A structural modal parameter identification method based on random subspace deep learning

Abstract

The application discloses a structural modal parameter identification method based on random subspace deep learning. A bridge measuring point data is used to construct a Hankel matrix and a Toeplitz matrix; based on the constructed Toeplitz matrix, singular values of the Toeplitz matrix are obtained; a machine learning neural network is established; the singular values of the Toeplitz matrix are taken as inputs of the established machine learning neural network, and then the order of the system is determined; based on the constructed Hankel matrix, Toeplitz matrix and the established machine learning neural network, a system matrix and an observation matrix are obtained, and a solving program of the system matrix and the observation matrix is automatically embedded into the machine learning neural network; the system matrix and the observation matrix obtained by the neural network are solved, and modal parameters of the structure are obtained. The application is used to solve the problems of false modal interference and the need for more artificial parameter setting in the prior art.

Description

Technical Field

[0001] This invention belongs to the field of civil engineering structure identification; specifically, it relates to a method for identifying structural modal parameters based on random subspace deep learning. Background Technology

[0002] Structural health monitoring technology is a crucial means of ensuring the structural safety of major engineering projects. It is widely used in numerous large-scale engineering structures in my country, playing a vital role in structural condition assessment and disaster early warning. Modal parameter identification is a critical component of the structural health monitoring technology system. Modal parameters are important indicators of a structure's "health," making accurate identification essential for understanding structural vibration characteristics and conducting health monitoring. The modal parameters (frequency, mode shape, damping ratio) of a structure are inherent characteristics that reflect its response to external forces, characterizing its "personality." They are crucial for understanding the dynamic characteristics of a structure, conducting structural damage detection, and safety assessments. Therefore, accurate identification of structural modal parameters is of paramount importance.

[0003] Modal parameter identification methods can be categorized into traditional methods and output-only methods, based on whether artificial excitation is required. Traditional methods obtain the structural response through artificial excitation testing and then use the excitation and response signals to identify the modal parameters. This primarily involves solving for the system's frequency response function or impulse response function using the system's input and output, and then using the relationship between the frequency response function or impulse response function and the modal parameters to obtain the structural modal parameters. These methods require ideal test conditions where the excitation of the structure can be controlled or measured. However, in many practical engineering structures, the excitation load is often difficult to measure; therefore, output-only modal parameter identification algorithms have greater advantages. Output-only modal parameter identification methods include time-domain, frequency-domain, and time-frequency-domain methods. The Ibrahim Time Domain (ITD) method uses the displacement, velocity, or acceleration time-domain signals of the structure's free vibration response to identify structural modal parameters. Peak picking (PP) is based on the principle that the frequency response function peaks near its natural frequency, and uses the power spectrum of the random response signal instead of the frequency response function. Time series analysis based on the Autoregressive Moving Average (ARMA) model is a method that uses a parametric model to process ordered random sampled data to obtain structural modal parameters. Stochastic Subspace Identification (SSI) is a method for identifying discrete state-space equations in linear systems and is suitable for stationary excitations. The Natural Excitation Technique (NExT) replaces the free vibration response or impulse response function in traditional time-domain modal analysis with a cross-correlation function between responses. The Eigensystem Realization Algorithm (ERA) uses measured impulse response or free response data to form a Hankel matrix and uses singular value decomposition to find the minimum realization of the system. Frequency-Domain Decomposition (FDD) is an extension of peak picking. The main idea is to perform singular value decomposition on the power spectrum of the response and decompose the power spectrum into a set of single-degree-of-freedom system power spectra corresponding to multiple modes.

[0004] However, in practical engineering applications, the above-mentioned modal parameter methods under environmental excitation all suffer from the interference of spurious modes and the need for a large number of manual parameter settings. Their automation and intelligence levels are not high, making it difficult to run automatically in structural health monitoring systems. Summary of the Invention

[0005] This invention provides a structural modality parameter identification method based on random subspace deep learning, which solves the problems of interference from spurious modalities and the need for a large number of manual parameter settings in the prior art.

[0006] This invention is achieved through the following technical solution:

[0007] A structural modality parameter identification method based on random subspace deep learning, the structural modality parameter identification method specifically includes the following steps:

[0008] Step 1: Construct the Hankel matrix and Toeplitz matrix using bridge measurement point data;

[0009] Step 2: Based on the Toeplitz matrix constructed in Step 1, obtain the singular values ​​of the Toeplitz matrix;

[0010] Step 3: Build a machine learning neural network;

[0011] Step 4: Use the singular values ​​of the Toeplitz matrix obtained in Step 2 as input to the machine learning neural network established in Step 3, and then determine the order of the system.

[0012] Step 5: Based on the Hankel matrix and Toeplitz matrix constructed in Step 1 and the machine learning neural network established in Step 3, obtain the system matrix and observation matrix, and automatically embed the solution program for the system matrix and observation matrix into the machine learning neural network;

[0013] Step 6: Solve the system matrix and observation matrix obtained from the neural network in Step 5 to obtain the modal parameters of the structure.

[0014] A structural modal parameter identification method based on random subspace deep learning, wherein step 2 specifically involves constructing a Hankel matrix from bridge measurement point data and processing the row space Y of the "future" output. f The line space Y output to the "past" p The Toeplitz matrix is ​​obtained by projection, and singular value decomposition is performed on the Toeplitz matrix.

[0015] A structural modality parameter identification method based on random subspace deep learning, wherein step 4 specifically involves inputting the singular values ​​obtained by singular value decomposition of the Toeplitz matrix into the order-determined neural network of the machine learning neural network established in step 3, and using the objective function (1) in the order-determined neural network for optimization to obtain the best estimate of the structural modality order; the objective function (1) is:

[0016]

[0017] in For the normalized singular values, s i Find the singular values ​​of the Toeplitz matrix, where i is the i-th singular value, l is the number of singular values, and R is the sum of the singular values. res The second-norm residual of the selected order and the threshold, where λ is a constant. c The threshold is set, n is the selected order, L is the loss function, m is the unselected order, and P is the threshold value. action E represents the probability that action = 0. p For R res The expectation.

[0018] A structural modality parameter identification method based on random subspace deep learning, wherein step 5 specifically involves integrating the solution of the system matrix and the observation matrix into the training process of the neural network by utilizing the principle of the state space model, and solving the system matrix and the observation matrix by utilizing the relationship between the row space of the "past" output and the row space of the "past" output shifted down by one block and the row space of the "future" output.

[0019] A structural modality parameter identification method based on random subspace deep learning, wherein obtaining the system matrix and observation matrix specifically involves dividing the row space Y of the "past" output... p and the line space Y of the "past" output shifted down one block line. p + and the line space Y of the "future" output f The first block of the input is the designed system solution neural network, which is then optimized using the objective function (2) to obtain the system matrix A and the observation matrix C;

[0020] The objective function (2) is specifically as follows:

[0021] T 1i =Y f Y p T =USV T

[0022]

[0023] Where T 1i The line space Y output for "past" p The line space Y output to the "future" f The Toeplitz matrix obtained by projection, where U and V are unitary matrices obtained from singular value decomposition, and S is the diagonal matrix obtained from singular value decomposition. Let A be the state vector at time i+1, and let A be the system matrix. Let Y be the state vector at time i. i Let C be the observation matrix. For Y f Move down one block row, where M is the number of measurement points and N is the modal order, which is half the system order.

[0024] A structural modal parameter identification method based on random subspace deep learning, wherein the modal parameters in step 6 include frequency, damping ratio and mode shape.

[0025] An electronic device includes a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other through the communication bus;

[0026] Memory, used to store computer programs;

[0027] When a processor executes a program stored in memory, it implements the steps of the method described above.

[0028] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the method described above.

[0029] The beneficial effects of this invention are:

[0030] This invention enables automatic processing of monitoring data, requires minimal human intervention, has a high degree of network automation and intelligence, and achieves good recognition accuracy.

[0031] This invention can reduce the amount of calculation and improve the calculation efficiency and accuracy in the process of modal parameter identification of civil engineering structures.

[0032] This invention enables fully intelligent identification of structural modal parameters under environmental excitation, eliminating the need for manual intervention. The entire process is convenient and accurate, improving the efficiency and reliability of structural health monitoring data analysis.

[0033] The entire process of this invention is convenient and accurate, improving the efficiency and reliability of structural health monitoring data analysis.

[0034] This invention can significantly reduce the degree of human intervention in the modality parameter identification process. During the training process, only the network hyperparameters and the threshold of the objective function need to be set.

[0035] This invention can meet the needs of online real-time data processing for structural health monitoring and has high identification accuracy. Attached Figure Description

[0036] Appendix Figure 1 This is a flowchart of the method of the present invention.

[0037] Appendix Figure 2This is a schematic diagram of the vibration acceleration data of a real bridge in Example 1 of the present invention, wherein (a) is a schematic diagram of the system response time; and (b) is a schematic diagram of the system response frequency.

[0038] Appendix Figure 3 This is a schematic diagram of the actual bridge vibration mode identification results in Example 1 of the present invention, wherein (a) is a schematic diagram of the first stage identification results in Example 1, (b) is a schematic diagram of the second stage identification results in Example 1, (c) is a schematic diagram of the third stage identification results in Example 1, (d) is a schematic diagram of the fourth stage identification results in Example 1, (e) is a schematic diagram of the fifth stage identification results in Example 1, (f) is a schematic diagram of the sixth stage identification results in Example 1, (g) is a schematic diagram of the seventh stage identification results in Example 1, (h) is a schematic diagram of the eighth stage identification results in Example 1, (i) is a schematic diagram of the ninth stage identification results in Example 1, and (j) is a schematic diagram of the tenth stage identification results in Example 1.

[0039] Appendix Figure 4 This is a schematic diagram of the actual bridge vibration acceleration data in Example 2 of the present invention, where (a) is a schematic diagram of the system response time; and (b) is a schematic diagram of the system response frequency.

[0040] Appendix Figure 5 This is a schematic diagram of the actual bridge vibration acceleration data in Example 2 of the present invention, wherein (a) is a schematic diagram of the first stage identification result of Example 2, (b) is a schematic diagram of the second stage identification result of Example 2, and (c) is a schematic diagram of the third stage identification result of Example 2. Detailed Implementation

[0041] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0042] A structural modality parameter identification method based on random subspace deep learning, the structural modality parameter identification method specifically includes the following steps:

[0043] Step 1: Construct the Hankel matrix and Toeplitz matrix using bridge measurement point data;

[0044] Step 2: Based on the Toeplitz matrix constructed in Step 1, obtain the singular values ​​of the Toeplitz matrix;

[0045] Step 3: Build a machine learning neural network;

[0046] Step 4: Use the singular values ​​of the Toeplitz matrix obtained in Step 2 as input to the machine learning neural network established in Step 3 to determine the order of the system; use the neural network to select the singular values ​​obtained from the singular value decomposition of the Toeplitz matrix to determine the singular values ​​of the signal and obtain the best estimate of the order of the system.

[0047] Step 5: Based on the Hankel matrix and Toeplitz matrix constructed in Step 1 and the machine learning neural network established in Step 3, obtain the system matrix and observation matrix, and automatically embed the solution program for the system matrix and observation matrix into the machine learning neural network;

[0048] Step 6: Solve the system matrix and observation matrix obtained from the neural network in Step 5 to obtain the modal parameters of the structure.

[0049] A structural modal parameter identification method based on random subspace deep learning, wherein step 2 specifically involves constructing a Hankel matrix from bridge measurement point data and processing the row space Y of the "future" output. f The line space Y output to the "past" p The Toeplitz matrix is ​​obtained by projection, and singular value decomposition is performed on the Toeplitz matrix.

[0050] A structural modality parameter identification method based on random subspace deep learning, wherein step 4 specifically involves inputting the singular values ​​obtained by singular value decomposition of the Toeplitz matrix into the order-determined neural network of the machine learning neural network established in step 3, and using the objective function (1) in the order-determined neural network for optimization to obtain the best estimate of the structural modality order; the objective function (1) is:

[0051]

[0052] in For the normalized singular values, s i Find the singular values ​​of the Toeplitz matrix, where i is the i-th singular value, l is the number of singular values, and R is the sum of the singular values. res The second-norm residual of the selected order and the threshold, where λ is a constant. c The threshold is set, n is the selected order, L is the loss function, m is the unselected order, and P is the threshold value. action E represents the probability that action = 0. p For R res The expectation.

[0053] A structural modality parameter identification method based on random subspace deep learning, wherein step 5 specifically involves integrating the solution of the system matrix and the observation matrix into the training process of the neural network by utilizing the principle of the state space model, and solving the system matrix and the observation matrix by utilizing the relationship between the row space of the "past" output and the row space of the "past" output shifted down by one block and the row space of the "future" output.

[0054] A structural modality parameter identification method based on random subspace deep learning, wherein obtaining the system matrix and observation matrix specifically involves dividing the row space Y of the "past" output... p and the line space Y of the "past" output shifted down one block line. p + and the line space Y of the "future" output f The first block of the input is the designed system solution neural network, which is then optimized using the objective function (2) to obtain the system matrix A and the observation matrix C;

[0055] The objective function (2) is specifically as follows:

[0056] T 1i =Y f Y p T =USV T

[0057]

[0058] Where T 1i The line space Y output for "past" p The line space Y output to the "future" f The Toeplitz matrix obtained by projection, where U and V are unitary matrices obtained from singular value decomposition, and S is the diagonal matrix obtained from singular value decomposition. Let A be the state vector at time i+1, and let A be the system matrix. Let Y be the state vector at time i. i Let C be the observation matrix, and Y be the observation matrix. f1 For Y f Move down one block row, where M is the number of measurement points and N is the modal order, which is half the system order.

[0059] A structural modal parameter identification method based on random subspace deep learning, wherein the modal parameters in step 6 include frequency, damping ratio and mode shape.

[0060] An electronic device includes a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other through the communication bus;

[0061] Memory, used to store computer programs;

[0062] When a processor executes a program stored in memory, it implements the steps of the method described above.

[0063] A computer-readable storage medium storing a computer program that, when executed by a processor, implements the steps of the method described above.

[0064] Example 1:

[0065] Figure 2 The structural vibration data from 10 accelerometers of an actual bridge are presented. Table 1 shows the results of the first ten modal parameters identified based on machine learning. In this case, the mode shape coefficients obtained from the system response of the structure are as follows: Figure 3 As shown.

[0066] Table 1. Results of structural modal parameters obtained from Example 1, the actual bridge calculation.

[0067]

[0068] Example 2:

[0069] Figure 4 The structural vibration data from five accelerometers of an actual bridge are presented. Table 2 shows the results of the third-order modal parameters identified based on machine learning. In this case, the mode shape coefficients obtained from the system response of the structure are as follows: Figure 5 As shown.

[0070] Table 2 shows the structural modal parameters obtained from the actual bridge example in Example 2.

[0071]

[0072] In the above examples, the accuracy of modal frequency, damping ratio, and mode shape identification is consistent with that of traditional classical frequency domain decomposition (FDD), covariance-driven and data-driven stochastic subspace methods (SSI-cov and SSI-data), and NExT+ERA methods, and the calculation is simpler and the response is faster.

Claims

1. A structural modality parameter recognition method based on random subspace deep learning, characterized in that, The structural modal parameter identification method specifically includes the following steps: Step 1: Construct the Hankel matrix and Toeplitz matrix using bridge measurement point data; Step 2: Based on the Toeplitz matrix constructed in Step 1, obtain the singular values ​​of the Toeplitz matrix; Step 3: Build a machine learning neural network; Step 4: Use the singular values ​​of the Toeplitz matrix obtained in Step 2 as input to the machine learning neural network established in Step 3, and then determine the order of the system. Step 5: Based on the Hankel matrix and Toeplitz matrix constructed in Step 1 and the machine learning neural network established in Step 3, obtain the system matrix and observation matrix, and automatically embed the solution program for the system matrix and observation matrix into the machine learning neural network; Step 6: Solve the system matrix and observation matrix obtained from the neural network in Step 5 to obtain the modal parameters of the structure; Step 4 specifically involves inputting the singular values ​​obtained from the singular value decomposition of the Toeplitz matrix into the fixed-order neural network of the machine learning neural network established in step 3, and using the objective function (1) in the fixed-order neural network for optimization to obtain the best estimate of the structural modal order; the objective function (1) is: in For normalized singular values, Find the singular values ​​for the Toeplitz matrix. For the first i A singular value, The number of singular values. The second-norm residual of the selected order and the threshold. It is a constant. For the set threshold, For the selected order, For loss function, For the order that was not selected, for action The probability that = 0, for The expectation.

2. The structural modality parameter recognition method based on random subspace deep learning according to claim 1, characterized in that, Step 2 specifically involves constructing a Hankel matrix from the bridge measurement point data and processing the row space of the "future" output. Line space output to "past" The Toeplitz matrix is ​​obtained by projection, and singular value decomposition is performed on the Toeplitz matrix.

3. The structural modality parameter recognition method based on random subspace deep learning according to claim 1, characterized in that, Specifically, step 5 involves integrating the solution of the system matrix and the observation matrix into the training process of the neural network using the principle of the state-space model. The system matrix and the observation matrix are solved by utilizing the relationship between the row space of the "past" output, the row space of the "past" output shifted down by one block, and the row space of the "future" output.

4. The structural modality parameter recognition method based on random subspace deep learning according to claim 3, characterized in that, Specifically, obtaining the system matrix and observation matrix involves dividing the row space of the "past" output. and the line space of the "past" output that is shifted down one block line. and the line space for "future" output The first block of input is the designed system solution neural network, which is then optimized using the objective function (2) to obtain the system matrix. and observation matrix ; The objective function (2) is specifically, in Line space for outputting "past" Line space output to the "future" The Toeplitz matrix obtained by projection, To obtain the unitary matrix from the singular value decomposition, The diagonal matrix obtained from singular value decomposition. For the first i The state vector at time +1 For the system matrix, For the first i The state vector at time t, for, For the observation matrix, for Move down one block row. The number of measurement points. It is the modal order, which is half the system order.

5. The structural modality parameter recognition method based on random subspace deep learning according to claim 1, characterized in that, The modal parameters in step 6 include frequency, damping ratio, and mode shape.

6. An electronic device, characterized in that, It includes a processor, a communication interface, a memory, and a communication bus, wherein the processor, the communication interface, and the memory communicate with each other through the communication bus; Memory, used to store computer programs; A processor, when executing a program stored in memory, implements the steps of the method described in any one of claims 1-5.

7. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores a computer program that, when executed by a processor, implements the steps of the method described in any one of claims 1-5.

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