Bridge vehicle-induced vibration prediction method based on modal expansion and residual CNN-LSTM network

Abstract

The application discloses a bridge vehicle-induced vibration prediction method based on a modal expansion and a residual CNN-LSTM network. According to the modal expansion method, the input vehicle parameters and road roughness are reconstructed into fixed-dimension features, and the concerned vehicle-induced vibration is analyzed and predicted by means of the multi-scale feature extraction and time sequence dependence extraction capacity of the residual convolution-long short-term memory network, so that the prediction precision of the vehicle-induced vibration is improved. The application generates training set samples by using a test design method and a numerical simulation method, so that the prediction precision and generalization ability of the obtained network model are ensured under the premise of controlling the number of training samples. The application has the beneficial effect of overcoming the time-consuming problem of traditional vehicle-bridge coupled vibration analysis, can quickly and reliably predict and analyze the vehicle-induced vibration of a target bridge according to vehicle parameters and road roughness, and is suitable for long-term safety evaluation of highway bridges under the action of random vehicle flow.

Description

Technical Field

[0001] This invention relates to the interdisciplinary field of bridge dynamic response analysis and computer science, and in particular to a method for predicting vehicle-induced vibrations of bridges based on modal extension and residual CNN-LSTM networks. Background Technology

[0002] Bridges are crucial hubs in highway transportation, and ensuring their safe operation is of great significance for smooth regional traffic flow and the orderly conduct of socio-economic activities. Vehicle load is one of the main loads that highway bridges must withstand, and it is a significant factor contributing to fatigue loss, concrete cracking, and even bridge collapse. Therefore, to prevent safety risks to highway bridges, it is necessary to accurately assess the structural response of bridges under vehicle loads to avoid serious damage caused by excessive vehicle loads.

[0003] Traditionally, influence line loading has been used to analyze the structural response of bridges under vehicle loads. However, influence line loading neglects the dynamic effects of vehicle loads and the complex coupling effects between the vehicle, bridge, and road, leading to insufficient accuracy in structural response analysis based on influence line loading. Furthermore, due to the neglect of dynamic effects, the analysis results using influence line loading often overestimate the fatigue life of the bridge. To obtain accurate analysis results, scholars and engineers both domestically and internationally have developed a series of vehicle-bridge coupled vibration analysis methods. However, vehicle-bridge coupled vibration analysis exhibits dual nonlinear characteristics in both time and space, resulting in significant computational time consumption. When analyzing the fatigue reliability of large bridge structures, the computational cost is often unacceptable. Therefore, there is an urgent need to develop an efficient and reliable method for analyzing vehicle-induced vibrations in bridges, controlling computational time while ensuring computational accuracy.

[0004] In recent years, machine learning and deep learning methods have developed rapidly, providing new solutions for analyzing vehicle-induced vibrations in bridges. Scholars both domestically and internationally have proposed several deep learning-assisted methods for analyzing vehicle-induced vibrations in bridges, significantly reducing computational time. However, the methods discussed above are only applicable to vibration response analysis when vehicles of a specified number and position of axles pass over a bridge at constant speeds. The vehicle distribution on highway bridges exhibits significant spatiotemporal variability and randomness, causing the dimensionality of input parameters to constantly change. Therefore, existing deep neural networks cannot be directly used to predict vehicle-induced vibrations in highway bridges. Furthermore, moving vehicles and road surface irregularities have completely different excitation frequencies, and existing deep learning methods do not fully utilize these differences in excitation frequencies to improve the prediction accuracy of vehicle-induced vibrations. Summary of the Invention

[0005] The purpose of this invention is to address the shortcomings of existing technologies by proposing a bridge vehicle-induced vibration prediction method based on modal extension and residual CNN-LSTM networks. This method can perform proxy prediction of the vibration response of a target bridge based on arbitrary input vehicle parameters, road surface unevenness information, and bridge mode shapes, and has good computational efficiency and relatively reliable analysis accuracy.

[0006] Technical Solution: To achieve the above objectives, this invention provides a method for predicting vehicle-induced vibrations in bridges based on modal extension and residual CNN-LSTM networks. The method includes the following specific steps:

[0007] S1 generates several sets of traffic flow parameters and road surface roughness levels, and generates corresponding road surface roughness according to the road surface roughness level, thereby obtaining the vehicle-induced vibration of the bridge under different traffic flow parameters and road surface roughness. The traffic flow parameters include the number of vehicles, vehicle mass, and vehicle position at each time. The vehicle-induced vibration includes the bridge displacement, velocity, acceleration, stress and strain.

[0008] S2, obtain the modal shapes of the target bridge, and use the modal extension method to reconstruct the features of the traffic flow parameters and road surface unevenness generated in step S1 to obtain the equivalent load of the vehicle mass. and the equivalent load of road surface unevenness. ;

[0009] S3, the training set for building a deep neural network model of the bridge;

[0010] S4, establish a residual convolutional-long short-term memory network;

[0011] S5, Use the training set from step S3 to train the residual convolutional-long short-term memory network established in step S4.

[0012] S6. Generate the traffic flow parameters and road surface unevenness for the expected analysis. Perform feature reconstruction on the newly generated traffic flow parameters and road surface unevenness according to the method in step S2. Input the reconstructed features into the residual convolutional-long short-term memory network obtained in step S5 to predict the vehicle-induced vibration of the bridge.

[0013] Furthermore, in step S1, the road surface roughness is generated according to the expected road surface roughness level using equations (1)-(2):

[0014] (1)

[0015] (2)

[0016] In the formula, For road surface unevenness; Indicates the spatial position along the bridge axis; It is the power spectral density function; It is the sampling interval within the spatial domain; It is the number of sampling points within the spatial domain; Spatial frequency; This is the lower cutoff frequency; The upper limit cutoff frequency; Reference spatial frequency; Spatial frequency The corresponding random phase.

[0017] Furthermore, in step S2, the feature reconstruction process is constructed using equations (3)-(6):

[0018] (3)

[0019] (4)

[0020] (5)

[0021] (6)

[0022] In the formula These are the positions of the k-th vehicle at various times; These are mass-normalized mode shapes; It refers to the spatial distribution of road surface unevenness; This is the modal shape interpolation result corresponding to the k-th vehicle; This is the interpolation result of the road surface roughness corresponding to the kth vehicle; It is the total weight of the kth vehicle; It is the equivalent load after the total vehicle weight is reconstructed using the modal expansion method; It is the equivalent load after the road surface roughness is reconstructed by the modal expansion method; It is the number of nodes in the numerical model along the length of the bridge; It analyzes the number of vehicles crossing the bridge within a given time period; It is the length of the time series; It is the number of dominant bridge modes; function This is an interpolation function. In planar vibration analysis, this function is a one-dimensional interpolation function; in spatial vibration analysis, this function is a two-dimensional interpolation function. (Operator) It is the element-wise multiplication operator.

[0023] Furthermore, in step S3, the training set consists of two types of equivalent loads after feature reconstruction. and This corresponds to vehicle-induced vibrations of the bridge, including displacement, velocity, acceleration, stress, and strain.

[0024] Furthermore, in step S3, the network model includes an input layer, three one-dimensional convolutional layers, one long short-term memory layer, two fully connected layers, and an output layer, along with the equivalent payload after feature reconstruction. and The input layer feeds into the network model. After passing through the first two convolutional layers, the initial input of the network and the output of the first two convolutional layers are added element by element to achieve multi-scale feature extraction. The output after addition is increased in dimensionality by the third convolutional layer, and the temporal dependencies are extracted by the long short-term memory layer. Finally, the vehicle-induced vibration of the bridge is obtained by the fully connected layer.

[0025] Furthermore, two convolutional layers are used for multi-scale feature extraction, with kernel sizes of 3 and 5 respectively; a third convolutional layer is used for upscaling the hidden layer features, with a kernel size of 1.

[0026] Furthermore, the mean squared error of the predicted values ​​is chosen as the loss function:

[0027] (7)

[0028] In the formula, It is a loss function. This is the predicted value of vehicle-induced vibration using the method of this invention. This is the true value of vehicle-induced vibration. It is the number of samples in the training or validation set.

[0029] Beneficial effects: Compared with the prior art, the technical solution of the present invention has the following beneficial technical effects:

[0030] This invention overcomes the computational time problem of traditional vehicle-bridge coupled vibration analysis methods. It can efficiently analyze vehicle-induced vibrations of bridges based on vehicle location, total vehicle weight, bridge road surface unevenness, and mode shapes. Furthermore, this invention can be used to predict vehicle-induced vibrations with any number of vehicles, effectively addressing the challenges posed by the spatiotemporal variability of vehicle distribution to neural network solutions. Therefore, this invention demonstrates good accuracy and applicability in predicting vehicle-induced vibrations of highway bridges and is expected to promote the development of data-driven bridge dynamic response analysis technology. Attached Figure Description

[0031] Figure 1 This is a schematic diagram of a numerical example;

[0032] Figure 2 This is a schematic diagram of the bridge vehicle-induced vibration prediction process of the present invention;

[0033] Figure 3 This is a schematic diagram of the residual convolutional-long short-term memory network of the present invention;

[0034] Figure 4a is a schematic diagram of the bridge displacement prediction result-time history curve of the method of the present invention;

[0035] Figure 4 b is a schematic diagram of the bridge displacement prediction result-power spectral density curve of the method of the present invention;

[0036] Figure 5 a is a schematic diagram of the bridge speed prediction result-time history curve of the method of the present invention;

[0037] Figure 5 b is a schematic diagram of the bridge speed prediction result-power spectral density curve of the method of the present invention;

[0038] Figure 6 a is a schematic diagram of the bridge acceleration prediction result-time history curve of the method of the present invention;

[0039] Figure 6 b is a schematic diagram of the bridge acceleration prediction result-power spectral density curve of the method of the present invention;

[0040] Figure 7 a is a schematic diagram of the mean square error of displacement prediction by the method of the present invention;

[0041] Figure 7 b is a schematic diagram of the mean square error of the speed prediction method of the present invention;

[0042] Figure 7 c is a schematic diagram of the mean square error of acceleration prediction by the method of the present invention. Detailed Implementation

[0043] The present invention will now be described in detail with reference to the accompanying drawings and preferred embodiments, making the objectives, implementation process, and effects of the invention clearer and more explicit. It should be noted that the specific embodiments described herein are for illustrative purposes only and are not intended to limit the scope of the invention.

[0044] Combination Figure 1 The numerical examples shown illustrate the specific implementation steps of the present invention. The numerical examples use a one-dimensional beam element model to simulate a single-span simply supported beam bridge, with a span of 3m and an elastic modulus of 3.45 × 10⁻⁶. 4 MPa, density 2.55×10 3 kg / m 3 The moment of inertia of the cross section is 0.018m. 4 The vehicle is simulated using a moving spring-mass model, with the total mass of the vehicle varying from 100kg to 2000kg and the vehicle speed varying from 1m / s to 5m / s. The output physical quantities of interest are the displacement, velocity, and acceleration at the bridge's centerline, i.e., the output dimension is 3; the analysis duration is 10s, the analysis step size is 0.02s, and the time series length is 500.

[0045] The bridge vehicle-induced vibration prediction method based on modal extension and residual CNN-LSTM network proposed in this invention and its calculation process are as follows: Figure 2 As shown, the required input features and predicted output features are as follows:

[0046] (1) Input features: real-time vehicle location, total vehicle weight, road surface unevenness of the bridge, and mode shape of the bridge.

[0047] (2) Output characteristics: Vibration response at the location of the bridge of interest, including but not limited to physical quantities such as displacement, velocity, and acceleration.

[0048] The specific implementation process of the method proposed in this invention includes the following five steps:

[0049] S1: Based on the modal shapes of the target bridge and the real-time position of the vehicle, the modal extension method is used to reconstruct the input features such as the total vehicle weight and road surface unevenness. In this example, the dominant modes of the bridge are set as the first 8 vertical bending modes, and the reconstructed input features are calculated using equations (1)-(4) according to the modal extension method:

[0050] (1)

[0051] (2)

[0052] (3)

[0053] (4)

[0054] In the formula, These are the real-time location coordinates of the kth vehicle; These are mass-normalized mode shapes; It refers to the spatial distribution of road surface unevenness; This is the modal shape interpolation result corresponding to the k-th vehicle; This is the interpolation result of the road surface roughness corresponding to the kth vehicle; It is the total weight of the kth vehicle; It is the equivalent load after the total vehicle weight is reconstructed using the modal expansion method; It is the equivalent load after the road surface roughness is reconstructed by the modal expansion method; This refers to the number of bridge nodes identified during vibration analysis. It analyzes the number of vehicles crossing the bridge within a given time period; It is the length of the time series; It is the number of dominant bridge modes; function It is an interpolation function; in this example, a spline function is used as the interpolation function; operators It is the element-wise multiplication operator.

[0055] Based on the calculation results of equations (1)-(4), the reconstructed input features and All are 500×8 two-dimensional arrays.

[0056] S2: Construct a residual convolutional-long short-term memory network based on the dimensions of the reconstructed input and output features. The structure of this residual convolutional-long short-term memory network is as follows: Figure 3 As shown, the system comprises an input layer, three one-dimensional convolutional layers, one long short-term memory layer, two fully connected layers, and an output layer. A skip connection from a residual neural network is introduced to element-wise add the outputs of the input layer and the hidden layers of the first two convolutional layers. The kernel sizes of the three convolutional layers are 3, 5, and 1, respectively, for multi-scale feature extraction and dimensionality upscaling of hidden layer features. The number of hidden nodes in the long short-term memory layer is set to 50; the number of hidden nodes in the two fully connected layers are 20 and 3, respectively.

[0057] S3: Database preparation for the deep neural network model. In this case, firstly, the sample parameters of the training set and the validation machine are generated using Latin cube design, and the sample parameters of the test set are generated randomly. Then, the samples of the training set, the validation machine, and the test set are generated based on the aforementioned sample parameters using a mature calculation program for vehicle-bridge coupled vibration analysis. The vehicle-bridge coupled vibration analysis process involves road surface unevenness, which is calculated using equations (5) and (6):

[0058] (5)

[0059] (6)

[0060] In the formula, For road surface unevenness; It is the power spectral density function; It is the sampling interval within the spatial domain; It is the number of sampling points within the spatial domain; Spatial frequency; The lower cutoff frequency, The upper limit cutoff frequency; Spatial frequency The corresponding random phase.

[0061] S4: Based on the training set and validation set samples obtained in step S3, train the deep neural network established in step S2, and normalize the reconstructed input features and output features to the [-1,1] interval before model training. During model training, the Adam optimization algorithm is used to train the network model, with a maximum iteration step of 20000, an initial learning rate of 0.001, and the remaining parameters of the optimization algorithm are set to default parameters. The loss function selected during model training is the mean square error between the predicted and actual values ​​of vehicle-induced vibration, i.e., the loss function is calculated using equation (7):

[0062] (7)

[0063] In the formula, It is a loss function. This is the predicted value of vehicle-induced vibration by the method proposed in this invention. This is the true value of vehicle-induced vibration. It is the number of samples in the training or validation set.

[0064] S5: Model validation of the deep neural network, which involves comparing the actual values ​​of vehicle-induced vibrations with the predicted values ​​output by the deep neural network model on the test set data. The comparison results of the time history curves of displacement, velocity, and acceleration, and the power spectral density are shown below. Figure 4 , Figure 5 , Figure 6 As shown in the figure. The model's prediction performance is evaluated using mean square error. The mean square error distributions of the displacement, velocity, and acceleration prediction results are shown in the figure. Figure 7 As shown, the prediction results of the method proposed in this invention match the actual values ​​well, with only a certain error in the high-frequency components of vehicle-induced vibration. This indicates that the present invention has good accuracy in predicting vehicle-induced vibration of bridges and is promising for long-term safety assessment of highway bridges.

Claims

1. A method for predicting vehicle-induced vibrations in bridges based on modal extension and residual CNN-LSTM networks, characterized in that, The method includes the following specific steps: S1 generates several sets of traffic flow parameters and road surface roughness levels, and generates corresponding road surface roughness according to the road surface roughness level, thereby obtaining the vehicle-induced vibration of the bridge under different traffic flow parameters and road surface roughness. The traffic flow parameters include the number of vehicles, vehicle mass, and vehicle position at each time. The vehicle-induced vibration includes the bridge displacement, velocity, acceleration, stress and strain. S2, obtain the modal shapes of the target bridge, and use the modal extension method to reconstruct the features of the traffic flow parameters and road surface unevenness generated in step S1 to obtain the equivalent load of the vehicle mass. and the equivalent load of road surface unevenness. ; S3, the training set for building a deep neural network model of the bridge; S4, establish a residual convolutional-long short-term memory network; S5, Use the training set from step S3 to train the residual convolutional-long short-term memory network established in step S4. S6, generate the traffic flow parameters and road surface unevenness to be analyzed, and reconstruct the features of the newly generated traffic flow parameters and road surface unevenness according to the method in step S2; input the reconstructed features into the residual convolutional-long short-term memory network obtained in step S5 to predict the vehicle-induced vibration of the bridge. In step S2, the feature reconstruction process is constructed using equations (3)-(6): （3） （4） （5） （6） In the formula These are the positions of the k-th vehicle at various times; These are mass-normalized mode shapes; It refers to the spatial distribution of road surface unevenness; This is the modal shape interpolation result corresponding to the k-th vehicle; This is the interpolation result of the road surface roughness corresponding to the k-th vehicle; It is the total weight of the kth vehicle; It is the equivalent load after the total vehicle weight is reconstructed using the modal extension method; It is the equivalent load after the road surface roughness is reconstructed by the modal expansion method; It is the number of nodes in the numerical model along the length of the bridge; It analyzes the number of vehicles crossing the bridge within a given time period; It is the length of the time series; It is the number of dominant bridge modes; function This is an interpolation function. In planar vibration analysis, this function is a one-dimensional interpolation function; in spatial vibration analysis, this function is a two-dimensional interpolation function. (Operator) It is the element-wise multiplication operator; In step S3, the network model includes an input layer, three one-dimensional convolutional layers, one long short-term memory layer, two fully connected layers, and an output layer. The equivalent payload after feature reconstruction is... and The input layer feeds into the network model. After passing through the first two convolutional layers, the initial input of the network and the output of the first two convolutional layers are added element by element to achieve multi-scale feature extraction. The output after addition is increased in dimensionality by the third convolutional layer, and the temporal dependencies are extracted by the long short-term memory layer. Finally, the vehicle-induced vibration of the bridge is obtained by the fully connected layer.

2. The method for predicting vehicle-induced vibration of bridges based on modal extension and residual CNN-LSTM network according to claim 1, characterized in that, In step S1, the road surface roughness is generated according to the expected road surface roughness level using equations (1) and (2): （1） （2） In the formula, For road surface unevenness; Indicates the spatial position along the bridge axis; It is the power spectral density function; It is the sampling interval within the spatial domain; It is the number of sampling points within the spatial domain; Spatial frequency; This is the lower cutoff frequency; The upper limit cutoff frequency; Reference spatial frequency; Spatial frequency The corresponding random phase.

3. The method for predicting vehicle-induced vibration of bridges based on modal extension and residual CNN-LSTM network according to claim 1, characterized in that, In step S3, the training set consists of two types of equivalent loads after feature reconstruction. and This corresponds to vehicle-induced vibrations of the bridge, including displacement, velocity, acceleration, stress, and strain.

4. The method for predicting vehicle-induced vibration of bridges based on modal extension and residual CNN-LSTM network according to claim 1, characterized in that, Two convolutional layers are used for multi-scale feature extraction, with kernel sizes of 3 and 5 respectively; a third convolutional layer is used for upscaling the hidden layer features, with a kernel size of 1.

5. A method for predicting vehicle-induced vibration of bridges based on modal extension and residual CNN-LSTM networks according to claim 1 or 4, characterized in that, Choose the mean squared error of the predicted values ​​as the loss function: （7） In the formula, It is a loss function. This is the predicted value of vehicle-induced vibration. This is the true value of vehicle-induced vibration. It is the number of samples in the training or validation set.

Images