Bridge finite element model correction method based on BP neural network

Abstract

The application discloses a bridge finite element model correction method based on a BP neural network, belongs to the technical field of finite element model correction, and comprises the steps of establishing a target function, selecting correction parameters and the like. The application adopts the BP neural network to correct the bridge finite element model, can avoid constructing a complex function expression, can quickly and effectively realize strain influence line error target minimization optimization through the construction of a two-layer feedforward neural network with a back propagation algorithm, more comprehensively evaluates model errors before and after correction, more completely reflects bridge mechanical characteristics, and can reduce the relative error of initial model calculation to below 10% from 38%.

Description

Technical Field

[0001] This invention relates to the field of finite element model correction technology, specifically to a method for correcting a bridge finite element model based on a BP neural network. Background Technology

[0002] Thanks to the continuous development of computer hardware and software, finite element modeling has gradually become a routine method for engineering structural analysis. However, even for ideal engineering structures, there are still significant deviations between the initial design model and existing actual projects. Finite element modeling rarely considers the discreteness of engineering materials, the fuzziness of construction errors, and the randomness of cross-sectional dimensions. This leads to the inaccuracy of previous models based solely on the geometric dimensions and material parameters of the engineering structure design, thus giving rise to the theory of finite element model correction. Therefore, this paper proposes a bridge finite element model correction method based on a backpropagation neural network. Summary of the Invention

[0003] The technical problem to be solved by this invention is: how to use the error between theoretical calculation and experimental results as the objective function to adjust and correct the physical parameters of the model multiple times in order to reduce the analytical deviation between the numerical model and the real structure. This invention provides a bridge finite element model correction method based on BP neural network. This method uses a well-trained BP neural network to predict the model structural parameters of the bridge under the measured strain influence line, and then optimizes the finite element model to make its cross-sectional stiffness and boundary characteristics more closely approximate the real bridge structure.

[0004] The present invention solves the above-mentioned technical problems through the following technical solution, and the present invention includes the following steps:

[0005] S1: Establish the objective function and select the correction parameters;

[0006] S2: Conduct bridge strain influence line tests, extract measured strain influence lines, and simultaneously establish an initial finite element model to extract calculated strain influence lines;

[0007] S3: Establish a BP neural network and use the trained BP neural network to correct the initial finite element model.

[0008] Furthermore, in step S1, the objective function corrects the finite element model by reducing the error between the measured strain influence line and the calculated strain influence line extracted by the finite element model.

[0009] Furthermore, in step S1, absolute error, percentage error, correlation coefficient, and relative error are selected to quantify the degree of agreement between the finite element model and the actual bridge structure. The specific calculation formulas are as follows:

[0010] Absolute error: ∑|ε a -ε m |;

[0011] Percentage error: ∑(ε) a -ε m ) 2 / ∑(ε m ) 2 ;

[0012] Relative error: ∑|ε a -ε m | / ∑|ε m |;

[0013] Correlation coefficient:

[0014] Where, ε a This indicates the calculated strain value along the influence line; ε m This represents the measured strain value of the influence line.

[0015] Furthermore, in step S1, the correction parameters include the elastic modulus E of the longitudinal main beam, the thickness T1 of the top plate, the thickness T2 of the bottom plate, and the thickness Tw of the web plate.

[0016] Furthermore, in step S2, the specific process of extracting the measured strain influence line is as follows:

[0017] S201: Define the test conditions and arrange the measuring points according to the actual bridge structure;

[0018] S202: Using a test loading vehicle, the strain influence line of the measuring point under a predetermined test load is tested;

[0019] S203: Extract the strain time history response of the bridge measuring points, use the vehicle information matrix of the structural test to remove the multi-axis effect of the vehicle, and then restore the bridge strain time history response to the bridge strain influence line under the unit concentrated load, that is, the measured strain influence line.

[0020] Furthermore, in step S2, the specific process for extracting and calculating the strain influence line is as follows:

[0021] S211: Based on the bridge structural dimensional information obtained from the design drawings and on-site conditions, establish an initial finite element model;

[0022] S212: Use strain influence line loading to define moving load analysis case;

[0023] S213: Apply a unit concentrated load to simulate strain influence lines and extract the calculated strain influence lines of the initial finite element model.

[0024] Furthermore, in step S3, the BP neural network is a multi-layer feedforward neural network based on the backpropagation algorithm, wherein the hidden layer node expressions are as follows:

[0025]

[0026] In the formula, y i For hidden layers; x j For the input layer; w ij θ represents the weights of the first layer network. i The threshold value for the first layer of the network;

[0027] The output layer node expression is as follows:

[0028]

[0029] In the formula, O l For output layer; T li The weights of the second-layer network; θ l The threshold for the second layer network;

[0030] Substitute the output value and the true sample value into the error formula:

[0031]

[0032] In the formula, t l Given the true values ​​of the samples, the weights T of the second-layer network are calculated using the error formula. li Expanding and differentiating, we get:

[0033]

[0034] Since E consists of multiple O k The functions, each O k If they are mutually independent, then:

[0035]

[0036]

[0037] Therefore, we get:

[0038]

[0039] Let the node error of the BP neural network be:

[0040] δ l =-(t) l -O l )×f'(net l )

[0041] The hidden layer expression is then obtained as follows:

[0042]

[0043] Similarly, the input layer expression can be obtained as follows:

[0044]

[0045] Due to the weight correction value ΔT li and Δw ij Proportional to the error function as it descends along the gradient, we obtain the following relationship:

[0046]

[0047]

[0048] Similarly, the correction values ​​Δθ for the thresholds of the first and second layers of the network can be obtained. i , Δθ l for:

[0049]

[0050]

[0051] Furthermore, in step S3, in the BP neural network, five shape control points in the strain influence line are selected as input layer parameters, and the input layer is set with five nodes. The five shape control points include three mid-span points and two mid-span 1 / 4 points. The output layer parameters are set with four nodes according to the definition of the correction parameters. The number of hidden layer nodes is calculated according to the following formula:

[0052]

[0053] In the formula, P is the number of hidden layer nodes, which is 12; m is the number of input layer nodes; n is the number of output layer nodes; and a is a constant in the interval [1, 10].

[0054] Furthermore, in step S3, the specific process of correcting the initial finite element model is as follows:

[0055] S301: Establish a BP neural network, import sample data into the established BP neural network, and train, verify and test the BP neural network.

[0056] S302: After the BP neural network has been trained and meets the computational error requirements, save the trained BP neural network.

[0057] S303: Extract 5 shape control points from the measured strain influence line of the bridge and import them as input parameters into the trained BP neural network;

[0058] S304: Input the correction parameters predicted by the trained BP neural network into the initial finite element model to correct the finite element model.

[0059] Compared with the prior art, the present invention has the following advantages: the bridge finite element model correction method based on BP neural network uses BP neural network to correct the bridge finite element model, which can avoid the construction of complex function expressions; and by constructing a two-layer feedforward neural network with backpropagation algorithm, it can quickly and effectively achieve the optimization of the strain influence line error target, more comprehensively evaluate the model error before and after correction, and more completely reflect the mechanical characteristics of the bridge, which can reduce the relative error of the initial model calculation from 38% to less than 10%. Attached Figure Description

[0060] Figure 1 This is a technical roadmap of the bridge finite element model correction method based on BP neural network in Embodiment 1 of the present invention;

[0061] Figure 2 This is a schematic diagram of a simply supported beam model with rotational elastic constraints at both ends in Embodiment 2 of the present invention;

[0062] Figure 3a This is a diagram showing the bridge dimensions (unit: mm) in Embodiment 2 of the present invention.

[0063] Figure 3b This is a cross-sectional view of the bridge in Embodiment 2 of the present invention (unit: mm);

[0064] Figure 4 This is a diagram of the measuring point layout in Embodiment 2 of the present invention (unit: mm);

[0065] Figure 5 This is the influence line of the measured strain of the bridge in Embodiment 2 of the present invention;

[0066] Figure 6 This refers to the strain influence line calculated in the bridge model of Embodiment 2 of the present invention;

[0067] Figure 7 This is a comparison diagram of the strain influence lines of the uncorrected model in Embodiment 2 of the present invention;

[0068] Figure 8 This is the BP neural network topology diagram in Embodiment 2 of the present invention;

[0069] Figure 9 This is a graph showing the relationship between the number of iterations and the mean square error in Embodiment 2 of the present invention;

[0070] Figure 10 This is a comparison diagram of the strain influence lines of the corrected model in Embodiment 2 of the present invention;

[0071] Figure 11 This is a comparison diagram of the relative error of the strain influence lines between the uncorrected model (initial model) and the corrected model (optimized model) in Embodiment 2 of the present invention. Detailed Implementation

[0072] The embodiments of the present invention are described in detail below. These embodiments are implemented based on the technical solution of the present invention, and provide detailed implementation methods and specific operation processes. However, the scope of protection of the present invention is not limited to the following embodiments.

[0073] Example 1

[0074] This embodiment provides a technical solution: a bridge finite element model correction method based on a BP neural network. This method selects the strain influence line of a continuous beam bridge as the target parameter, constructs a two-layer feedforward neural network using MATLAB, establishes a finite element model, and generates 30 sample data points to train the BP neural network. The well-trained neural network predicts the model's structural parameters under the measured strain influence line, thereby optimizing the finite element model to make its cross-sectional stiffness and boundary properties more closely approximate the real bridge structure. This provides a new approach to correcting finite element model structures. The technical route is as follows: Figure 1 As shown.

[0075] Specifically, the present invention mainly includes the following main steps:

[0076] S1: Establish the objective function and select the correction parameters;

[0077] S2: Testing and identification of bridge strain influence lines;

[0078] S3: Correcting the bridge finite element model based on BP neural network.

[0079] The main technical aspects of this method are explained in detail below:

[0080] (1) Objective function

[0081] The objective function aims to correct the finite element model by reducing the error between the measured strain influence line and the strain influence line extracted from the finite element model. In this invention, absolute error, percentage error, correlation coefficient, and relative error are selected to quantify the degree of agreement between the finite element model and the actual structure. The calculation formulas are shown in Table 1.

[0082] Table 1 Calculation formula for correction parameters

[0083]

[0084] Where, ε a This indicates the calculated strain value along the influence line; ε m This represents the measured strain value of the influence line.

[0085] (2) Correction parameters

[0086] Correction parameters can be divided into matrix parameters and physical parameters. Matrix parameters are the structural mass matrix and stiffness matrix in the finite element model. The correction process can achieve the purpose of model correction by directly correcting the correlation matrix of the results. However, the substructure parameters of this method do not have clear physical meaning, and may even lead to abnormal situations such as negative stiffness parameters. In view of this, this invention selects physical parameters in the finite element model that can describe material properties or geometric properties for correction. Through sensitivity analysis of various parameters of the bridge finite element model, the following four physical parameters are selected for correction: the elastic modulus E of the longitudinal main beam, the thickness T1 of the top plate, the thickness T2 of the bottom plate, and the thickness Tw of the web plate.

[0087] (3) Correction method

[0088] Model correction is a typical inverse nonlinear problem. Finite element model correction achieves the minimization of the objective function by iteratively adjusting the relationship between physical parameters and the correction results. Neural networks simulate the information processing and transmission of the human brain in terms of physical mechanisms, possessing good learning and nonlinear mapping capabilities. Finite element model correction based on BP (BackPropagation) neural networks avoids constructing complex mathematical function expressions. It achieves finite element model correction by constructing a two-layer feedforward neural network with a backpropagation algorithm.

[0089] Example 2

[0090] In this embodiment, taking the elastically supported constrained main beam model as an example, the finite element correction method in Embodiment 1 is further explained. Considering the uncertainty of the bending stiffness of the bridge main beam section, and introducing non-ideal boundaries of vertical elastic supports and rotational elastic constraints at both ends of the main beam, an elastically supported constrained main beam model is constructed to simulate the uncertainty of structural model parameters in existing bridges. Figure 2 As shown.

[0091] The virtual concentrated bending moment M A M B Replace the redundant rotational constraints at both ends and establish the displacement compatibility equations for points A and B:

[0092] M A δ AA +M B δ AB +Δ AP =-(2M) A / h 2 ·K'1) (5)

[0093] M A δ BA +M B δ BB +Δ BP =-(2M)B / h 2 ·K'2) (6)

[0094] In the formula, δij is the compliance coefficient, representing the angle of rotation produced at point i when a unit force is applied at point j; Δ iP K is the free term in the displacement compatibility equation, representing the rotation angle produced at position i under the action of external force P; i For rotational constraint stiffness;

[0095] Calculate δij and Δ using the graphical multiplication method iP Substituting the displacement compatibility equation, compliance coefficient, and free term of the model into equations (5) and (6) above, we can obtain:

[0096]

[0097]

[0098] Among them, the virtual concentrated bending moment M A M B The denominator does not contain the position parameter x' of the moving concentrated force, while the degree of the parameter x' in the numerator is related to Δ. iP Since the internal forces are consistent, substituting the elastic constraint forces, the influence line of the bending moment at any section C is:

[0099]

[0100] In the formula, l is the beam length; c is the distance from point C to the beam end.

[0101] Therefore, further calculations yield the strain influence line at any cross section C as follows:

[0102] ε C (x')=σ C (x') / E C =M C (x') / W C ·E C (9)

[0103] In the formula, σ C The stress influence line at point C; E C Let W be the elastic modulus at any cross section C; C Let C be the section modulus of any cross section.

[0104] As can be seen from the above formula, the strain influence line of a bridge is mainly related to factors such as the structural span, the elastic modulus of the material, the moment of inertia of the cross section, and the boundary constraint stiffness of the bridge. Therefore, using the strain influence line as the target parameter to carry out model correction research can comprehensively consider important modeling information such as the geometric dimensions of the bridge cross section, the structural constraint stiffness, and the elastic modulus of the material, so that the physical meaning of the correction is clear and the correction calculation results are scientific and reliable.

[0105] (1) Project Overview

[0106] Taking a steel plate composite continuous beam bridge as the test object, this study investigates the correction of the bridge's finite element model based on a backpropagation neural network. The bridge structure has a total length of 105m (35m+35m+35m) and a width of 12m, arranged orthogonally. The superstructure consists of a composite beam of I-beams and concrete panels. The main bridge steel structure uses Q345 steel, and the substructure uses circular column piers and C40 sulfur-resistant concrete. The bridge bearings are sliding pendulum bearings. The bridge deck pavement consists of a reinforced waterproof coating, 60mm medium-grained asphalt pavement, and 40mm fine-grained asphalt pavement. The bridge's geometric dimensions are as follows: Figure 3a , 3b As shown.

[0107] (2) Experimental process

[0108] In order to conduct bridge finite element model correction more scientifically and provide reliable data support for the selection of model correction parameters, the main geometric dimensions of the bridge section were verified on-site in conjunction with the design drawings.

[0109] The test loading vehicle was a single two-axle heavy truck with a load capacity of 37 tons. The vehicle moved slowly along the designated loading path on the bridge deck at minimum idle speed, with the loading path 6.375m from the bridge centerline. For the bridge influence line test, surface strain sensors were installed at the mid-span section of the bridge's middle span, at the bottom of the No. 1 main beam. The data acquisition equipment used was a DH3821 strain testing and analysis system. The vehicle moved at minimum idle speed, and the acquisition frequency was set to 2Hz. The strain influence line of the mid-span measuring point (S1) under the predetermined test load was tested. The measuring point layout diagram is shown below. Figure 4 .

[0110] (3) Identification of bridge influence lines

[0111] A loading test was conducted using a single heavy vehicle moving across a three-span steel plate composite continuous beam. The test extracted the mid-span strain time-history response of the bridge. A constructed vehicle information matrix was used to isolate the multi-axis effect of the vehicle, and the bridge strain time-history response was then restored to the bridge strain influence line under a unit concentrated load (1 kN). (See...) Figure 5 .

[0112] Based on the bridge structural dimensions obtained from the design drawings and on-site measurements, an initial finite element model was established. A moving load analysis case was defined using strain influence lines. To accurately align with the measured strain influence lines, a loading step size of 403.846 mm was selected. A total of 261 loading steps were generated for the moving load analysis case. Strain influence line loading was simulated using a unit concentrated load, and the calculated strain influence lines of the bridge model (initial finite element model) were extracted. Figure 6As shown. A comparison of the measured strain influence lines and the calculated strain influence lines is shown in the figure. Figure 7 .

[0113] Depend on Figures 5-7 It is known that the strain influence line at the mid-span of the bridge, measured through the influence line loading test by moving vehicles, conforms to the general law of the theoretical influence line of a three-span continuous beam bridge. The troughs on the left and right sides of the influence line are basically the same, indicating that the overall stiffness distribution of the bridge is uniform, the curve has no obvious abrupt changes, and the bridge structure has no obvious damage. The maximum value of the strain influence line at the mid-span of the bridge structure under unit load is 0.1489με. Under the same loading condition, the maximum value of the strain influence line of the finite element model established solely based on the design information is 0.2270με. It is not difficult to see that the actual bridge structure is safer than the theoretical design model. However, precisely because of the large deviation between the two, further research is needed to revise the initial finite element model.

[0114] (4) Principles and Theory of BP Neural Network

[0115] A BP neural network is a multi-layer feedforward neural network based on the backpropagation algorithm, where the hidden layer node expressions are as follows:

[0116]

[0117] In the formula, y i For hidden layers; x j For the input layer; w ij θ represents the weights of the first layer network. i This is the threshold value for the first layer of the network.

[0118] The output layer node expression is as follows:

[0119]

[0120] In the formula, O l For output layer; T li The weights for the second layer network; θ l This is the threshold for the second layer network.

[0121] Substitute the output value and the true sample value into the error formula:

[0122]

[0123] In the formula, t l Given the true values ​​of the samples, the weights T of the second-layer network are calculated using the error formula. li Expanding and differentiating, we get:

[0124]

[0125] Because E is multiple O k The functions, each O kIf they are mutually independent, then the following exists:

[0126]

[0127]

[0128] By combining equations (15) and (16), equation (14) can be calculated to obtain:

[0129]

[0130] Let the node error of the BP neural network be:

[0131] δ l =-(t) l -O l )×f'(net l (18)

[0132] Substituting equation (18) into equation (17), we obtain the hidden layer expression as follows:

[0133]

[0134] Similarly, the input layer expression can be obtained as:

[0135]

[0136] Due to the weight adjustment value ΔT li and Δw ij Proportional to the error function as it descends along the gradient, hence the following relationship is obtained:

[0137]

[0138]

[0139] Similarly, the correction values ​​Δθ for the thresholds of the first and second layers of the network can be obtained. i , Δθ l for:

[0140]

[0141]

[0142] (5) Neural network topology based on model correction

[0143] The bridge influence line theory is essentially a continuous function curve. Given the discreteness of the observation methods, five shape control points (three mid-span points and two mid-span 1 / 4 points) in the strain influence line are extracted as input layer parameters, and five nodes are set for the input layer. The output layer parameters are set with four nodes according to the definition of the above-mentioned correction parameters.

[0144] Since the input layer parameters and the output layer parameters are not on the same order of magnitude, Min-Max normalization is used to process the data.

[0145]

[0146] In the formula, x j The normalized value of the parameter; x i For parameter values; x max and x min These represent the maximum and minimum values ​​of the parameter, respectively.

[0147] Regarding the number of hidden layer nodes, according to the empirical formula:

[0148]

[0149] In the formula, P is the number of hidden layer nodes, which is 12 in this invention; m is the number of input layer nodes; n is the number of output layer nodes; and a is a constant in the interval [1, 10].

[0150] Based on the determined number of nodes in each layer, a 5-12-4-4 BP neural network topology was constructed for finite element model correction. Feedforward neural networks without feedback were used between neurons. The tansig and pureline functions were used for network node transfer functions. The Levenberg-Marquardt algorithm was used for backpropagation. The BP neural network topology is shown below. Figure 8 .

[0151] The structural parameters of the initial finite element model were randomly scaled 30 times, and the strain influence lines of the bridge under the corresponding structural parameters were extracted (the strain influence lines were calculated). These were used as 30 training samples for the BP neural network, as shown in Table 2. The 30 sample data were then imported into the established BP neural network for training, validation, and testing.

[0152] Table 2 Sample Parameter Table

[0153]

[0154]

[0155]

[0156] Note: p is the sample value; q is the initial value.

[0157] (6) Model correction of network training results

[0158] The results of training a BP neural network (model correction network) and iterating the LM backpropagation algorithm (Levonburg-Marquardt algorithm) multiple times are shown in Table 3. Figure 9As shown in Table 3, the goodness of fit for the training, validation, and test samples all exceeded 0.90, and the overall regression fit evaluation reached over 0.95, indicating that the BP neural network has strong fitting ability and can be used to correct parameters in the prediction model. Figure 9 It is known that the constructed BP neural network underwent 34 iterations. The optimal iteration number was the 28th iteration, at which point the mean squared error was the lowest, at only 4.69 × 10⁻⁶. -4 This meets the calculation error requirements.

[0159] Table 3 Sample Fitting Results

[0160]

[0161] (7) Model correction test verification

[0162] Five shape control points were extracted from the measured strain influence line of the bridge and imported as input parameters into the trained BP neural network. The structural physical parameters predicted by the BP neural network were then input into the finite element model. The strain influence line of the model after correction was extracted, and the error between the corrected model and the initial model was analyzed, as shown in Table 4. Figure 10 , Figure 11 As shown.

[0163] Table 4 Error Comparison

[0164]

[0165] Table 4 shows that using a BP neural network to correct the finite element model of a bridge can effectively optimize the finite element parameters of the bridge structure. Figure 10 It can be seen that the strain influence line of the model is closer to the measured influence line of the structure, with its percentage error decreasing to 0.89% and its relative error decreasing to 9.43%, both within 10%. Compared with the model before the correction, the correlation coefficient of the strain influence line after the correction increased from 0.99669 to 0.99671.

[0166] Depend on Figure 11 It can be seen that the relative error of the model before and after the correction at each strain influence line loading step has a maximum value near the support of the continuous beam bridge. This is caused by the small absolute value of the strain influence line coefficient near the support. The relative error is within the control line of ±5%. Compared with the initial model, the absolute value of the relative error of the optimized model is smaller, indicating that the strain influence line of the optimized model has a better fit with the measured strain influence line.

[0167] Although embodiments of the present invention have been shown and described above, it is understood that the above embodiments are exemplary and should not be construed as limiting the present invention. Those skilled in the art can make changes, modifications, substitutions and variations to the above embodiments within the scope of the present invention.

Claims

1. A method for correcting a bridge finite element model based on a BP neural network, characterized in that, Includes the following steps: S1: Establish the objective function and select the correction parameters; S2: Conduct bridge strain influence line tests, extract measured strain influence lines, and simultaneously establish an initial finite element model to extract calculated strain influence lines; S3: Establish a BP neural network and use the trained BP neural network to correct the initial finite element model; In step S1, the correction parameters include the elastic modulus E of the longitudinal main beam, the top plate thickness T1, the bottom plate thickness T2, and the web thickness Tw. In step S2, the specific process of extracting the measured strain influence line is as follows: S201: Define the test conditions and arrange the measuring points according to the actual bridge structure; S202: Using a test loading vehicle, the strain influence line of the measuring point under a predetermined test load is tested; S203: Extract the strain time history response of the bridge measuring points, use the constructed test loading vehicle information matrix to remove the multi-axle effect of the vehicle, and then restore the bridge strain time history response to the bridge strain influence line under the unit concentrated load, that is, the measured strain influence line. The test loading vehicle is a single two-axle heavy vehicle. In step S2, the specific process for extracting and calculating the strain influence line is as follows: S211: Based on the bridge structural dimensional information obtained from the design drawings and on-site conditions, establish an initial finite element model; S212: Use strain influence line loading to define moving load analysis case; S213: Simulate strain influence line loading with unit concentrated load, extract the calculated strain influence line of the initial finite element model; perform 30 random scaling operations on the structural parameters of the initial finite element model, extract the bridge strain influence line under the corresponding structural parameters, i.e., the calculated strain influence line, as 30 training samples for the BP neural network; import the 30 sample data into the established BP neural network, and train, verify and test the BP neural network. In step S3, the specific process of correcting the initial finite element model is as follows: S301: Establish a BP neural network, import sample data into the established BP neural network, and train, verify and test the BP neural network. S302: After the BP neural network has been trained and meets the computational error requirements, save the trained BP neural network. S303: Extract 5 shape control points from the measured strain influence line of the bridge and import them as input parameters into the trained BP neural network; S304: Input the correction parameters predicted by the trained BP neural network into the initial finite element model to correct the finite element model.

2. The bridge finite element model correction method based on BP neural network according to claim 1, characterized in that: In step S1, the objective function corrects the finite element model by reducing the error between the measured strain influence line and the calculated strain influence line extracted from the finite element model.

3. The bridge finite element model correction method based on BP neural network according to claim 2, characterized in that: In step S1, absolute error, percentage error, correlation coefficient, and relative error are selected to quantify the degree of agreement between the finite element model and the actual bridge structure. The specific calculation formulas are as follows: Absolute error: ∑|ε a -ε m |; Percentage error: ∑(ε) a -ε m ) 2 / ∑(ε m ) 2 ; Relative error: ∑|ε a -ε m | / ∑|ε m |; Correlation coefficient: Where, ε a This indicates the calculated strain value along the influence line; ε m This represents the measured strain value of the influence line.

4. The bridge finite element model correction method based on BP neural network according to claim 3, characterized in that: In step S3, the BP neural network is a multilayer feedforward neural network based on the backpropagation algorithm, wherein the hidden layer node expressions are as follows: In the formula, y i For hidden layers; x j For the input layer; w ij θ represents the weights of the first layer network. i The threshold value for the first layer of the network; The output layer node expression is as follows: In the formula, O l For output layer; T li The weights for the second layer network; θ l The threshold for the second layer network; Substitute the output value and the true sample value into the error formula: In the formula, t l Given the true values ​​of the samples, the weights T of the second-layer network are calculated using the error formula. li Expanding and differentiating, we get: Since E consists of multiple O k The functions, each O k If they are mutually independent, then: Therefore, we get: Let the node error of the BP neural network be: δ l =-(t l -O l )×f'(net l ) The hidden layer expression is then obtained as follows: Similarly, the input layer expression can be obtained as: Due to the weight correction value ΔT li and Δw ij Proportional to the error function as it descends along the gradient, we obtain the following relationship: Similarly, the correction values ​​Δθ for the thresholds of the first and second layers of the network can be obtained. i , Δθ l for:

5. The bridge finite element model correction method based on BP neural network according to claim 4, characterized in that: In step S3, in the BP neural network, five shape control points in the strain influence line are selected as input layer parameters, and the input layer is set with five nodes. The five shape control points include three mid-span points and two mid-span 1 / 4 points. The output layer parameters are set with four nodes according to the definition of the correction parameters. The number of hidden layer nodes is calculated according to the following formula: In the formula, P is the number of hidden layer nodes, which is 12; m is the number of input layer nodes; n is the number of output layer nodes; and a is a constant in the interval [1, 10].

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