Sensor optimization arrangement method and system based on structural vibration response

Abstract

The application provides a sensor optimization arrangement method and system based on structural vibration response, and belongs to the technical field of equipment safety detection. The application comprises the following steps: establishing a finite element model of a structure to be monitored; calculating an equivalent energy matrix and an average value of diagonal elements of the equivalent energy matrix; starting from all degrees of freedom, sequentially deleting the minimum value on the diagonal of the equivalent energy matrix, and simultaneously deleting the degree of freedom represented by the value; using the remaining degrees of freedom to construct an iteration matrix; sorting the main diagonal elements on the iteration matrix, selecting the smallest element, and deleting the degree of freedom vector corresponding to the element from the modal matrix; repeating the step until the number of remaining degrees of freedom is equal to the number of sensors to be arranged, wherein the sensors are arranged on the remaining degrees of freedom. The application not only considers high-energy measuring points and improves the noise resistance of the measuring point combination, but also fully guarantees the modal independence and modal information amount of the measuring point combination, and is more suitable for the application of sensor optimization arrangement in actual engineering practice.

Description

Technical Field

[0001] This invention relates to the field of equipment safety testing technology, specifically to a sensor optimization arrangement method and system based on structural vibration response. Background Technology

[0002] Structural health monitoring is a non-destructive testing technique for structures that uses sensors installed at specific locations to perform modal identification, analysis, and evaluation. The placement of sensors directly affects the composition and quality of the acquired signals, making it crucial for structural health monitoring. How to strategically place sensors to acquire the most accurate and representative structural response information using a limited number of sensors has become a prominent issue in structural health monitoring.

[0003] To address the sensor placement optimization problem, the most representative existing methods are traditional approaches with rigorous mathematical foundations, optimizing based on evaluation criteria, such as the effective independence method, modal kinetic energy method, and QR decomposition method. However, due to the one-sidedness of the evaluation criteria, these methods all have their limitations. With the development of intelligent optimization algorithms, the solution to the sensor placement optimization problem has also introduced highly adaptable intelligent methods that optimize search techniques, such as genetic algorithms, particle swarm optimization, artificial fish swarm optimization, and Bayesian theory algorithms. The goal of these methods is to search for the global optimum of the objective function; therefore, the selection of the objective function determines the accuracy and convergence of the optimization. At the same time, these methods are prone to getting trapped in local optima, and their computational speed is affected by computer performance.

[0004] Based on traditional and intelligent optimization methods, many improved methods have emerged that consider multiple evaluation criteria or combine traditional and intelligent methods for optimization. For example, Yao et al. first proposed an improved method based on the effective independence method, using the determinant of the information matrix as the fitness value and applying a genetic algorithm for iterative optimization. Xie Jianhong et al. proposed a genetic neural network algorithm that combines a genetic algorithm with a neural network. These methods are improvements on the first two methods and are more effective in practical engineering applications of sensor optimization placement problems because they take into account more influencing factors.

[0005] In 1991, Kamer proposed the Effective Independence Method (EI method), which is currently the most widely used sensor layout optimization method. It optimizes the Fisher information matrix to keep the selected modal vectors as linearly independent as possible. However, the EI method only considers the linear contribution of the measuring points to the modal matrix and does not take into account the energy contribution of the measuring points, easily missing measuring points with high vibration energy, thus reducing the noise resistance of the sensor layout. To address this shortcoming of the EI method, many scholars have introduced various energy factors to propose improved methods. Yang Yaxun et al. proposed the Energy Coefficient-Effective Independence Method (EI-MSE method) using nodal degree-of-freedom modal strain energy as correction coefficients, overcoming the deficiency of the EI method's information matrix not containing energy elements; Liu Wei et al. proposed the Effective Independence-Modal Kinetic Energy Method (EI-MKE method) using modal kinetic energy to correct the EI method; Fan Hengcheng et al. proposed the Multi-Energy Parameter Improved Effective Independence Method (EI-MEP method) using modal strain energy and modal kinetic energy as correction coefficients for the EI method.

[0006] The above improved method obtains the optimal arrangement scheme by multiplying the iteration matrix of the EI method by a coefficient matrix containing vibration energy. However, introducing the coefficient matrix changes the numerical distribution of the original iteration matrix. While selecting high-energy measurement points, it reduces the modal independence of the measurement points, thus diminishing the advantage of high modal independence of the EI method. Summary of the Invention

[0007] The purpose of this invention is to provide a sensor optimization arrangement method and system based on structural vibration response, so as to solve at least one of the technical problems existing in the background art.

[0008] To achieve the above objectives, the present invention adopts the following technical solution:

[0009] On one hand, the present invention provides a sensor optimization arrangement method based on structural vibration response, comprising:

[0010] A finite element model of the structure to be monitored is established, the number of modes is selected, modal analysis is performed, and the modal vector matrix, mass matrix and stiffness matrix of the structure to be monitored are obtained.

[0011] Calculate the equivalent energy matrix and the average value of the diagonal elements of the equivalent energy matrix based on the modal vector matrix, mass matrix, stiffness matrix, and number of modes;

[0012] Starting from all degrees of freedom, the minimum value on the diagonal of the equivalent energy matrix is ​​deleted in turn, and the degree of freedom represented by that value is also deleted, until the minimum value deleted is greater than the average value of the diagonal elements or the number of remaining candidate degrees of freedom is equal to twice the number of sensors that need to be deployed.

[0013] Construct an iterative matrix using the remaining degrees of freedom, sort the diagonal elements of the iterative matrix, select the smallest element and remove the degree of freedom vector corresponding to that element from the modal vector matrix; continue constructing iterative matrices to delete degree of freedom vectors from the modal vector matrix until the number of remaining degrees of freedom is the number of sensors to be arranged, where the sensors will be arranged on the remaining degrees of freedom.

[0014] Preferably, calculating the equivalent energy matrix includes:

[0015] Calculate the modal kinetic energy and modal strain energy corresponding to the k-th mode of the i-th degree of freedom of the structure to be monitored;

[0016] Normalize the modal kinetic energy and modal strain energy;

[0017] The sum of the normalized modal kinetic energy and the normalized modal strain energy is taken as the relative total energy corresponding to the k-th mode of the i-th degree of freedom, and the equivalent energy matrix is ​​calculated.

[0018] Preferably, the modal kinetic energy MKE corresponding to the k-th mode of the i-th degree of freedom. ik for:

[0019] Where, φ ik M represents the k-th modal component of the i-th degree of freedom. ij φ represents the value in the i-th row and j-th column of the mass matrix. jk This represents the k-th modal component of the j-th degree of freedom.

[0020] Preferably, the modal strain energy (MSE) corresponding to the k-th mode in the i-th degree of freedom. ik for: Among them, K ij This represents the value in the i-th row and j-th column of the stiffness matrix.

[0021] Preferably, the modal kinetic energy and modal strain energy are normalized, including:

[0022] Among them, GMKE ik GMSE represents the modal kinetic energy after normalization transformation. ik denoted as modal strain energy after normalization transformation, where n represents the total number of degrees of freedom and N represents the modal order.

[0023] Preferably, calculating the equivalent energy matrix includes:

[0024] Take GMKE ik and GMSE ik The sum of these values ​​represents the relative total energy GE corresponding to the k-th mode in the i-th degree of freedom. ikCalculate the equivalent energy matrix EEM: EEM = diag((GE)(GE)) T ).

[0025] Secondly, the present invention provides a sensor optimization arrangement system based on structural vibration response, comprising:

[0026] The module is used to build a finite element model of the structure to be monitored, select the number of modes, perform modal analysis, and obtain the modal vector matrix, mass matrix, and stiffness matrix of the structure to be monitored.

[0027] The calculation module is used to calculate the equivalent energy matrix and the average value of the diagonal elements of the equivalent energy matrix based on the modal vector matrix, mass matrix, stiffness matrix and number of modes;

[0028] The filtering module is used to start from all degrees of freedom and sequentially delete the minimum value on the diagonal of the equivalent energy matrix, while also deleting the degree of freedom represented by that value, until the minimum value deleted is greater than the average value of the diagonal elements or the number of remaining candidate degrees of freedom is equal to twice the number of sensors that need to be deployed.

[0029] The iteration module is used to construct an iteration matrix using the remaining degrees of freedom, sort the diagonal elements of the iteration matrix, select the smallest element and delete the degree of freedom vector corresponding to that element from the modal vector matrix; continue to construct the iteration matrix and delete degree of freedom vectors from the modal vector matrix until the number of remaining degrees of freedom is the number of sensors to be arranged, where the sensors will be arranged on the remaining degrees of freedom.

[0030] Thirdly, the present invention provides a non-transitory computer-readable storage medium for storing computer instructions, which, when executed by a processor, implement the sensor optimization arrangement method based on structural vibration response as described above.

[0031] Fourthly, the present invention provides a computer program product, including a computer program that, when run on one or more processors, is used to implement the sensor optimization arrangement method based on structural vibration response as described above.

[0032] Fifthly, the present invention provides an electronic device, comprising: a processor, a memory, and a computer program; wherein the processor is connected to the memory, the computer program is stored in the memory, and when the electronic device is running, the processor executes the computer program stored in the memory to cause the electronic device to execute instructions for implementing the sensor optimization arrangement method based on structural vibration response as described above.

[0033] The beneficial effects of this invention are as follows: By introducing modal kinetic energy and modal strain energy, a normalized equivalent energy matrix (EEM) with multiple energy parameters is derived. The size of the diagonal elements of the EEM is used to screen out a subset of measurement points with high energy, and the high-energy measurement point subset is further screened by the EI method. Without changing the effectiveness of the EI method, this invention not only considers high-energy measurement points and improves the noise resistance of the measurement point combination, but also fully guarantees the modal independence and modal information content of the measurement point combination, making it more suitable for the application of sensor optimization layout in practical engineering.

[0034] The advantages of additional aspects of the invention will be set forth more clearly in the following description or will be learned by practice of the invention. Attached Figure Description

[0035] To more clearly illustrate the technical solutions of the embodiments of the present invention, the drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0036] Figure 1 This is a flowchart of the sensor optimization arrangement method based on structural vibration response according to an embodiment of the present invention.

[0037] Figure 2 The diagram shows the effects of various methods under the MAC matrix off-diagonal element average criterion described in the embodiments of the present invention.

[0038] Figure 3 The diagram shows the effects of various methods under the MAC matrix off-diagonal element maximum value criterion described in the embodiments of the present invention.

[0039] Figure 4 The diagram shows the effects of various methods under the modal kinetic energy criterion described in the embodiments of the present invention.

[0040] Figure 5 The diagram shows the effects of various methods under the modal strain energy criterion described in the embodiments of the present invention.

[0041] Figure 6 The diagram shows the effects of various methods under the Fisher matrix determinant criterion described in the embodiments of the present invention.

[0042] Figure 7 This is the stability graph measured according to the embodiments of the present invention. Detailed Implementation

[0043] Embodiments of the present invention are described in detail below, examples of which are shown in the accompanying drawings, wherein the same or similar reference numerals denote the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0044] 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.

[0045] It should also be understood that terms such as those defined in general dictionaries should be understood to have meanings consistent with their meanings in the context of the prior art, and should not be interpreted in an idealized or overly formal sense unless defined as here.

[0046] Those skilled in the art will understand that, unless specifically stated otherwise, the singular forms “a,” “an,” “the,” and “the” used herein may also include the plural forms. It should be further understood that the term “comprising” as used in this specification means the presence of the stated features, integers, steps, operations, elements, and / or components, but does not exclude the presence or addition of one or more other features, integers, steps, operations, elements, and / or groups thereof.

[0047] In the description of this specification, references to terms such as "one embodiment," "some embodiments," "example," "specific example," or "some examples," etc., indicate that a specific feature, structure, material, or characteristic described in connection with that embodiment or example is included in at least one embodiment or example of the present invention. Furthermore, the specific features, structures, materials, or characteristics described may be combined in any suitable manner in one or more embodiments or examples. Moreover, without contradiction, those skilled in the art can combine and integrate the different embodiments or examples described in this specification, as well as the features of those different embodiments or examples.

[0048] To facilitate understanding of the present invention, the present invention will be further explained and described below with reference to the accompanying drawings and specific embodiments. However, the specific embodiments do not constitute a limitation on the embodiments of the present invention.

[0049] Those skilled in the art should understand that the accompanying drawings are merely schematic diagrams of embodiments, and the components in the drawings are not necessarily essential for implementing the present invention.

[0050] Example 1

[0051] This embodiment 1 provides a sensor optimization arrangement system based on structural vibration response, including:

[0052] The module is used to build a finite element model of the structure to be monitored, select the number of modes, perform modal analysis, and obtain the modal vector matrix, mass matrix, and stiffness matrix of the structure to be monitored.

[0053] The calculation module is used to calculate the equivalent energy matrix and the average value of the diagonal elements of the equivalent energy matrix based on the modal vector matrix, mass matrix, stiffness matrix and number of modes;

[0054] The filtering module is used to start from all degrees of freedom and sequentially delete the minimum value on the diagonal of the equivalent energy matrix, while also deleting the degree of freedom represented by that value, until the minimum value deleted is greater than the average value of the diagonal elements or the number of remaining candidate degrees of freedom is equal to twice the number of sensors that need to be deployed.

[0055] The iteration module is used to construct an iteration matrix using the remaining degrees of freedom, sort the diagonal elements of the iteration matrix, select the smallest element and delete the degree of freedom vector corresponding to that element from the modal vector matrix; the iteration matrix is ​​repeatedly constructed to delete degrees of freedom in the modal vector matrix until the number of remaining degrees of freedom is the number of sensors to be arranged, where the sensors will be arranged on the remaining degrees of freedom.

[0056] In this embodiment 1, the above-described system is used to implement a sensor optimization arrangement method based on structural vibration response, including:

[0057] Using the building module, a finite element model of the structure to be monitored is established, the number of modes is selected, modal analysis is performed, and the modal vector matrix, mass matrix and stiffness matrix of the structure to be monitored are obtained.

[0058] Using the calculation module, based on the modal vector matrix, mass matrix, stiffness matrix, and number of modes, the equivalent energy matrix and the average value of the diagonal elements of the equivalent energy matrix are calculated;

[0059] Using the filtering module, starting from all degrees of freedom, the minimum value on the diagonal of the equivalent energy matrix is ​​deleted in turn, and the degree of freedom represented by that value is also deleted, until the minimum value deleted is greater than the average value of the diagonal elements or the number of remaining candidate degrees of freedom is equal to twice the number of sensors that need to be deployed.

[0060] Using the iterative module, an iterative matrix is ​​constructed using the remaining degrees of freedom. The diagonal elements of the iterative matrix are sorted, the smallest element is selected, and the degree of freedom vector corresponding to that element is deleted from the modal vector matrix. The iterative matrix is ​​constructed repeatedly to delete degree of freedom vectors until the number of remaining degrees of freedom is the number of sensors to be arranged. The sensors will be arranged on the remaining degrees of freedom.

[0061] The calculation of the equivalent energy matrix includes:

[0062] Calculate the modal kinetic energy and modal strain energy corresponding to the k-th mode of the i-th degree of freedom of the structure to be monitored;

[0063] Normalize the modal kinetic energy and modal strain energy;

[0064] The sum of the normalized modal kinetic energy and the normalized modal strain energy is taken as the relative total energy corresponding to the k-th mode of the i-th degree of freedom, and the equivalent energy matrix is ​​calculated.

[0065] The modal kinetic energy MKE corresponding to the k-th mode in the i-th degree of freedom ik for:

[0066] Where, φ ik M represents the k-th order modal vector matrix with the i-th degree of freedom. ij φ represents the value in the i-th row and j-th column of the mass matrix. jk This represents the k-th modal component of the j-th degree of freedom.

[0067] Modal strain energy MSE corresponding to the k-th mode in the i-th degree of freedom ik for: Among them, K ij This represents the value in the i-th row and j-th column of the stiffness matrix.

[0068] Normalization transformations of modal kinetic energy and modal strain energy include:

[0069] Among them, GMKE ik GMSE represents the modal kinetic energy after normalization transformation. ik denoted as modal strain energy after normalization transformation, where n represents the total number of degrees of freedom and N represents the modal order.

[0070] Calculate the equivalent energy matrix, including:

[0071] Take GMKE ik and GMSE ik The sum of these values ​​represents the relative total energy GE corresponding to the k-th mode in the i-th degree of freedom. ik Calculate the equivalent energy matrix EEM: EEM = diag((GE)(GE)) T ).

[0072] In this process, an iterative matrix E is constructed using the remaining degrees of freedom. The diagonal elements of matrix E are sorted, and the smallest element is selected. The degree of freedom vector corresponding to this element is then removed from the modality matrix.

[0073] In the formula Φ s It is the modal matrix of the structural residual degrees of freedom.

[0074] Example 2

[0075] Combination Figure 1 As shown in Embodiment 2, a sensor optimization arrangement method based on vibration response is provided, including the following steps:

[0076] (1) Establish a finite element model, select the number of modes, perform modal analysis, and obtain the modal vector matrix Φ, mass matrix M, and stiffness matrix K of the structure.

[0077] A truss model of a space power transmission tower was constructed, with the truss members using the Link180 element type. Link180 elements are tension / compression elements along the member axis, each node having three translational degrees of freedom and not subjected to bending or torsion; they can be used to simulate trusses, cables, and connecting rods. The member cross-sectional area is 1×10⁻⁶. -3 m 2 Its elastic modulus is 210 GPa and its density is 7850 kg / m³. 3 The structure measures 5m × 2m × 4.5m. The dimensions of the horizontal and vertical members are 1m, 1.5m, and 2m, respectively. The dimensions of the remaining diagonal members can be derived from the dimensions of the horizontal and vertical members. The finite element model has 28 nodes and 84 degrees of freedom, excluding the four nodes whose degrees of freedom are fully constrained. Simulation using ANSYS software yielded the modal vector matrix Φ, mass matrix M, and stiffness matrix K of the finite element structure.

[0078] (2) Select the number of modes n and determine the number of sensors h.

[0079] Considering the capabilities of on-site testing techniques and the requirements of damage identification technology, the measured mode order should not be too high and should include the main modes of the structure. The first six modes of the structure are selected for analysis, encompassing roll, yaw, pitch, and heave degrees of freedom. The number of sensors installed must satisfy the modal observability of the structure; that is, the number of sensors should be greater than the number of modes being analyzed. However, installing too many sensors is meaningless for evaluating the merits of various arrangement schemes. Schemes with 6 to 40 sensors are selected for evaluation.

[0080] (3) Calculate the equivalent energy matrix EEM and the average value of its diagonal elements.

[0081] ① Calculate the modal kinetic energy and modal strain energy corresponding to the k-th mode of the i-th degree of freedom of the structure:

[0082]

[0083]

[0084] ② Normalize the modal kinetic energy and modal strain energy as required:

[0085]

[0086]

[0087] ③ Take GMKE ik and GMSE ik The sum of these values ​​represents the relative total energy GE corresponding to the k-th mode in the i-th degree of freedom. ik Calculate the equivalent energy matrix EEM: EEM = diag(GE)(GE) T )

[0088] ④ Calculate the average value of the diagonal elements of the equivalent energy matrix (EEM).

[0089] (4) Starting from all degrees of freedom, successively delete the minimum value on the diagonal of the equivalent energy matrix EEM, and at the same time delete the degree of freedom represented by its value, until the deleted minimum value is greater than the average value of the diagonal elements. Or the number of remaining degrees of freedom is equal to 2h.

[0090] (5) Construct an iterative matrix E using the remaining degrees of freedom from step (4), sort the diagonal elements of matrix E, select the smallest element, and remove the corresponding degree of freedom vector from the modality matrix, where: In the formula φ s It is the modal matrix of the structural residual degrees of freedom.

[0091] (6) Repeat step (5) until the h degrees of freedom with the highest linear independence are selected.

[0092] (7) Selecting the same number of modes n and the desired number of sensors h, the EI method, EI-MKE method, EI-MSE method, and EI-MEP method are used to optimize the sensor arrangement. The schemes with different numbers of sensors arranged structurally are evaluated for each method. Considering the characteristics of each evaluation criterion, the modal confidence average and modal confidence maximum are used to evaluate the orthogonality of the arranged measurement points; the modal kinetic energy and modal strain energy are used to evaluate the energy distribution of the arranged measurement points; and the Fisher information determinant is used to evaluate the modal information contained in the arranged measurement points. The evaluation results are as follows: Figures 2-6 As shown in the figure. The modal kinetic energy and modal strain energy values ​​are related to the normalization factor of the mode shape, and only their relative magnitudes need to be compared in the figure.

[0093] The evaluation results of this embodiment show that, based on the modal confidence mean criterion and modal confidence maximum criterion, the E-EI method and the EI method are significantly superior to other methods. Furthermore, when a small number of sensors are deployed, the E-EI method outperforms the EI method in terms of modal confidence maximum criterion, making it the optimal method among the several. When the number of sensors is greater than 9, based on the modal kinetic energy criterion and modal strain energy criterion, all four improved methods achieve the goal of improving the EI method. The EI-MKE method has an advantage in modal kinetic energy, while the EI-MSE method has an advantage in modal strain energy. The E-EI method and the EI-MEP method have the best overall performance. Based on the Fisher information matrix determinant criterion, both the E-EI method and the EI method are the optimal methods. In summary, the E-EI method comprehensively considers both modal kinetic energy and modal strain energy, maintaining high levels of both energies at the selected measurement points, and its performance is similar to that of the EI-MEP method. In terms of orthogonality and information content, the E-EI method is comparable to the EI method and is even superior to the EI method in terms of modal confidence criterion evaluation. That is, the E-EI method, while maintaining the orthogonality of the modal matrix vectors and the information content, incorporates energy into the optimal sensor arrangement, effectively improving the EI method, and has the best overall performance among various improvement methods.

[0094] Example 3

[0095] In this embodiment 3, a switch rail is selected as an example to provide a method for arranging sensors on the switch rail. The switch rail is an important component of the switch, and its movement can guide the train into the mainline or siding direction. Compared with constant cross-section rails, switch rails are variable cross-section rails, which are more prone to cracking and deformation. Real-time health monitoring of the switch rail is of significant engineering importance for rail transit safety. In this embodiment 3, an experiment is conducted using railway switch rail quality monitoring as an engineering background to further verify the effectiveness and generalization of the E-EI method. The following operational steps are included:

[0096] (1) Establish a finite element model, select the number of modes, perform modal analysis, and obtain the modal vector matrix φ, mass matrix M, and stiffness matrix K of the structure.

[0097] Using a 12.48m long switch rail as the experimental model, vertical acceleration sensors were arranged on the upper surface of the switch rail at equal intervals with a step size of 0.2m, with a sampling frequency of 1000Hz. Modal testing of the structure was conducted using the exciter method. Due to the large number of measurement points, response information was collected multiple times in groups and then processed and analyzed centrally to extract the modal frequencies of the switch rail. The first five modal frequencies were extracted and analyzed using the random subspace method and peak picking method. The stability diagram is shown below. Figure 7As shown, a finite element solid model of the switch rail was established based on the actual model. After modal correction, modal analysis was performed. The switch rail was divided into 125 elements with a step size of 0.1m. All element nodes were studied, resulting in a total of 124 nodes and 372 degrees of freedom. Using the modal information of the corrected model, the modal matrix φ, stiffness matrix K, and mass matrix M of the selected measurement points were derived.

[0098] (2) Select the number of modes n and determine the number of sensors h.

[0099] Considering the capabilities of on-site testing technology and the requirements of damage identification technology, the measured mode order should not be too high and should include the main mode shapes of the structure. The first five mode orders are extracted for analysis, and sensors are arranged at 12 and 24 degrees of freedom.

[0100] (3) Calculate the equivalent energy matrix EEM and the average value of its diagonal elements.

[0101] ① Calculate the modal kinetic energy and modal dynamic energy corresponding to the k-th mode of the i-th degree of freedom of the structure:

[0102]

[0103]

[0104] ② Normalize the modal kinetic energy and modal strain energy as required:

[0105]

[0106]

[0107] ③ Take GMKE ik and GMSE ik The sum of these values ​​represents the relative total energy GE corresponding to the k-th mode in the i-th degree of freedom. ik Calculate the equivalent energy matrix EEM: EEM = diag((GE)(GE)) T )

[0108] ④ Calculate the average value of the diagonal elements of the equivalent energy matrix (EEM).

[0109] (4) Starting from all degrees of freedom, successively delete the minimum value on the diagonal of the equivalent energy matrix EEM, and at the same time delete the degree of freedom represented by its value, until the deleted minimum value is greater than the average value of the diagonal elements. Or the number of remaining degrees of freedom is equal to 2h.

[0110] (5) Construct matrix E using the remaining degrees of freedom from step (4), sort the diagonal elements of matrix E, select the smallest element, and remove the degree of freedom vector corresponding to that element from the modal matrix, where: In the formula Φ s It is the modal matrix of the structural residual degrees of freedom.

[0111] (6) Repeat step (5) until the h degrees of freedom with the highest linear independence are selected.

[0112] (7) Selecting the same number of modes n and the desired number of sensors h, the EI method, EI-MKE method, EI-MSE method, and EI-MEP method were used to optimize the sensor arrangement, and the schemes with different numbers of sensors arranged in the structure were evaluated for each method. The results of the arrangement using the five methods are shown in Tables 1 and 2. The evaluation results of each scheme are shown in Tables 3 and 4.

[0113] Table 1 shows the deployment results of various schemes for arranging 12 sensors.

[0114]

[0115] Table 2 shows the deployment results of various schemes for arranging 24 sensors.

[0116]

[0117] Table 3 Evaluation results of various schemes for deploying 12 sensors

[0118]

[0119] Table 4 Evaluation results of various schemes for deploying 24 sensors

[0120]

[0121] f1, f2, f3, f4, and f5 represent the mean of the diagonal elements of the modal confidence matrix, the maximum value of the diagonal elements of the modal confidence matrix, and the modal kinetic energy value (on the order of 10), respectively. -4 Modal strain energy value (on the order of 10) 8 The determinant values ​​of the Fisher information matrix are also considered. For f3 and f4, only their relative sizes need to be compared.

[0122] In this embodiment, Tables 1 and 2 show that the arrangement results of each method are concentrated at both ends and the middle of the switch rail, with many overlapping measurement points. This proves the rationality of the various schemes approaching the optimal arrangement. Among them, the E-EI method has a more uniform arrangement, reflecting its reliability. Tables 3 and 4 show that the E-EI method effectively improves the EI method in terms of both measurement point energy and linear independence. Furthermore, in terms of measurement point independence, the values ​​of f1 and f2 in the E-EI method are significantly lower than the other three methods, indicating the highest linear independence between measurement points. In terms of measurement point energy, the values ​​of f3 and f4 are very close to the other three improved methods, indicating a high level of total measurement point energy. Regarding ensuring the amount of information contained in the measurement points, the value of f5 in the E-EI method is greater than that in the EI-MKE method and very close to the other two improved methods. Therefore, the E-EI method has no obvious shortcomings in the three aspects of evaluation, and its strong linear independence is a prominent advantage, making it a stable, accurate, and reliable method for solving the problem of optimal sensor arrangement.

[0123] Example 4

[0124] Embodiment 4 of the present invention provides a non-transitory computer-readable storage medium for storing computer instructions. When executed by a processor, the computer instructions implement a sensor optimization arrangement method based on structural vibration response. The method includes:

[0125] A finite element model of the structure to be monitored is established, the number of modes is selected, modal analysis is performed, and the modal vector matrix, mass matrix and stiffness matrix of the structure to be monitored are obtained.

[0126] Calculate the equivalent energy matrix and the average value of the diagonal elements of the equivalent energy matrix based on the modal vector matrix, mass matrix, stiffness matrix, and number of modes;

[0127] Starting from all degrees of freedom, the minimum value on the diagonal of the equivalent energy matrix is ​​deleted in turn, and the degree of freedom represented by that value is also deleted, until the minimum value deleted is greater than the average value of the diagonal elements or the number of remaining candidate degrees of freedom is equal to twice the number of sensors that need to be deployed.

[0128] An iterative matrix is ​​constructed using the remaining degrees of freedom. The diagonal elements of the iterative matrix are sorted, the smallest element is selected, and the degree of freedom vector corresponding to that element is removed from the modal vector matrix. The iterative matrix is ​​then constructed to remove degree of freedom vectors from the modal vector matrix until the number of remaining degrees of freedom is equal to the number of sensors to be arranged. The sensors will be arranged on the remaining degrees of freedom.

[0129] Example 5

[0130] Embodiment 5 of the present invention provides a computer program (product), including a computer program that, when run on one or more processors, is used to implement a sensor optimization arrangement method based on structural vibration response, the method comprising:

[0131] A finite element model of the structure to be monitored is established, the number of modes is selected, modal analysis is performed, and the modal vector matrix, mass matrix and stiffness matrix of the structure to be monitored are obtained.

[0132] Calculate the equivalent energy matrix and the average value of the diagonal elements of the equivalent energy matrix based on the modal vector matrix, mass matrix, stiffness matrix, and number of modes;

[0133] Starting from all degrees of freedom, the minimum value on the diagonal of the equivalent energy matrix is ​​deleted in turn, and the degree of freedom represented by that value is also deleted, until the minimum value deleted is greater than the average value of the diagonal elements or the number of remaining candidate degrees of freedom is equal to twice the number of sensors that need to be deployed.

[0134] An iterative matrix is ​​constructed using the remaining degrees of freedom. The diagonal elements of the iterative matrix are sorted, the smallest element is selected, and the degree of freedom vector corresponding to that element is removed from the modal vector matrix. The iterative matrix is ​​then constructed to remove degree of freedom vectors from the modal vector matrix until the number of remaining degrees of freedom is equal to the number of sensors to be arranged. The sensors will be arranged on the remaining degrees of freedom.

[0135] Example 6

[0136] Embodiment 6 of the present invention provides an electronic device, including: a processor, a memory, and a computer program; wherein, the processor is connected to the memory, and the computer program is stored in the memory. When the electronic device is running, the processor executes the computer program stored in the memory to cause the electronic device to execute instructions for implementing a sensor optimization arrangement method based on structural vibration response, the method including:

[0137] A finite element model of the structure to be monitored is established, the number of modes is selected, modal analysis is performed, and the modal vector matrix, mass matrix and stiffness matrix of the structure to be monitored are obtained.

[0138] Calculate the equivalent energy matrix and the average value of the diagonal elements of the equivalent energy matrix based on the modal vector matrix, mass matrix, stiffness matrix, and number of modes;

[0139] Starting from all degrees of freedom, the minimum value on the diagonal of the equivalent energy matrix is ​​deleted in turn, and the degree of freedom represented by that value is also deleted, until the minimum value deleted is greater than the average value of the diagonal elements or the number of remaining candidate degrees of freedom is equal to twice the number of sensors that need to be deployed.

[0140] An iterative matrix is ​​constructed using the remaining degrees of freedom. The diagonal elements of the iterative matrix are sorted, the smallest element is selected, and the degree of freedom vector corresponding to that element is removed from the modal vector matrix. The iterative matrix is ​​then constructed to remove degree of freedom vectors from the modal vector matrix until the number of remaining degrees of freedom is equal to the number of sensors to be arranged. The sensors will be arranged on the remaining degrees of freedom.

[0141] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0142] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0143] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0144] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment, whereby a series of operational steps are performed to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0145] While the specific embodiments of the present invention have been described above in conjunction with the accompanying drawings, this is not intended to limit the scope of protection of the present invention. Those skilled in the art should understand that, based on the technical solutions disclosed in the present invention, various modifications or variations that can be made by those skilled in the art without creative effort should be included within the scope of protection of the present invention.

Claims

1. A method for optimizing sensor placement based on structural vibration response, characterized in that, The method comprises the following steps: A finite element model of the structure to be monitored is established, the number of modes is selected, modal analysis is performed, and a modal vector matrix, a mass matrix and a stiffness matrix of the structure to be monitored are obtained; An equivalent energy matrix and an average value of diagonal elements of the equivalent energy matrix are calculated according to the modal vector matrix, the mass matrix, the stiffness matrix and the number of modes; wherein, modal kinetic energy and modal strain energy corresponding to the i-th degree of freedom and the k-th mode of the structure to be monitored are calculated, the modal kinetic energy and the modal strain energy are normalized, and a sum of the normalized modal kinetic energy and the normalized modal strain energy is taken as relative total energy corresponding to the i-th degree of freedom and the k-th mode, and the equivalent energy matrix is calculated; Starting from all degrees of freedom, the minimum value on the diagonal of the equivalent energy matrix is sequentially deleted, and the degree of freedom represented by the minimum value is also deleted, until the deleted minimum value is greater than the average value of the diagonal elements or the number of remaining degrees of freedom to be selected is equal to twice the number of sensors to be arranged; An iteration matrix is constructed using the remaining degrees of freedom, main diagonal elements on the iteration matrix are sorted, the smallest element is selected, and a degree of freedom vector corresponding to the element is deleted from the modal vector matrix, the iteration matrix is continuously constructed to delete the degree of freedom vector from the modal vector matrix, until the number of remaining degrees of freedom is equal to the number of sensors to be arranged, wherein the sensors are arranged on the remaining degrees of freedom.

2. The method of claim 1, wherein, The first degree of freedom corresponds to the first order modal energy is: ; where, represents the th modal vector matrix of the th degree of freedom, represents the value of the th row and th column of the mass matrix, represents the th modal component of the th degree of freedom.

3. The method of claim 2, wherein, The first degree of freedom corresponds to the first order modal strain energy : ; wherein represents the value of the stiffness matrix in the first row and the first column.

4. The method of claim 3, wherein, The modal kinetic energy and the modal strain energy are normalized, comprising: ; ; wherein, denotes the normalized transformed modal kinetic energy, denotes the normalized transformed modal strain energy, denotes the number of all degrees of freedom, denotes the order of the mode.

5. The method of claim 4, wherein, The equivalent energy matrix is calculated, comprising: Take and and the sum as the first degree of freedom of the first order modal corresponding to the relative total energy , calculate the equivalent energy matrix : .

6. A sensor optimization arrangement system based on structural vibration response, characterized in that, The method comprises the following steps: The construction module is configured to establish a finite element model of the structure to be monitored, select the number of modes, perform modal analysis, and obtain a modal vector matrix, a mass matrix and a stiffness matrix of the structure to be monitored; The calculation module is configured to calculate an equivalent energy matrix and an average value of diagonal elements of the equivalent energy matrix according to the modal vector matrix, the mass matrix, the stiffness matrix and the number of modes; wherein, modal kinetic energy and modal strain energy corresponding to the i-th degree of freedom and the k-th mode of the structure to be monitored are calculated, the modal kinetic energy and the modal strain energy are normalized, and a sum of the normalized modal kinetic energy and the normalized modal strain energy is taken as relative total energy corresponding to the i-th degree of freedom and the k-th mode, and the equivalent energy matrix is calculated; The screening module is configured to start from all degrees of freedom, sequentially delete the minimum value on the diagonal of the equivalent energy matrix, and delete the degree of freedom represented by the minimum value, until the deleted minimum value is greater than the average value of the diagonal elements or the number of remaining degrees of freedom to be selected is equal to twice the number of sensors to be arranged; The iteration module is configured to construct an iteration matrix using the remaining degrees of freedom, sort main diagonal elements on the iteration matrix, select the smallest element, delete a degree of freedom vector corresponding to the element from the modal vector matrix, continuously construct the iteration matrix to delete the degree of freedom vector from the modal vector matrix, until the number of remaining degrees of freedom is equal to the number of sensors to be arranged, wherein the sensors are arranged on the remaining degrees of freedom.

7. A non-transitory computer-readable storage medium, comprising: The non-transitory computer readable storage medium is configured to store computer instructions, and the computer instructions are executed by a processor to implement the sensor optimal arrangement method based on structural vibration response according to any one of claims 1-5.

8. A computer program product, characterised in that, A computer program that, when run on one or more processors, implements the method of optimizing placement of sensors based on structural vibration response according to any one of claims 1-5.

9. An electronic device, comprising: Comprising: a processor, a memory, and a computer program; wherein the processor is connected with the memory, and the computer program is stored in the memory; when the electronic device is running, the processor executes the computer program stored in the memory, so that the electronic device executes the instructions of implementing the method of optimizing placement of sensors based on structural vibration response according to any one of claims 1-5.

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