CN110889249A - Resistivity karst cave identification method based on population evolution algorithm - Google Patents

Resistivity karst cave identification method based on population evolution algorithm Download PDF

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CN110889249A
CN110889249A CN201911082582.1A CN201911082582A CN110889249A CN 110889249 A CN110889249 A CN 110889249A CN 201911082582 A CN201911082582 A CN 201911082582A CN 110889249 A CN110889249 A CN 110889249A
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李晓阳
孙瑞甲
卢春燕
罗盈洲
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Abstract

The invention discloses a resistivity karst cave identification method based on a population evolution algorithm, which mainly comprises the following steps: s1, constructing a karst cave finite element model, and solving potential distribution data of a structural measurement point by using an electric impedance method positive problem correlation formula; s2, constructing a target function of the karst cave structure, namely the target function to be optimized; and S3, continuously and iteratively optimizing the target function by using a population evolution algorithm, and storing the optimal solution after meeting the stopping criterion so as to identify the karst cave position. Compared with the traditional sensitivity or gradient matrix method, the method can accurately detect the positions of various karst caves without initial values and gradient information and is insensitive to noise. The effectiveness and robustness of the method are illustrated through two embodiments of a single karst cave and a plurality of karst caves, and compared with a particle swarm algorithm, the method has better detection precision even under certain measurement noise and good engineering application capability.

Description

Resistivity karst cave identification method based on population evolution algorithm
Technical Field
The invention relates to a resistivity karst cave identification method based on a population evolution algorithm, and belongs to the technical field of underground karst cave detection.
Background
At present, in the area where the limestone underground karst cave develops, the underground karst cave of a construction engineering field is often positioned below an underground water level, each building party aims at ensuring the safety of the building foundation, and a large amount of manpower, financial resources and time are invested to carry out the exploration work of the limestone underground karst cave of the construction engineering field in the limestone area. The underground karst cave can cause certain dangers to buildings, subways and the like, the underground karst cave is detected and processed in time, and the method has important significance to safety in construction, use and the like of the structure.
The resistivity method for detecting the karst cave problem is an optimization problem in the identification research of inverse problems, and the basic idea is as follows: the detection area, the electrode scheme and the karst cave are determined, the measured electric potential distribution data are changed, and the karst cave position can be positioned by using the changes in response to the change of the apparent resistivity of the soil layer. Namely, the method is realized by defining an objective function related to the karst cave structure and then utilizing various optimization methods to detect the position of the karst cave. The traditional resistivity cavern detection method introduces a regularization method, adopts sensitivity or a gradient matrix to identify the position of the cavern, and has the following defects: the method is sensitive to initial values and noise, and is easy to fall into a local optimal solution, so that the identification effect is poor.
Disclosure of Invention
The invention aims to provide a cross-hole resistivity karst cave identification method with practicability, effectiveness and accuracy, which can accurately detect the positions of various karst caves, is not sensitive to noise and has good engineering application capability.
The technical scheme of the invention is as follows: a cross-hole resistivity karst cave identification method comprises the following steps:
the method comprises the following steps: establishing a finite element model of a karst cave soil layer, determining an electrode scheme, and obtaining potential distribution data of a measuring point by using an electrical impedance method;
step two: constructing an objective function of the karst cave structure, namely an optimized objective function, wherein the objective function is as follows:
Figure BDA0002264411290000021
c＝[c1；c2；...；cm](1)
Figure BDA0002264411290000022
Figure BDA0002264411290000023
where g (c) is the objective function, | () | represents the 2 norm of the vector, i.e.
Figure BDA0002264411290000024
c is the apparent resistivity of each cell, Su represents the data on the set of measured potential points,
Figure BDA0002264411290000025
is the potential distribution data measured by the ith set of electrode schemes,
Figure BDA0002264411290000026
is the potential distribution data identified by the ith electrode scheme,
Figure BDA0002264411290000027
is a matrix formed by s sets of measurement data, and R (c) is a matrix formed by s sets of identification data;
step three: and continuously optimizing the objective function by using a population evolution algorithm, and finally obtaining the identification position of the karst cave after meeting the stop criterion.
In the third step of the method, the specific process of optimizing the objective function by using the population evolution algorithm is as follows:
s1, population parameters and initialization: the control parameters include the maximum number of iterations ItermaxNumber of seed groups Np, number of decision variables n, upper bound X of decision variablesmaxAnd lower bound Xmin：
Xp，q＝Xmin+r and·(Xmax-Xmin)，p＝1，2，...，Np，q＝1，2，...，n (1)
Wherein rand is in [0,1 ]]Uniformly distributed random numbers in the range, and the adaptive value f ═ of the candidate solution (f ═ f)1，f2，...，fNp) Calculated according to the following objective function:
fp＝obj(Xp，1，Xp，2，…，Xp，n)，p＝1，2，…，Np (2)
s2, new position generation stage: at this stage, the population candidate solution is considered to move around its own initial position to a better position, for candidate solution p, another candidate solution 1 is randomly selected from the population (p ≠ 1) for generating potential search directions, and the positions are updated according to the distance between the old and new positions of the candidate solution p by the following two models:
(i) model 1: the new position of the candidate solution p is directly learned to the candidate solution 1, and the exploration radius dynamically changes along with iteration:
Figure BDA0002264411290000031
Figure BDA0002264411290000032
(ii) model 2: a new position of the solution candidate p is generated around the home position:
Figure BDA0002264411290000033
s3, spatial search enhancement stage: to further enhance the in-depth search for each dimension, the following steps are taken for each iteration: (i) finding the best and worst candidate solutions in the population; (ii) by changing the value of one dimension while maintaining the values of the other dimensions; (iii) comparing the newly generated solution with the fitness value of the original solution, and reserving a better solution; (iv) repeating steps (ii) and (iii) for other aspects, respectively, the newly created solution being generated by the following formula:
Figure BDA0002264411290000034
s4, stop criterion stage: saving the current optimal solution, and if the maximum iteration times are met, terminating the algorithm; otherwise, steps S2 and S3 will be repeated.
Compared with the prior art, the technical scheme of the invention has the beneficial effects that: the method constructs the target function through the potential distribution data of the karst cave structure measuring points, utilizes the metaheuristic algorithm to identify the karst cave position, is insensitive to initial values and noise, is not easy to fall into a local optimal solution, and has better efficiency and precision.
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FIG. 1 is a flow chart of a solution cavity identification problem normalized to an optimization problem;
FIG. 2 is a schematic diagram of a flow chart of an implementation of a population evolution algorithm;
FIG. 3 is a finite element model of a single karst cave in example 1 of the present invention;
FIG. 4 is a finite element model of a plurality of karsts in embodiment 2 of the present invention;
FIG. 5 shows the result of the detection in the absence of noise by the method of the present invention in example 1 of the present invention;
FIG. 6 shows the results of the detection in the presence of 0.1% noise in example 1 of the present invention;
FIG. 7 is a detection result of the particle swarm optimization under the noise-free condition in embodiment 1 of the present invention;
FIG. 8 is a graph showing the detection result of the particle swarm optimization in the presence of 0.1% noise in example 1 of the present invention;
FIG. 9 is a comparison graph of the convergence curves of the algorithm for a single cave with 0.1% noise in example 1 of the present invention.
FIG. 10 shows the result of the detection in the absence of noise by the method of the present invention in example 2 of the present invention;
FIG. 11 shows the results of the detection in the presence of noise by the method of the present invention in example 2 of the present invention;
FIG. 12 shows the detection result of the particle swarm optimization in the noise-free case in embodiment 2 of the present invention;
FIG. 13 shows the detection results of the particle swarm optimization in the presence of 0.1% noise in example 2 of the present invention;
FIG. 14 is a comparison graph of the convergence curves of the algorithm for multiple caverns with 0.1% noise in example 2 of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention will be further described in detail with reference to the accompanying drawings and examples.
Referring to fig. 1, the specific process of the resistivity karst cave identification method based on the population evolution algorithm of the invention comprises two steps:
(1) objective function
The karst cave model is simplified into a rectangular detection area. The current points are not identical to the potential points, but are equal in number. The positive problem solution is performed using finite elements, as follows:
Ku＝f
Figure BDA0002264411290000051
Figure BDA0002264411290000052
wherein u ═ u1；u2；…；un]Comprises all thatMeasuring node potential, f ═ f1；f2；…；fn]The current vector is characterized, different electrode schemes, and f is different. K is a stiffness matrix and the apparent resistivity c of each unit is ═ c1；c2；…；cm]Is linearly related to where KjIs a matrix of cell stiffness at unit resistivity.
When no karst cave exists in the soil layer, the apparent resistivity of all the units is taken as c0When the solution holes appear, the apparent resistivity of the unit is reduced, and the apparent resistivity of the unit with the solution holes is 3, namely cjThat is, 3( j 1,2, 3.., m) indicates that the jth unit has a cavity. By the formula of the finite element, c has a functional relation with u, and the electric potential distribution data calculated by c can be identified
Figure BDA0002264411290000067
The objective function constructed based on the potential distribution data is as follows:
Figure BDA0002264411290000061
c＝[c1；c2；...；cm](2)
Figure BDA0002264411290000062
Figure BDA0002264411290000063
where c is the apparent resistivity of each cell, Su represents the data on the set of measured potential points,
Figure BDA0002264411290000064
is the potential distribution data measured by the ith set of electrode schemes,
Figure BDA0002264411290000065
is the number of potential distributions identified by the ith group of electrode schemesAccording to the above-mentioned technical scheme,
Figure BDA0002264411290000066
is a matrix of s sets of measured data, and R (c) is a matrix of s sets of calculated data. When the measured potential distribution data and the identified potential distribution data are completely matched, the numerical value is minimum, the karst cave identification problem is equivalent to an optimization problem, a certain individual position of the population is an apparent resistivity distribution condition, and when the objective function reaches a minimum value, the position of the karst cave can be reflected through the identified apparent resistivity c, namely an optimal solution.
(2) And optimizing the target function by using a population evolution algorithm to obtain a recognition result.
Referring to fig. 2, the population evolution algorithm can be divided into the following 7 stages:
stage 1: population parameters and initialization: the control parameters include the maximum number of iterations ItermaxGroup size number Np, decision variable number n, upper bound X of decision variablesmaxAnd lower bound Xmin. These parameters are given at the start of the algorithm. Similar to other naturally inspired metaheuristic optimization algorithms, the initial population positions are randomly generated as follows:
Xp，q＝Xmin+r and·(Xmax-Xmin)，p＝1，2，...，Np，q＝1，2，...，n (1)
wherein rand is in [0,1 ]]Uniformly distributed random numbers within the range. The adaptive value f ═ f (f) of the solution candidates1，f2，...，fNp) Calculated according to the following objective function:
fp＝obj(Xp，1，Xp，2，...，Xp，n)，p＝1，2，...，Np (2)
and (2) stage: and a new position generation stage: at this stage, the population candidate solution is considered to move around its initial position to a better position. For a candidate solution p, another candidate solution l is randomly selected from the population (p ≠ l) for generating potential search directions. According to the distance between the new position and the old position of the candidate solution p, the positions are updated through the following two models:
(i) model 1: the new position of the candidate solution p is directly learned to the candidate solution l, and the exploration radius dynamically changes along with iteration:
Figure BDA0002264411290000071
Figure BDA0002264411290000072
(ii) model 2: a new position of the solution candidate p is generated around the home position:
Figure BDA0002264411290000073
in the two models, the purpose of the model 1 is to explore a solution in a feasible space, so that the exploration capability of the algorithm is improved, and the situation that the solution falls into a local optimal solution is avoided; the model 2 is used for improving the convergence performance of the algorithm, so that the development capability of the algorithm is enhanced. During each iteration, in order to balance the exploration and development capabilities of the algorithm in the search process, the two models are randomly invoked.
If the fitness value of the new location is better than the old location, the location of the candidate solution is updated, otherwise the old location is retained:
Figure BDA0002264411290000081
and (3) stage: and (3) a spatial search enhancement stage: during the search, all dimensions of each candidate solution are updated simultaneously. However, the variation of one-dimensional variables may have a negative effect on other dimensional variables, resulting in poor convergence performance for each dimension. To further enhance the in-depth search for each dimension, the following steps are taken for each iteration: (i) finding the best and worst candidate solutions in the population; (ii) generating another solution from the best candidate by changing the value of one dimension while maintaining the values of the other dimensions; (iii) comparing the newly generated solution with the fitness value of the original solution, and reserving a better solution; (iv) (iv) repeating steps (ii) and (iii) separately for other aspects. The newly generated solution is generated by the following formula:
Figure BDA0002264411290000082
and (4) stage: a stopping criterion stage: if the maximum number of iterations is met, the algorithm will terminate: otherwise, the two processes of the stage 2 and the stage 3 are repeated, and a new position and an enhanced dimension search are generated.
As the population evolution algorithm belongs to a population intelligent algorithm, the population evolution algorithm can be used for solving a nonlinear problem, and the resistivity method for detecting the karst cave problem is a typical nonlinear problem. In combination with a population evolution algorithm, firstly, a finite element model of a karst cave is identified according to a resistivity method of a detection area, the corresponding karst cave position is calibrated according to the apparent resistivity of a unit, the set input and output currents (an electrode scheme) are solved according to a positive problem formula, the potential distribution of the detection area is solved, in the practical engineering, only the potential distribution condition can be obtained, but the apparent resistivity distribution is solved according to the potential distribution, the problem is nonlinear, therefore, the apparent resistivity distribution condition of the detection area is solved by combining the population evolution algorithm, the position of the karst cave is obtained (an objective function is established according to the potential distribution condition obtained by the positive problem, a certain body position of a population is the apparent resistivity distribution condition, parameters such as the initial position of the individual, the number of the individual and the like are set, then, the continuous iteration of the algorithm is carried out, after the stopping criterion is met, the resulting optimal individual location is the identified apparent resistivity profile).
Example 1: single karst cave model location identification
And establishing a single karst cave finite element model as shown in FIG. 3, dividing the rectangular detection area into 64 units, and detecting by adopting an underground karst cave model with 64 units. The length and width of the rectangular detection area are 4m by 4m, and each side is uniformly divided into 8 units; and detecting the underground karst cave by adopting an electrical impedance imaging method. Assuming that cell number 28 is equivalent to 3 in apparent resistivity, the parameters in the algorithm are set: maximum number of iterations ItermaxThe number of population sizes Np and the number of decision variables n are respectively 200, 250 and64. the noise levels were 0% and 0.1%, respectively.
As can be seen from FIGS. 5-8, the position of the karst cave can be detected by the population evolution algorithm, and the particle swarm algorithm gives a lot of wrong identifications. The karst cave position can be accurately identified by a population evolution algorithm, and the relative error of actual data and identification data is extremely small. Even under the influence of artificial noise, the relative error is within 1.3 percent; as can be seen from the convergence curve of the algorithm in FIG. 9, the convergence rate of the population evolution algorithm is significantly faster than that of the particle swarm algorithm, and the final convergence value is much smaller.
Example 2: multiple karst cave model position identification
As shown in FIG. 4, in the present embodiment, for multi-unit cavern detection, an electrical impedance imaging method is used to detect the underground cavern. Assuming that cells 12 and 47 are equivalent to 3 in apparent resistivity, the parameters in the algorithm are set: maximum number of iterations ItermaxThe population size number Np and the decision variable number n are 200, 250 and 64, respectively. The noise levels were 0% and 0.1%, respectively.
As can be seen from FIGS. 10-13, the population evolution algorithm can accurately identify the karst cave position in the absence of noise. In contrast, particle swarm optimization cannot detect efficiently; it can be seen from the convergence curve of the algorithm in fig. 14 that the convergence rate of the population evolution algorithm is significantly faster than that of the particle swarm algorithm, and the final convergence value is much smaller, although the number of the recognition units is larger, the population evolution algorithm is still feasible and accurate in the aspect of karst cave detection and is insensitive to noise.
It should be understood that the above-described embodiments of the present invention are only examples for clearly illustrating the present invention, and those skilled in the art can modify the forms of the present invention based on the above description, such as expanding the detection range, changing the location of the cavern, etc., and are not exhaustive herein. Any modification, equivalent replacement, and improvement made within the spirit and principle of the present invention should be included in the protection scope of the claims of the present invention.

Claims (2)

1. A resistivity karst cave identification method based on a population evolution algorithm is characterized by comprising the following steps:
the method comprises the following steps: establishing a finite element model of a karst cave soil layer, determining an electrode scheme, and obtaining potential distribution data of a measuring point by using an electrical impedance method;
step two: constructing an objective function of the karst cave structure, namely an optimized objective function, wherein the objective function is as follows:
Figure FDA0002264411280000011
where g (c) is the objective function, | () | represents the 2 norm of the vector, i.e.
Figure FDA0002264411280000012
c is the apparent resistivity of each cell, Su represents the data on the set of measured potential points,
Figure FDA0002264411280000013
is the potential distribution data measured by the ith set of electrode schemes,
Figure FDA0002264411280000014
is the potential distribution data identified by the ith group of electrode schemes,
Figure FDA0002264411280000015
is a matrix formed by s sets of measurement data, and R (c) is a matrix formed by s sets of identification data;
step three: and continuously optimizing the objective function by using a population evolution algorithm, and finally obtaining the identification position of the karst cave after meeting the stop criterion.
2. The resistivity-cave identification method based on the population evolution algorithm according to claim 1, characterized in that: the specific process of optimizing the objective function by using the population evolution algorithm in the third step is as follows:
s1, population parameters and initialization: the control parameters include iterative optimizationLarge number ItermaxGroup size number Np, decision variable number n, upper bound X of decision variablesmaxAnd lower bound Xmin：
Xp，q＝Xmin+rand·(Xmax-Xmin)，p＝1，2，...，Np，q＝1，2，...，n (1)
Wherein rand is in [0,1 ]]Uniformly distributed random numbers in the range, and the adaptation value f ═ of the solution candidate (f ═ f)1，f2，...，fNp) Calculated according to the following objective function:
fp＝obj(Xp，1，Xp，2，…，Xp，n)，p＝1，2，…，Np (2)
s2, new position generation stage: at this stage, the population candidate solution is considered to move around its initial position to a better position, for candidate solution p, another candidate solution l is randomly selected from the population (p ≠ l) for generating potential search directions, and the position is updated according to the distance between the old and new positions of the candidate solution p by the following two models:
(i) model 1, learning the new position of the candidate solution p directly to the candidate solution l, and dynamically changing the exploration radius along with iteration:
Figure FDA0002264411280000021
Figure FDA0002264411280000022
(ii) model 2 New positions that produce candidate solutions p near the original position:
Figure FDA0002264411280000023
s3, spatial search enhancement stage: to further enhance the in-depth search for each dimension, the following steps are taken for each iteration: (i) finding the best and worst candidate solutions in the population; (ii) by changing the value of one dimension while maintaining the values of the other dimensions; (iii) comparing the newly generated solution with the fitness value of the original solution, and reserving a better solution; (iv) repeating steps (ii) and (iii) for other aspects, respectively, the newly created solution is generated by the following formula:
Figure FDA0002264411280000031
s4, stop criterion stage: saving the current optimal solution, and if the maximum iteration times are met, terminating the algorithm; otherwise, steps S2 and S3 will be repeated.
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