Multi-batch three-dimensional sensor optimization layout method in modal test

Abstract

The invention discloses a multi-batch three-dimensional sensor optimization layout method in a modal test, which is used for extracting candidate sensor positions from a finite element model and solving the optimization problem by simultaneously considering a reference sensor and a mobile sensor. Firstly, a modal addition method is carried out on candidate sensor positions extracted from a finite element model, a reference sensor candidate set is selected, then an improved three-dimensional independence criterion and a minimum variance criterion of structural response estimation errors are combined, and three-dimensional sensor optimization layout is achieved by optimizing a batch with the worst objective function result. According to the method, the modal test precision of a large-scale structure or a complex structure can be effectively improved.

Description

Technical Field

[0001] This invention relates to the field of mechanical engineering, and more particularly to a method for optimizing the layout of multiple batches of three-dimensional sensors in modal testing. Background Technology

[0002] Rotating machinery often operates under harsh conditions such as high temperatures and alternating loads. Influenced by complex nonlinear load excitations, it is prone to dynamic structural problems and fatigue failure. Therefore, modal identification under operating conditions is of great significance. Its dynamic characteristics are not only core indicators for system condition monitoring but also the foundation for ensuring reliable and stable operation of the rotor system, fault and damage diagnosis, and system life prediction. Furthermore, a thorough understanding of the stress-strain response of the structure under actual operating conditions is equally crucial for reliability monitoring. However, due to limitations in the number of sensors and the difficulty in deploying them in critical locations, related assessment work often faces challenges. Continuous monitoring in high-risk areas is even more difficult and costly. Virtual sensing, by introducing process models, can estimate and extend the response of unmeasured locations based on limited sensor data, providing an efficient and feasible technical approach for structural health monitoring.

[0003] The accuracy of modal testing depends on the number and location of sensors. For small, simple test structures, the number of sensors and the location of measurement points can often be determined based on expert experience. However, for large, complex structures, intricate spatial structures, hardware limitations, and harsh operating environments can all affect the arrangement of sensors and the quality of data acquisition. To ensure the accuracy of data collection, it is necessary to study optimized layout methods for multiple batches of three-dimensional sensors in modal testing to maximize the effectiveness of the measurement system.

[0004] In 1991, Kamer proposed a criterion called the Fisher information matrix, which ranks candidate sensor locations based on their contribution to the linear independence of the target modality. By minimizing the condition number of the Fisher information matrix or maximizing the determinant, minimum eigenvalue, or norm, the locations with the smallest contribution can be removed, thus achieving the optimal sensor layout.

[0005] To avoid selecting sensor locations with low energy, a commonly used objective function is modal kinetic energy, which typically prioritizes locations with high amplitude responses to improve the signal-to-noise ratio. A drawback of modal kinetic energy is its heavy dependence on the finite element mesh size. Specifically, it tends to select regions with coarser meshes and higher mass. A similar objective function is the driving point residual. The driving point residual assesses the effectiveness of a specific degree of freedom in exciting a specific mode, and locations with higher driving point residual values ​​are considered optimal locations for modal excitation.

[0006] Another commonly used standard is the modal confidence criterion, which quantifies the similarity between mode shapes obtained from sensor locations. Optimal sensor locations can be achieved by minimizing the maximum value or sum of the off-diagonal elements in the MAC (Modal Assurance Criterion) matrix.

[0007] Furthermore, sensor optimization methods considering model uncertainty have attracted considerable attention. Kim proposed the stochastic effective independence method, an extension of the effective independence method, which combines deterministic and stochastic components to explain model uncertainty. Jaya investigated the impact of modeling error and measurement noise on modal extension sensor location. However, the results show that modeling error varies with the degrees of freedom. Papadimitriou proposed information entropy as a criterion for sensor optimization; his research examined the impact of measurement noise and modeling error on sensor optimization, aiming to minimize redundant data from neighboring sensors. Vincenzi used the same information entropy (IE) method to explore the impact of model and parameter uncertainties on sensor optimization in modal testing and structural health monitoring.

[0008] Current research primarily focuses on optimal sensor placement in single-batch measurements, with relatively little attention paid to optimizing the positions of reference and moving sensors in multi-batch modal identification. However, data merging is a crucial step in multi-batch modal analysis. Inappropriate sensor placement can lead to certain modes failing to be accurately identified in specific batches, especially modes with similar frequencies, making effective modal matching and pairing difficult and impacting the overall accuracy of modal parameter identification. Therefore, developing sensor optimization methods for multi-batch testing, and rationally configuring the positions of reference and moving sensors to ensure high-quality and consistent data across batches, is of great significance for improving the accuracy and reliability of modal analysis of large or complex structures. Summary of the Invention

[0009] The technical problem to be solved by the present invention is to address the deficiencies mentioned in the background art by providing a method for optimizing the layout of multiple batches of three-dimensional sensors in modal testing. By optimizing the sensor layout and parameter settings, this method can improve the accuracy of structural vibration data acquisition, the efficiency of analysis, and reduce the number of sensors used.

[0010] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0011] A method for optimizing the layout of multiple batches of 3D sensors in modal testing includes the following steps:

[0012] Step 1), initialize the number of selected moving sensors to n. rov=0, the location number of the motion sensor i rov =0, let N ref For the preset number of required reference sensors, N rov The number of required moving sensors is preset, and n is the preset modal order;

[0013] Step 2) Extract the positions and three-dimensional mode shapes of all candidate sensors from the finite element model. Perform modal summation on the three-dimensional mode shape of each candidate sensor, and select the sensor with the largest modal component summation index, N. c The locations of the candidate sensors are used as a reference sensor candidate set Set. ref Let the number of all candidate sensors be N. all Set all Let N be the set of locations of all candidate sensors. ref <N c <N all ;

[0014] Step 3), Set ref The reference sensor positions are numbered sequentially from 1 to N. c Set all Except for Set ref Other candidate sensor locations are used as the candidate set for mobile sensors. rov and Set rov Divide the data into p equal batches, each batch containing (N... all -N ref ) / p positions of moving sensors; initialize reference sensor position number i r =0;

[0015] Step 4), let i r =i r +1, b = 0;

[0016] Step 5), from Set ref Delete number i r Based on the reference sensor position, the remaining N is obtained. c -1 reference sensor position set (ref-1) and add it to the measurement sensor candidate set Set mea At this time, Set mea＝ [Set (ref-1) ];

[0017] Step 6), let b = b + 1;

[0018] Step 7), use the candidate set of mobile sensors in the b-th batch as the control sensor candidate set Set. b ;

[0019] Step 8), calculate Set mea The three-dimensional information matrix Q0 is obtained, and the orthogonal projection vector P = φ0φ0 is established. T Where φ0 represents the set of eigenvectors corresponding to the zero eigenvalues ​​of Q0, and the filtered Set is calculated using P. b Information matrix Q cf =PQ c P T Q c For Set b A three-dimensional information matrix;

[0020] Step 9), calculate Set according to the following formula b EfI3 at each moving sensor location fi Value and press EfI3 fi Rank the locations of the moving sensors from largest to smallest:

[0021]

[0022] Where det(.) represents the determinant of the matrix within the parentheses, I3 is a 3x3 identity matrix, and Ф 3i Let be the three-dimensional mode shape vector of the i-th sensor position. Indicates the pseudo-inverse of the matrix within the brackets;

[0023] From Set b Remove EfI3 fi The location of the moving sensor with the largest value is deleted and added to the optimal moving sensor candidate set Set as the b-th batch's optimal moving sensor location. (rov，b) and put it into Set mea At this time, Set mea =[Set (ref-1) Set (rov，b) Let n rov =n rov +1;

[0024] Step 10), calculate Set mea The three-dimensional information matrix Q0;

[0025] Step 11): Determine if Q0 is full rank. If not, proceed to step 9. If it is full rank, proceed to step 12.

[0026] Step 12), let i rov =i rov +1, Set (com，b) =Set (rov，b) Set comea =Set mea ;

[0027] Step 13), let Set b The number of sensor positions is N b Let Set all Not belonging to Set comea The sensor locations are named as the Unmeasured Sensor Candidate Set. unmea ;

[0028] Select Set b The i-th rov Each sensor location is placed in Set (com，b) and put it into Set comea ; Calculate Set unmea The average value of the displacement estimation error variance in Σ um For Set unmea The displacement error covariance matrix, Φ um For Set unmea The modal shape matrix, Where W is the diagonal weighting matrix, and under the assumption that the measurement noise is uncorrelated, the weighting matrix W can be regarded as the identity matrix; Φ m For Set mea The modal shape matrix, tr(.) is the rank of the matrix within the brackets, and d is the set... unmea The number of positions in the middle;

[0029] Step 14), determine i rov Is it equal to N? b If they are not equal, proceed to step 12); if they are equal, proceed to step 15.

[0030] Step 15), find the average value. The smallest i rov and assign it to i opr Set b The i-th opr Delete each sensor location and add the deleted sensor locations to the Set. (rov，b) and Set mea In the middle, at this time, Set mea =[Set (ref-1) Set (rov，b) Let n rov =n rov +1, i rov =0;

[0031] Step 16), determine n rov Is it equal to N? rov If they are not equal, proceed to step 12); if they are equal, proceed to step 17.

[0032] Step 17), let

[0033] Step 18): Determine if b is equal to p. If not, proceed to step 6); if equal, proceed to step 19.

[0034] Step 19): Compare and extract the maximum average value across p batches.

[0035] Step 20, determine i r Is it equal to N? c If not equal, proceed to step 4); if equal, proceed to step 21.

[0036] Step 21), compare i r =1,2,3……N c In the case of turn up The minimum i r and assign it to i t Set ref Subtract the i-th from the middle t Let the set of 10 reference sensor locations be the optimal reference sensor candidate set Set. opt ;

[0037] Step 22), let Set ref =Set opt N c =N c -1;

[0038] Step 23), determine N c Is it equal to N? ref If they are not equal, proceed to step 3); if they are equal, proceed to step 24.

[0039] Step 24), P optimal =[Set ref， Set (rov,b) [This is] the optimal sensor configuration.

[0040] As a further optimization scheme of the multi-batch three-dimensional sensor optimization layout method in modal testing of the present invention, N ref Take 2.

[0041] As a further optimization scheme of the multi-batch three-dimensional sensor layout optimization method in modal testing of the present invention, p is set to 2.

[0042] Compared with the prior art, the present invention, employing the above technical solution, has the following technical effects:

[0043] By optimizing the batch with the worst objective function result, the layout of the 3D sensor reference points and the moving points of each batch can be optimized simultaneously, ensuring the high quality and consistency of data from each batch. This is of great significance for improving the accuracy and reliability of modal analysis of large or complex structures. Attached Figure Description

[0044] Figure 1 This is a schematic diagram of the process of the present invention;

[0045] Figure 2 The research object is a thin plate structure;

[0046] Figure 3 A schematic diagram showing the optimized sensor layout for a thin-plate structure.

[0047] Figure 4 This is a schematic diagram of the optimized MAC values ​​for each mode shape. Detailed Implementation

[0048] The technical solution of the present invention will be further described in detail below with reference to the accompanying drawings:

[0049] This invention can be implemented in many different forms and should not be considered limited to the embodiments described herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully express the scope of the invention to those skilled in the art. In the drawings, components are enlarged for clarity.

[0050] It should be understood that although the terms first, second, third, etc., may be used herein to describe various elements, components, and / or parts, these elements, components, and / or parts are not limited by these terms. These terms are merely used to distinguish elements, components, and / or parts from one another. Therefore, the first element, component, and / or part discussed below may be a second element, component, or part without departing from the teachings of this invention.

[0051] The optimization layout problem of multiple batches of 3D sensors in modal testing can be expressed as: given the number of available reference sensors, the number of moving sensors, and the number of batches, how should the reference and moving sensors be placed to maximize modal observability? Therefore, it is necessary to solve the optimization problem by simultaneously considering the positions of the reference and moving sensors. The optimization approach is as follows:

[0052] The accuracy of multi-batch modal testing depends on the batch with the worst test quality. Therefore, this invention considers optimizing the batch with the worst test quality to maximize the quality of all batches, thereby improving the accuracy of modal testing. The optimization formula is as follows:

[0053]

[0054] Where P optimalTo determine the optimal location for multiple batches of sensors. d is the set of locations where no sensors are placed (Set). unmea The number of positions included, ∑ um Set of locations where no sensors are placed unmea The displacement error covariance matrix is ​​given by tr(.), where tr(.) is the trace of the matrix within the brackets. The objective of this formula is to minimize (1 / d)·tr(Σ) over all batches. um The maximum value of ).

[0055] To achieve the above approach, the first step is to select an initial set of candidate reference sensors. In practical scenarios involving modal testing of large structures, limitations such as the limited number of sensors often prevent the simultaneous measurement of all degrees of freedom within a single batch, thus affecting the accuracy of modal analysis and virtual sensing. Therefore, employing multi-batch measurement techniques to cover all degrees of freedom of interest is crucial.

[0056] Multi-batch measurement techniques categorize sensors into two types: reference sensors and moving sensors. In each batch of tests, some reference sensors remain in fixed positions, while moving sensors cover different areas.

[0057] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0058] A method for optimizing the layout of multiple batches of 3D sensors in modal testing includes the following steps:

[0059] Step 1), initialize the number of selected moving sensors to n. rov =0, the location number of the motion sensor i rov =0, let N ref For the preset number of required reference sensors, N rov The number of required moving sensors is preset, and n is the preset modal order;

[0060] Step 2) Extract the positions and three-dimensional mode shapes of all candidate sensors from the finite element model. Perform modal summation on the three-dimensional mode shape of each candidate sensor, and select the sensor with the largest modal component summation index, N. c The locations of the candidate sensors are used as a reference sensor candidate set Set. ref Let the number of all candidate sensors be N. all Set all Let N be the set of locations of all candidate sensors. ref <N c <N all ;

[0061] In step 2), the core idea of ​​the eigenvector summation method is: based on finite element analysis, obtain the eigenvectors (mode shapes) of the three-dimensional modes of the structure within the target frequency band, and calculate the sum of the absolute values ​​of the normalized mode shape amplitudes at each candidate location. The sum of the absolute values ​​of the normalized displacement amplitudes comprehensively reflects the activity and energy level of that location in the overall modal response. The N with the largest sum of absolute values ​​is selected. c (N c >N ref Using N points as the initial reference sensor candidate set can effectively enhance the signal-to-noise ratio and prevent sensors from being placed at mode shape nodes. ref This represents the required number of reference sensors.

[0062]

[0063] In the formula, MSSP i φ represents the modal component summation index at the i-th sensor position; in This represents the modal component of the i-th sensor position in the n-th mode shape, where N is the mode order.

[0064] Step 3), Set ref The reference sensor positions are numbered sequentially from 1 to N. c Set all Except for Set ref Other candidate sensor locations are used as the candidate set for mobile sensors. rov and Set rov Divide the data into p equal batches, each batch containing (N... all -N ref ) / p positions of moving sensors; initialize reference sensor position number i r =0;

[0065] Step 4), let i r =i r +1; b = 0;

[0066] Step 5), from Set ref Delete number i r Based on the reference sensor position, the remaining N is obtained. c -1 reference sensor position set (ref-1) and add it to the measurement sensor candidate set Set mea At this time, Set mea =[Set (ref-1) ];

[0067] Step 6), let b = b + 1;

[0068] Step 7), use the candidate set of mobile sensors in the b-th batch as the control sensor candidate set Set. b ;

[0069] Step 8), calculate Set mea The three-dimensional information matrix Q0 is obtained, and the orthogonal projection vector P = φ0φ0 is established. T Where φ0 represents the set of eigenvectors corresponding to the zero eigenvalues ​​of Q0, and the filtered Set is calculated using P. b Information matrix Q cf =PQ c P T Q c For Set b A three-dimensional information matrix;

[0070] Step 9), calculate Set according to the following formula b EfI3 at each moving sensor location fi Value and press EfI3 fi Rank the locations of the moving sensors from largest to smallest:

[0071]

[0072] Where det(.) represents the determinant of the matrix within the parentheses, I3 is a 3x3 identity matrix, and Ф 3i Let be the three-dimensional mode shape vector of the i-th sensor position. Indicates the pseudo-inverse of the matrix within the brackets;

[0073] From Set b Remove EfI3 fi The location of the moving sensor with the largest value is deleted and added to the optimal moving sensor candidate set Set as the b-th batch's optimal moving sensor location. (rov，b) and put it into Set mea At this time, Set mea =[Set (ref-1) Set (rov，b) Let n rov =n rov +1;

[0074] Step 10), calculate Set mea The three-dimensional information matrix Q0;

[0075] Step 11): Determine if Q0 is full rank. If not, proceed to step 9. If it is full rank, proceed to step 12.

[0076] Step 12), let i rov =i rov +1, Set (com，b)=Set (rov，b) Set comea =Set mea ;

[0077] Step 13), let Set b The number of sensor positions is N b Let Set all Not belonging to Set comea The sensor locations are named as the Unmeasured Sensor Candidate Set. unmea ;

[0078] Select Set b The i-th rov Each sensor location is placed in Set (com，b) and put it into Set comea ; Calculate Set unmea The average value of the displacement estimation error variance in ∑ um For Set unmea The displacement error covariance matrix, Φ um For Set unmea The modal shape matrix, Where W is the diagonal weighting matrix, and under the assumption that the measurement noise is uncorrelated, the weighting matrix W can be regarded as the identity matrix; Φ m For Set mea The modal shape matrix, tr(.) is the rank of the matrix within the brackets, and d is the set... unmea The number of positions in the middle;

[0079] In step 13): Since continuing to select the moving sensor based on the effective independence criterion after Q0 reaches full rank is prone to information redundancy, we consider using the minimum variance criterion of structural response estimation error to continue seeking the optimal moving sensor point.

[0080] According to the theory of modal superposition Φ is a subset of N all Candidate sensor locations, Nth-order mode shape φ n The modal shape matrix is ​​given, q(t) represents the modal coordinates, and the displacement response x(t) can be divided into displacements xt at the sensor placement position and the sensorless position. m and x um As shown below:

[0081]

[0082] Therefore, the modal shape matrix Φ is also correspondingly divided into Φ for the sensor placement location. m Φ at the location where no sensor is placed um .

[0083] The measurement response y(t) considering the measurement error ε(t) can be expressed as:

[0084] y(t)=x m (t)+ε(t)=Φ m q(t)+ε(t);

[0085] Assume the measurement error follows a Gaussian distribution with a zero mean and is uncorrelated across all sensor locations. The least-squares solution for the modal coordinates is:

[0086]

[0087] in Here are the estimated values ​​for the modal coordinates, (.). + It indicates a false reversal.

[0088] The error covariance matrix ∑ of the weighted least squares estimate q for

[0089]

[0090] Where W is the diagonal weighted matrix, and under the assumption that the measurement noise is uncorrelated, the weighted matrix W can be regarded as the identity matrix.

[0091] Based on the above equations, the displacement estimation error covariance matrix ∑ at the location where no sensor is placed can be calculated. um as follows:

[0092]

[0093] By minimizing the average of the displacement estimation error variance of the set of locations where no sensors are placed, i.e. The quality of modal testing under this sensor configuration can be evaluated.

[0094] Step 14), determine i rov Is it equal to N? b If they are not equal, proceed to step 12); if they are equal, proceed to step 15.

[0095] Step 15), find the average value. The smallest i rov and assign it to i opr Set b The i-th opr Delete each sensor location and add the deleted sensor locations to the Set. (rov，b) and Set mea In the middle, at this time, Set mea =[Set (ref-1) Set(rov，b) Let n rov =n rov +1, i rov =0;

[0096] Step 16), determine n rov Is it equal to N? rov If they are not equal, proceed to step 12); if they are equal, proceed to step 17.

[0097] Step 17), let

[0098] Step 18): Determine if b is equal to p. If not, proceed to step 6); if equal, proceed to step 19.

[0099] Step 19): Compare and extract the maximum average value across p batches.

[0100] Step 20, determine i r Is it equal to N? c If not equal, proceed to step 4); if equal, proceed to step 21.

[0101] Step 21), compare i r =1,2,3……N c In the case of turn up The minimum i r and assign it to i t Set ref Subtract the i-th from the middle t Let the set of 10 reference sensor locations be the optimal reference sensor candidate set Set. opt ;

[0102] Step 22), let Set ref =Set opt N c =N c -1;

[0103] Step 23), determine N c Is it equal to N? ref If they are not equal, proceed to step 3); if they are equal, proceed to step 24.

[0104] Step 24), P optimal =[Set ref， Set (rov,b) [This is] the optimal sensor configuration.

[0105] To verify the generality of the proposed method, the following methods were used: Figure 2The thin plate shown is used for verification. One end of the plate is fixed, and the other end is free. The fixed end is marked in blue. The material of the thin plate is structural steel, and the elastic modulus is 2 × 10⁻⁶. 11 Pa, Poisson's ratio is 0.3, and density is 7850 kg / m³. 3 Assuming the modes of interest are the first five modes, including three bending modes and two torsional modes, according to the present invention... Figure 1 The flowchart shown illustrates the optimal sensor arrangement. Figure 3 As shown in the figure, solid dots represent the reference sensor positions, and hollow dots represent the moving sensor positions. To measure the quality of the sensor configuration, the Modal Assurance Criterion (MAC) is used as the evaluation standard. The MAC values ​​between the measured modes of this sensor configuration are shown below. Figure 4 As shown in the figure, Ph1 is the actual value and Ph2 is the optimized simulation value. It can be found that the method can restore the modal shape of the target structure and distinguish the modes when two batches of tests are conducted, and obtain a very good MAC value. The maximum value on the off-diagonal is only the MAC value between mode 1 and mode 3, which is 0.28.

[0106] Sensor placement is a crucial factor affecting the accuracy of modal testing. This invention presents a method for optimizing the layout of multiple batches of three-dimensional sensors in modal testing. This method extracts candidate sensor positions from the finite element model and addresses the optimization problem by simultaneously considering both reference and moving sensors. First, modal summation is applied to the candidate sensor positions extracted from the finite element model to select a candidate set of reference sensors. Then, combined with a modified three-dimensional independence criterion and a minimum variance criterion for structural response estimation error, the optimal layout of the three-dimensional sensors is achieved by optimizing the batch with the worst objective function result. This method can effectively improve the modal testing accuracy of large or complex structures. Finally, simulation data verifies the feasibility of this optimization method.

[0107] It will be understood by those skilled in the art that, unless otherwise defined, all terms used herein (including technical and scientific terms) have the same meaning as commonly understood by one of ordinary skill in the art to which this invention pertains. It should also be understood that terms such as those defined in general dictionaries should be understood to have the same meaning as in the context of the prior art, and should not be interpreted in an idealized or overly formal sense unless defined as herein.

[0108] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for optimizing the layout of multiple batches of three-dimensional sensors in modal testing, characterized in that, Includes the following steps: Step 1), initialize the number of selected moving sensors to n. rov =0, the location number of the motion sensor i rov =0, let N ref For the preset number of required reference sensors, N rov The number of mobile sensors is the preset number, and p is the preset number of batches. Step 2) Extract the positions and three-dimensional mode shapes of all candidate sensors from the finite element model. Perform modal summation on the three-dimensional mode shape of each candidate sensor, and select the sensor with the largest modal component summation index, N. c The locations of the candidate sensors are used as a reference sensor candidate set Set. ref Let the number of all candidate sensors be N. all Set all Let N be the set of locations of all candidate sensors. ref <N c <N all ; Step 3), Set ref The reference sensor positions are numbered sequentially from 1 to N. c Set all Except for Set ref Other candidate sensor locations are used as the candidate set for mobile sensors. rov and Set rov Divide the data into p equal batches, each batch containing (N... all -N ref ) / p positions of moving sensors; initialize reference sensor position number i r =0; Step 4), let i r =i r +1, b = 0; Step 5), from Set ref Delete number i r Based on the reference sensor position, the remaining N is obtained. c -1 reference sensor position set (ref-1) and add it to the measurement sensor candidate set Set mea At this time, Set mea =[Set (ref-1) ]; Step 6), let b = b + 1; Step 7), use the candidate set of mobile sensors in the b-th batch as the control sensor candidate set Set. b ; Step 8), calculate Set mea The three-dimensional information matrix Q0 is obtained, and the orthogonal projection vector P = φ0φ0 is established. T Where φ0 represents the set of eigenvectors corresponding to the zero eigenvalues ​​of Q0, and the filtered Set is calculated using P. b Information matrix Q cf =PQ c P T Q c For Set b A three-dimensional information matrix; Step 9), calculate Set according to the following formula b EfI3 at each moving sensor location fi Value and press EfI3 fi Rank the locations of the moving sensors from largest to smallest: Where det(.) represents the determinant of the matrix within the parentheses, I3 is a 3x3 identity matrix, and Ф 3i Let be the three-dimensional mode shape vector of the i-th sensor position. This represents the pseudo-inverse of the matrix within the brackets; From Set b Remove EfI3 fi The location of the moving sensor with the largest value is deleted and added to the optimal moving sensor candidate set Set as the b-th batch's optimal moving sensor location. (rov，b) and put it into Set mea At this time, Set mea =[Set (ref-1) Set (rov，b) Let n rov =n rov +1; Step 10), calculate Set mea The three-dimensional information matrix Q0; Step 11): Determine if Q0 is full rank. If not, proceed to step 9. If it is full rank, proceed to step 12. Step 12), let i rov =i rov +1, Set (com，b) =Set (r ov, b), Set comea =Set mea ; Step 13), let Set b The number of sensor positions is N b Let Set all Not belonging to Set comea The sensor locations are named as the Unmeasured Sensor Candidate Set. unmea ; Select Set b The i-th rov Each sensor location is placed in Set (com，b) and put it into Set comea ; Calculate Set unmea The average value of the displacement estimation error variance in ∑ um For Set unmea The displacement error covariance matrix, Φ um For Set unmea The modal shape matrix, Where W is the diagonal weighting matrix, and under the assumption that the measurement noise is uncorrelated, the weighting matrix W can be regarded as the identity matrix; Φ m For Set mea The modal shape matrix, tr(.) is the rank of the matrix within the brackets, and d is the set... unmea The number of positions in the middle; Step 14), determine i rov Is it equal to N? b If they are not equal, proceed to step 12); if they are equal, proceed to step 15. Step 15), find the average value. The smallest i rov and assign it to i opr Set b The i-th opr Delete each sensor location and add the deleted sensor locations to the Set. (rov，b) and Set mea In the middle, at this time, Set mea =[Set (ref-1 ), Set (rov，b) Let n rov =n rov +1, i rov =0; Step 16), determine n rov Is it equal to N? rov If they are not equal, proceed to step 12); if they are equal, proceed to step 17. Step 17), let Step 18): Determine if b is equal to p. If not, proceed to step 6); if equal, proceed to step 19. Step 19): Compare and extract the maximum average value across p batches. Step 20, determine i r Is it equal to N? c If not equal, proceed to step 4); if equal, proceed to step 21. Step 21), compare i r =1,2,3……N c In the case of turn up The minimum i r and assign it to i t Set ref Subtract the i-th from the middle t Let the set of 10 reference sensor locations be the optimal reference sensor candidate set Set. opt ; Step 22), let Set ref =Set opt N c =N c -1; Step 23), determine N c Is it equal to N? ref If they are not equal, proceed to step 3); if they are equal, proceed to step 24. Step 24), P optimal =[Set ref Set (rov,b) [This is] the optimal sensor configuration.

2. The method for optimizing the layout of multiple batches of three-dimensional sensors in modal testing according to claim 1, characterized in that, N ref Take 2.

3. The method for optimizing the layout of multiple batches of three-dimensional sensors in modal testing according to claim 1, characterized in that, p is set to 2.

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