CN117057136A - Optimized layout method of elastic wave tomography sensor - Google Patents
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Abstract
Aiming at the sensor layout problem in the elastic wave tomography technology, the invention provides an evaluation function of the sensor optimization layout, and the optimization algorithm is adopted to optimize the sensor layout. From the angle of elastic wave tomography generalized inverse solution evaluation, an objective function of sensor optimization layout is established by utilizing a data resolution matrix, a model resolution matrix and a covariance matrix of solution, and an improved adaptive longicorn group optimization algorithm (AEPSO-BAS) is adopted for target optimization, so that an optimal sensor layout is obtained, basis is provided for experimental design, and meanwhile, the accuracy of elastic wave tomography is improved.
Description
Technical Field
The invention relates to the field of array information processing, in particular to an optimal layout method of an elastic wave tomography sensor.
Background
Elastic wave tomography (including seismic wave tomography, acoustic wave tomography, etc.) is one of the techniques for engineering geophysical prospecting by using geophysical methods. The method utilizes the difference of propagation speeds or attenuation coefficients of elastic waves in different media, records parameters such as travel time, amplitude, mass center frequency and the like of the elastic waves between a receiving point and an excitation point, and utilizes a computer mathematical method to reconstruct a distribution image of the speed or attenuation coefficients of the media, thereby realizing nondestructive detection of the internal structure distribution or defects of the media.
The elastic wave tomography test has complex operation, the sensor arrangement is limited by field conditions, the number of used sensors is limited, the target object cannot be observed in all directions like medical tomography, and the engineering problem necessarily causes incomplete tomography data. Therefore, in the case of low-density rays, how to ensure the authenticity of the elastography results is an urgent problem to be solved by the current elastography.
In order to perform omnibearing observation on a detection target, the sensors are arranged to cover a test area as much as possible, and meanwhile, the test data of each sensor used in a test are ensured to be as effective as possible, so that the sensors are required to be optimally distributed, and the accuracy and the test precision of the test are improved. The establishment of an evaluation function of the optimized layout of the elastic wave tomography sensor is a key and basis for realizing the optimized layout of the sensor.
Disclosure of Invention
In order to solve the defects in the prior art, the invention provides an optimal layout method of an elastic wave tomography sensor, which is characterized in that from the perspective of elastic wave tomography generalized inverse solution evaluation, an objective function of the optimal layout of the sensor is established by utilizing a data resolution matrix, a model resolution matrix and a covariance matrix of the solution, and an improved adaptive longicorn group optimization algorithm (AEPSO-BAS) is adopted for carrying out target optimization, so that the optimal sensor layout is obtained, the basis is provided for experimental design, and meanwhile, the precision of elastic wave tomography is improved.
The invention adopts the technical proposal for solving the technical problems that: the method for optimizing the layout of the elastic wave tomography sensor comprises the following steps:
s1, constructing a sensor optimization layout objective function according to an elastic wave tomography principle;
s2, obtaining the minimum value of the sensor optimization layout objective function by adopting an improved self-adaptive longhorn beetle group optimization method, so as to perform the sensor optimization layout.
The sensor optimization layout objective function described in step S1 is:
ξ＝ω 1 ·||H-I r || 2 +ω 2 ·||R-I N || 2 +ω 3 ·||C|| 2
r＝min{M,N}
where ζ is the target value of the sensor optimized layout objective function, I r And I N The unit matrix is of order r and the unit matrix is of order N, r is the rank of distance matrix A in elastic wave tomography matrix equation ax=b, and b= (b) in elastic wave tomography matrix equation ax=b 1 ,b 2 …b M ) ' is M-dimensional column vector of wave arrival time of each sensor in elastic wave tomography model, and is a test value, x= (x) 1 ,x 2 …x N ) ' is a slowness value of a discrete unit to be solved, and is an N-dimensional unknown column vector; I.I 2 The 2 norms of the matrix are represented, and the calculation formula of the data resolution matrix H is as follows:
wherein G is the generalized inverse of distance matrix A, and U is AA T Is a eigenvector matrix of (1), U r M x r submatrices consisting of the first r columns of U, V being A T A eigenvector matrix, V r An N x r sub-matrix of the first r columns of V,Σ r ＝diag(σ 1 ,σ 2 ,…,σ r )，σ i singular values for distance matrix a;
the calculation formula of the model resolution matrix R is as follows:
the covariance matrix calculation formula of the solution of the matrix equation ax=b is:
omega in sensor optimization layout objective function 1 、ω 2 And omega 3 The values of the first weighting coefficient, the second weighting coefficient and the third weighting coefficient are respectively 0.5-1.
The step S2 specifically comprises the following steps:
s2.1, carrying out grid division on a test range, wherein the number of grids is N, connecting an excitation source and each sensor to obtain M rays, writing M ray equations according to the excitation source coordinates and each sensor coordinate, respectively calculating the lengths of the M rays in the N grids, and recording the ray length of the p-th ray in the q-th grid as a pq P=1, …, M, q=1, …, N, will a pq As the p-th row and q-th column elements of the distance matrix A, obtaining the distance matrix A corresponding to the longhorn beetle and calculating the rank of the matrix A;
s2.2, randomly giving K sensor layout modes on the grid boundary, namely randomly generating K longhorns, wherein the initial positions of the longhorns are respectively expressed as S i ＝(x i1 ,…x iM ,y i1 ,…y iM ) I= … K, K being the number of longicorn;
s2.3, if all column vectors of the distance matrix A are not zero vectors and the matrix A is of full rank, adding the longhorn beetles into a longhorn beetle group, and entering a step S2.4; otherwise, discarding the longicorn, and returning to the step S2.2;
s2.4, returning to the step S2.2 when the number of the longicorn in the current day of cattle group does not reach K; otherwise, calculating a sensor optimization layout objective function of each longicorn to obtain the adaptability of each longicornAnd population fitness->i= … K, the initial value of the iteration number K is 0;
s2.5, accumulating the iteration times k to 1, and for each longicorn, calculating the speed of the ith longicorn in the iteration through the following formulaAnd position->
Wherein c 1 And c 2 A first constant and a second constant which are non-negative, each taking a random number between (0, 2), r 1 And r 2 And the random numbers are respectively (0 and 1), k is the current iteration number, w (k) is the inertia weight, and each iteration is updated by the following formula:
wherein w is max And w min Is the maximum and minimum value of the weight, q max For maximum iteration number, q max ≥200；
S2.6, substituting the updated position information into a sensor optimization layout objective function, and calculating the fitness of each longhorn beetle;
s2.7, updating individual extremum: for each longicorn, the current fitness value is compared with the optimal value of the experienced fitness values, namely the historical optimal fitness p i Comparing, if the current fitness value is smaller than the historical optimal fitness value and meets the condition described in the step S2.3, replacing the historical optimal value with the current fitness value;
s2.8, updating population extremum: the optimal fitness value of each longicorn is matched with the optimal fitness p of the group g Comparing, if the optimal fitness value of a certain longicorn is smaller than the optimal fitness value of the group, replacing the optimal fitness of the group with the optimal fitness value of the longicorn, and recording the position of the optimal longicorn;
s2.9, for the optimal longicorn, calculating the left whisker by using the following formulaAnd right whisker->Is defined by the position of:
wherein the method comprises the steps ofrands () represents a random vector, d represents a spatial dimension, s kt Is the position of longicorn, d 0 Distance between two beards, d 0 ＝step/c'，c'＝5，t＝(0…t max ) The number of iterations is the number of times of the inner part of the longicorn;
the longhorn beetle position was updated and internal iterations were performed using the following formula:
wherein the method comprises the steps ofAnd->When the kth iteration is performed on the optimal longhorn beetle, the left and right whisker positions are substituted into the objective function value calculated after the sensor is optimized and laid out to be the objective function value, and the minimum objective function value is obtained after the internal iteration is completed, wherein the value is the global optimal value of the kth iteration, theta and step are constants, the value range of the theta is 0-1, and the value range of the theta is 0-1>Long is the area diameter, step is less than or equal to 10;
s2.10, recording a global optimal value, if the global optimal value is not improved in the set continuous L generation, entering a step S2.11, and executing an escape strategy, otherwise, returning to the step S2.5;
s2.11, adopting an escape strategy to divide the longicorn in the longicorn crowd into two parts, and updating the speed of one part of the longicorn by adopting the following formula:
the other part of the longhorn beetle speed is updated by adopting the following formula:
wherein r is 3 And r 4 Respectively r 4 Is a random number between (0, 1), F is a constant, and is used for controlling the speed of the longicorn, and F=1.5v max v max Maximum speed value;
s2.11, checking a termination condition, terminating iteration to output the optimal sensor layout when the iteration times reach a preset value, otherwise returning to the step S2.5 to enter the next iteration calculation.
The invention has the beneficial effects based on the technical scheme that: the invention establishes an evaluation function of sensor optimization layout, optimizes the sensor layout by adopting an optimization algorithm, establishes an objective function of the sensor optimization layout by utilizing a data resolution matrix, a model resolution matrix and a covariance matrix of solution from the perspective of generalized inverse solution evaluation of elastic wave tomography, and adopts an improved adaptive longicorn group optimization algorithm (AEPSO-BAS) to perform objective optimization, thereby obtaining the optimal sensor layout, providing basis for experimental design and improving the precision of elastic wave tomography.
Drawings
Fig. 1 is a grid illustration intent.
Fig. 2 is a schematic flow chart.
Fig. 3 is a schematic diagram of a data resolution matrix.
Fig. 4 is a schematic diagram of a model resolution matrix.
Fig. 5 is a covariance matrix schematic.
FIG. 6 is a diagram of grid tomography inversion relative error.
Detailed Description
The invention is further described below with reference to the drawings and examples.
The principle of the invention is explained:
1. according to the elastic wave tomography principle, the invention obtains the objective function of the sensor optimization layout from the angle of the elastic wave tomography generalized inverse solution evaluation.
Taking explosion tomography as an example, referring to fig. 1, a schematic diagram of an explosion test field after meshing is shown. Elastic wave tomography matrix equation:
Ax＝b (1)
wherein b= (b) 1 ,b 2 …b M ) ' is M-dimensional column vector of each ray travel time, and is a test value; x= (x 1 ,x 2 …x N ) ' as waiting to be solvedThe discrete unit slowness value is an N-dimensional unknown column vector; a is M×N distance matrix, its element is a pq ，p＝1,…,M，q＝1,…,N，
(1) Data resolution matrix
For equation (1), based on the generalized inverse inversion of singular value decomposition, if the rank of coefficient matrix a is r, the data resolution matrix calculation formula is:
wherein G is the generalized inverse matrix of matrix A, and U is AA T Is a eigenvector matrix of (1), U r M x r submatrices consisting of the first r columns of U, V being A T A eigenvector matrix, V r Is an N x r sub-matrix of the first r columns of V,Σ r ＝diag(σ 1 ,σ 2 ,…,σ r )，σ i is the singular value of matrix a. The closer H is to the identity matrix I, the closer the estimated value of the model parameter is to the observed value, the less closely the components of the data theoretical value are related to the adjacent detection data, and the higher the resolution of the data estimation. Since there is an error between the model parameter estimate and the actual detection value, h+.i. It is an important index of the degree of the fitting observation value of the reconstruction result.
(2) Model resolution matrix
The model resolution matrix is calculated as:
it can be seen that the model resolution matrix is only equal to V r Related, and V r Nor is it an orthogonal matrix. The method is an important index of the inversion result obtained by the generalized inverse inversion algorithm and the real physical model proximity. If R is an identity matrix, the inversion result is completely consistent with the real result, namely the inversion is unique, and the situation is called full resolution;otherwise, if R approximates a diagonal matrix, the matrix elements of R vary relatively slowly, although they have peaks, or the peaks are not on the main diagonal, then the resolution of R is not high.
(3) Covariance matrix of solution estimation
Suppose that element b of observation data b i Is independent of linearity, and has zero mean value and delta variance 2 For generalized inverse inversion based on singular value decomposition, the covariance matrix of the solution is calculated as:
it follows that the covariance matrix of the solution estimate is a function of δ, V, and Σ. The covariance of the model parameters depends on the covariance of the observed data and the way in which the observed data errors map to errors of the solution, which is also a basis for the design of the test.
(4) Establishment of optimized layout evaluation function
According to the analysis, the closer the data resolution matrix is to the identity matrix, the closer the data prediction value is to the actual measurement value, the closer the model resolution matrix is to the identity matrix, and the closer the inversion result is to the real physical model; meanwhile, the smaller the covariance matrix value of the solution is, the smaller the error is, and according to the relation, an objective function of the sensor optimization layout is constructed:
ξ＝ω 1 ·||H-I r || 2 +ω 2 ·||R-I N || 2 +ω 3 ·||C|| 2 (5)
wherein I is r ，I N The r-order and N-order identity matrices respectively, I.I 2 Representing the matrix 2 norm. Omega 1 ，ω 2 ，ω 3 Is a weighting coefficient. The smaller the xi is, the closer the data resolution matrix and the model resolution matrix corresponding to the matrix A are to the identity matrix, and the smaller the covariance matrix value of the solution is. Meanwhile, in order to fully utilize the test data of each sensor and avoid the linear correlation or near linear correlation of certain row vectors of the matrix A, the rank of the matrix A should be increased as much as possible to reach the maximum value, namely fullRank, therefore, additional conditions are added, causing the rank of matrix a to: r=min { M, N }.
And evaluating the distribution mode of the elastic wave tomography sensor by adopting an objective function xi, and obtaining a minimum xi value by adopting an optimization algorithm so as to obtain the optimal sensor layout.
2. Sensor optimization layout was performed using an improved adaptive longhorn beetle swarm optimization algorithm (AEPSO-BAS).
Embedding a longhorn beetle whisker search algorithm into a particle swarm optimization algorithm to form a longhorn beetle swarm optimization algorithm, taking the longhorn beetles as particles in the particle swarm, carrying out individual and group optimization on the longhorn beetles by adopting the longhorn beetle swarm optimization algorithm to obtain an optimal longhorn beetle, and then adopting the longhorn beetle whisker search algorithm to obtain an optimal objective function.
Using d-dimensional vectors s i ＝(x i1 ,…x iM ,y i1 ,…y iM ) (d=2m) to indicate the position of the ith longicorn, M indicating the number of sensors used in the test. By v i ＝(v i1 ,v i2 ,…,v id ) To represent the speed of the ith longicorn, the optimal position searched by the ith longicorn so far is p i The optimal position searched so far for by the whole longicorn group is p g 。
Based on the above principle, referring to fig. 2, the present invention provides an optimized layout method of an elastic wave tomography sensor, including the following steps:
s1, constructing a sensor optimization layout objective function according to an elastic wave tomography principle. The sensor optimization layout objective function is as follows:
ξ＝ω 1 ·||H-I r || 2 +ω 2 ·||R-I N || 2 +ω 3 ·||C|| 2
r＝min{M,N}
where ζ is the target value of the sensor optimized layout objective function, I r And I N The unit matrix is of order r and the unit matrix is of order N, r is the rank of distance matrix A in elastic wave tomography matrix equation ax=b, and b= (b) in elastic wave tomography matrix equation ax=b 1 ,b 2 …b M ) ' elastic waveM-dimensional column vectors of arrival times of waves in the tomography model at each sensor are experimental test values, and x= (x) 1 ,x 2 …x N ) ' is a slowness value of a discrete unit to be solved, and is an N-dimensional unknown column vector; I.I 2 The 2 norms of the matrix are represented, and the calculation formula of the data resolution matrix H is as follows:
wherein G is the generalized inverse of distance matrix A, and U is AA T Is a eigenvector matrix of (1), U r M x r submatrices consisting of the first r columns of U, V being A T A eigenvector matrix, V r An N x r sub-matrix of the first r columns of V,Σ r ＝diag(σ 1 ,σ 2 ,…,σ r )，σ i singular values for distance matrix a;
the calculation formula of the model resolution matrix R is as follows:
the covariance matrix calculation formula of the solution of the matrix equation ax=b is:
omega in sensor optimization layout objective function 1 、ω 2 And omega 3 The first weighting coefficient, the second weighting coefficient and the third weighting coefficient are respectively, and the values are according to H-I r || 2 、||R-I N || 2 And C 2 The value of (2) is determined, and the value range is generally 0.5-1.
S2, adopting an improved self-adaptive longhorn beetle group optimization method to enable the sensor optimization layout objective function to obtain the minimum value, so that the sensor optimization layout is carried out. The method specifically comprises the following steps:
s2.1, carrying out grid division on a test range, wherein the number of grids is N, connecting an excitation source and each sensor to obtain M rays, writing M ray equations according to the excitation source coordinates and each sensor coordinate, respectively calculating the lengths of the M rays in the N grids, and recording the ray length of the p-th ray in the q-th grid as a pq P=1, …, M, q=1, …, N, will a pq And (3) obtaining a distance matrix A corresponding to the longhorn beetle as the p-th row and the q-th column elements of the distance matrix A, and calculating the rank of the matrix A.
S2.2, randomly giving K sensor layout modes on the grid boundary, namely randomly generating K longhorns, wherein the initial positions of the longhorns are respectively expressed as S i ＝(x i1 ,…x iM ,y i1 ,…y iM ) I= … K, K being the number of longhorn beetles.
S2.3, if all column vectors of the distance matrix A are not zero vectors and the matrix A is of full rank, adding the longicorn into the longicorn crowd, and entering a step S2.4; otherwise, the longhorn beetle is abandoned, and the step S2.2 is returned.
S2.4, returning to the step S2.2 when the number of the longicorn in the current day of cattle group does not reach K; otherwise, calculating a sensor optimization layout objective function of each longicorn to obtain the adaptability of each longicornAnd population fitness->i= … K, and the initial value of the iteration number K is 0.
S2.5, accumulating the iteration times k to 1, and for each longicorn, calculating the speed of the ith longicorn in the iteration through the following formulaAnd position->
Wherein c 1 And c 2 A first constant and a second constant which are non-negative, each taking a random number between (0, 2), r 1 And r 2 And the random numbers are respectively (0 and 1), k is the current iteration number, w (k) is the inertia weight, and each iteration is updated by the following formula:
wherein w is max And w min Respectively the maximum and minimum values of the weights, q max For maximum iteration number, q max ≥200。
S2.6, substituting the updated position information into a sensor optimization layout objective function, and calculating the fitness of each longhorn beetle.
S2.7, updating individual extremum: for each longicorn, the current fitness value is compared with the optimal value of the experienced fitness values, namely the historical optimal fitness p i If the current fitness value is smaller than its historical optimal fitness value and the condition described in step S2.3 is fulfilled, the historical optimal value is replaced with the current fitness value.
S2.8, updating population extremum: the optimal fitness value of each longicorn is matched with the optimal fitness p of the group g And comparing, if the optimal fitness value of a certain longicorn is smaller than the optimal fitness value of the group, replacing the optimal fitness of the group with the optimal fitness value of the longicorn, and recording the position of the certain longicorn.
S2.9, for the optimal longicorn, calculating the left whisker by using the following formulaAnd right whisker->Is defined by the position of:
wherein the method comprises the steps ofrands () represents a random vector, d represents a spatial dimension, s kt Is the position of longicorn, d 0 Distance between two beards, d 0 ＝step/c'，c'＝5，t＝(0…t max ) The number of iterations is the number of times of the inner part of the longicorn;
the longhorn beetle position was updated and internal iterations were performed using the following formula:
wherein the method comprises the steps ofAnd->When the kth iteration is performed on the optimal longhorn beetle, the left and right whisker positions are substituted into the objective function value calculated after the sensor is optimized and laid out to be the objective function value, and the minimum objective function value is obtained after the internal iteration is completed, wherein the value is the global optimal value of the kth iteration, theta and step are constants, the value range of the theta is 0-1, and the value range of the theta is 0-1>Long is the area diameter, step.ltoreq.10, d in this example 0 ＝step/c'，c'＝5。
S2.10, recording a global optimal value, if the global optimal value is not improved in the set continuous L generation, entering a step S2.11, and executing an escape strategy, otherwise, returning to the step S2.5;
s2.11, adopting an escape strategy to divide the longicorn in the longicorn crowd into two parts, and updating the speed of one part of the longicorn by adopting the following formula:
the other part of the longhorn beetle speed is updated by adopting the following formula:
wherein r is 3 And r 4 Respectively r 4 Is a random number between (0, 1), F is a constant, and is used for controlling the speed of the longicorn, and F=1.5v max v max Is the maximum speed value.
S2.11, checking a termination condition, terminating iteration to output the optimal sensor layout when the iteration times reach a preset value, otherwise returning to the step S2.5 to enter the next iteration calculation.
In the experiment of this embodiment, 13 sensors (i.e., m=13) are distributed on the boundary of the grid area as shown in fig. 1, the grid number n=58, and the random distribution mode and the sensor distribution mode optimized by this patent are respectively adopted to perform evaluation of solution estimation, and parameter setting: omega 1 ＝0.8，ω 2 ＝0.1，ω 3 ＝1，δ 2 ＝1，k 1 ＝0.1，k 2 ＝0.9，w max ＝0.9，w min ＝0.4，q max ＝1000，c 1 ＝c 2 ＝1.49，θ＝0.95，step＝1，t max ＝300，F＝1，L＝20。
The model resolution matrix, the data resolution matrix and the unit covariance matrix are obtained, and numerical comparison of each index under different sensor distributions is shown in table 1 as shown in fig. 3, 4 and 5.
Table 1 comparison of the indices under different sensor profiles
The data resolution matrix of the random distribution mode is a non-complete unit matrix, which indicates that the data of the underdetermined equation set is not fully utilized, and the rank is 11; the data resolution matrix of the optimized distribution is a unit matrix, the data of the equation set is fully utilized without redundancy, and the rank is 13. Because both distribution models form an underdetermined equation set, the model resolution matrix is a non-unit matrix, but the model resolution matrix of the optimized distribution is less in burrs and is closer to the unit matrix than the random model, which indicates that the estimation resolution of the optimized model solution is higher. The covariance of the solution estimation of the optimal distribution mode is smaller than that of the solution estimation of the optimal distribution mode in a random mode. FIG. 6 shows the relative error of grid tomography inversion in a random distribution and an optimized distribution. From the analysis, the sensor optimizing distribution mode provided by the invention is more beneficial to tomographic inversion calculation.
Claims (3)
1. An elastic wave tomography sensor optimizing layout method is characterized by comprising the following steps:
s1, constructing a sensor optimization layout objective function according to an elastic wave tomography principle;
s2, obtaining the minimum value of the sensor optimization layout objective function by adopting an improved self-adaptive longhorn beetle group optimization method, so as to perform the sensor optimization layout.
2. The method for optimizing layout of an elastic wave tomography sensor according to claim 1, wherein: the sensor optimization layout objective function described in step S1 is:
ξ＝ω 1 ·||H-I r || 2 +ω 2 ·||R-I N || 2 +ω 3 ·||C|| 2
r＝min{M,N}
where ζ is the target value of the sensor optimized layout objective function, I r And I N The unit matrix is of order r and the unit matrix is of order N, r is the rank of distance matrix A in the equation Ax=b of the elastic wave tomography matrix, and b=in the equation Ax=b of the elastic wave tomography matrix(b 1 ,b 2 …b M ) ' is M-dimensional column vector of wave arrival time of each sensor in elastic wave tomography model, and is a test value, x= (x) 1 ,x 2 …x N ) ' is a slowness value of a discrete unit to be solved, and is an N-dimensional unknown column vector; I.I 2 The 2 norms of the matrix are represented, and the calculation formula of the data resolution matrix H is as follows:
wherein G is the generalized inverse of distance matrix A, and U is AA T Is a eigenvector matrix of (1), U r M x r submatrices consisting of the first r columns of U, V being A T A eigenvector matrix, V r An N x r sub-matrix of the first r columns of V,Σ r ＝diag(σ 1 ,σ 2 ,…,σ r )，σ i singular values for distance matrix a;
the calculation formula of the model resolution matrix R is as follows:
the covariance matrix calculation formula of the solution of the matrix equation ax=b is:
omega in sensor optimization layout objective function 1 、ω 2 And omega 3 The values of the first weighting coefficient, the second weighting coefficient and the third weighting coefficient are respectively 0.5-1.
3. The method for optimizing layout of an elastic wave tomography sensor according to claim 1, wherein: the step S2 specifically comprises the following steps:
s2.1, carrying out grid division on a test range, wherein the number of grids is N, connecting an excitation source and each sensor to obtain M rays, writing M ray equations according to the excitation source coordinates and each sensor coordinate, respectively calculating the lengths of the M rays in the N grids, and recording the ray length of the p-th ray in the q-th grid as a pq P=1, …, M, q=1, …, N, will a pq As the p-th row and q-th column elements of the distance matrix A, obtaining the distance matrix A corresponding to the longhorn beetle and calculating the rank of the matrix A;
s2.2, randomly giving K sensor layout modes on the grid boundary, namely randomly generating K longhorns, wherein the initial positions of the longhorns are respectively expressed as S i ＝(x i1 ,…x iM ,y i1 ,…y iM ) I= … K, K being the number of longicorn;
s2.3, if all column vectors of the distance matrix A are not zero vectors and the matrix A is of full rank, adding the longhorn beetles into a longhorn beetle group, and entering a step S2.4; otherwise, discarding the longicorn, and returning to the step S2.2;
s2.4, returning to the step S2.2 when the number of the longicorn in the current day of cattle group does not reach K; otherwise, calculating a sensor optimization layout objective function of each longicorn to obtain the adaptability of each longicornAnd population fitness->i= … K, the initial value of the iteration number K is 0;
s2.5, accumulating the iteration times k to 1, and for each longicorn, calculating the speed of the ith longicorn in the iteration through the following formulaAnd position->
Wherein c 1 And c 2 A first constant and a second constant which are non-negative, each taking a random number between (0, 2), r 1 And r 2 And the random numbers are respectively (0 and 1), k is the current iteration number, w (k) is the inertia weight, and each iteration is updated by the following formula:
wherein w is max And w min Is the maximum and minimum value of the weight, q max For maximum iteration number, q max ≥200；
S2.6, substituting the updated position information into a sensor optimization layout objective function, and calculating the fitness of each longhorn beetle;
s2.7, updating individual extremum: for each longicorn, the current fitness value is compared with the optimal value of the experienced fitness values, namely the historical optimal fitness p i Comparing, if the current fitness value is smaller than the historical optimal fitness value and meets the condition described in the step S2.3, replacing the historical optimal value with the current fitness value;
s2.8, updating population extremum: the optimal fitness value of each longicorn is matched with the optimal fitness p of the group g Comparing, if the optimal fitness value of a certain longicorn is smaller than the optimal fitness value of the group, replacing the optimal fitness of the group with the optimal fitness value of the longicorn, and recording the position of the optimal longicorn;
s2.9, for the optimal longicorn, calculating the left whisker by using the following formulaAnd right whisker->Is defined by the position of:
wherein the method comprises the steps ofrands () represents a random vector, d represents a spatial dimension, s kt Is the position of longicorn, d 0 Distance between two beards, d 0 ＝step/c'，c'＝5，t＝(0…t max ) The number of iterations is the number of times of the inner part of the longicorn;
the longhorn beetle position was updated and internal iterations were performed using the following formula:
wherein the method comprises the steps ofAnd->When the kth iteration is performed on the optimal longhorn beetle, the left and right whisker positions are substituted into the objective function value calculated after the sensor is optimized and laid out to be the objective function value, and the minimum objective function value is obtained after the internal iteration is completed, wherein the value is the global optimal value of the kth iteration, theta and step are constants, the value range of the theta is 0-1, and the value range of the theta is 0-1>Long is the area diameter, step is less than or equal to 10;
s2.10, recording a global optimal value, if the global optimal value is not improved in the set continuous L generation, entering a step S2.11, and executing an escape strategy, otherwise, returning to the step S2.5;
s2.11, adopting an escape strategy to divide the longicorn in the longicorn group into two parts, and updating the speed of one part of the longicorn by adopting the following formula:
the other part of the longhorn beetle speed is updated by adopting the following formula:
wherein r is 3 And r 4 Respectively r 4 Is a random number between (0, 1), F is a constant, and is used for controlling the speed of the longicorn, and F=1.5v max v max Maximum speed value;
s2.11, checking a termination condition, terminating iteration to output the optimal sensor layout when the iteration times reach a preset value, otherwise returning to the step S2.5 to enter the next iteration calculation.
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