Bridge moving load identification method based on displacement response power spectrum

Abstract

The application discloses a bridge moving load identification method based on displacement response power spectrum, which comprises the following steps: (1) acquiring bridge displacement response power spectrum corresponding to different moving loads; (2) converting the bridge displacement response power spectrum into a color picture, taking the color picture and the corresponding moving load as the input and output of an AlexNet model respectively, and constructing a sample database; (3) training the mapping relationship between the color picture and the moving load by using the AlexNet model; and (4) identifying the moving load from the measured bridge displacement response power spectrum by using the trained mapping relationship. The application adopts a new bridge moving load identification method, considers the interference of random road excitation, directly identifies the moving load through the bridge displacement response power spectrum, is more in line with engineering practice, effectively solves the moving load identification under the influence of random road excitation, and provides support for efficient and accurate identification of the bridge moving load.

Description

Technical Field

[0001] This invention relates to the field of bridges, and more specifically to a method for identifying bridge moving loads based on displacement response power spectrum. Background Technology

[0002] Moving loads, as the primary external excitation for bridges, play a crucial role in many load combinations. Due to the dynamic effects of moving loads, bridges are prone to fatigue damage and even collapse. Therefore, accurate identification of moving loads is of great significance in preventing catastrophic events and can provide a reference for bridge design, monitoring, and evaluation.

[0003] Currently, moving load identification methods can be divided into two categories: direct methods and indirect methods. Direct methods acquire vehicle weight through force sensors installed under the road surface, i.e., bridge dynamic weighing systems. While this system provides a direct measurement method, its expensive hardware and cumbersome maintenance limit its widespread application.

[0004] Indirect methods identify vehicle loads from the dynamic response of the vehicle-axle coupling system without the need for expensive hardware, making them more promising for application.

[0005] Typically, indirect methods primarily utilize machine learning algorithms. By establishing a mapping relationship between input and output beforehand—that is, between the structural response and the moving load matching the structural response—the corresponding vehicle load can be identified from the measured structural response. However, indirect methods generally use response time series as input, failing to consider the randomness of the structural response caused by random road surface excitation. This does not match the actual service environment of bridges, leading to unreasonable identification results.

[0006] In summary, how to identify moving loads under random road surface excitation disturbances has become an urgent problem for those skilled in the art. Summary of the Invention

[0007] In view of the shortcomings of the prior art, the actual problem solved by the present invention is: how to identify bridge moving loads under random excitation disturbances on the road surface.

[0008] To solve the above-mentioned technical problems, the present invention adopts the following technical solution:

[0009] Includes the following steps:

[0010] S1. Obtain the bridge displacement response power spectrum corresponding to different moving loads;

[0011] S2. Convert the bridge displacement response power spectrum into a color image, use the color image as the input of the AlexNet model, and use the corresponding moving load as the output of the AlexNet model to establish a sample database of the correspondence between the bridge displacement response power spectrum and the moving load.

[0012] S3. Use the AlexNet model to train the mapping relationship between color images and moving loads;

[0013] S4. Identify moving loads from the measured bridge displacement response power spectrum using the trained mapping relationship.

[0014] Preferably, step S1 includes:

[0015] S101. Establish the vehicle-bridge coupled dynamic equations considering the random excitation effect of the road surface:

[0016] S102. Divide the vehicles into five levels according to their weight variation range, and randomly generate n vehicle weight samples in each level, for a total of 5n vehicle weight samples. in, Let represent the vehicle weight of the h-th sample, where h∈{1,2,...,5n};

[0017] S103, Regarding vehicle weight Randomly generate the power spectral density of road surface roughness for the h-th vehicle weight sample. in, Let ω represent the weight of the vehicle in the h-th sample, where h∈{1,2,...,5n}. j This represents the frequency corresponding to the j-th spectral line within the first three natural frequencies of the bridge, where j∈{1,2,...,M} and M is the number of spectral lines within the first three natural frequencies of the bridge.

[0018] S104. For each randomly generated road surface roughness power spectral density obtained in step S103... Substitute these values ​​into the vehicle-bridge coupled dynamics equations in step S101, and solve the vehicle-bridge coupled dynamics equations using the Newmark-β method to obtain the bridge displacement response power spectrum for the h-th vehicle weight sample.

[0019] S105. Repeat steps S103 and S104 multiple times to obtain the weights of different vehicles. Corresponding bridge displacement response power spectrum Where h∈{1,2,...,5n}, ω j This represents the frequency corresponding to the j-th spectral line within the first three natural frequencies of the bridge, where j∈{1,2,...,M} and M is the number of spectral lines within the first three natural frequencies of the bridge.

[0020] Preferably, the vehicle-bridge coupled dynamic equation considering the random excitation effect of the road surface in step S101 is:

[0021]

[0022] in, C vb =c v ·N b ,

[0023]

[0024]

[0025]

[0026] In the formula, M b The mass matrix representing the bridge, C b The damping matrix of the bridge, K b The stiffness matrix of the bridge; m v c represents the mass of the vehicle. v k represents the vehicle's damping. v Represents the spring stiffness of a vehicle; y b Represents the displacement response of the bridge. For y b The first derivative, For y b The second derivative; y v Represents the vehicle's displacement response. For y v The first derivative, For y v The second derivative; N b The shape function representing the bridge, For N b The first derivative; C bb C vb and C bv Both represent the additional damping term generated by vehicle-axle coupling; K bb K bc K bv and K vb Both represent the additional stiffness term resulting from vehicle-axle coupling; F R F represents the random excitation caused by road surface unevenness; G S represents vehicle load excitation; rr (ω) represents the power spectral density of road surface roughness; ω represents the frequency; F G Represents vehicle weight; superscript T represents matrix transpose; i represents imaginary unit; t represents time;

[0027] Preferably, the power spectral density of road surface roughness for the h-th vehicle weight sample in step S103 is... Randomly generated according to the following formula:

[0028]

[0029] In the formula, h∈{1,2,...,5n}; ω j ωj represents the frequency corresponding to the j-th spectral line within the first three natural frequencies of the bridge, where j∈{1,2,...,M}, and M represents the number of spectral lines within the first three natural frequencies of the bridge; ω0 represents the standard frequency, in units of (cycle / s), and ω0=0.16·v, where v represents the uniform speed of the vehicle; S rr (ω0) represents the power spectral density of road surface roughness at the standard frequency, ranging from 2 to 512 (unit: 10). -6 m 2 / (cycle / s)).

[0030] Preferably, step S2 includes:

[0031] S201. Assemble the bridge displacement response power spectrum for each vehicle weight into a global matrix using the following formula.

[0032] In the formula, M represents the number of spectral lines within the first three natural frequencies of the bridge, h represents the h-th vehicle weight sample, and h∈{1,2,...,5n};

[0033] S202. Calculate the modulus, real part, and imaginary part of the above global matrix, and use them as the R, G, and B channels of the pixel matrix, respectively, to generate the color image P of the h-th vehicle weight sample. h Where h∈{1,2,...,5n};

[0034] S203, P each color image h and the corresponding vehicle weight Using these as inputs and outputs to construct a sample database of size 5n, the database is divided into training, validation, and test sets in an 8:1:1 ratio.

[0035] Preferably, step S3 includes:

[0036] S301. Use the pre-trained AlexNet model to extract shallow features from the training set. Based on the number of samples in the training set, computer hardware performance, and network depth, select 9 layers for retraining.

[0037] S302. Based on the five levels of output requirements described in step S102, redesign the structure of the fully connected layer as AveragePooling2D+Dense+Dense.

[0038] S303. The AlexNet model is trained using a deep learning platform. The hyperparameters during training are set as follows: Learning Rate is 0.0001, Momentum is 0.9, the loss function is cross-entropy, Batch Size is 32, and Epoch is 100.

[0039] S304. The trained AlexNet model is validated using a validation set. After validation, the mapping relationship between color images and vehicle weight is obtained.

[0040] Preferably, the AlexNet model in step S301 is pre-trained on the ImageNet dataset.

[0041] Preferably, the deep learning platform mentioned in step S303 is the Keras deep learning platform.

[0042] The present invention has the following beneficial effects:

[0043] 1. The present invention discloses a bridge moving load identification method based on displacement response power spectrum, which takes into account the interference of random road surface excitation. It can directly identify moving loads through bridge displacement response power spectrum using trained mapping relationship, which is more in line with engineering practice and effectively solves the problem of moving load identification under the influence of random road surface excitation, providing support for efficient and accurate identification of bridge moving loads.

[0044] 2. The method disclosed in this invention does not require expensive hardware facilities or cumbersome post-maintenance work, and has broad application prospects. Attached Figure Description

[0045] To make the objectives, technical solutions, and advantages of the invention clearer, the invention will now be described in further detail with reference to the accompanying drawings, wherein:

[0046] Figure 1 This is a flowchart of a bridge moving load identification method based on displacement response power spectrum according to the present invention;

[0047] Figure 2 This is a schematic diagram of a simply supported beam structure monitoring system used for identifying moving loads in an embodiment of the present invention.

[0048] Figure 3 This is a power spectral density curve of displacement response under five vehicle weight categories at measurement point 1 in an embodiment of the present invention;

[0049] Figure 4 These are color images of the displacement response power spectral density of five vehicle weight categories at measurement point 1 in this embodiment of the invention.

[0050] Figure 5 This is the accuracy curve of the training set in an embodiment of the present invention;

[0051] Figure 6 The loss function curve of the training set in this embodiment of the invention;

[0052] Figure 7 This is the accuracy curve of the validation set in the embodiments of the present invention;

[0053] Figure 8 The loss function curves for the validation set in this embodiment of the invention;

[0054] Figure 9 This is the confusion matrix of the recognition results of the test set in the embodiments of the present invention. Detailed Implementation

[0055] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0056] The problem that this invention actually solves is: how to identify bridge moving loads under random road surface excitation disturbances.

[0057] like Figure 1 As shown, this invention discloses a method for identifying bridge moving loads based on displacement response power spectrum, comprising the following steps:

[0058] S1. Obtain the bridge displacement response power spectrum corresponding to different moving loads;

[0059] S2. Convert the bridge displacement response power spectrum into a color image, use the color image as the input of the AlexNet model, and use the corresponding moving load as the output of the AlexNet model to establish a sample database of the correspondence between the bridge displacement response power spectrum and the moving load.

[0060] S3. Use the AlexNet model to train the mapping relationship between color images and moving loads;

[0061] S4. Identify moving loads from the measured bridge displacement response power spectrum using the trained mapping relationship.

[0062] Compared with existing technologies, the bridge moving load identification method based on displacement response power spectrum disclosed in this invention takes into account the interference of random road surface excitation. It can directly identify moving loads through bridge displacement response power spectrum using trained mapping relationships, which is more in line with engineering practice and effectively solves the problem of moving load identification under the influence of random road surface excitation. This provides support for the efficient and accurate identification of bridge moving loads. Moreover, the method disclosed in this invention does not require expensive hardware facilities and cumbersome post-maintenance work, and has broad application prospects.

[0063] In specific implementation, step S1 includes:

[0064] S101. Establish the vehicle-bridge coupled dynamic equations considering the random excitation effect of the road surface:

[0065]

[0066] in, C vb =c v ·N b ,

[0067]

[0068]

[0069]

[0070] In the formula, M b The mass matrix representing the bridge, C b The damping matrix of the bridge, K b The stiffness matrix of the bridge; m v c represents the mass of the vehicle. v k represents the vehicle's damping. v Represents the spring stiffness of a vehicle; y b Represents the displacement response of the bridge. For y b The first derivative, For y b The second derivative; y v Represents the vehicle's displacement response. For y v The first derivative, For y v The second derivative; N b The shape function representing the bridge, For N b The first derivative; C bb C vb and C bv Both represent the additional damping term generated by vehicle-axle coupling; Kbb K bc K bv and K vb Both represent the additional stiffness term resulting from vehicle-axle coupling; F R F represents the random excitation caused by road surface unevenness; G S represents vehicle load excitation; rr (ω) represents the power spectral density of road surface roughness; ω represents the frequency; F G Represents vehicle weight; superscript T represents matrix transpose; i represents imaginary unit; t represents time;

[0071] S102. Divide the vehicles into five levels according to their weight variation range, and randomly generate n vehicle weight samples in each level, for a total of 5n vehicle weight samples. in, Let represent the vehicle weight of the h-th sample, where h∈{1,2,...,5n};

[0072] S103, Regarding vehicle weight Randomly generate the power spectral density of road surface roughness for the h-th vehicle weight sample. in, Let ω represent the weight of the vehicle in the h-th sample, where h∈{1,2,...,5n}. j This represents the frequency corresponding to the j-th spectral line within the first three natural frequencies of the bridge, where j∈{1,2,...,M} and M is the number of spectral lines within the first three natural frequencies of the bridge.

[0073] The power spectral density of road surface unevenness for the h-th vehicle weight sample Randomly generated according to the following formula:

[0074]

[0075] In the formula, h∈{1,2,...,5n}; ω j ωj represents the frequency corresponding to the j-th spectral line within the first three natural frequencies of the bridge, where j∈{1,2,...,M}, and M represents the number of spectral lines within the first three natural frequencies of the bridge; ω0 represents the standard frequency, in units of (cycle / s), and ω0=0.16·v, where v represents the uniform speed of the vehicle; S rr (ω0) represents the power spectral density of road surface roughness at the standard frequency, ranging from 2 to 512 (unit: 10). -6 m 2 / (cycle / s)).

[0076] S104. For each randomly generated road surface roughness power spectral density obtained in step S103... Substitute these values ​​into the vehicle-bridge coupled dynamics equations in step S101, and solve the vehicle-bridge coupled dynamics equations using the Newmark-β method to obtain the bridge displacement response power spectrum for the h-th vehicle weight sample.

[0077] S105. Repeat steps S103 and S104 multiple times to obtain the weights of different vehicles. Corresponding bridge displacement response power spectrum Where h∈{1,2,...,5n}, ω j This represents the frequency corresponding to the j-th spectral line within the first three natural frequencies of the bridge, where j∈{1,2,...,M} and M is the number of spectral lines within the first three natural frequencies of the bridge.

[0078] In specific implementation, step S2 includes:

[0079] S201. Assemble the bridge displacement response power spectrum for each vehicle weight into a global matrix using the following formula.

[0080] In the formula, M represents the number of spectral lines within the first three natural frequencies of the bridge, h represents the h-th vehicle weight sample, and h∈{1,2,...,5n};

[0081] S202. Calculate the modulus, real part, and imaginary part of the above global matrix, and use them as the R, G, and B channels of the pixel matrix, respectively, to generate the color image P of the h-th vehicle weight sample. h Where h∈{1,2,...,5n};

[0082] S203, P each color image h and the corresponding vehicle weight Using these as inputs and outputs to construct a sample database of size 5n, the database is divided into training, validation, and test sets in an 8:1:1 ratio.

[0083] In specific implementation, step S3 includes:

[0084] S301. The AlexNet model pre-trained on the ImageNet dataset will be used to extract shallow features from the training set. The number of layers to be retrained is selected as 9 based on the number of samples in the training set, the performance of the computer hardware, and the depth of the network.

[0085] S302. Based on the five levels of output requirements described in step S102, the structure of the fully connected layer is redesigned as AveragePooling2D+Dense+Dense. The purpose of redesigning the fully connected layer is to adapt to the output requirements of the vehicle load recognition task and accelerate the training speed.

[0086] S303. The AlexNet model was trained using the Keras deep learning platform. The hyperparameters during training were set as follows: Learning Rate was 0.0001, Momentum was 0.9, the loss function was cross-entropy, Batch Size was 32, and Epoch was 100.

[0087] S304. The trained AlexNet model is validated using a validation set. After validation, the mapping relationship between color images and vehicle weight is obtained.

[0088] Example

[0089] To further describe in detail the bridge moving load identification method based on displacement response power spectrum of the present invention, Figure 2 Taking the simply supported beam shown as an example, we will perform specific moving load identification operations and result verification on the bridge deck, such as... Figure 2 As shown, the bridge used in this embodiment is a 50m span prestressed concrete simply supported box girder bridge, with four measuring points arranged longitudinally along the beam (numbered 1 to 4 from left to right). The concrete specification is C50, and the elastic modulus is 3.45 × 10⁻⁶. 4 MPa, Poisson's ratio is 0.2, and mass density is 2650 kg / m³ 3 The prestressed steel strands have a tensile strength standard value of 1860 MPa and an elastic modulus of 1.95 × 10⁻⁶ MPa. 5 MPa, high-strength low-relaxation steel strand with a nominal diameter of 15.2 mm.

[0090] The bridge moving load identification in this embodiment adopts the following steps:

[0091] S1. Obtain the bridge displacement response power spectrum corresponding to different moving loads;

[0092] Specifically, a finite element model of the bridge was established using ANSYS, with an element length set to 0.5m. To prevent the structural response from tending to infinity at the resonant frequency, a constant damping ratio of 0.05 was set. The finite element model calculation results showed that the first three natural frequencies of the simply supported beam bridge were 2.76Hz, 10.57Hz, and 22.26Hz. Based on the finite element model, the mass matrix M of the bridge was extracted. b Damping matrix C b Stiffness matrix Kb The vehicle is a single-degree-of-freedom unicycle model. The unicycle travels at a constant speed of v = 10 m / s on a bridge, with a spring stiffness k. v =190kN / m, damping is c v = 5kN·s / m.

[0093] Vehicle weights were pre-classified into five levels (Level A, Level B, Level C, Level D, and Level E), with Levels A through E representing the change from small vehicles to heavy vehicles, as shown in Table 1. Within each level, n = 100 vehicle weight data points were randomly generated, resulting in a total of 500 vehicle weight samples.

[0094] Table 1 Vehicle Weight Classification

[0095]

[0096] There are M=81 spectral lines in the first three natural frequencies of the bridge. Based on the 81 spectral lines and the five levels of vehicle weight, 81 sets of power spectral density values ​​of road surface roughness are randomly generated. The vehicle-bridge coupled dynamic equation is solved using the Newmark-β method to obtain the power spectrum of bridge displacement response.

[0097] Figure 3 The displacement response power spectral density at measuring point 1 is shown for five vehicle weight categories. From Figure 3 As can be seen, there are significant differences among these power spectral densities, indicating that the bridge displacement response power spectrum calculated through the above steps can serve as effective information for identifying moving loads on bridges.

[0098] S2. Convert the bridge displacement response power spectrum into a color image, use the color image as the input of the AlexNet model, and use the corresponding moving load as the output of the AlexNet model to establish a sample database of the correspondence between the bridge displacement response power spectrum and the moving load.

[0099] In specific implementation, step S2 includes:

[0100] S201. Assemble the bridge displacement response power spectrum for each vehicle weight into a global matrix using the following formula.

[0101] In the formula, M represents the number of spectral lines in the first three natural frequencies of the bridge, and M is 81; h represents the h-th vehicle weight sample, and h∈{1,2,...,500}.

[0102] S202. Calculate the modulus, real part, and imaginary part of the above global matrix, and use them as the R, G, and B channels of the pixel matrix, respectively, to generate the color image P of the h-th vehicle weight sample.h Where h∈{1,2,...,500};

[0103] S203, P each color image h and the corresponding vehicle weight Using these as input and output terms for the AlexNet model, a sample database of 500 samples was constructed, and the sample database was divided into training, validation, and test sets in an 8:1:1 ratio.

[0104] The power spectrum conversion result of bridge displacement response is as follows: Figure 4 As shown, Figure 4 Color images of five different vehicle weight categories were randomly displayed. From Figure 4 Significant differences can be observed, indicating that the AlexNet model can achieve accurate identification results for bridge moving loads.

[0105] S3. Use the AlexNet model to train the mapping relationship between color images and moving loads;

[0106] In specific implementation, step S3 includes:

[0107] S301. The AlexNet model pre-trained on the ImageNet dataset will be used to extract shallow features from the training set. The number of layers to be retrained is selected as 9 based on the number of samples in the training set, the performance of the computer hardware, and the depth of the network.

[0108] S302. Based on the five levels of output requirements described in step S1, redesign the structure of the fully connected layer as AveragePooling2D+Dense+Dense.

[0109] S303. The AlexNet model was trained using the Keras deep learning platform. The hyperparameters during training were set as follows: Learning Rate was 0.0001, Momentum was 0.9, the loss function was cross-entropy, Batch Size was 32, and Epoch was 100.

[0110] S304. The trained AlexNet model is validated using a validation set. After validation, the mapping relationship between color images and vehicle weight is obtained.

[0111] S4. Identify moving loads from the measured bridge displacement response power spectrum using the trained mapping relationship.

[0112] To verify the effectiveness and generalization ability of this invention, vehicle weight identification was performed using test set samples. The confusion matrix of the identification results is as follows: Figure 9 As shown. From Figure 9 As can be seen from the above, the test accuracy using the method disclosed in this invention reaches 98%, and it can effectively identify bridge moving loads under random excitation interference on the road surface.

[0113] To verify the effectiveness of this invention, the training and validation results of the method of this invention were compared with those of the VGG16 model, InceptionV3 model, and ResNet50 model. The results are as follows: Figures 5 to 8 As shown in Table 2, the accuracy, loss value, and total training time of each model after 100 training iterations are as follows.

[0114] Table 2 shows the accuracy, loss value, and total training time of each model after 100 training iterations.

[0115]

[0116] After the Figures 5 to 8 Based on a careful analysis of Table 2, the following conclusion can be drawn: the AlexNet model disclosed in this invention performs better than other models in identifying bridge moving loads.

[0117] Specifically, from Figures 5 to 8 As can be seen from the data, the AlexNet model shows the fastest and most stable increase in accuracy on both the training and validation sets, followed by the InceptionV3 and VGG16 models, while the ResNet50 model shows the slowest increase and the largest fluctuations. Similarly, the loss values ​​on the training and validation sets also exhibit the same pattern: the AlexNet model decreases the fastest, followed by the InceptionV3 and VGG16 models, and the ResNet50 model decreases the slowest. Furthermore, as shown in Table 2, after 100 training iterations, although the AlexNet model ranks second in training and validation set accuracy, its total training time is only 1 / 8 of that of the VGG16 model, 1 / 5 of that of the ResNet50 model, and 1 / 4 of that of the InceptionV3 model.

[0118] The above comparison results show that, considering the data characteristics and scale of this embodiment, the performance of the AlexNet model disclosed in this invention in identifying bridge moving loads surpasses that of several other models.

[0119] In summary, the bridge moving load identification method based on displacement response power spectrum disclosed in this invention takes into account the interference of random road surface excitation. It can directly identify moving loads through the bridge displacement response power spectrum using trained mapping relationships, which is more in line with engineering practice and effectively solves the problem of moving load identification under the influence of random road surface excitation. This provides support for the efficient and accurate identification of bridge moving loads. Moreover, the method disclosed in this invention does not require expensive hardware facilities or cumbersome post-maintenance work, and has broad application prospects.

[0120] It is understood that the present invention has been described through some embodiments, and those skilled in the art will recognize that various changes or equivalent substitutions can be made to these features and embodiments without departing from the spirit and scope of the invention. Under the teachings of the present invention, modifications can be made to these features and embodiments to adapt to specific situations and materials without departing from the spirit and scope of the invention. The embodiments described in this invention are only a part of the embodiments of the invention, not all of them. The components of the embodiments of the invention described and shown in the accompanying drawings can generally be arranged and designed in various different configurations. Therefore, the following detailed description of the embodiments of the invention provided in the accompanying drawings is not intended to limit the scope of the claimed invention, but merely to illustrate selected embodiments of the invention. Therefore, the invention is not limited to the specific embodiments disclosed herein, and all other embodiments obtained by those skilled in the art based on the embodiments of the invention without inventive effort are within the scope of protection of the present invention.

Claims

1. A bridge moving load identification method based on displacement response power spectrum, characterized by, The method comprises the following steps: S1, acquiring bridge displacement response power spectrum corresponding to different moving loads; step S1 comprises: S101, establishing a vehicle-bridge coupling dynamics equation considering random excitation of the pavement; wherein the vehicle-bridge coupling dynamics equation considering random excitation of the pavement is: wherein , , ; ， ， ， ； ； ； wherein M represents a mass matrix of the bridge, C represents a damping matrix of the bridge, K represents a stiffness matrix of the bridge; m represents a mass of the vehicle, c represents a damping of the vehicle, k represents a spring stiffness of the vehicle; y represents a displacement response of the bridge, is a first derivative of , is a second derivative of ; y represents a displacement response of the vehicle, is a first derivative of , is a second derivative of ; φ represents a shape function of the bridge, is a first derivative of ; , and all represent additional damping terms due to vehicle-bridge coupling; , , and all represent additional stiffness terms due to vehicle-bridge coupling; w represents a random excitation due to road roughness; f represents a vehicle load excitation; S represents a road roughness power spectral density; ω represents a frequency; m represents a vehicle weight; superscript T represents matrix transpose; i represents an imaginary unit; t represents time; S102. Divide the vehicles into five levels according to their weight variation range, and randomly generate n vehicle weight samples in each level, for a total of 5n vehicle weight samples. ,in, Let represent the vehicle weight of the h-th sample, where h∈{1, 2,... , 5n}; S103, Regarding vehicle weight Randomly generate the power spectral density of road surface roughness for the h-th vehicle weight sample. ,in, Let represent the vehicle weight of the h-th sample, where h ∈ {1, 2, ..., 5n}. The frequency corresponding to the j-th spectral line within the first three natural frequencies of the bridge, where j∈{1, 2, ..., M}, and M is the number of spectral lines within the first three natural frequencies of the bridge; the power spectral density of the road surface roughness of the h-th vehicle weight sample. Randomly generated according to the following formula: ； wherein h e {1, 2,..., 5n}; represents the frequency corresponding to the jth spectral line within the first three natural frequencies of the bridge, and j e {1, 2,..., M}, M represents the number of spectral lines within the first three natural frequencies of the bridge; represents the standard frequency, with the unit of (cycle / s), and wherein, represents the uniform driving speed of the vehicle; represents the power spectral density of the road roughness at the standard frequency, with the value range of 2~512 (unit: 10 -6 m 2 / (cycle / s)); S104, for each randomly generated road roughness power spectrum density obtained in step S103 are substituted into the vehicle-bridge coupling dynamics equation in step S101 respectively, and the Newmark-β method is used to solve the vehicle-bridge coupling dynamics equation to obtain the bridge displacement response power spectrum of the hth vehicle weight sample ; S105, repeatedly steps S103 and S104 to obtain different vehicle weights Corresponding bridge displacement response power spectrum ; wherein h ∈ {1, 2,..., 5n}, represent the frequency corresponding to the jth spectral line within the first three natural frequencies of the bridge, and j ∈ {1, 2,..., M}, M is the number of spectral lines within the first three natural frequencies of the bridge; S2, converting the bridge displacement response power spectrum into a color picture, taking the color picture as an input item of an AlexNet model, taking the corresponding moving load as an output item of the AlexNet model, and establishing a sample database of the corresponding relationship between the bridge displacement response power spectrum and the moving load; S3, training a mapping relationship between the color picture and the moving load by using the AlexNet model; S4, identifying the moving load from the measured bridge displacement response power spectrum by using the trained mapping relationship.

2. The bridge moving load identification method based on displacement response power spectrum according to claim 1, wherein, Step S2 comprises: S201, assemble the bridge displacement response power spectrum under each vehicle weight into a global matrix : wherein M represents the number of spectral lines within the first three natural frequencies of the bridge, h represents the hth vehicle weight sample, and h e {1, 2,..., 5n}. S202. Calculate the modulus, real part, and imaginary part of the above global matrix, and use them as the R, G, and B channels of the pixel matrix, respectively, to generate the color image P of the h-th vehicle weight sample. h Where h∈{1, 2, ... , 5n}; S203, P each color image h and the corresponding vehicle weight Using these as inputs and outputs to construct a sample database of size 5n, the database is divided into training, validation, and test sets in an 8:1:1 ratio.

3. The bridge moving load identification method based on displacement response power spectrum according to claim 1, characterized in that, Step S3 comprises: S301, using the pre-trained AlexNet model to extract shallow features of the training set, and comprehensively selecting the number of layers for retraining as 9 according to the sample number of the training set, the computer hardware performance and the network depth; S302, redesigning the structure of the fully connected layer as AveragePooling2D + Dense + Dense according to the output requirements of the five levels in step S102; S303, training the AlexNet model by using a deep learning platform, and the hyperparameter settings of the training process are as follows: the Learning Rate is 0.0001, the Momentum is 0.9, the loss function is selected as a cross-entropy function, the Batch Size is 32, and the Epoch is 100; S304, verifying the trained AlexNet model by using a verification set, and obtaining the mapping relationship between the color picture and the vehicle weight after verification.

4. The bridge moving load identification method based on displacement response power spectrum according to claim 3, characterized in that, The AlexNet model in step S301 is pre-trained on an ImageNet data set.

5. The bridge moving load identification method based on displacement response power spectrum according to claim 3, characterized in that, The deep learning platform in step S303 is a Keras deep learning platform.

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