Hybrid sensor configuration method based on clustering and global spatial distance distribution coefficient

Abstract

The present invention relates to a hybrid sensor configuration method based on clustering and global spatial distance distribution coefficient, and belongs to the technical field of sensor optimization layout for structural health monitoring. The method comprises the following steps: Step 1: Establish a structural finite element model and calculate the information matrix of candidate sensors; Step 2: In view of the information redundancy problem, use K-means clustering to cluster the strain information matrix of the sensor in Step 1; Step 3: Propose a global spatial distance distribution index and establish a spatial redundancy-related objective function; Step 4: Determine the calculation formula of the relative error of morphological estimation; Step 5: Establish a sensor layout optimization objective function for morphological estimation; Step 6: Use an adaptive search algorithm to solve the objective function of minimizing the relative error of morphological estimation and maximizing the spatial distance distribution index, and output the final result of sensor configuration. The sensor configuration algorithm described in the present invention has the characteristics of fast convergence, strong practicality, and applicability to large and complex structures.

Description

Technical Field

[0001] The present invention belongs to the field of morphology estimation for structural health monitoring, and specifically proposes a hybrid sensor configuration method based on clustering and global space distance distribution coefficient. Background Art

[0002] The optimal layout of sensors is a primary link in structural health monitoring. The measurement data of these sensors are converted into corresponding structural response characteristics, and these characteristics are analyzed to determine the current health status of the structure. Due to the limitations of monitoring costs and monitoring environment, a limited number of sensors need to be arranged in the best position to ensure that important system characteristics can be obtained experimentally to achieve accurate identification of the health status of the structure. In order to accurately obtain the response of the structure, appropriate optimization methods must be used to place sensors at key locations. At present, some classic sensor configuration methods have been successfully applied to actual engineering verification. However, these methods do not consider the redundancy problem in sensor layout, or only consider one of the two factors, information redundancy or spatial redundancy, and there are few methods that combine the two. Therefore, in order to use fewer sensors to obtain better morphological estimation effects, solve the spatial and information redundancy problems of sensors, and avoid wasting sensors, it is necessary to optimize the sensor layout position of the structure.

[0003] To this end, the main purpose of this invention is to study the optimal sensor configuration for morphology estimation, and propose a sensor configuration method that considers information and spatial redundancy. For information redundancy and spatial redundancy, the K-means clustering method and a global spatial distance distribution index are respectively used, and the minimum relative error of morphology estimation and the maximum spatial distance distribution index are taken as an objective function of effective sensor layout. An adaptive direct search algorithm is used to iteratively solve the optimization problem to achieve the optimal configuration of the sensor, which has obvious advantages over traditional methods. Summary of the invention

[0004] The technical problem to be solved by the present invention is to provide a sensor configuration method for morphology estimation. The method aims at solving the information redundancy and spatial redundancy problems in sensor layout, proposes to use K-means clustering and global spatial distance distribution index to solve the problem, and selects the sensor position according to the principle of minimum relative error of morphology estimation. The method can be applied to the sensor layout of large or complex mechanisms in the aerospace field, and has the characteristics of being simple and fast, fast convergence, convenient and reliable, and highly practical.

[0005] The hybrid sensor configuration method based on clustering and global space distance distribution coefficient of the present invention comprises the following steps:

[0006] A hybrid sensor configuration method based on clustering and global space distance distribution coefficient, characterized by comprising the following steps:

[0007] 1. A hybrid sensor configuration method based on clustering and global spatial distance distribution coefficient, characterized in that it includes the following steps:

[0008] Step 1: Calculate the information matrix of candidate sensors;

[0009] First, a finite element model of the structure is established. The number of finite element nodes is N, and each finite element unit node corresponds to a candidate sensor position. The sensors to be configured on the structure are preset to be n FBG sensors. The problem of sensor layout is to select n positions from N candidate positions and apply them to morphological monitoring. The information matrix of all candidate position sensors on the structure is equal to the sum of the information matrices of a single sensor:

[0010]

[0011] Among them, Φ i and Q i Respectively represent the strain modal vector and strain information matrix corresponding to the i-th sensor, This matrix is ​​a semi-positive definite matrix. The strain mode of the structure is obtained by finite element analysis, and the strain mode information matrix corresponding to the sensors at all candidate positions is calculated by the above formula;

[0012] Step 2: To address the information redundancy problem, K-means clustering is used to cluster the strain information matrix of the sensor in step 1 to obtain k different sensor groups;

[0013] 2-1 First, the strain modal information matrix of each sensor obtained in step 1 is used as the sample set to be clustered, the number of clustering groups is set to k, and the information matrices corresponding to k structurally randomly distributed sensors are selected from the sample set as the initial clustering center Q0 = [Q 01 ,Q 02 ,…,Q 0k ];

[0014] 2-2 Calculate the distance between the sample points in each sensor sample set and the center points of each cluster. The distance from the jth sample point to the i-th cluster grouping center is d ji =||Q j -Q 0i ||, and assign it to the group that is closest to the cluster center, i.e., the group with the highest similarity;

[0015] 2-3 Calculate and update the cluster center of each group based on the redistributed sample set;

[0016] 2-4 Repeat steps 2-2 to 2-3 until the standard measurement function converges or reaches the set number of clustering iterations. The standard measurement function is:

[0017]

[0018] Among them, ||·||2 represents the Euclidean norm, C i and m i Respectively represent the sample set and center of the i-th cluster;

[0019] Step 3: Propose a global spatial distance distribution index and establish an objective function related to spatial redundancy;

[0020] Select n sensors from the sensor group obtained in step 2, and establish an index coefficient for evaluating the global spatial distance distribution of these sensors;

[0021] 3-1 First calculate the distance from a single sensor location to every other sensor location and select the minimum distance; then take the next sensor location and calculate its distance to all other sensor locations including the first sensor measured, again select the minimum value and add it to the first minimum distance; this process is repeated until the nearest sensor location of all sensor locations has been selected; then divide the sum of the minimum distances by the number of sensors to get the average minimum distance:

[0022]

[0023] Among them, min(D ij ) is the distance between each sensor and its nearest neighbor sensor;

[0024] 3-2 Assuming that the distribution of sensors is completely random, the average random distance based on probability is:

[0025]

[0026] Among them, D ran is the average random distance, A is the area of ​​the sensor distribution area;

[0027] 3-3 Use the distances between all sensors to form a distance matrix and calculate the distance d from the i-th sensor to the j-th sensor ij , the calculated result is used as the element of the i-th row and j-th column in the distance matrix DD, and the norm of the distance matrix is ​​calculated as Considering the ratio of the range of all sensor positions to the structural area, the calculation formula of the global space distance distribution coefficient DI is proposed as follows:

[0028]

[0029] 3-4 According to the distribution coefficient in step 3-3, an optimization function f1 for evaluating the spatial distribution of sensors is established. This function is an objective function related to spatial redundancy and is defined as the maximum value of the global spatial distribution coefficient:

[0030]

[0031] Among them, d1 is the spatial distance value when all candidate sensors are distributed adjacently, and d is the sensor position to be optimized;

[0032] Step 4: Determine the calculation formula for the relative error of morphological estimation;

[0033] Since this layout method is structure-oriented morphological estimation, in addition to ensuring the integrity of the information of the sensor network and the rationality of the spatial distribution, it is necessary to introduce the morphological estimation error function as another optimization target of the hybrid sensor layout method;

[0034] 4-1 Dynamic displacement w of N nodes of the structure N×1 The modal displacement vibration shape Φ N×M To represent, M is the selected structural modal order. Relatively speaking, the strain ε of the n sensors to be arranged on the structure n×1 The strain mode shape Ψ can be used n×M To express, the above vibration modes are respectively transformed into their modal coordinates q M×1 Multiplication:

[0035] w N×1 =Φ N×M ·q M×1 ,ε n×1 =Ψ n×M ·q M×1 (7)

[0036] 4-2 Introducing a relative estimation error That is, the ratio of the covariance matrix of the morphology estimation error to the measurement noise:

[0037]

[0038] 4-3 Based on the relative error obtained in 4-2, the optimization objective function with the minimum relative error of morphological estimation is established:

[0039]

[0040] Step 5: Through steps 3 and 4, the calculation formula of the optimization objective function f of the sensor configuration for morphology estimation can be established as follows:

[0041]

[0042] Among them, w2 and w1 represent the weight coefficients related to the morphological estimation error and the spatial distance distribution coefficient, respectively;

[0043] Step 6: Then, an adaptive search optimization algorithm is used to solve the objective function given in step 5 with the minimum relative error of morphological estimation and the maximum spatial distance distribution index, and the final result of the sensor configuration is output;

[0044] The adaptive search algorithm uses reflection, expansion, contraction, compression and other operations to optimize the function. The process will continue until the termination condition is met. The four scalar parameters in the operation are: reflection coefficient α′, expansion coefficient β′, contraction coefficient γ′, compression coefficient σ′, and their values ​​are related to the dimension. Their values ​​are as follows:

[0045]

[0046] Where n is the dimension of the corresponding optimization function, that is, the number of sensors to be deployed. The result of each iteration of the algorithm is to generate a new single vertex x′ e , x′ r , x′ oc , x′ ic Replace x n+1 , or a compression step occurs, then n new vertices v′ are generated i , together with x1, constitute all the vertices of the simplex in the next iteration; its main iterative steps are:

[0047] 6-1 Define the initial simplex and sort it: Given a non-degenerate simplex Δ(x1, x2, …, x n+1 ), the simplex is a convex polyhedron with n+1 vertices, In order to find the minimum value of the objective function, firstly set x1,x2,…x n+1 The corresponding function value Sort by f(x1)≤f(x2)≤…f(x n )≤f(x n+1 ); determine the lowest point x1 as a good point, the second highest point x n Worst point, highest point x n+1 As the worst point;

[0048] 6-2 Calculate the reflection point in, It is represented as except for point x n+1 The centroid of the n vertices other than r )If f(x1)<f(x r )<f(x n ), then the vertex x′ of the new simplex n+1 =x r ;

[0049] 6-3 Extension, if f(x r )<f(x1), then calculate the extension point If f(x e )<f(x r ), x′ n+1 =x e , otherwise accept x r And terminate the iteration;

[0050] 6-4 Contraction, if f(x r )≥f(x n ), then between x and x r With x n+1 Contraction between the better

[0051] a) If f(x n )≤f(x r )≤f(x n+1 )(Point x r Strictly x n+1 Good), then perform external contraction,

[0052]

[0053] If f(x oc )<f(x r ), then x′ n+1 =x oc Terminate this iteration, otherwise execute step 6-5;

[0054] b) If f(x r )>f(x n+1 ), then an internal shrink operation is performed:

[0055]

[0056] If f(x ic )<f(x n+1 ), then x′ n+1 =x ic And terminate this iteration, otherwise execute step 6-5;

[0057] 6-5 compression, calculate n points, v i =x1+σ(x i -x1),i=2,…,n+1,x i ′=v i ′, then the vertices of the simplex in the next iteration are Δ=Δ(x1,v2,…v n+1 )composition;

[0058] 6-6 Repeat steps 6-1 to 6-5 in each iteration until the termination condition is met;

[0059] After iteration 6-7, the solution of the objective function in step 5 is output, i.e., the layout positions of n sensors;

[0060] Firstly, based on the information matrix of the sensor, the sensors are divided into several groups by clustering method. Then, the positions that meet the above conditions are selected from several groups according to the criteria of maximum global spatial distribution distance and minimum morphological relative estimation error. The positions of the sensors are continuously updated and optimized in the iterative process, and it is judged whether the termination conditions are finally met, so as to determine the optimal position of the sensor.

[0061] The sensor optimization layout result is obtained through the above steps, and the sensor placement position is determined. The sensor configuration method based on clustering and global space distance distribution coefficient of the present invention has the following beneficial effects:

[0062] (1) The proposed sensor layout method for morphology estimation can simultaneously solve the two problems of information redundancy and spatial redundancy in sensor layout, thus avoiding the waste of sensors.

[0063] (2) Based on the finite element model of the structure, the influence of shape estimation error and global spatial distribution distance on the sensor configuration result is considered, which can be applied to the structural shape reconstruction problem under different constraints and loading conditions;

[0064] (3) For the problem of morphology estimation using fewer sensors for large or complex structures, the hybrid optimization layout method can effectively avoid redundant information and improve the morphology reconstruction accuracy and computational efficiency. BRIEF DESCRIPTION OF THE DRAWINGS

[0065] Figure 1 Sensor optimization configuration flow chart;

[0066] Figure 2 Simplex vertices based on adaptive search algorithm;

[0067] Figure 3 Adaptive Nelder-Mead algorithm flow chart;

[0068] Figure 4 Cantilever beam sensor location selection obtained using effective independent sensor method;

[0069] Figure 5 Cantilever beam sensor location selection obtained based on the hybrid sensor layout approach. DETAILED DESCRIPTION

[0070] A hybrid sensor configuration method based on clustering and global space distance distribution coefficient, characterized by comprising the following steps:

[0071] 1. A hybrid sensor configuration method based on clustering and global spatial distance distribution coefficient, characterized in that it includes the following steps:

[0072] Step 1: Calculate the information matrix of candidate sensors;

[0073] First, a finite element model of the structure is established. The number of finite element nodes is N, and each finite element unit node corresponds to a candidate sensor position. The sensors to be configured on the structure are preset to be n FBG sensors. The problem of sensor layout is to select n positions from N candidate positions and apply them to morphological monitoring. The information matrix of all candidate position sensors on the structure is equal to the sum of the information matrices of a single sensor:

[0074]

[0075] Among them, Φ i and Q i Respectively represent the strain modal vector and strain information matrix corresponding to the i-th sensor, This matrix is ​​a semi-positive definite matrix. The strain mode of the structure is obtained by finite element analysis, and the strain mode information matrix corresponding to the sensors at all candidate positions is calculated by the above formula;

[0076] Step 2: To address the information redundancy problem, K-means clustering is used to cluster the strain information matrix of the sensor in step 1 to obtain k different sensor groups;

[0077] 2-1 First, the strain modal information matrix of each sensor obtained in step 1 is used as the sample set to be clustered, the number of clustering groups is set to k, and the information matrices corresponding to k structurally randomly distributed sensors are selected from the sample set as the initial clustering center Q0 = [Q 01 ,Q 02 ,…,Q 0k ];

[0078] 2-2 Calculate the distance between the sample points in each sensor sample set and the center points of each cluster. The distance from the jth sample point to the i-th cluster grouping center is d ji =‖Q j -Q 0i ‖, and assign it to the group that is closest to the cluster center, i.e., the group with the highest similarity;

[0079] 2-3 Calculate and update the cluster center of each group based on the redistributed sample set;

[0080] 2-4 Repeat steps 2-2 to 2-3 until the standard measurement function converges or reaches the set number of clustering iterations. Different numbers of iterations can be set for different sample sets. In the implementation process of the present invention, the number of iterations set is 1000. Set the standard measurement function to:

[0081]

[0082] Among them, ||·||2 represents the Euclidean norm, C i and m i Respectively represent the sample set and center of the i-th cluster;

[0083] Step 3: Propose a global spatial distance distribution index and establish an objective function related to spatial redundancy;

[0084] Select n sensors from the sensor group obtained in step 2, and establish an index coefficient for evaluating the global spatial distance distribution of these sensors;

[0085] 3-1 First calculate the distance from a single sensor location to every other sensor location and select the minimum distance; then take the next sensor location and calculate its distance to all other sensor locations including the first sensor measured, again select the minimum value and add it to the first minimum distance; this process is repeated until the nearest sensor location of all sensor locations has been selected; then divide the sum of the minimum distances by the number of sensors to get the average minimum distance:

[0086]

[0087] Among them, min(D ij ) is the distance between each sensor and its nearest neighbor sensor;

[0088] 3-2 Assuming that the distribution of sensors is completely random, the average random distance based on probability is:

[0089]

[0090] Among them, D ran is the average random distance, A is the area of ​​the sensor distribution area;

[0091] 3-3 Use the distances between all sensors to form a distance matrix and calculate the distance d from the i-th sensor to the j-th sensor ij , the calculated result is used as the element of the i-th row and j-th column in the distance matrix DD, and the norm of the distance matrix is ​​calculated as Considering the ratio of the range of all sensor positions to the structural area, the calculation formula of the global space distance distribution coefficient DI is proposed as follows:

[0092]

[0093] 3-4 According to the distribution coefficient in step 3-3, an optimization function f1 for evaluating the spatial distribution of sensors is established. This function is an objective function related to spatial redundancy and is defined as the maximum value of the global spatial distribution coefficient:

[0094]

[0095] Among them, d1 is the spatial distance value when all candidate sensors are distributed adjacently, and d is the sensor position to be optimized;

[0096] Step 4: Determine the calculation formula for the relative error of morphological estimation;

[0097] Since this layout method is structure-oriented morphological estimation, in addition to ensuring the integrity of the information of the sensor network and the rationality of the spatial distribution, it is necessary to introduce the morphological estimation error function as another optimization target of the hybrid sensor layout method;

[0098] 4-1 Dynamic displacement w of N nodes of the structure N×1 The modal displacement vibration shape Φ N×M To represent, M is the selected structural modal order. Relatively speaking, the strain ε of the n sensors to be arranged on the structure n×1 The strain mode shape Ψ can be used n×M To express, the above vibration modes are respectively transformed into their modal coordinates q M×1 Multiplication:

[0099] w N×1 =Φ N×M ·q M×1 ,ε n×1 =Ψ n×M ·q M×1 (7)

[0100] 4-2 Introducing a relative estimation error That is, the ratio of the covariance matrix of the morphology estimation error to the measurement noise:

[0101]

[0102] 4-3 Based on the relative error obtained in 4-2, the optimization objective function with the minimum relative error of morphological estimation is established:

[0103]

[0104] Step 5: Through steps 3 and 4, the calculation formula of the optimization objective function f of the sensor configuration for morphology estimation can be established as follows:

[0105]

[0106] Among them, w2 and w1 represent the weight coefficients related to the morphological estimation error and the spatial distance distribution coefficient, respectively;

[0107] Step 6: Then, the adaptive search optimization algorithm is used to solve the objective function given in step 5 with the minimum relative error of morphological estimation and the maximum spatial distance distribution index, and the final result of the sensor configuration is output. The flow chart of the hybrid sensor layout method is as follows: Figure 1 ;

[0108] The adaptive search algorithm uses operations such as reflection expansion, contraction, and compression to optimize the function. The process will continue until the termination condition is met. The four scalar parameters in the operation are: reflection coefficient α′, expansion coefficient β′, contraction coefficient γ′, and compression coefficient σ′. Their values ​​are related to the dimension and are as follows:

[0109]

[0110] Where n is the dimension of the corresponding optimization function, that is, the number of sensors to be deployed. The result of each iteration of the algorithm is to generate a new single vertex x e ′、x r ′、x o ' c 、x i ' c Replace x n+1 , or a compression step occurs, then n new vertices v are generated i ′, together with x1, constitute all the vertices of the simplex in the next iteration, such as Figure 2 ; Its main iterative steps are:

[0111] 6-1 Define the initial simplex and sort it: Given a non-degenerate simplex Δ(x1, x2, …, x n+1 ), the simplex is a convex polyhedron with n+1 vertices, In order to find the minimum value of the objective function, firstly set x1,x2,…x n+1 The corresponding function value Sort by f(x1)≤f(x2)≤…f(x n )≤f(x n+1 ); determine the lowest point x1 as a good point, the second highest point x n Worst point, highest point x n+1 As the worst point;

[0112] 6-2 Calculate the reflection point in, It is represented as except for point x n+1 The centroid of the n vertices other thanr )If f(x1)<f(x r )<f(x n ), then the vertex x′ of the new simplex n+1 =x r ;

[0113] 6-3 Extension, if f(x r )<f(x1), then calculate the extension point If f(x e )<f(x r ), x′ n+1 =x e , otherwise accept x r And terminate the iteration;

[0114] 6-4 Contraction, if f(x r )≥f(x n ), then between x and x r With x n+1 Contraction between the better

[0115] a) If f(x n )≤f(x r )≤f(x n+1 )(Point x r Strictly x n+1 Good), then perform external contraction,

[0116]

[0117] If f(x oc )<f(x r ), then x′ n+1 =x oc Terminate this iteration, otherwise execute step 6-5;

[0118] b) If f(x r )>f(x n+1 ), then an internal shrink operation is performed:

[0119]

[0120] If f(x ic )<f(x n+1 ), then x′ n+1 =x ic And terminate this iteration, otherwise execute step 6-5;

[0121] 6-5 compression, calculate n points, v i =x1+σ(x i -x1),i=2,…,n+1,x i ′=v i′, then the vertices of the simplex in the next iteration are Δ=Δ(x1,v2,…v n+1 )composition;

[0122] 6-6 Repeat steps 6-1 to 6-5 in each iteration until the termination condition is met, such as Figure 3 ;

[0123] After iteration 6-7, the solution of the objective function in step 5 is output, i.e., the layout positions of n sensors;

[0124] Firstly, based on the information matrix of the sensor, the sensors are divided into several groups by clustering method. Then, the positions that meet the above conditions are selected from several groups according to the criteria of maximum global spatial distribution distance and minimum morphological relative estimation error. The positions of the sensors are continuously updated and optimized in the iterative process, and it is judged whether the termination conditions are finally met, so as to determine the optimal position of the sensor.

[0125] Reference Figure 4 The cantilever beam model was established using Patran finite element method. The geometric dimensions of the cantilever beam were 450 mm × 20 mm × 2 mm, the elastic modulus was 7.2 GPa, the Poisson's ratio was 0.33, and the density was 2.75 × 10 3 kg / m 3 The finite element unit is 30 QUAD4 shell elements, and the number of sensors to be selected is set to 5. The first three-order displacement and strain modal matrices, mass matrix, stiffness matrix and node numbers of the structure are obtained through finite element calculation.

[0126] Reference Figure 4 and Figure 5 They are the sensor point locations after optimization by the hybrid sensor optimization configuration method and the effective independence method (EFI) disclosed in the present invention. When the EFI method is used for sensor layout, clustering will occur at the positions of nodes 10, 11 and 20, 21, which is a bad sensor configuration result. The concentrated sensors are highly correlated. In contrast, the sensor positions obtained by the hybrid sensor layout method do not have the phenomenon of concentrated sensor distribution, which shows that the sensor redundancy problem is better solved.

Claims

1. A hybrid sensor configuration method based on clustering and global spatial distance distribution coefficient, characterized in that: The following steps are involved: Step 1: Calculate the information matrix of candidate sensors; First, a finite element model of the structure is established. The number of finite element nodes is N, and each finite element unit node corresponds to a candidate sensor position. The sensors to be configured on the structure are assumed to be n FBG sensors. The problem of sensor layout is to select n positions from N candidate positions and apply them to morphological monitoring. The information matrix of all candidate position sensors on the structure is equal to the sum of the information matrices of a single sensor: Among them, Φ i and Q i Respectively represent the strain modal vector and strain information matrix corresponding to the i-th sensor, The matrix is ​​a semi-positive definite matrix; the strain mode of the structure is obtained by finite element analysis, and the strain mode information matrix corresponding to the sensors at all candidate positions is calculated by the above formula; Step 2: To address the information redundancy problem, K-means clustering is used to cluster the strain information matrix of the sensor in step 1 to obtain k different sensor groups; 2-1 First, the strain modal information matrix of each sensor obtained in step 1 is used as the sample set to be clustered, the number of clustering groups is set to k, and the information matrices of k sensors randomly distributed in the structure are selected from the sample set as the initial clustering center Q0 = [Q 01 ,Q 02 ,…,Q 0k ]; 2-2 Calculate the distance between the sample points in each sensor sample set and the center points of each cluster. The distance from the jth sample point to the i-th cluster grouping center is d ji =||Q j -Q 0i ||, and assign it to the group that is closest to the cluster center, i.e., the group with the highest similarity; 2-3 Calculate and update the cluster center of each group based on the redistributed sample set; 2-4 Repeat steps 2-2 to 2-3 until the standard measurement function converges or reaches the set number of clustering iterations. The standard measurement function is: Among them, ||·||2 represents the Euclidean norm, C i and m i Respectively represent the sample set and center of the i-th cluster; Step 3: Propose a global spatial distance distribution index and establish an objective function related to spatial redundancy; Select n sensors from the sensor group obtained in step 2, and establish an index coefficient for evaluating the global spatial distance distribution of these sensors; 3-1 First calculate the distance from a single sensor location to every other sensor location and select the minimum distance; then take the next sensor location and calculate its distance to all other sensor locations including the first sensor measured, again select the minimum value and add it to the first minimum distance; this process is repeated until the nearest sensor location of all sensor locations has been selected; then divide the sum of the minimum distances by the number of sensors to get the average minimum distance: Among them, min(D ij ) is the distance between each sensor and its nearest neighbor sensor; 3-2 Assuming that the distribution of sensors is completely random, the average random distance based on probability is: Among them, D ran is the average random distance, A is the area of ​​the sensor distribution area; 3-3 Use the distances between all sensors to form a distance matrix and calculate the distance d from the i-th sensor to the j-th sensor ij , the calculated result is used as the element of the i-th row and j-th column in the distance matrix DD, and the norm of the distance matrix is ​​calculated as Considering the ratio of the range of all sensor positions to the structural area, the calculation formula of the global space distance distribution coefficient DI is proposed as follows: 3-4 According to the distribution coefficient in step 3-3, an optimization function f1 for evaluating the spatial distribution of sensors is established. This function is an objective function related to spatial redundancy and is defined as the maximum value of the global spatial distribution coefficient: Among them, d1 is the spatial distance value when all candidate sensors are distributed adjacently, and d is the sensor position to be optimized; Step 4: Determine the calculation formula for the relative error of morphological estimation; Since this layout method is structure-oriented morphological estimation, in addition to ensuring the integrity of the information of the sensor network and the rationality of the spatial distribution, it is necessary to introduce the morphological estimation error function as another optimization target of the hybrid sensor layout method; 4-1 Dynamic displacement w of N nodes of the structure N×1 The modal displacement vibration shape Φ N×M is represented by M, where M is the selected structural modal order; correspondingly, the n sensors to be arranged on the structure have strain ε n×1 The strain mode shape Ψ can be used n×M To express, the above vibration modes are respectively transformed into their modal coordinates q M×1 Multiplication: w N×1 =Φ N×M ·q M×1 , eh n×1 =Ψ n×M ·q M×1 (7) 4-2 Introducing a relative estimation error That is, the ratio of the covariance matrix of the morphology estimation error to the measurement noise: 4-3 Based on the relative error obtained in 4-2, the optimization objective function with the minimum relative error of morphological estimation is established: Step 5: Through steps 3 and 4, the calculation formula of the optimization objective function f of the sensor configuration for morphology estimation can be established as follows: Among them, w2 and w1 represent the weight coefficients related to the morphological estimation error and the spatial distance distribution coefficient, respectively; Step 6: Then, an adaptive search optimization algorithm is used to solve the objective function given in step 5 with the minimum relative error of morphological estimation and the maximum spatial distance distribution index, and the final result of the sensor configuration is output; The adaptive search algorithm uses reflection, expansion, contraction, and compression operations to optimize the function. The process will continue until the termination condition is met. The four scalar parameters in the operation are: reflection coefficient α′, expansion coefficient β′, contraction coefficient γ′, and compression coefficient σ′. Their values ​​are related to the dimension and are as follows: Where n is the dimension of the corresponding optimization function, that is, the number of sensors to be deployed; the result of each iteration of the algorithm is to generate a new single vertex x e ′、x r ′、x o ' c 、x i ' c Replace x n+1 , or a compression step occurs, then n new vertices v are generated i ′, together with x1, constitute all the vertices of the simplex in the next iteration; its main iterative steps are: 6-1 Define the initial simplex and sort it: Given a non-degenerate simplex Δ(x1, x2, …, x n+1 ), the simplex is a convex polyhedron with n+1 vertices, In order to find the minimum value of the objective function, firstly set x1,x2,…x n+1 The corresponding function value Sort by f(x1)≤f(x2)≤…f(x n )≤f(x n+1 ); determine the lowest point x1 as a good point, the second highest point x n Worst point, highest point x n+1 As the worst point; 6-2 Calculate the reflection point in, It is represented as except for point x n+1 The centroid of the n vertices other than r )If f(x1)<f(x r )<f(x n ), then the vertex x′ of the new simplex n+1 =x r ; 6-3 Extension, if f(x r )<f(x1), then calculate the extension point If f(x e )<f(x r ), x′ n+1 =x e , otherwise accept x r And terminate the iteration; 6-4 Contraction, if f(x r )≥f(x n ), then in and x r With x n+1 Contraction between the better a) If f(x n )≤f(x r )≤f(x n+1 )(Point x r Strictly x n+1 Good), then perform external contraction, If f(x oc )<f(x r ), then x′ n+1 =x oc Terminate this iteration, otherwise execute step 6-5; b) If f(x r )>f(x n+1 ), then an internal shrink operation is performed: If f(x ic )<f(x n+1 ), then x′ n+1 =x ic And terminate this iteration, otherwise execute step 6-5; 6-5 compression, calculate n points, v i =x1+σ(x i -x1),i=2,…,n+1,x i ′=v i ′, then the vertices of the simplex in the next iteration are Δ=Δ(x1,v2,…v n+1 )composition; 6-6 Repeat steps 6-1 to 6-5 in each iteration until the termination condition is met; After iteration 6-7, the solution of the objective function in step 5 is output, i.e., the layout positions of n sensors; Firstly, based on the information matrix of the sensor, the sensors are divided into several groups by clustering method. Then, the positions that meet the above conditions are selected from several groups according to the criteria of maximum global spatial distribution distance and minimum morphological relative estimation error. The positions of the sensors are continuously updated and optimized in the iterative process, and it is judged whether the termination conditions are finally met, so as to determine the optimal position of the sensor.

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