A distributed dynamic load identification method combining wavelet decomposition and LSTM deep learning network

Abstract

The application discloses a distributed dynamic load identification method combining wavelet decomposition and an LSTM deep learning network. The method comprises the following steps: 1. establishing a finite element model of a vehicle panel structure; 2. dividing sub-regions on the surface of the vehicle panel structure subjected to the distributed dynamic load, constructing the transmission relationship between the dynamic load on the sub-regions and the dynamic responses of the measuring points of the finite element model, and establishing a sample library of the strain dynamic response time domain information at the multiple measuring points and the distributed dynamic load time domain information on the nodes of the sub-regions; 3. extracting the time-frequency characteristics of the response and load time domain information in the sample library; taking the time-frequency characteristics of the measuring point response as input and the time-frequency characteristics of the distributed dynamic load on the nodes of the sub-regions as output, and training the deep learning network; 4. taking the time-frequency characteristics of the strain response obtained at the measured measuring points as input, and solving the load values on the nodes of each sub-region through the deep learning network proxy model obtained through the training, and superimposing to obtain the distributed dynamic load on the surface of the vehicle panel structure.

Description

Technical fields:

[0001] This invention relates to a distributed dynamic load identification method that combines wavelet decomposition and LSTM deep learning network, belonging to the field of structural dynamic load identification technology. Background technology:

[0002] External load information of engineering structures is crucial for structural dynamics analysis and condition monitoring. However, many engineering structures, under service conditions, cannot directly obtain external dynamic load information by deploying force sensors on their surfaces. Therefore, it is necessary to develop dynamic load identification methods that utilize structural response to invert the external loads acting upon them.

[0003] Traditional methods for identifying distributed dynamic loads construct a distributed dynamic load identification model, transforming the problem into estimating a small number of parameters within the model. Existing deep learning-based methods primarily target concentrated dynamic loads and impact loads. Identifying continuous distributed dynamic loads with complex spatial and temporal characteristics requires considering both spatial distribution and time history information, making it significantly more challenging. Therefore, a new method is needed to identify dynamic loads with complex spatial distribution characteristics. Summary of the Invention

[0004] The purpose of this invention is to provide a distributed dynamic load identification method that combines wavelet decomposition and LSTM deep learning network to solve the problem of identifying three-dimensional distributed dynamic loads that have non-stationary characteristics in spatial distribution but stationary random characteristics in time history. This provides an indirect means of obtaining dynamic loads for the design and condition monitoring of engineering structures in service under distributed dynamic load environments.

[0005] Technical Solution: To achieve the above objectives, this invention proposes a distributed dynamic load identification method combining wavelet decomposition and LSTM deep learning networks. This method includes the following steps:

[0006] S1. Establish a finite element model of the vehicle's wall panel structure;

[0007] S2. Divide the surface of the vehicle wall panel structure under the action of distributed dynamic load into sub-regions, construct the transmission relationship between the dynamic load distributed in the form of shape function on the sub-region and the dynamic response of the finite element model measurement points, and establish a sample library based on the time domain information of strain dynamic response at multiple measurement points and the time domain information of distributed dynamic load on the corresponding sub-region nodes;

[0008] S3. Use Meyer wavelets to extract time-frequency features from the time-domain information of response and load in the sample library; take the time-frequency features of the response at the measurement point as input and the time-frequency features of the distributed dynamic load on the sub-region nodes as output, and train an LSTM deep learning network to obtain the relationship between the time-frequency features of the distributed dynamic load on the sub-region and the time-frequency features of the dynamic strain response at the measurement point of the finite element model;

[0009] S4. Using the time-frequency characteristics of the strain response obtained at the measured points as input, the load values ​​on each sub-region node are solved by the trained LSTM deep learning network proxy model, and the distributed dynamic load on the surface of the vehicle panel structure is obtained by superposition.

[0010] Furthermore, in step S2, the process of dividing the structural surface under the action of the distributed dynamic load into sub-regions, constructing the transmission relationship between the dynamic load distributed in the form of shape functions on the sub-regions and the dynamic response at the measurement points of the finite element model, and establishing a sample library based on the time-domain information of the strain dynamic response at multiple measurement points and the time-domain information of the distributed dynamic load on the corresponding sub-region nodes, specifically involves the following steps:

[0011] S21: To obtain the strain response at the measuring point, the distributed dynamic load on the vehicle's wall panel structure is first transformed into nodal loads on the structural finite element model using the finite element method. The element nodal loads are obtained by integration within the structural finite element model.

[0012]

[0013] In the formula, N e (x,y) represents the shape function of the element in the structural finite element model, N i (x,y) represents the interpolation function corresponding to the i-th node in this sub-region, p i (t) represents the nodal load value that varies with time; the nodal loads on the structural finite element model, which are equivalent to the distributed dynamic loads on the sub-region, are applied to the finite element model, and the strain response at the model measurement points is calculated.

[0014] S22: Based on the Green's function of a linear system, the transfer function relationship between the distributed dynamic load and the strain response at the measuring point over the sub-region is obtained as follows:

[0015]

[0016] In the formula, ε i The strain response ε at the i-th measuring point i (t), p i The distributed dynamic load p at the node of the i-th sub-region i (t), m S m represents the number of strain measurement points. P G represents the number of nodes in the load sub-region. i,jThis represents the transfer matrix between the distributed load corresponding to the node in the j-th sub-region and the strain response at the i-th measuring point;

[0017] Equation (2) can be simplified to the following:

[0018] Y * =GP * (3)

[0019] In the formula, Y * Let G be the response matrix, G be the transfer matrix, and P be the response matrix. * The load matrix;

[0020] S23: Set batch distributed dynamic load information as input, calculate the time domain information of strain change response at multiple measurement points through finite element software, and establish a sample library based on the time domain information of strain change response at measurement points and the time domain information of distributed dynamic load on all sub-region nodes.

[0021] Furthermore, in step S2, when the sub-region is a quadrilateral, the load magnitude within each sub-region is obtained by multiplying the load values ​​at the four nodes of that region by the corresponding interpolation function and then summing them. Also, when the sub-region is a quadrilateral, the specific expression for the interpolation function of a single node in the four adjacent sub-regions is:

[0022]

[0023] In the formula, L x ,L y These represent the lengths of each sub-region along the x and y directions, respectively, and D1 to D4 represent the four sub-regions connected by this node.

[0024] Furthermore, in step S3, Meyer wavelets are used to extract time-frequency features from the time-domain information of the response and load in the sample library; the time-frequency features of the measurement point response are used as input, and the time-frequency features of the distributed dynamic load on the sub-region nodes are used as output. Based on the LSTM deep learning network training, the relationship between the time-frequency features of the distributed dynamic load on the sub-region and the time-frequency features of the dynamic strain response of the measurement point in the finite element model is obtained. The specific steps are as follows:

[0025] S31. Using Meyer wavelets to analyze the load matrix P * With the response vector Y of the measuring point * Frequency band feature extraction is performed on the time-domain signal to obtain P. * and Y * Signal components P in each frequency band * 1、…、P * J and Y * 1、…、Y * J , where J is the order of the Meyer wavelet;

[0026] S32. The response vector Y at the measurement point * Signal components Y in each frequency band * 1、…、Y * J As the sequence input to the LSTM deep learning network, the sample distribution is normalized through a batch normalization layer; the LSTM layer processes the time-series signal; activation is performed using the Leaky-ReLU activation function; and the sequence output layer is connected to the sequence output layer through a fully connected layer. The sequence output layer outputs the component samples P of the dynamic load in each frequency band. * 1、…、P * J ;

[0027] S33. Use 70% of the sample data as the training set to train the network, 15% as the validation set to prevent overfitting, and 15% as the test set to test the network model. The network uses the Adam optimizer with a learning rate of 0.001, the root mean square error (RMSE) as the loss function, and a maximum of 1000 iterations. A neural network model is trained to determine the transmission relationship between the distributed dynamic load on the sub-region and the dynamic strain response at the measuring points of the finite element model.

[0028] Furthermore, in step S4, the time-frequency characteristics of the measured strain response are used as input, and the load values ​​on each sub-region node are solved through the trained LSTM deep learning network proxy model. The distributed dynamic load on the structural surface is then obtained by superposition. The specific steps are as follows:

[0029] The response vector of the measurement point to be identified Frequency band feature extraction is performed on the time-domain signal to obtain Signal components in each frequency band After inputting the signal components into the network trained in step 3, component samples of the recognition payload in each frequency band are obtained. The identification load vector is obtained by superimposing these vectors.

[0030] Beneficial effects: Compared with the prior art, the technical solution of the present invention has the following beneficial technical effects:

[0031] 1. Existing distributed dynamic load identification technologies are generally applicable to the identification of regular two-dimensional distributed loads. For distributed dynamic loads with more complex spatial distributions, there is a lack of effective identification methods. The method for identifying distributed dynamic loads using strain response information from a limited number of measuring points provided in this invention can accurately identify distributed dynamic loads on structural surfaces, and has certain advantages.

[0032] 2. Compared with traditional distributed dynamic load identification methods based on dynamic models, the distributed dynamic load identification method combining wavelet decomposition and LSTM deep learning network avoids ill-conditioned matrix inversion and has better identification efficiency and noise resistance. At the same time, the method in this paper has a lower requirement for the number of measurement points and can be better applied to online identification of distributed dynamic loads over a long period of time.

[0033] 3. This invention provides a method for indirectly obtaining distributed dynamic loads on engineering structures by inverting the strain response of a limited number of measuring points to obtain the distributed dynamic loads on the entire surface of the structure. This provides real and effective load information for the condition monitoring and safety design of engineering structures. Attached Figure Description

[0034] Figure 1 This is a flowchart illustrating the logic of the method of the present invention.

[0035] Figure 2 This is a schematic diagram of a wall panel subjected to distributed dynamic loads.

[0036] Figure 3 This is a graph showing the power spectral density of the distributed dynamic load.

[0037] Figure 4 The diagram shows the time history q(t) of dynamic loads distributed at typical locations.

[0038] Figure 5 This is a schematic diagram of the load sub-region.

[0039] Figure 6 This is a diagram of a distributed dynamic load identification model based on an LSTM neural network.

[0040] Figure 7 (a) is a schematic diagram of the actual distributed load acting on the plate structure at t=0.15s, (b) is a schematic diagram of the identified distributed load, and (c) is a schematic diagram comparing the identification result of the time history distribution of the distributed dynamic load with the reference value. Detailed Implementation

[0041] The technical solution of the present invention will be described in detail below through embodiments. However, the embodiments are only preferred embodiments of the present invention. It should be noted that for those skilled in the art, several improvements and equivalent substitutions can be made to the structure and dynamic load form without departing from the principle of the present invention. These improved and equivalent substitutions of the technical solutions of the claims of the present invention all fall within the protection scope of the present invention.

[0042] Example: For example Figure 2 The diagram shows a wall panel structure with four fixed sides. Identify the distributed dynamic load acting on the panel surface. The panel is 0.2m long, 0.15m wide, and 0.002m thick, with fixed boundaries on all four sides. The material is steel with an elastic modulus of 2.1 × 10⁻⁶.11 Pa, Poisson's ratio is 0.3, and density is 7850 kg·m³. -3 The structure uses Rayleigh damping, with a damping ratio of ξ for each mode. i =0.02. The expression for the distributed dynamic load to be identified is:

[0043] P(x,y,t)=s(x,y)q(t) (1)

[0044] In the formula, s(x,y)=0.0001*(ax) 2 +by 2 Let a∈(1,5), b∈(1,5), be the spatial distribution function of the dynamic load, with x and y in mm; q(t) be the time history of the load, with the load in Pa. Assume that... Figure 3 The load power spectral density curve in the image is used to generate dynamic load time history samples using the harmonic superposition method, such as... Figure 4 As shown.

[0045] The technique of this invention for identifying distributed dynamic loads from measured structural strain response data specifically includes the following steps:

[0046] S1. Establish the finite element model of the vehicle's wall panel structure. In this example, the structure is a wall panel structure with fixed supports on all four sides. This includes the following steps:

[0047] S11: Establish the initial finite element model of the actual structure;

[0048] S12: Obtain modal data of the actual structure based on modal testing;

[0049] S13: Based on the modal data from the modal tests, the initial finite element model is modified to obtain the modified finite element model.

[0050] The distributed dynamic load time-domain identification method, in step S2, divides the structural surface on which the distributed dynamic load acts into sub-regions, constructs the transmission relationship between the dynamic load distributed in the form of shape functions on the sub-regions and the dynamic response of the finite element model nodes, and establishes a sample library based on the strain dynamic response at the measuring point and the distributed dynamic load on the corresponding sub-region. The specific method includes the following steps:

[0051] S21. Using the finite element method, the distributed dynamic load is transformed into nodal loads on the finite element structure: the sub-regions of the load-bearing surface are divided as follows: Figure 5 As shown, it includes 36 rectangular regions and 49 shared nodes. The load magnitude within each sub-region is obtained by multiplying the load values ​​at the four nodes of that region by their corresponding interpolation functions and then summing the results. The specific expression for the interpolation function of a single node in its four adjacent sub-regions is as follows:

[0052]

[0053] In the formula, L x ,L y These represent the lengths of each sub-region along the x and y directions, respectively, and D1 to D4 represent the four sub-regions connected by this node.

[0054] Therefore, the distributed dynamic load within a single sub-region can be expressed as:

[0055]

[0056] In the formula, m N N represents the number of nodes in this sub-region. i (x,y) represents the interpolation function corresponding to the i-th node in this sub-region, p i (t) represents the load value at the center node of the sub-region that varies with time. After dividing the load sub-regions, the interpolation function corresponding to each node is selected. Here, the shape function of the finite element corresponding to the sub-region can be directly selected as the interpolation function. The interpolation function determines the distribution of the load in each sub-region, and the load value at the center node controls the coefficient of the distribution function. The distributed dynamic load on the entire structural surface can be reconstructed by solving for the load values ​​at all nodes. The distributed dynamic load on the structural surface is shown in the following equation:

[0057]

[0058] In the formula, m P m represents the number of nodes contained in the subregion. e This represents the number of sub-regions connected to the j-th node.

[0059] Distributed dynamic loads can then be expressed as nodal loads on the finite element structure:

[0060]

[0061] In the formula, N e N represents the shape function of an element in a structural finite element model. i (x,y) represents the interpolation function corresponding to the i-th node in this sub-region, p i (t) represents the nodal load value that varies with time.

[0062] The nodal loads on the structural finite element model, which are equivalent to the distributed dynamic loads on the sub-region, are applied to the finite element model, and the strain response at the model measurement points is calculated.

[0063] S22: Based on the Green's function of a linear system, the transfer function relationship between the distributed dynamic load and the strain response at the measuring point is obtained as follows:

[0064]

[0065] In the formula, ε i The strain response ε at the i-th measuring point i (t), p i The distributed dynamic load p at the node of the i-th sub-region i (t), m S m represents the number of strain measurement points. P G represents the number of nodes in the load sub-region. i,j This represents the transfer matrix between the distributed load corresponding to the node in the j-th sub-region and the strain response at the i-th measuring point.

[0066] Equation (2) can be simplified to the following:

[0067] Y * =GP * (3)

[0068] In the formula, Y * Let G be the response matrix, G be the transfer matrix, and P be the response matrix. * This is the load matrix.

[0069] S23: Generate 200 sets of distributed dynamic load samples based on the given dynamic load form. Calculate the strain response at the measuring points using finite element software, and establish a sample library based on the strain response at the measuring points and the distributed dynamic loads on the corresponding sub-regions. In this embodiment, there are 13 virtual strain measuring points, evenly distributed on the plate, and the triaxial strain (ε) is measured. x ,ε y ,τ xy As a response, the strain sampling frequency is 5000Hz. Data is collected and a sample library is established based on the time-domain information of strain-variable response at the measuring points and the time-domain information of distributed dynamic loads on all sub-region nodes.

[0070] The distributed dynamic load time-domain identification method described above, in step S3, uses Meyer wavelets to extract features from time-domain samples in the sample library; based on an LSTM deep learning network, it constructs the relationship between the distributed dynamic load on the sub-region and the dynamic strain response of the finite element model measurement points. The specific method includes the following steps:

[0071] S31. In this embodiment, the 4th-order Meyer wavelet is used to process the load matrix P respectively. * With the response vector Y of the measuring point * Frequency band feature extraction is performed on the time-domain signal.

[0072] S32. The response vector Y at the measurement point * Signal components Y in each frequency band * 1、…、Y * JThe sequence input to the LSTM deep learning network is normalized by a batch normalization layer; then, an LSTM layer is used to process the time-series signal; activation is performed using the Leaky-ReLU activation function; and finally, a fully connected layer connects to the sequence output layer, which outputs the component samples P of the dynamic load in each frequency band. * 1、…、P * J ;

[0073] S33. Use 70% of the sample data as the training set to train the network, 15% of the data as the validation set to prevent overfitting, and 15% of the data as the test set to test the network model. The network uses the Adam optimizer with a learning rate of 0.001, the loss function is the root mean square error (RMSE), and the maximum number of iterations is 100. A surrogate model is trained to obtain the transmission relationship between the distributed dynamic load on the sub-region and the dynamic strain response at the measuring point of the finite element model.

[0074] The distributed dynamic load time-domain identification method described above uses the time-frequency characteristics of the measured strain response as input in step S4. Based on the trained LSTM deep learning network, the load values ​​on the common nodes of each sub-region boundary are calculated to obtain the distributed dynamic load on the structural surface. The specific method includes the following steps:

[0075] S41. The measured strain response is processed using a 4th-order Meyer wavelet to extract the characteristic signals, obtaining the components of the response signal in each frequency band, which are then used as network inputs. The load values ​​acting on each node in the model sub-region are reconstructed by superimposing the characteristic components of the load vector at each frequency band.

[0076] After solving for the load values ​​at each node in the sub-region, the distributed dynamic load on the entire structural surface is expressed as:

[0077]

[0078] In the formula, m P m represents the number of nodes contained in the entire sub-region of the structure's surface. N N represents the number of sub-regions connected to the j-th node. ji This represents the interpolation function for the j-th node within the i-th subregion it is connected to.

[0079] Figure 7Figures a and b show the actual spatial distribution and identification results of the distributed dynamic load at time t = 0.15s, respectively, while Figure c shows the identification results of the time history distribution of the dynamic load. It can be seen that the identification method in this invention can accurately identify the distributed dynamic load whose spatial distribution changes over time through the strain sequence at the measuring point. Compared with common deep learning-based distributed dynamic load identification methods, the method in this invention can more accurately characterize the temporal and spatial features of the dynamic load, and its technical solution is advanced.

Claims

1. A method for identifying distributed dynamic loads combining wavelet decomposition and LSTM deep learning networks, characterized in that, The method includes the following steps: S1. Establish a finite element model of the vehicle's wall panel structure; S2. Divide the surface of the vehicle wall panel structure under the action of distributed dynamic load into sub-regions, construct the transmission relationship between the dynamic load distributed in the form of shape function on the sub-region and the dynamic response of the finite element model measurement points, and establish a sample library based on the time domain information of strain dynamic response at multiple measurement points and the time domain information of distributed dynamic load on the corresponding sub-region nodes; S3. Use Meyer wavelets to extract time-frequency features from the time-domain information of response and load in the sample library; take the time-frequency features of the response at the measurement point as input and the time-frequency features of the distributed dynamic load on the sub-region nodes as output, and train an LSTM deep learning network to obtain the relationship between the time-frequency features of the distributed dynamic load on the sub-region and the time-frequency features of the dynamic strain response at the measurement point of the finite element model; S4. Using the time-frequency characteristics of the strain response obtained at the measured points as input, the load values ​​on each sub-region node are solved by the trained LSTM deep learning network proxy model, and the distributed dynamic load on the surface of the vehicle wall panel structure is obtained by superposition. In step S2, the structural surface subjected to the distributed dynamic load is divided into sub-regions, and the transfer relationship between the dynamic load distributed in the form of shape functions on the sub-regions and the dynamic response of the finite element model measurement points is constructed. A sample library is established based on the time-domain information of strain dynamic response at multiple measurement points and the time-domain information of distributed dynamic load on the corresponding sub-region nodes. The specific steps are as follows: S21: To obtain the strain response at the measuring point, the distributed dynamic load on the vehicle's wall panel structure is transformed into nodal loads on the structural finite element model using the finite element method. The element nodal loads are obtained by integration within the structural finite element model. (1) In the formula, N e (x,y) represents the shape function of the element in the structural finite element model, N i (x,y) represents the interpolation function corresponding to the i-th node in this sub-region, p i (t) represents the nodal load value as a function of time; The nodal loads on the structural finite element model, which are equivalent to the distributed dynamic loads on the sub-region, are applied to the finite element model, and the strain response at the model measurement points is calculated. S22: Based on the Green's function of a linear system, the transfer function relationship between the distributed dynamic load and the strain response at the measuring point over the sub-region is obtained as follows: (2) In the formula, i The strain response at the i-th measuring point , i The distributed dynamic load at the node of the i-th sub-region m S m represents the number of strain measurement points. P G represents the number of nodes in the load sub-region. i,j This represents the transfer matrix between the distributed load corresponding to the node in the j-th sub-region and the strain response at the i-th measuring point; Equation (2) can be simplified to the following: (3) In the formula, Y * Let G be the response matrix, G be the transfer matrix, and P be the response matrix. * The load matrix; S23: Set batch distributed dynamic load information as input, calculate the time domain information of strain change response at multiple measurement points through finite element software, and establish a sample library based on the time domain information of strain change response at measurement points and the time domain information of distributed dynamic load on all sub-region nodes.

2. The distributed dynamic load identification method combining wavelet decomposition and LSTM deep learning network according to claim 1, characterized in that, In step S2, when the sub-region is a quadrilateral, the load magnitude within each sub-region is obtained by multiplying the load values ​​at the four nodes of that region by the corresponding interpolation function and then summing them. Furthermore, when the sub-region is a quadrilateral, the specific expression for the interpolation function of a single node in its four adjacent sub-regions is as follows: (4) In the formula, L x ,L y These represent the lengths of each sub-region along the x and y directions, respectively, and D1~D4 represent the four sub-regions connected by this node.

3. The distributed dynamic load identification method combining wavelet decomposition and LSTM deep learning network according to claim 1, characterized in that, In step S3, the time-frequency features of the response and load in the sample library are extracted using Meyer wavelets. The time-frequency features of the measurement point response are used as input, and the time-frequency features of the distributed dynamic load on the sub-region nodes are used as output. Based on an LSTM deep learning network, the relationship between the time-frequency features of the distributed dynamic load on the sub-region and the time-frequency features of the dynamic strain response at the measurement points of the finite element model is obtained through training. The specific steps are as follows: S31. Using Meyer wavelets to analyze the load matrix P * With the response vector Y of the measuring point * Frequency band feature extraction is performed on the time-domain signal to obtain P. * and Y * Signal components P in each frequency band * 1、…、P * J and Y * 1、…、Y * J , where J is the order of the Meyer wavelet; S32. Transfer the response vector Y of the measurement point. * Signal components Y in each frequency band * 1、…、Y * J The sequence input to the LSTM deep learning network is normalized by a batch normalization layer; the time-series signal is processed using an LSTM layer; activation is performed using the Leaky-ReLU activation function; and a fully connected layer connects to the sequence output layer, which outputs the component samples P of the dynamic load in each frequency band. * 1、…、P * J .

4. The distributed dynamic load identification method combining wavelet decomposition and LSTM deep learning network according to claim 3, characterized in that, During training, 70% of the sample data was used as the training set to train the network, and 15% of the data was used as the test set to test the network model. The neural network was optimized using the Adam optimizer with a learning rate of 0.001 and the root mean square error (RMSE) loss function. The maximum number of iterations was 1000. The neural network model of the transmission relationship between the distributed dynamic load on the sub-region and the dynamic strain response of the finite element model measuring points was obtained through training.

5. A distributed dynamic load identification method combining wavelet decomposition and LSTM deep learning network according to claim 1, 3, or 4, characterized in that, In step S4, the time-frequency characteristics of the measured strain response are used as input, and the load values ​​on each sub-region node are solved through the trained LSTM deep learning network proxy model. The distributed dynamic load on the structural surface is then obtained by superposition. The specific steps are as follows: The response vector of the measurement point to be identified Frequency band feature extraction is performed on the time-domain signal to obtain Signal components in each frequency band … After inputting the signal components into the network trained in step 3, component samples of the recognition payload in each frequency band are obtained. … The identification load vector is obtained by superimposing these vectors. .

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