阅读说明：本技术 一种水下地形空间无失真监测方法及系统 (Underwater terrain space distortion-free monitoring method and system ) 是由 徐春莺 于 2020-10-30 设计创作，主要内容包括：本发明公开了一种水下地形空间无失真监测方法及系统,为克服水下地形难以进行有限元分析等缺点,将无失真重构水下地形形态的问题转化为弹性铁条的问题,因此对弹性的特性进行分析,获得传感器间的最大间隔,针对随机非均匀采样情况所需的采样密度较小,并且测量的误差小,能够适用于水下地形的空间异质性与复杂性。(The invention discloses a method and a system for monitoring underwater topography space without distortion, which aim to overcome the defects that finite element analysis is difficult to perform on underwater topography and the like, and convert the problem of reconstructing underwater topography form without distortion into the problem of elastic iron bars, so that the characteristics of elasticity are analyzed to obtain the maximum interval between sensors, the sampling density required by random non-uniform sampling conditions is small, the measurement error is small, and the method and the system can be suitable for the spatial heterogeneity and complexity of underwater topography.)

1. An underwater terrain space distortion-free monitoring method, characterized by comprising the steps of:

s100, obtaining characteristic data of the substrate according to the range to be monitored and the intensity of topographic relief change, wherein the characteristic data comprises the length, the elastic modulus, the unit volume mass and the cross section area of the substrate;

s200, calculating the vibration frequency of the substrate according to the characteristic data to obtain the main vibration mode of the substrate;

s300, selecting the first n-order master vibration mode of the substrate to synthesize the root of the underwater topography form and calculating the frequency equation of the substrate;

s400, solving a required maximum sampling interval according to the root of the fundamental frequency equation to serve as a maximum interval between the sensors;

s500, arranging a plurality of sensors on the selected elastic iron strips according to the maximum intervals among the sensors, and laying the elastic iron strips on the underwater terrain according to the maximum intervals among the sensors.

2. An underwater terrain space distortion-free monitoring method according to claim 1, wherein in S100, the substrate is an elastic iron bar, and the free vibration of the substrate can be regarded as linear superposition of a plurality of main vibration modes.

3. The method for undistorted monitoring of underwater topographic space as claimed in claim 2, wherein in S400, the main vibration mode of the substrate is a fixed vibration mode, also called a natural vibration mode, when the substrate is subjected to main vibration, the main vibration is a free vibration of the substrate according to any natural frequency; the natural mode shape is the same as the natural frequency, and only depends on the inherent physical properties of the system, and is not related to the initial condition.

4. The method for monitoring the underwater topography space without distortion according to claim 1, wherein in S300, the method for selecting the root of the frequency equation of the substrate of the first n-order dominant mode synthesis underwater topography form of the substrate comprises:

the transverse free vibration equation, the frequency equation and the principal mode of vibration of the substrate can be deduced by a force balance equation or a moment balance equation, and the equations are respectively as follows:

lateral free vibration equation of the substrate:

the mass of the substrate in unit volume is rho, the cross-sectional area of the substrate is A, the elastic modulus of the material is E, the moment of inertia of the cross section to a neutral axis is J, and the bending rigidity EJ is a constant;

frequency equation: the root of the fundamental frequency equation is β l: tg β l ═ th β l (2);

where l is the length of the substrate and β is the angular frequency of the spatial domain.

5. The method for undistorted monitoring of underwater topography space according to claim 4, wherein in S400, the method for solving the root of the required maximum sampling interval from the root of the fundamental frequency equation is:

the main vibration mode is as follows: y is_i(x)＝C_i[cosβ_ix-chβ_ix+r_i(sinβ_ix-shβ_ix)] (3)；

Wherein: c_iIs a coefficient; r is_iIn formula (4), the index i in the lower right corner represents the order;

for the principal mode shape of the substrate, β_iI.e. the angular frequency of the spatial domain, thenIs the frequency of the spatial domain and is,for the spatial domain period, the spatial domain period is recorded asThe nyquist sampling theorem for the analog time domain is:

where k is the space domain sampling interval, k_MAXFor the maximum sampling interval of the spatial domain, the original continuous signal can be recovered through the sampling points at this time, that is, the original form of the substrate can be recovered, and equation (5) can be specifically expressed as:

substituting the formula (2) into the formula (6), and obtaining the maximum sampling interval of the distortion-free recovered substrate by knowing the length of the substrate; the sensor monitors according to the maximum sampling interval of the largest substrate.

6. An underwater terrain space distortion-free monitoring system, the system comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, the processor executing the computer program to run in the units of the following system:

the device comprises a substrate characteristic acquisition unit, a data acquisition unit and a data acquisition unit, wherein the substrate characteristic acquisition unit is used for acquiring characteristic data of a substrate according to a range to be monitored and the intensity of topographic relief change, and the characteristic data comprises the length, the elastic modulus, the unit volume mass and the cross sectional area of the substrate;

the main vibration mode calculation unit is used for calculating and obtaining the vibration frequency of the substrate according to the characteristic data so as to obtain the main vibration mode of the substrate;

the base frequency calculation unit is used for selecting the first n-order master vibration mode of the base to synthesize the root of the underwater topography equation and calculating the base frequency equation;

the maximum sampling interval calculation unit is used for solving the required maximum sampling interval according to the root of the fundamental frequency equation to be used as the maximum interval between the sensors;

and the sensor laying unit is used for laying the plurality of sensors on the selected plurality of elastic iron strips according to the maximum intervals among the sensors and laying the elastic iron strips on the underwater terrain according to the maximum intervals among the sensors, so that the non-distortion monitoring of the terrain is realized.

Technical Field

The disclosure relates to the technical field of underwater topography measurement, in particular to a distortion-free monitoring method and system for an underwater topography space, and more particularly relates to a contact-type sensing array-based research method for distortion-free monitoring characteristics of the underwater topography space.

Background

Underwater terrain monitoring is the observation of the deformation of the terrain over a period of time. Unlike static measurement, the process is a space-time dynamic process continuously changing along with time or space, monitoring data has obvious time sequence characteristics and space regional characteristics, and two factors of sensing distance and sampling period need to be considered. At a certain moment, the morphology of the terrain at the moment is formed through sampling, quantization and reconstruction of the sensing array which is distributed in space, and the process must meet the sampling condition of the space domain. Even if the sensing array is linearly arranged on the underwater terrain at equal intervals, when the sensing array deforms along with the terrain, the sampling intervals are not equal any more, and the uniform sampling of the space domain is changed into the non-uniform sampling of the space domain. For a certain sensor to move along with the terrain in a time domain, the sampling theorem in the time domain must be satisfied in order to ensure that the deformation process of the monitored terrain is not distorted, and the process generally satisfies the Nyquist sampling theorem. Therefore, this patent will focus on spatial domain sampling conditions.

Kadec et al studied the non-uniform sampling condition of the integer point perturbation, called Kadec theorem. Hyun et al analyzed the reconstruction technique of random non-uniformly sampled signals from the practical application of non-uniformly sampled signal reconstruction. Hu and the like research the structure of a non-uniform sequence set by using an abstract mathematical method, and provide a transformation set and a Lagrangian interpolation function set which can decompose a non-uniform sampling sequence of band-limited signals into unit pulses sin pi t. Souglo discusses the sampling problem with randomness using multidimensional linear theory. Guni uses the Cauchy residual theory to derive a reconstruction formula that can be used for finite point non-uniformly sampled signals.

In addition, the optimal arrangement criterion theory of the sensor also comprises an identification error minimum criterion, a modal strain energy criterion, a model reduction criterion, an interpolation fitting criterion and the like. The optimization layout problem is equivalent to a combined optimization problem, and m sensors are arranged on n positions by taking the minimum recognition error of system parameters or finite element analysis as a criterion. Aiming at different optimization criteria, corresponding processing methods are provided, and the processing methods comprise a nonlinear programming optimization method, a sequence method, an inference algorithm, a random algorithm, a genetic algorithm and the like. At present, the following two problems mainly exist in the existing technical scheme: (1) the Kadec theorem is directed to the random non-uniform sampling case, which requires a large sampling density. (2) The minimum error criterion is a probability-based statistical method, while the modal strain energy criterion is a finite element analysis method for the object to be measured, and the minimum error criterion and the modal strain energy criterion are not suitable for the spatial heterogeneity and complexity of the underwater terrain.

Disclosure of Invention

The invention aims to provide a method and a system for monitoring underwater terrain space without distortion, which are used for solving one or more technical problems in the prior art and at least provide a beneficial selection or creation condition.

In order to solve the problems, the present disclosure provides a technical scheme of a method and a system for monitoring an underwater topography space without distortion, which converts the problem of reconstructing the underwater topography form without distortion into the problem of an elastic iron bar in order to overcome the defects that finite element analysis is difficult to perform on the underwater topography, and the like, thereby analyzing the elastic characteristic and obtaining the maximum interval between sensors.

In order to achieve the above object, according to an aspect of the present disclosure, there is provided an underwater terrain space distortion-free monitoring method, the method including the steps of:

s100, obtaining characteristic data of the substrate according to the range to be monitored and the intensity of topographic relief change, wherein the characteristic data comprises the length, the elastic modulus, the unit volume mass and the cross section area of the substrate;

s200, calculating the vibration frequency of the substrate according to the characteristic data to obtain the main vibration mode of the substrate;

s300, selecting the first n-order master vibration mode of the substrate to synthesize the root of the underwater topography form and calculating the frequency equation of the substrate;

s400, solving a required maximum sampling interval according to the root of the fundamental frequency equation to serve as a maximum interval between the sensors;

s500, arranging a plurality of sensors on the selected elastic iron strips according to the maximum intervals among the sensors, and laying the elastic iron strips on the underwater terrain according to the maximum intervals among the sensors. Further, in S100, the substrate is an elastic iron bar, and the free vibration of the substrate (the elastic iron bar) can be regarded as linear superposition of a plurality of main vibration modes.

Further, in S300, the main vibration mode of the substrate is a fixed vibration mode, also called a natural vibration mode, when the substrate performs main vibration, the main vibration mode is a free vibration of the substrate according to any natural frequency; the natural mode shape is the same as the natural frequency, and only depends on the inherent physical properties of the system, and is not related to the initial condition.

Further, in S400, the method for calculating the root of the frequency equation of the substrate by selecting the first n-th order dominant mode synthetic underwater topography of the substrate comprises:

the transverse free vibration equation, the frequency equation and the principal mode of vibration of the substrate can be deduced by a force balance equation or a moment balance equation, and the equations are respectively as follows:

lateral free vibration equation of the substrate:

the mass of the substrate in unit volume is rho, the cross-sectional area of the substrate is A, the elastic modulus of the material is E, the moment of inertia of the cross section to a neutral axis is J, the bending rigidity EJ is a constant, and x and y are respectively an abscissa value and an ordinate value on the substrate;

frequency equation: the root of the fundamental frequency equation is β l: tg β l ═ th β l (2);

where l is the length of the substrate and β is the angular frequency of the spatial domain;

further, in S600, the method for solving the root of the required maximum sampling interval according to the root of the fundamental frequency equation is as follows:

the main vibration mode is as follows:

Y_i(x)＝C_i[cosβ_ix-chβ_ix+r_i(sinβ_ix-shβ_ix)] (3)

wherein: c_iIs a coefficient; r is_iFor equation (4), the index i in the lower right hand corner represents the order of the variable, e.g. β_iRepresenting the angular frequency β, k of the ith order spatial domain_iA spatial domain sampling interval (spatial domain period) representing the ith order;

for the principal mode shape of the substrate, β_iI.e. the angular frequency of the spatial domain, thenIs the frequency of the spatial domain and is,is a spatial domain period. Noting the spatial domain period asThe nyquist sampling theorem for the analog time domain is:

where k is the space domain sampling interval, k_MAXThe maximum sampling interval in the spatial domain is that the original continuous signal can be recovered through the sampling points, namely the original form of the substrate can be recovered. Formula (6) may be embodied as:

by substituting equation (2) for equation (6), and knowing the length of the substrate (monitoring), the maximum sampling interval of the substrate which can be recovered without distortion can be obtained, i.e. the arrangement interval between the sensors should not be greater than the obtained maximum interval, and the substrate shape can be recovered from the data of the sensors without distortion.

The invention also provides an underwater terrain space distortion-free monitoring system, which comprises: a memory, a processor, and a computer program stored in the memory and executable on the processor, the processor executing the computer program to run in the units of the following system:

the device comprises a substrate characteristic acquisition unit, a data acquisition unit and a data acquisition unit, wherein the substrate characteristic acquisition unit is used for acquiring characteristic data of a substrate according to a range to be monitored and the intensity of topographic relief change, and the characteristic data comprises the length, the elastic modulus, the unit volume mass and the cross sectional area of the substrate;

the main vibration mode calculation unit is used for calculating and obtaining the vibration frequency of the substrate according to the characteristic data so as to obtain the main vibration mode of the substrate;

the base frequency calculation unit is used for selecting the first n-order master vibration mode of the base to synthesize the root of the underwater topography equation and calculating the base frequency equation;

the maximum sampling interval calculation unit is used for solving the required maximum sampling interval according to the root of the fundamental frequency equation to be used as the maximum interval between the sensors;

and the sensor laying unit is used for laying the plurality of sensors on the selected plurality of elastic iron strips according to the maximum intervals among the sensors and laying the elastic iron strips on the underwater terrain according to the maximum intervals among the sensors, so that the non-distortion monitoring of the terrain is realized.

The beneficial effect of this disclosure does: the invention provides a method and a system for monitoring underwater topography space without distortion, which are small in sampling density and small in measurement error and can be suitable for spatial heterogeneity and complexity of underwater topography aiming at random non-uniform sampling conditions.

Drawings

The foregoing and other features of the present disclosure will become more apparent from the detailed description of the embodiments shown in conjunction with the drawings in which like reference characters designate the same or similar elements throughout the several views, and it is apparent that the drawings in the following description are merely some examples of the present disclosure and that other drawings may be derived therefrom by those skilled in the art without the benefit of any inventive faculty, and in which:

FIG. 1 is a comparison of the time and spatial domains;

FIG. 2 is a graph of the base stress and external moment coordinate system;

FIG. 3 is a diagram showing the stress condition of the micro-segment of the substrate;

fig. 4 is a block diagram of an underwater terrain space distortion-free monitoring system according to the present disclosure.

Detailed Description

The conception, specific structure and technical effects of the present disclosure will be clearly and completely described below in conjunction with the embodiments and the accompanying drawings to fully understand the objects, aspects and effects of the present disclosure. It should be noted that the embodiments and features of the embodiments in the present application may be combined with each other without conflict.

The utility model provides a distortion-free monitoring method for underwater terrain space, which comprises the following steps:

a complex signal of the underwater terrain is decomposed into a composite of a plurality of sinusoidal signals. In the time domain, there is the nyquist sampling theorem, but the underwater terrain is a signal in the spatial domain. In the spatial domain, the arrangement of the sensors must satisfy the nyquist theorem for the morphology at a certain time in order to guarantee a distortion-free reconstruction of the morphology. As shown in fig. 1, in the spatial domain, the waveform is related to the spatial position, and the time domain is related to the waveform and the time. Due to the difference between the terrain form and the deformation range, the spatial frequency characteristics are different, and a uniform numerical value or a calculation formula is difficult to provide.

Therefore, the technical problem to be solved by the invention is to overcome the defects of the prior art and provide a method for researching undistorted time-space monitoring characteristics of underwater terrain deformation based on a contact type sensing array. In order to solve the technical problem, the invention is realized by the following technical scheme:

the method comprises the steps of taking an elastic iron strip as a substrate, arranging a sensing array on the elastic iron strip, and obtaining monitoring conditions of the underwater terrain by researching the monitoring conditions of the substrate, namely the space arrangement intervals of sensors.

According to the synthesis of a plurality of sinusoidal signals, the free vibration of the elastic iron strip can be regarded as the linear superposition of a plurality of main vibration modes. The free vibration of the substrate at any natural frequency is called the primary vibration, and when the primary vibration is made, the substrate has a fixed vibration form, called the natural vibration mode or the primary vibration mode. The natural mode shape is the same as the natural frequency, and only depends on the inherent physical properties of the system, and is not related to the initial condition. In the application, the first n order natural frequencies are selected. According to the spatial sampling theorem, the maximum spacing between sensors can be determined.

Establishing a coordinate system as shown in fig. 2, let y (x, t) be the transverse displacement of the cross section at the position x from the origin on the substrate at the time t, p (x, t) be the external stress distributed on the substrate per unit length, and m (x, t) be the external moment distributed on the substrate per unit length. Let the mass of the substrate per unit volume be ρ, the cross-sectional area of the substrate be A, the elastic modulus of the material be E, and the moment of inertia of the cross-section to the neutral axis be J.

As shown in fig. 3, the micro-segment dx is stressed, wherein Q, M is the shearing force and bending moment on the cross section,is the inertia force of the micro-segment, all the forces and moments in FIG. 3 are in the positive directionIs drawn.

The force balance equation has:

or written as:

wherein p is an abbreviation for p (x, t), p (x, t) is the external stress distributed on the substrate per unit length, and the mass per unit volume of the substrate is ρ; from the moment balance equation (omitting the high order small quantities) there are:

m is an abbreviation for m (x, t) which is the external moment distributed on the substrate per unit length;

or written as:

the substitution of the moment balance equation into the force balance equation is:

the relationship between bending moment and deflection is known from the assumption of a flat section of material mechanicsFor the substrate with the equal section, the bending rigidity EJ is constant, so that the transverse vibration equation of the substrate can be obtained as follows:

let p (x, t) be m (x, t) be 0 in the above equation, giving the following equation for the lateral free vibration of the substrate:

the principal vibration of the substrate can be assumed to be:

where Y (x) is the dominant mode shape or mode shape function, which is the basis function for the vibration of the substrate in space. Substituting the above equation into the free vibration equation yields:

(EJY″)″-ω²ρAY＝0 (9)；

wherein Y is an abbreviation for principal mode shape Y (x);

converting equation (9) to:

Y^Ⅳ-β⁴Y＝0 (10)；

wherein: y is^ⅣIs the 4 th derivative of y (x), β is a coefficient, is a transformation to equation (9), β specifically means the angular frequency of the spatial domain;

according to the boundary conditions, the left end of the substrate is a fixed end, the deflection y and the cornerEqual to 0, i.e.:

Y(x)＝0，EJY″(x)＝0，x＝0 (12)；

the right end of the basement is simply supported end, and amount of deflection y and moment of flexure M equals zero, promptly:

Y(x)＝0，EJY″(x)＝0，x＝l (13)；

wherein l is the length of the substrate;

then there are:

Y(0)＝Y′(0)＝0； (14)；

Y(l)＝Y″(l)＝0；

the frequency equation and the main vibration mode of the substrate vibration equation are obtained by solving the boundary condition:

tgβl＝thβl (15)；

Y_i(x)＝C_i[cosβ_ix-chβ_ix+r_i(sinβ_ix-shβ_ix)] (16)；

wherein, C_iIs a coefficient, takes on a value of [0.1,10](ii) a The index i in the lower right corner represents the order;

wherein:

for the principal mode shape of the substrate, β_iI.e. the angular frequency of the spatial domain, thenIs the frequency of the spatial domain and is,for the spatial domain period, i in the lower right corner represents the order; . Noting the spatial domain period asThe nyquist sampling theorem for the analog time domain is:

where k is the space domain sampling interval, k_MAXIs the spatial domain maximum sampling interval. At this time, the original continuous signal can be recovered through the sampling points, namely, the original form of the substrate can be recovered. Formula (18) may be embodied as:

by substituting equation (15) for equation (19), and knowing the substrate (monitoring) length l, the maximum sampling interval of the undistorted recoverable substrate, i.e., the maximum sensor placement interval, can be obtained, i.e., the maximum sensor placement interval.

An undistorted monitoring system for an underwater topographic space according to an embodiment of the present disclosure is shown in fig. 4, where the undistorted monitoring system for an underwater topographic space according to the embodiment includes: a processor, a memory and a computer program stored in and executable on the memory, the processor when executing the computer program implementing the steps in an embodiment of an underwater terrain space distortion-free monitoring system as described above.

The system comprises: a memory, a processor, and a computer program stored in the memory and executable on the processor, the processor executing the computer program to run in the units of the following system:

the device comprises a substrate characteristic acquisition unit, a data acquisition unit and a data acquisition unit, wherein the substrate characteristic acquisition unit is used for acquiring characteristic data of a substrate according to a range to be monitored and the intensity of topographic relief change, and the characteristic data comprises the length, the elastic modulus, the unit volume mass and the cross sectional area of the substrate;

the main vibration mode calculation unit is used for calculating and obtaining the vibration frequency of the substrate according to the characteristic data so as to obtain the main vibration mode of the substrate;

the base frequency calculation unit is used for selecting the first n-order master vibration mode of the base to synthesize the root of the underwater topography equation and calculating the base frequency equation;

the maximum sampling interval calculation unit is used for solving the required maximum sampling interval according to the root of the fundamental frequency equation to be used as the maximum interval between the sensors;

and the sensor laying unit is used for laying the plurality of sensors on the selected plurality of elastic iron strips according to the maximum intervals among the sensors and laying the elastic iron strips on the underwater terrain according to the maximum intervals among the sensors, so that the non-distortion monitoring of the terrain is realized. The underwater terrain space distortion-free monitoring system can be operated in computing equipment such as desktop computers, notebooks, palm computers and cloud servers. The underwater terrain space distortion-free monitoring system can be operated by a system comprising, but not limited to, a processor and a memory. It will be appreciated by those skilled in the art that the examples are merely illustrative of an undistorted monitoring system for an underwater terrain space and are not intended to be limiting, and may include more or less than a few components, or some combination of components, or different components, for example, an input output device, a network access device, a bus, etc.

The Processor may be a Central Processing Unit (CPU), other general purpose Processor, a Digital Signal Processor (DSP), an Application Specific Integrated Circuit (ASIC), a Field Programmable Gate Array (FPGA) or other Programmable logic device, discrete Gate or transistor logic device, discrete hardware component, or the like. The general purpose processor may be a microprocessor or the processor may be any conventional processor or the like, the processor is a control center of the system for operating the system for monitoring undistorted underwater topography space, and various interfaces and lines are used to connect various parts of the system for operating the entire system for monitoring undistorted underwater topography space.

The memory may be used to store the computer programs and/or modules, and the processor may implement the various functions of the system by running or executing the computer programs and/or modules stored in the memory and invoking the data stored in the memory. The memory may mainly include a storage program area and a storage data area, wherein the storage program area may store an operating system, an application program required by at least one function (such as a sound playing function, an image playing function, etc.), and the like; the storage data area may store data (such as audio data, a phonebook, etc.) created according to the use of the cellular phone, and the like. In addition, the memory may include high speed random access memory, and may also include non-volatile memory, such as a hard disk, a memory, a plug-in hard disk, a Smart Media Card (SMC), a Secure Digital (SD) Card, a Flash memory Card (Flash Card), at least one magnetic disk storage device, a Flash memory device, or other volatile solid state storage device.

While the present disclosure has been described in considerable detail and with particular reference to a few illustrative embodiments thereof, it is not intended to be limited to any such details or embodiments or any particular embodiments, but it is to be construed as effectively covering the intended scope of the disclosure by providing a broad, potential interpretation of such claims in view of the prior art with reference to the appended claims. Furthermore, the foregoing describes the disclosure in terms of embodiments foreseen by the inventor for which an enabling description was available, notwithstanding that insubstantial modifications of the disclosure, not presently foreseen, may nonetheless represent equivalent modifications thereto.