Finite space electric field distribution determining method and system
阅读说明：本技术 有限空间电场分布确定方法及系统 (Finite space electric field distribution determining method and system ) 是由 黄俊革 刘宇 漆玉茂 张彧 裴健 卢思同 鲁宁琦 谢圣 于 2019-11-22 设计创作，主要内容包括：本发明提供了一种有限空间电场分布确定方法及系统,本发明适用于电法在有限空间中的应用,本发明结合实际应用,提出了有限空间中受边界影响下的电场分布规律,并利用镜像法进行建模计算的方法。所述方法包括：获取有限空间的大小、介质电阻率和供电点、观测点的位置,将所述大小及位置输入到基于镜像法的成像器中,再将所述成像器的输出输入到预设分类器中,基于所述分类器的输出和介质电阻率计算电场分布。该方法及系统适用于任意装置下、各种边界的有限空间电场分布计算,使得有限空间中电场分布的理论值计算更贴近实际测量下的真实情况。(The invention provides a method and a system for determining electric field distribution in a finite space, which are suitable for application of an electric method in the finite space. The method comprises the following steps: the method comprises the steps of obtaining the size of a limited space, the resistivity of a medium, the position of a power supply point and the position of an observation point, inputting the size and the position into an imager based on a mirror image method, inputting the output of the imager into a preset classifier, and calculating the distribution of an electric field based on the output of the classifier and the resistivity of the medium. The method and the system are suitable for the finite space electric field distribution calculation of various boundaries under any device, so that the theoretical value calculation of the electric field distribution in the finite space is closer to the real situation under actual measurement.)
1. A method for determining electric field distribution in a finite space, comprising:
acquiring the size of a limited space, the resistivity of a medium, the positions of a power supply point and an observation point;
inputting the size of the finite space, the resistivity of the medium, the positions of the power supply point and the observation point into an imager based on a mirror image method to obtain corresponding output;
inputting the output of the imager into a classifier based on a mirror image set to obtain corresponding output;
calculating an electric field distribution based on the output of the classifier and the medium resistivity.
2. The finite space electric field distribution determining method according to claim 1, wherein acquiring the size of the finite space, the medium resistivity, and the positions of the feeding point and the observation point comprises:
and acquiring the length, width and height of the limited space, and establishing a space model and converting an analytic space.
3. The finite space electric field distribution determining method of claim 2, wherein resolving the spatial transformation comprises:
the translation of the analysis space includes a representation of the finite space and a representation of the location of the supply points, which refer to the location of the two opposite point current sources A, B, and the observation points, which refer to the location of the two measurement electrodes M, N.
4. The finite space electric field distribution determining method of claim 3, wherein calculating an electric field distribution based on the output of the classifier and the medium resistivity comprises:
the potential values, the electric field strengths and the MN potential differences of the two opposite point current sources A, B or mirror images thereof on the two measuring electrodes M, N are calculated in a layered mode according to the following formula:
in the formula, I is the current intensity of the power supply loop; rho is the dielectric resistivity;distances a to M, B to N, respectively;
calculating the potential difference variation of each layer of the measuring electrode M, N, wherein the formula is as follows:
finding the potential difference of the measuring electrode M, N with the variation smaller than 1%, and calculating the corresponding apparent resistivity, wherein the formula is as follows:
in the formula, ρsIs the apparent resistivity of the medium; and K is a device coefficient and is related to power supply and measurement of electrode spacing.
5. The finite space electric field distribution determining method according to claim 1, wherein before obtaining the size of the finite space, the medium resistivity, the power feeding point, and the position of the observation point, the method further comprises:
and deducing and verifying the electric field distribution rule of the finite space.
6. The finite space electric field distribution determining method according to claim 5, wherein the deriving and verifying of the electric field distribution law of the finite space includes:
the method comprises the steps of imager model building based on a mirror image method and classifier model building based on a mirror image set.
7. The finite space electric field distribution determining method of claim 1, wherein the imager based on the mirror method includes an imaging model of a point current source at a power supply point with respect to a boundary of a finite space and an imaging model of a point current source at a power supply point with respect to a corner of a finite space.
8. The finite space electric field distribution determining method of claim 1, wherein the classifier based on the mirror image set is used for performing hierarchical classification on the parent-child relationship of the mirror image; and calculating the importance of the mirror on the influence of the electric field, and classifying the effective mirror and the ineffective mirror.
9. A finite spatial electric field distribution determining system, comprising:
the acquisition unit of the finite space is used for acquiring the size of the finite space, the resistivity of the medium, the position of the power supply point and the position of the observation point;
the finite space conversion unit is used for establishing a space model and converting the acquired attribute into the representation of an analysis space;
the imaging unit is used for inputting the size of the finite space, the resistivity of the medium, the power supply point and the position of the observation point into an imager based on a mirror image method to obtain corresponding output;
the classification unit is used for inputting the output of the imager into a classifier based on a mirror image set to obtain corresponding output;
and the electric field distribution calculation unit is used for calculating the potential value of an observation point in the electric field of the finite space, the electric field strength and the potential difference thereof according to the output of the classifier, and further calculating the change rate of the potential difference of each layer and the apparent resistivity of the finite space.
Technical Field
The invention relates to a method and a system for determining electric field distribution in a limited space.
Background
When a direct current method is adopted to conduct exploration of a limited space medium, certain deviation of electric field distribution and actual exists due to the influence of experiments and field environments. In addition, the internal electric field of the limited space is difficult to analyze by using the edge value effect of the half space or the full space, and an analytic solution is given.
Therefore, the distribution rule of the electric field in the limited space in the medium is researched, the influence factor is large, and the theoretical support is lacked.
Disclosure of Invention
The invention aims to provide a method and a system for determining electric field distribution in a limited space.
In order to solve the above problems, the present invention provides a method and a system for determining electric field distribution in a limited space, comprising:
acquiring the size of a limited space, the resistivity of a medium, the positions of a power supply point and an observation point;
inputting the size of the finite space, the resistivity of the medium, the positions of the power supply point and the observation point into an imager based on a mirror image method to obtain corresponding output;
inputting the output of the imager into a classifier based on a mirror image set to obtain corresponding output;
calculating an electric field distribution based on the output of the classifier and the medium resistivity.
Further, in the above method, acquiring the size of the finite space, the medium resistivity, and the position of the power supply point and the observation point includes:
and acquiring the length, width and height of the limited space, and establishing a space model and converting an analytic space.
Further, in the above method, resolving the spatial transformation includes:
the translation of the analysis space includes a representation of the finite space and a representation of the location of the supply points, which refer to the location of the two opposite point current sources A, B, and the observation points, which refer to the location of the two measurement electrodes M, N.
Further, in the above method, calculating an electric field distribution based on the output of the classifier and the medium resistivity includes:
the potential values, the electric field strengths and the MN potential differences of the two opposite point current sources A, B or mirror images thereof on the two measuring electrodes M, N are calculated in a layered mode according to the following formula:
in the formula, I is the current intensity of the power supply loop; rho is the dielectric resistivity;
calculating the potential difference variation of each layer of the measuring electrode M, N, wherein the formula is as follows:
finding the potential difference of the measuring electrode M, N with the variation smaller than 1%, and calculating the corresponding apparent resistivity, wherein the formula is as follows:
in the formula, ρsIs the apparent resistivity of the medium; and K is a device coefficient and is related to power supply and measurement of electrode spacing.
Further, in the above method, before obtaining the size of the finite space, the medium resistivity, and the position of the feeding point and the observation point, the method further includes:
and deducing and verifying the electric field distribution rule of the finite space.
Further, in the above method, derivation and verification of the electric field distribution law in the finite space includes:
the method comprises the steps of imager model building based on a mirror image method and classifier model building based on a mirror image set.
Further, in the above method, the imager based on the mirror method includes an imaging model of a point current source at the power supply point with respect to a boundary of the limited space and an imaging model of a point current source at the power supply point with respect to a corner of the limited space.
Further, in the above method, the classifier based on the mirror image set is used for performing hierarchical classification on parent-child relationships of mirror images; and calculating the importance of the mirror on the influence of the electric field, and classifying the effective mirror and the ineffective mirror.
According to another aspect of the present invention, there is also provided a finite spatial electric field distribution determining system, including:
the acquisition unit of the finite space is used for acquiring the size of the finite space, the resistivity of the medium, the position of the power supply point and the position of the observation point;
the finite space conversion unit is used for establishing a space model and converting the acquired attribute into the representation of an analysis space;
the imaging unit is used for inputting the size of the finite space, the resistivity of the medium, the power supply point and the position of the observation point into an imager based on a mirror image method to obtain corresponding output;
the classification unit is used for inputting the output of the imager into a classifier based on a mirror image set to obtain corresponding output;
and the electric field distribution calculation unit is used for calculating the potential value of an observation point in the electric field of the finite space, the electric field strength and the potential difference thereof according to the output of the classifier, and further calculating the change rate of the potential difference of each layer and the apparent resistivity of the finite space.
Compared with the prior art, the invention provides the method for solving the electric field distribution condition of the finite space by adopting the mirror image method, realizes the calculation of the electric field distribution of the finite space under any device and various boundaries, and leads the theoretical derivation value to be closer to the measurement value under the actual condition.
In addition, the method is combined with practical application and research, is suitable for tests of randomly selecting the positions of a limited space, a power supply point and an observation point, and develops a new analytical calculation method and a new analytical calculation system for the limited space-oriented electrical method application research.
Drawings
FIG. 1 is a flow chart of an implementation of a finite space electric field distribution calculation method provided by an embodiment of the present invention;
FIG. 2 is a diagram of a finite space model provided by an embodiment of the present invention;
FIG. 3 is a schematic diagram of imaging a surface of a limited space based on a mirror image method according to an embodiment of the present invention;
FIG. 4 is a schematic diagram of imaging a bottom surface of a limited space based on a mirror image method according to an embodiment of the present invention;
FIG. 5 is a schematic diagram of measuring the distribution of an applied electric field on a surface in a finite space based on a symmetric four-stage method according to an embodiment of the present invention;
FIG. 6 is a schematic structural diagram of a finite space electric field distribution computing system according to an embodiment of the present invention.
Detailed Description
In order to make the aforementioned objects, features and advantages of the present invention comprehensible, embodiments accompanied with figures are described in further detail below.
As shown in fig. 1, the present invention provides a method for determining electric field distribution in a limited space, comprising:
step S1, obtaining the size of the finite space, the medium resistivity, the power supply point and the position of the observation point;
step S2, inputting the size of the finite space, the medium resistivity, the power supply point and the position of the observation point into an imager based on a mirror image method to obtain corresponding output;
step S3, inputting the output of the imager into a classifier based on a mirror image set to obtain corresponding output;
step S4, calculating an electric field distribution based on the output of the classifier and the medium resistivity.
The method is suitable for application of an electrical method in a limited space, provides an electric field distribution rule under the influence of a boundary in the limited space by combining practical application, and utilizes a mirror image method to perform modeling calculation. The method comprises the following steps: the method comprises the steps of obtaining the size of a limited space, the resistivity of a medium, the position of a power supply point and the position of an observation point, inputting the size and the position into an imager based on a mirror image method, inputting the output of the imager into a preset classifier, and calculating the distribution of an electric field based on the output of the classifier and the resistivity of the medium. The method is suitable for the finite space electric field distribution calculation of various boundaries under any device, so that the theoretical value calculation of the electric field distribution in the finite space is closer to the real situation under actual measurement.
In an embodiment of the method for determining electric field distribution in finite space of the present invention, obtaining the size of finite space, the resistivity of medium, and the positions of power supply points and observation points includes:
and acquiring the length, width and height of the limited space, and establishing a space model and converting an analytic space.
In an embodiment of the finite space electric field distribution determining method of the present invention, the resolving the transformation of the space includes:
the translation of the analysis space includes a representation of the finite space and a representation of the location of the supply points, which refer to the location of the two opposite point current sources A, B, and the observation points, which refer to the location of the two measurement electrodes M, N.
In an embodiment of the method for determining electric field distribution in finite space of the present invention, before obtaining the size of finite space, the resistivity of medium, the positions of power supply points and observation points, the method further includes:
and deducing and verifying the electric field distribution rule of the finite space.
In an embodiment of the method for determining electric field distribution in a finite space of the present invention, deriving and verifying an electric field distribution law in a finite space includes:
the method comprises the steps of imager model building based on a mirror image method and classifier model building based on a mirror image set.
In an embodiment of the finite space electric field distribution determining method of the invention, the imager based on the mirror image method comprises an imaging model of a point current source at a power supply point relative to a boundary of a finite space and an imaging model of a point current source at a power supply point relative to a corner of the finite space.
In an embodiment of the finite space electric field distribution determining method of the present invention, the classifier based on the mirror image set is configured to perform hierarchical classification on parent-child relationships of mirror images; and calculating the importance of the mirror on the influence of the electric field, and classifying the effective mirror and the ineffective mirror.
In an embodiment of the finite space electric field distribution determining method of the present invention, calculating an electric field distribution based on the output of the classifier and the medium resistivity includes:
the potential values, the electric field strengths and the MN potential differences of the two opposite point current sources A, B or mirror images thereof on the two measuring electrodes M, N are calculated in a layered manner, and the formula (the potential values and the electric field strengths take the observation point M as an example) is as follows:
in the formula, I is the current intensity of a power supply loop, and the unit is mA; rho is the dielectric resistivity, and the unit is omega m;
calculating the potential difference variation of each layer of the measuring electrode M, N, wherein the formula is as follows:
finding the potential difference of the measuring electrode M, N with the variation smaller than 1%, and calculating the corresponding apparent resistivity, wherein the formula is as follows:
in the formula, ρsApparent resistivity of the medium is shown in units of omega-m; and K is a device coefficient and is related to power supply and measurement of electrode spacing.
Specifically, in the embodiment of the present invention, the size of the finite space and the resistivity of the medium are obtained, specifically, the length, the width, and the height of the finite space medium are obtained by a distance measuring device based on an electronic sensor through a measuring device, and the resistivity of the finite space medium is obtained by a resistivity measuring device based on a specimen holder.
Here, the obtained attribute parameters of the finite space need to be transformed by a transformation unit device, as shown in fig. 2, which is a schematic diagram of a finite space model transformed by the transformation unit device.
In the figure, a space rectangular coordinate system formed by an x axis, a y axis, a z axis and an o point is an analytical model of a space; a. b and c respectively represent the length, width and height of a limited space; A. b is a power supply point, namely the positions of two opposite-point current sources; m, N are observation points, i.e. the positions of the two measuring electrodes.
Further, the transformation model is stored in the finite space electric field distribution calculation system.
The storage expresses the finite space as a plane formula in a space rectangular coordinate system, and the formula is as follows:
Ax+By+Cz+D＝0；
the A, B, M, N point location is represented as a coordinate point in a rectangular spatial coordinate system, such as a (3, 2, 7).
It should be noted that, because the size of the finite space is uncertain, the transformation project after the acquisition is located at the first octave of the rectangular spatial coordinate system as much as possible, which is convenient for the subsequent steps.
Step S2, inputting the size and position into a mirror method based imager;
in the embodiment of the invention, the imager based on the mirror image method is constructed in advance, the size of the acquired limited space, the power supply point and the observation point position are input into the imager, and the imager performs imaging on each boundary and each corner or iterative imaging on the point current source.
The iterative imaging means imaging the mirror image of the point current source and sequentially iterating.
Exemplarily, the point current source is used for imaging of each boundary, as shown in fig. 3 and 4, the point power source a
In addition to the above description, the mirror image points a (12 or 21), a (23 or 32), a (34 or 43), and a (14 or 41) of the point current source, which are quadratic mirror symmetry in the embodiment of imaging with respect to each boundary, are substantially mirror images of the point current source with respect to the imaging of each corner, that is, the right angle space surrounded by the two intersecting surfaces.
Illustratively, as shown in fig. 3, there is a mirror image a (12 or 21) generated in the right-angle space surrounded by the surfaces No. 1 and No. 2, and similarly, the mirror images a (23 or 32), a (34 or 43), a (14 or 41) generated in the right-angle space surrounded by the other two intersecting surfaces.
Each of the above-described mirror images plus the image about the corner is calculated as one image of the imager; the output of the imager is input to the next step according to the output of each imaging until the imaging is terminated after the stop signal is fed back.
A step S3 of inputting the output based on the imager into a preset classifier;
in the embodiment of the invention, a classifier for carrying out parent-child relationship hierarchical classification and effective classification on the mirror image is constructed in advance, the output based on the imager is input into a preset classifier, and the classifier is used for identifying and classifying the output of each imaging so as to output the effective mirror image with the hierarchical attribute of the imaging.
Optionally, in order to make the output result of the classifier more accurate, before the 3 steps, the electric field distribution rule of the finite space is derived and verified, a mirror image sample is collected to form a mirror image set, and the classifier is optimized through the mirror image set, wherein the mirror image set sample includes the guess of the distribution situation of the current source mirror image of the finite space point in the
Illustratively, in the above embodiments, the point current sources are classified with respect to the imaging output of each boundary and corner, as shown in fig. 3 and 4, the imaging of a in the first-order imager is divided into a1, a2, A3, a4 (shown in fig. 3) and a bottom 1 (shown in fig. 4), and a (12 or 21), a (23 or 32), a (34 or 43), a (14 or 41), that is, the imaging including the first-order mirror plus the imaging with respect to the corner, for 9 mirror point current sources. FIG. 5 is a schematic diagram of measuring the distribution of an applied electric field on a surface of a finite space based on a symmetric four-stage method according to an embodiment of the present invention
Further, calculating the potential value and the electric field intensity of the mirror image at the observation point, the ratio of the potential value and the electric field intensity of the current source at the observation point and the potential difference change rate of the M, N two observation electrodes in the above embodiment, and evaluating the importance of the influence on the electric field; and the regulation is carried out by the M, N that the potential difference change rate of the two observation electrodes is less than 1%.
It should be added that the above steps need to be looped according to the imaging times of the imager, the greater the times, the lower the importance of the influence of the image on the electric field, and when it is lower than the above specification set value (1%), the feedback stop signal is sent to step S2.
Optionally, based on
the superposition of the images of the corners influences the guess; illustratively, the imaging of a in the corner is divided into the superposition of two mirror point current sources a12 and a 21.
The guessing of the layering is performed according to the mirror symmetry times in the above steps.
Here, based on the above guesses, comparison with experimental data measured on a surface in a limited space based on the symmetric quaternary method is performed; compared with the electrical method simulation result based on the finite element method. It is found that only the theoretical data provided by the classification method described in the above embodiment is close to experimental data and simulation data.
It has to be noted here that the finite space electric field distribution calculation method provided by the present invention does not detail the theoretical derivation verification, nor refute other theoretical guesses, but only clearly describes the embodiment of the present invention.
Step S4, calculating an electric field distribution based on the output of the classifier and the medium resistivity.
Here, based on the output of the classifier and the dielectric resistivity, the potential values, the electric field strengths, and the MN potential differences of the A, B two electrodes or mirror images thereof at the observation points M and N are sequentially calculated in layers, and the formula (the potential values and the electric field strengths are exemplified by the observation point M) is as follows:
wherein I is the current intensity of the power supply loop, and the unit is mA; rho is the dielectric resistivity, and the unit is omega m;
calculating the potential difference variation of each layer MN, wherein the formula is as follows:
finding the potential difference of MN with the variable quantity less than 1%, and calculating the corresponding apparent resistivity, wherein the formula is as follows:
where rhosApparent resistivity of the medium is shown in units of omega-m; and K is a device coefficient and is related to power supply and measurement of electrode spacing.
In this embodiment, the electric field distribution law of the finite space can be reflected.
According to another aspect of the present invention, there is also provided a finite spatial electric field distribution determining system, including:
the acquisition unit of the finite space is used for acquiring the size of the finite space, the resistivity of the medium, the position of the power supply point and the position of the observation point;
the finite space conversion unit is used for establishing a space model and converting the acquired attribute into the representation of an analysis space;
the imaging unit is used for inputting the size of the finite space, the resistivity of the medium, the power supply point and the position of the observation point into an imager based on a mirror image method to obtain corresponding output;
the classification unit is used for inputting the output of the imager into a classifier based on a mirror image set to obtain corresponding output;
and the electric field distribution calculation unit is used for calculating the potential value of an observation point in the electric field of the finite space, the electric field strength and the potential difference thereof according to the output of the classifier, and further calculating the change rate of the potential difference of each layer and the apparent resistivity of the finite space.
Here, as shown in fig. 6, the finite space electric field distribution calculation system 6 includes: a first device, a limited-space acquisition unit 61; a second device, a space-limited conversion unit 62; third means, an imaging unit 63; fourth means, a classification unit 64; fifth means, an electric field distribution calculation unit 65.
In the above system, the specific working process of the unit may refer to the corresponding process in the foregoing method embodiment, and is not described herein again.
The embodiments in the present description are described in a progressive manner, each embodiment focuses on differences from other embodiments, and the same and similar parts among the embodiments are referred to each other.
Those of skill would further appreciate that the various illustrative elements and algorithm steps described in connection with the embodiments disclosed herein may be implemented as electronic hardware, computer software, or combinations of both, and that the various illustrative components and steps have been described above generally in terms of their functionality in order to clearly illustrate this interchangeability of hardware and software. Whether such functionality is implemented as hardware or software depends upon the particular application and design constraints imposed on the implementation. Skilled artisans may implement the described functionality in varying ways for each particular application, but such implementation decisions should not be interpreted as causing a departure from the scope of the present invention.
It will be apparent to those skilled in the art that various changes and modifications may be made in the invention without departing from the spirit and scope of the invention. Thus, if such modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include such modifications and variations.
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