Modal parameter identification method based on long short-term memory neural network

Abstract

The invention discloses a modal parameter identification method based on a long short-term memory neural network, belongs to the field of artificial intelligence, system identification and structural health monitoring, and aims to improve the precision of modal parameter identification by using the neural network. The method comprises the following steps: firstly, acquiring response data of a structure model after excitation, preprocessing the response data to obtain a sample set, and dividing the sample set into a training set and a test set; then, a neural network based on long and short term memory is constructed, wherein the neural network is mainly composed of an encoder (MLP), an LSTM feature extractor, a decoder (MLP) and a linear reconstructor; training the neural network by using the training set data until the loss function converges, identifying by using the test set data, and finally obtaining the natural frequency of the structure through the power spectral density analysis of the obtained data. According to the method, the modal frequency identification precision is remarkably improved, and an efficient solution is provided for intelligent health monitoring of a complex structure.

Description

Technical Field

[0001] The present invention belongs to the fields of artificial intelligence, system identification, structural health monitoring, etc., and relates to a modal parameter identification method based on long short-term memory neural network. Background Art

[0002] Structural modal parameter identification technology is an important research direction in the field of system identification. Its core goal is to accurately obtain the inherent vibration characteristic parameters of the structure (such as natural frequency, damping ratio, vibration mode, etc.) to provide theoretical support for structural dynamics modeling, health monitoring and control strategy optimization. Especially in the fields of complex structures such as aerospace and bridge engineering, the accurate identification of modal parameters is directly related to the safety and reliability of the system. However, traditional identification methods often have problems such as insufficient accuracy and poor robustness when faced with nonlinear, high-dimensional and noisy measured data, and a more efficient and intelligent identification framework is urgently needed.

[0003] Early modal parameter identification methods were mainly based on time domain or frequency domain analysis techniques. In the time domain method, the eigensystem realization algorithm (ERA) has become a widely used mainstream method due to its multiple-input multiple-output (MIMO) characteristics and robustness to noise. ERA constructs a generalized Hankel matrix and uses singular value decomposition (SVD) to extract the minimum realization of the system, and then obtains the modal parameters through eigenvalue decomposition. However, the traditional ERA algorithm relies on deterministic model assumptions and is difficult to effectively deal with parameter uncertainties that are common in actual engineering (such as material property deviations, environmental disturbances, etc.). If such uncertainties are not quantified, the identification results will deviate from the true value, which will affect subsequent model corrections and control decisions. To address this problem, statistical methods such as Monte Carlo simulation are used for uncertainty propagation analysis, but their computational cost is high, especially in large-scale structural scenarios, and it is difficult to meet real-time requirements.

[0004] In recent years, the rapid development of deep learning technology has injected new vitality into modal parameter identification. With its powerful nonlinear mapping ability, neural networks can directly learn modal features from raw vibration data, avoiding the reliance of traditional methods on model assumptions. For example, multi-layer perceptrons (MLPs) are used for end-to-end mapping of vibration responses and modal parameters, but their static network structure is difficult to effectively capture the temporal dependencies in vibration signals, resulting in limited ability to extract dynamic features. Although recurrent neural networks (RNNs) have temporal modeling capabilities, traditional RNNs are difficult to process long sequence data due to the vanishing gradient problem, which limits their application in long-term vibration signal analysis. The long short-term memory (LSTM) network has significantly improved the long sequence modeling capability by introducing gating mechanisms and memory units, and has made breakthroughs in speech recognition, natural language processing and other fields, but its potential in the field of structural dynamics has not yet been fully explored.

[0005] Existing neural network-based modal parameter identification methods still face the following challenges: First, most studies focus on static feature extraction, ignoring the temporal correlation hidden in vibration signals, resulting in limited accuracy of modal parameter estimation; Second, the network structure design lacks physical interpretability and is difficult to effectively combine with classical dynamics theories (such as the modal superposition principle), restricting the generalization ability of the model; Third, it is vulnerable to noise interference during the training process and is sensitive to hyperparameters, with insufficient model robustness. In addition, traditional methods usually process modal responses and reconstruction processes independently and fail to improve the overall identification performance through joint optimization. Summary of the Invention

[0006] The object of the present invention is to overcome the problems such as low accuracy of existing neural network-based modal parameter identification methods, and propose a modal parameter identification method based on long short-term memory neural network, which deeply integrates temporal feature extraction and physical mechanism constraints through an encoder-decoder architecture. Specifically, the encoder uses MLP to perform high-dimensional mapping on vibration displacement data, the long short-term memory neural network is used as a feature extractor to capture temporal dependence relationships, the decoder further converts the intermediate features into modal responses, and finally the vibration data is reconstructed through a linear layer. This framework innovatively combines the gating mechanism of the long short-term memory neural network with the modal superposition principle. While improving the temporal modeling ability, the network parameters are jointly optimized through reconstruction error and independence constraints, significantly improving the identification accuracy and robustness. In addition, power spectral density analysis is introduced to post-process the modal responses output by the decoder, further ensuring the physical rationality of parameter extraction. Compared with traditional neural network methods, this framework not only overcomes the problem of gradient disappearance, but also provides a new technical approach for the intelligent identification of complex structures through multi-level feature fusion and physical constraints.

[0007] Technical solution of the present invention:

[0008] A modal parameter identification method based on long short-term memory neural network, comprising the following steps:

[0009] Step 1: Obtain the response data of the structure after being excited by a load;

[0010] Step 2: Divide the collected data into a training set and a test set;

[0011] Step 3: Construct a modal parameter identification neural network framework based on long short-term memory, and train the network parameters of the modal parameter identification neural network framework on the training set;

[0012] Step 4: Input the test set data into the trained model for prediction, and obtain the modal responses of each order of the structure through power spectral density analysis.

[0013] The beneficial effects of the present invention compared with the prior art are as follows:

[0014] (1) Significantly improved temporal feature extraction ability: By introducing the gating mechanism and memory cell structure of the long short-term memory (LSTM) network, the problem of gradient disappearance in traditional recurrent neural networks (RNNs) in long sequence modeling is effectively solved. It can accurately capture the temporal dependence in vibration signals, significantly improve the dynamic feature extraction ability, and is especially suitable for long-term vibration data analysis.

[0015] (2) Combination of multi-level feature fusion and physical constraints: An encoder-decoder architecture is adopted. Through the synergistic effect of multi-layer perceptrons (MLPs) and long short-term memory neural networks, high-dimensional mapping of vibration data, temporal feature extraction, and low-dimensional modal response conversion are achieved. At the same time, the linear reconstruction layer integrates the principle of modal superposition, embeds physical mechanisms into network design, enhances the interpretability and generalization ability of the model, and avoids the limitations of traditional neural networks being divorced from the physical background.

[0016] (3) Joint optimization of the loss function to improve robustness: The loss function comprehensively considers the reconstruction error, modal response independence constraint, and Gaussianity constraint. By jointly optimizing network parameters through multi-objective optimization, noise interference is effectively suppressed, the sensitivity of the model to hyperparameters is reduced, and the stability and robustness of the identification results are significantly improved.

[0017] (4) Physical post-processing to ensure parameter rationality: Power spectral density analysis is introduced at the output end of the neural network to post-process the modal responses extracted by the decoder, ensuring the physical rationality of parameters such as natural frequencies and vibration modes, making up for the defect that pure data-driven methods may deviate from actual dynamic laws, and providing a reliable guarantee for engineering applications. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] Figure 1 Shows the flowchart of the modal parameter identification method based on long short-term memory neural network proposed by the present invention;

[0019] Figure 2 Shows the neural network structure according to an embodiment of the present invention;

[0020] Figure 3 Shows the training process of the neural network based on long short-term memory. DETAILED DESCRIPTION OF THE EMBODIMENTS

[0021] Hereinafter, the exemplary embodiments of the present disclosure will be described in more detail with reference to the drawings. Although the exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure can be implemented in various forms and should not be limited by the embodiments set forth herein. On the contrary, these embodiments are provided so that the present disclosure can be more thoroughly understood and the scope of the present disclosure can be fully conveyed to those skilled in the art.

[0022] Figure 1The flowchart of the modal parameter identification method based on the long short-term memory neural network proposed by the present invention is as follows. As Figure 1 shown, the method includes the following steps:

[0023] Step 1: Obtain the response data after the structure is excited by the load. Among them, the response data can be collected from various sensors arranged on the structure, and the displacement data is obtained from the response data.

[0024] Step 2: Divide the collected data according to a predetermined ratio to generate a training set and a test set. The predetermined ratio can be 4:1.

[0025] Step 3: Construct a modal parameter identification neural network framework based on long short-term memory, and train the network parameters of the modal parameter identification neural network framework on the training set. The modal parameter identification neural network framework mainly includes an encoder, a feature extractor, a decoder, and a reconstructor. Specifically, the first layer is a multi-layer perceptron (MLP), that is, the encoder; the second layer is a long short-term memory neural network (LSTM), that is, the feature extractor; the third layer is a multi-layer perceptron (MLP), that is, the decoder; the fourth layer is a linear layer, that is, the reconstructor. The proposed neural network structure is as Figure 2 shown.

[0026] The training process of the long short-term memory-based neural network is as Figure 3 shown, and the specific steps are as follows:

[0027] Step 3.1: The encoder receives the original vibration displacement data in the training set , and then maps it to a high-dimensional representation ;

[0028] Step 3.2: The feature extractor receives the high-dimensional representation , and obtains an intermediate representation by extracting features;

[0029] Among them, the feature extractor is a long short-term memory neural network, which introduces a gating mechanism and a memory cell structure, effectively captures the time dependence of the input data, and overcomes the problem of gradient disappearance in traditional recurrent neural networks in long sequence modeling. The long short-term memory neural network unit gradually updates the hidden state and memory cell state at the current moment through the cooperation of the gating mechanism and the memory cell. The specific calculation process is as follows:

[0030] Calculate the forgetting coefficient at the current moment, which is used to determine how much information from the previous moment to retain:

[0031] (1)

[0032] Calculate the current Input coefficient at a moment and update the candidate memory cell state :

[0033] (2)

[0034] (3)

[0035] According to and output, update the memory cell state at the current moment :

[0036] (4)

[0037] Calculate the output coefficient at the current moment and generate a new hidden state :

[0038] (5)

[0039] (6)

[0040] In equations (1)-(6), , , are the forgetting coefficient, input coefficient, and output coefficient respectively, , are the candidate memory cell state and memory cell state respectively, , are the hidden states output by the long short-term memory neural network unit at times and respectively, is the input to the long short-term memory neural network at time , , are both activation functions, is element-wise multiplication, and the subscripted and are the weight matrix and bias vector respectively.

[0041] Step 3.3: The decoder receives the intermediate representation , then maps it to a low-dimensional space and outputs the modal response ;

[0042] Step 3.4: The reconstructor receives the modal response and outputs the reconstructed vibration displacement data ;

[0043] The reconstructor is used to reconstruct the response data of the model, and its corresponding physical equation is:

[0044] (7)

[0045] Among them, represents the structural vibration displacement data obtained by reconstruction; represents the modal matrix, which is composed of the modal shape vectors ; represents the modal response matrix, which is composed of the modal response vectors ; represents the -th order modal shape vector; represents the -th order modal response vector.

[0046] The role of the reconstructor is to fit the modal shape matrix . After the MLP outputs the modal response Q described in step 3.3, the vibration displacement data is reconstructed through a linear layer to obtain .

[0047] Step 3.5: Calculate the loss function based on the reconstructed vibration displacement data and the original vibration displacement data, and update the parameters of the neural network and then go through steps 3.1 - 3.4 again until the loss function converges finally.

[0048] The loss function includes the reconstruction error , the independence constraint of the modal response and the Gaussianity constraint :

[0049] (8)

[0050] (9)

[0051] (10)

[0052] (11)

[0053] Among them, represents the element in the -th row and -th column of the original vibration displacement data ; represents the element in the -th row and -th column of the vibration displacement data obtained by reconstruction; respectively represent the total number of rows and total number of columns of the displacement data, and also represent the number of sampling times of the sensors and the number of sensors respectively; represents the output of the third middle layer: the modal response of the structure; represents the identity matrix; represents the transfer matrix corresponding to the linear layer; respectively represent the hyperparameters of the neural network, which are random numbers between 0 and 1; represents the covariance operation; represents the determinant operation.

[0054] Step 4: After inputting the test set into the modal parameter identification neural network framework, obtain the modal responses obtained by the decoder layer described in step 3.3 , and perform power spectral density analysis on this modal response to obtain the modal shapes of each order.

[0055] Perform power spectral density analysis using the built-in functions in the numerical analysis software.

[0056] As Figure 2 shown, taking a five-span truss structure as a basic example, the Young's modulus of the truss material is , and the density is . In step 4: After inputting the test set into the modal parameter identification neural network framework, obtain the modal responses obtained by the decoder layer described in step 3.3 , perform power spectral density analysis to obtain the frequencies of each order of the modes. Finally, the obtained frequencies are shown in Table 1, and in the table, they are compared with the theoretical values and the results obtained by other identification methods, including the Eigensystem Realization Algorithm (ERA), Multi-Layer Perceptron (MLP), a Recurrent Neural Network Model (GRU), and a Deep Learning Model Architecture (Transformer).

[0057] Table 1 Frequency identification results obtained by different methods

[0058] Through the above comparison, it can be seen that the method described in the present invention is more accurate than other existing modal parameter identification methods, and the structural modal parameters obtained by this method can be used as important parameters for structural control and health monitoring.

[0059] In summary, the above is only a preferred embodiment of the present invention and is not used to limit the protection scope of the present invention. Any modifications, equivalent replacements, improvements, etc. made within the spirit and principle of the present invention shall be included within the protection scope of the present invention.

Claims

1. A modal parameter identification method based on long short-term memory neural network, characterized in that: The following steps are involved: Step 1: Obtain the response data of the structure after being excited by the load; Step 2: Divide the collected data into training set and test set; Step 3: Construct a modal parameter identification neural network framework based on long short-term memory, and train the network parameters of the modal parameter identification neural network framework on the training set; Step 4: Input the test set data into the trained model for prediction, and obtain the modal response by power spectral density analysis to obtain the frequencies of each order of the structure.

2. The modal parameter identification method based on long short-term memory neural network according to claim 1, characterized in that: In step one, response data is collected from various sensors arranged on the structure, and displacement data is obtained from the response data.

3. The modal parameter identification method based on long short-term memory neural network according to claim 1 is characterized in that: In step 2, the collected data is divided into 4:1 to generate training set and test set.

4. The modal parameter identification method based on long short-term memory neural network according to claim 2 is characterized in that: In step three, the long short-term memory-based modal parameter identification neural network framework includes an encoder, a feature extractor, a decoder and a reconstructor.

5. The modal parameter identification method based on long short-term memory neural network according to claim 4 is characterized in that: In the long short-term memory-based modal parameter identification neural network framework, the first layer is a multi-layer perceptron, i.e., an encoder; the second layer is a long short-term memory neural network, i.e., a feature extractor; the third layer is a multi-layer perceptron, i.e., a decoder; and the fourth layer is a linear layer, i.e., a reconstructor.

6. The modal parameter identification method based on long short-term memory neural network according to claim 5 is characterized in that: The training process of the long short-term memory based modal parameter identification neural network framework includes: Step 3.1: The encoder receives the raw vibration displacement data in the training set , and then mapped it to a high-dimensional representation ; Step 3.2: Feature extractor receives high-dimensional representation , by extracting features to obtain the intermediate representation ; Step 3.3: Decoder receives intermediate representation , and then map it to a low-dimensional space to output the modal response ; Step 3.4: Reconstructor receives modal response , output the reconstructed vibration displacement data ; Step 3.5: Calculate the loss function based on the reconstructed vibration displacement data and the original vibration displacement data, and update the parameters of the modal parameter identification neural network framework and go through steps 3.1-3.4 again, and finally make the loss function converge.

7. The modal parameter identification method based on long short-term memory neural network according to claim 6 is characterized in that: The working process of the feature extractor in step 3.2 includes: Calculate current The forgetting coefficient of time , used to decide how much information from the previous moment to retain: （1） Calculate current Input coefficient at time , and update the candidate memory cell state : （2） （3） according to and Output, update the memory cell state at the current moment : （4） Calculate the output coefficient at the current moment , and generate a new hidden state : （5） （6） In formulas (1) to (6), , , They are the forgetting coefficient, input coefficient, and output coefficient. , are the candidate memory cell state and the memory cell state respectively, , Separate moments and The hidden state of the LSTM neural network output at time, It's time The input of the long short-term memory neural network, , are activation functions, is element-wise multiplication, with subscripts and are the weight matrix and bias vector respectively.

8. The modal parameter identification method based on long short-term memory neural network according to claim 1 is characterized in that: In step 3.4, the reconstructor is used to reconstruct the response data of the model, and the corresponding physical equation is: （7） in, Represents the structural vibration displacement data obtained by reconstruction; Represents the modal matrix, which consists of the modal vibration vector composition; Represents the modal response matrix, which consists of the modal response vector composition; Representative The first mode shape vector; Representative The modal response vector.

9. The modal parameter identification method based on long short-term memory neural network according to claim 1, characterized in that: In step 3.5, the loss function Contains reconstruction error , independence constraints of modal responses and Gaussianity constraints : （8） （9） （10） （11） in, Indicates the original vibration displacement data Line Elements of a column; Represents the first Line Elements of a column; They represent the total number of rows and columns of vibration displacement data, and also represent the sampling times and number of sensors of the sensor respectively; Represents the output of the third intermediate layer: the modal response of the structure; represents the identity matrix; represents the transfer matrix corresponding to the linear layer; They represent the hyperparameters of the neural network, which are random numbers between 0 and 1; represents the covariance operation; Represents determinant operation.

10. The modal parameter identification method based on long short-term memory neural network according to claim 1, characterized in that: In step 4, power spectral density analysis is performed using built-in functions in numerical analysis software.

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