response of the action of (c). The measuring device 1 is based on relative observation point P₁～P_NObtains first observation point information based on the sound of (1) relative to observation point Q₁～Q_NThe second observation point information is obtained. The strain gauges and the load cells detect the change in stress as respective axle pair observation points P for the vehicle 6₁～P_N、Q₁～Q_NThe response of the action of (c). The measuring device 1 is based on the observation point P₁～P_NObtaining information of a first observation point according to the stress change, and obtaining the information of the first observation point according to the observation point Q₁～Q_NThe second observation point information is obtained.

In each of the above embodiments, the vehicle 6 is in the lane L₁～L_NThe traveling directions are all the same, but the traveling direction of the vehicle 6 may be in the lane L₁～L_NIs different from the other lanes. For example, the vehicle 6 may be in the lane L₁Middle border slave observation point P₁Towards observation point Q₁Is traveling in the direction of the lane L₂Middle border slave observation point Q₂Towards observation point P₂Is driven in the direction of (1). In this case, the measuring apparatus 1 observes the observation point P based on the observation₁Acceleration data acquisition vehicle output from sensor 21The vehicle 6 enters the lane L₁According to the time of entry from observation point Q₁The acceleration data output by the sensor 22 of (6) acquires the lane L of the vehicle 6₁Exit time of exit. In addition, the measuring device 1 observes the observation point Q according to the observation₂Obtaining the vehicle 6 entering the lane L from the acceleration data outputted from the sensor 22₂According to the time of entry from observation point P₂Acquire the acceleration data output from the sensor 21 of the vehicle 6 from the lane L₂Exit time of exit.

In the above embodiments, the sensors 21, 22, and 23 are provided on the girders G of the superstructure 7, but may be provided on the surface, the inside, the lower surface of the floor F, the piers 8a, and the like of the superstructure 7. In the above embodiments, the bridge 5 is exemplified by a road bridge, but the present invention is not limited to this, and the bridge 5 may be a railway bridge, for example. In the above embodiments, the upper structure of the bridge is taken as an example of the structure, but the structure is not limited to this, and the structure may be any object that deforms by the movement of the moving body.

The above embodiment and modification are merely examples, and are not limited thereto. For example, the embodiments and the modifications may be combined as appropriate.

The present invention includes substantially the same configurations as those described in the embodiments, for example, configurations having the same functions, methods, and results, or configurations having the same objects and effects. The present invention includes a configuration in which the immaterial portions of the configurations described in the embodiments are replaced. The present invention includes a configuration that achieves the same operational effects as the configurations described in the embodiments or a configuration that achieves the same object. The present invention includes a configuration in which a known technique is added to the configuration described in the embodiment.