Bridge finite element model correction method based on deep learning

Abstract

The invention relates to a bridge finite element model correction method based on deep learning, and belongs to the field of structural health monitoring. According to the method for bridge finite element correction based on an inverse agent model of deep learning, structural response serves as an independent variable, structural attributes serve as dependent variables, and the structural response is trained by inputting a finite element model of the structural attributes to be updated. The training set is obtained by executing a plurality of finite element model instances, wherein each instance is formed by assigning random values to structural attributes. Structural response measured by an experiment can be used as input of a trained inverse proxy model, and structural attributes used for updating a finite element model are used as output. The method can overcome the problem that the number of to-be-corrected parameters in a traditional correction method is limited, and is suitable for correction of various bridge finite element models.

Description

Technical Field

[0001] The invention relates to a bridge finite element model correction method based on deep learning, and belongs to the field of structural health monitoring. Background Art

[0002] Establishing an accurate finite element model that reflects the actual situation at the time is a necessary prerequisite and foundation for safety monitoring, disease assessment, performance evaluation, and repair and reinforcement of large bridges. Due to the influence of model errors, parameter errors, and long-term structural damage, the finite element model established according to the original design drawings and relevant standards is often different from the actual structure. At this time, the finite element model cannot reflect the true stress state of the structure. Therefore, an iterative procedure is usually used to calibrate certain parameters of the model to minimize the difference between the measured structural response and the model output. This process is usually called finite element model correction, which corrects and adjusts the finite element model of the structure so that it can truly reflect the current status of the actual structure and obtain a more accurate finite element model.

[0003] Existing finite element model updating methods can be classified into deterministic methods and stochastic methods. Deterministic methods are usually optimization problems, in which unknown parameters are regarded as fixed constants and an objective function is defined to measure the residual between numerical and experimental data sets. Stochastic methods regard unknown parameters as random variables and aim to quantify their uncertainty distribution. These methods can be based on frequentist or Bayesian methods. Frequentist methods operate in random scenarios through optimization techniques, and the objectives to be minimized are usually frequency properties such as the mean and covariance of the data. In the Bayesian framework, the prior distribution of the parameters is first assumed, and then the likelihood function is derived from the experimental data, and the posterior probability is updated using this information. Although stochastic methods can produce better results, they usually require a large amount of experimental data and are very computationally intensive. Therefore, deterministic methods are still widely used in practical applications.

[0004] One of the limitations of finite element model updating is the time consumption of performing the finite element dynamic analysis process. In order to solve this problem, scholars have proposed using alternative models to replace traditional finite element models to speed up model updating. These alternative models express the relationship between finite element responses and correction parameters through mathematical functions. These functions are in various forms, such as neural network regression models, Kriging models, radial basis functions, and adaptive Gaussian proxy models. These proxy models have limitations, and there are multiple combinations of finite element model update parameters, which may lead to similar objective function values. Most of them can only correct a few parameters and have low computational efficiency. In fact, the finite element model of a complex bridge often requires dozens or even hundreds of parameters to be defined. It is difficult to ensure that the corrected finite element model can reliably simulate the real bridge structure by only correcting a few parameters of the bridge finite element model. Summary of the invention

[0005] The present invention provides a method for correcting a bridge finite element model based on a deep learning inverse proxy model. By constructing a correction parameter regression prediction model based on a deep residual network structure, accurate prediction of the optimal value of the parameter to be corrected is achieved. Data of the finite element model of a complex bridge is collected, and the powerful fitting ability of the deep learning model is used to ensure that all parameters to be corrected in the bridge finite element model are accurately corrected, and the optimal values ​​of all parameters to be corrected are quickly found, ensuring that the finite element can simulate the real bridge structure with high fidelity.

[0006] The present invention adopts the following technical solution:

[0007] The present invention provides a bridge finite element model correction method based on deep learning, comprising the following steps:

[0008] Step 1: According to the as-built drawing information of the bridge, establish the initial single-tower span finite element model of the bridge;

[0009] Step 2: Identify the true frequency of the bridge based on the measured vibration response data;

[0010] Step 3: Take the longitudinal spring stiffness of the main beam, main tower, support and the transverse spring stiffness of the support in the single-tower span finite element model as the parameters to be corrected;

[0011] Step 4: Use the sensitivity method to select the parameters to be corrected of the finite element and define the target structural parameters M of the finite element model that needs to be updated;

[0012] The target structure is: main beam concrete elastic modulus, main beam concrete density, main tower concrete elastic modulus, main tower concrete density, transverse spring stiffness, longitudinal spring stiffness;

[0013] Step 5: Based on the target structure in step 4, define the parameter correction range of the target structure;

[0014] Step 6: Based on the parameter correction range set in step 5, generate S Each vector contains a set of values ​​randomly selected within their respective boundaries and assigned to the target parameter; the vector representation is as follows:

[0015] y s =I y +(U y -I y )·r

[0016] Step 7: For each s sample, y s Parameters are assigned to the finite element model and the number N of structural responses is calculated and collected; the vector representation is as follows:

[0017] XS =[x s1 ,x s2 ,…,x sN ]

[0018] Step 8. Collect all vectors X s and s , forming the feature matrix:

[0019]

[0020] Target matrix:

[0021]

[0022] Step 9: Using the data collected in step 8, randomly select 70% as training samples, build a convolutional residual network model to train the data, and use the remaining 30% as prediction samples;

[0023] Step 10: The training samples are subjected to a one-dimensional convolution layer, batch normalization, and global pooling layer for local feature extraction, and then output through a swish activation function;

[0024] Construct three fully connected layers in the direct connection layer, set one fully connected layer in the skip layer, and output the features of the direct connection layer and the skip layer after fusion through the Addition layer;

[0025] The fused features are processed through a fully connected layer and a regression loss function to complete the training of the one-dimensional convolutional residual network;

[0026] Step 11: Use the remaining 30% of the prediction samples to make predictions using the model trained in step 10, and use the mean absolute error and root mean square error as evaluation indicators to evaluate the accuracy of the model;

[0027] Step 12: based on the prediction results of the parameters to be corrected by the one-dimensional convolutional residual network model in step 11, update the single tower span finite element model;

[0028] Step 13: Calculate the error between the modal frequency of the updated and corrected single-tower span finite element model and the modal frequency identified by the actual bridge tower sensor. If the error is closer to 0 than before correction, it is determined that the bridge finite element model is effectively corrected.

[0029] In the bridge finite element model correction method based on deep learning described in the present invention, the sensitivity method is used in step 4 to select the finite element parameters to be corrected, and the sensitivity k of each parameter is calculated by the following formula:

[0030]

[0031] Where Δf is the frequency change rate, and Δω is the parameter change rate.

[0032] In the bridge finite element model correction method based on deep learning described in the present invention, the lower limit and upper limit expressions of the parameters to be corrected in step 5 are as follows:

[0033] I y =[l1,l2,…,l M ]

[0034] U y =[u1,u2,…,u M ]

[0035] in and are vectors of lower and upper bounds on the structural parameters, respectively.

[0036] In the bridge finite element model correction method based on deep learning described in the present invention, a convolutional residual network model is constructed in step 9, and a local representation of features is extracted through a one-dimensional convolution layer, batch normalization and global pooling, and then output through a swish activation function;

[0037] The one-dimensional convolution layer operation can be expressed as:

[0038]

[0039] Where Y[i] is the value of the output feature map at position i, W[j] is the jth element in the convolution kernel, X[i+j] is the value of the input feature map at position i+j, and K is the size of the convolution kernel;

[0040] The batch normalization operation includes three steps: calculating the mean and variance, standardization, scaling, and offset;

[0041] (1.1), the mean and variance are calculated as follows:

[0042]

[0043] Where x represents the input data, usually the output of a layer of the neural network, m is the number of samples in the current batch, μ is the mean of the current batch, which is used to standardize the input, and σ 2 is the variance of the current batch, used to standardize the input;

[0044] (1.2), the standardization operation is expressed as follows:

[0045]

[0046] is the standardized output, ò is a small constant to avoid zero values ​​when calculating the variance;

[0047] (1.3), scaling and offset operations are expressed as follows:

[0048]

[0049] Among them, γ and β are learnable parameters, the scaling parameter is used to adjust the scale of the standardized value, and the offset parameter is used to adjust the center position of the standardized value;

[0050] For a feature map F, the formula for global average pooling can be expressed as:

[0051]

[0052] Where H and W are the height and width of the feature map, respectively, and G is the global feature of the output; global maximum pooling is similar, except that the maximum value is taken; the ultimate goal of this operation is to retain the most important features and simplify the model;

[0053] The Swish activation function is a nonlinear activation function, and the formula is defined as follows:

[0054]

[0055] σ(x) is the Sigmoid function, which is used to map the input value x to between 0 and 1; Swish(x) is the output of the Swish activation function, which represents the nonlinear transformation of the input value x;

[0056] The Addition layer is used to add the output of the convolutional layer to the previous input, which can be expressed as follows:

[0057] y=x+f(x)

[0058] Where f(x) represents the input value after the activation function, x is the input value of the convolutional layer, and y is the result of the corresponding addition of the elements;

[0059] The weighted regression loss function can be expressed as follows:

[0060]

[0061] Where β is a non-negative trade-off parameter set to 0.01 in the present invention, y is the observed value, is the mean of all observations, is the predicted value and n is the number of observations.

[0062] The bridge finite element model correction method based on deep learning of the present invention is based on the one-dimensional convolution residual network model completed in step 11, and the single tower span finite element model is updated through the experimental structural response state data of the line; a set of new experimental structural response is obtained. When the finite element model is updated, the updated target parameters Assigned to this model, the expression is as follows;

[0063]

[0064] Beneficial Effects

[0065] The bridge finite element model correction method based on deep learning adopted by the present invention has the following effects:

[0066] (1) The present invention is a method for bridge finite element correction based on a deep learning "inverse proxy model". The method uses the structural response as an independent variable and the structural attribute as a dependent variable, and trains the structural response by inputting a finite element model of the structural attribute to be updated. The training set is obtained by executing multiple finite element model instances, each of which is formed by assigning random values ​​to the structural attributes. The experimentally measured structural response can be used as the input of the trained "inverse proxy model", and the structural attributes used to update the finite element model are used as output.

[0067] (2) The finite element model of a complex bridge often requires dozens or even hundreds of parameters to be defined. It is difficult to ensure that the corrected finite element model can reliably simulate the real bridge structure by only correcting a few parameters of the bridge finite element model. The present invention can overcome the problem of the limited number of parameters to be corrected in the traditional correction method and is suitable for the correction of various bridge finite element models.

[0068] (3) The convolutional residual network model proposed in the present invention can reliably and accurately determine the optimal value of the parameter to be corrected. The model training error is within the allowable range and has good universality. The single-tower span finite element model after inversion correction based on the convolutional residual network model has high accuracy and can more realistically reflect the actual situation. It can be used as a replacement model for the safety prognosis study of bridges. BRIEF DESCRIPTION OF THE DRAWINGS

[0069] Figure 1 It is the finite element update flow chart of the present invention;

[0070] Figure 2 It is a structural diagram of the convolutional residual network model of the present invention;

[0071] Figure 3 This is a structural diagram of the initial single-tower span finite element model of the present invention;

[0072] Figure 4 It is a schematic diagram of the local sensitivity of each parameter perturbation to the modal frequency of the present invention;

[0073] Figure 5 It is a schematic diagram of vibration modes of the finite element model after vertical 1st order to vertical 6th order correction of the present invention. DETAILED DESCRIPTION

[0074] In order to make the purpose and technical solution of the embodiment of the present invention clearer, the technical solution of the embodiment of the present invention will be clearly and completely described below in conjunction with the drawings of the embodiment of the present invention. Obviously, the described embodiment is a part of the embodiment of the present invention, not all of the embodiments. Based on the described embodiment of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0075] Step 1: Establish the initial single-tower span finite element model of the bridge according to the as-built drawings, such as Figure 3 As shown;

[0076] Step 2: Identify the actual frequency of the bridge based on the measured vibration response data, as shown in Table 1

[0077] Table 1 Comparison between the calculated frequency and measured frequency of the initial model of a single tower span

[0078]

[0079]

[0080] Note: Error = (measured frequency / initial calculated frequency-1) × 100%.

[0081] Step 3: The physical meaning of the mass parameter ρ not only reflects the discreteness of the material density itself, but also includes the mass of the non-main force-bearing components that are not modeled and the external loads included under normal operating conditions; the stiffness of the system can be reflected by the elastic modulus E of the component material and the spring stiffness K at the support, as shown in the following table:

[0082] Table 2 shows the parameters to be corrected selected according to the empirical method.

[0083]

[0084] Step 4: Use the sensitivity method to select the parameters to be corrected in the finite element. The sensitivity k of each parameter is calculated by formula (1), where Δf is the frequency change rate, Δω is the parameter change rate, and the sensitivity calculation results of each modal frequency to each parameter are as follows: Figure 4 As shown. And define the "target" structural parameter M of the finite element model that needs to be updated;

[0085]

[0086] Step 5: For each target parameter, i.e., the parameter to be corrected, the acceptable lower and upper limits are defined, such as

[0087] As shown in Table 3:

[0088]

[0089] in and are vectors of lower and upper bounds on the structural parameters, respectively.

[0090] Step 6: Figure 1 In the “sampling” phase, S , each containing a set of values ​​randomly selected within their respective bounds and assigned to the target parameter, as follows:

[0091] y s =I y +(U y -I y )·r (3)

[0092] Where, s = [1, S], r ~ U M (0,1) is a vector of M random numbers with standard uniform distribution, which is redrawn for each sample s.

[0093] Step 7: For each s sample, convert y s Parameters are assigned to the finite element model and the number N of structural responses is calculated and collected.

[0094] X S =[x s1 ,x s2 ,…,x sN ] (4)

[0095] Only modal data, i.e. individual natural frequencies, are considered as structural responses.

[0096] Step 8: Collect all vectors X s and s , forming a "feature" matrix and the "target" matrix

[0097] Step 9: Figure 1 In the "training" phase, the convolutional residual network model The convolutional residual network model structure is as follows: Figure 2 As shown in the figure, the local representation of the feature is extracted through a one-dimensional convolution layer, batch normalization and global pooling, and then output through the swish activation function. Then, three fully connected layers are designed in the direct connection layer, and a fully connected layer is set in the jump layer. The direct connection layer and the jump layer are fused and output through the Addition layer. Finally, the fused features are output through a fully connected layer and a regression loss function. The regression prediction of the parameters to be corrected in the final experiment based on the design of each module. The specific formulas of each module are as follows:

[0098] The one-dimensional convolutional layer operation can be expressed as:

[0099]

[0100] Where Y[i] is the value of the output feature map at position i, W[j] is the jth element in the convolution kernel, X[i+j] is the value of the input feature map at position i+j, and K is the size of the convolution kernel.

[0101] The batch normalization operation includes three steps: calculating the mean and variance, standardization, scaling, and offset. Specifically, the mean and variance are calculated as follows:

[0102]

[0103] Where x represents the input data, usually the output of a layer of the neural network, m is the number of samples in the current batch, μ is the mean of the current batch, which is used to standardize the input, and σ 2 is the variance of the current batch, used to standardize the input.

[0104] The standardization operation is expressed as follows:

[0105]

[0106] is the normalized output, and ò is a small constant to avoid zero values ​​when calculating the variance.

[0107] Scaling and offset operations are expressed as follows:

[0108]

[0109] Where γ and β are learnable parameters, respectively, the scaling parameter is used to adjust the scale of the standardized value, and the offset parameter is used to adjust the center position of the standardized value.

[0110] Global pooling can reduce the size of feature maps by applying average or maximum pooling to each feature channel. For a feature map F, the formula for global average pooling can be expressed as:

[0111]

[0112] Where H and W are the height and width of the feature map, respectively, and G is the global feature of the output. Global maximum pooling is similar, except that the maximum value is taken. The ultimate goal of this operation is to retain the most important features and simplify the model. The Swish activation function is a nonlinear activation function, and the formula is defined as follows:

[0113]

[0114] σ(x) is the Sigmoid function, which is used to map the input value x to between 0 and 1. Swish(x) is the output of the Swish activation function, which represents the nonlinear transformation of the input value x. Compared with activation functions such as ReLU, Swish is smooth and does not have discontinuous points, and may perform better during optimization.

[0115] In the residual network structure of the present invention, the output of the convolutional layer is added to the previous input using the Addition layer, which is specifically expressed as follows:

[0116] y = x + f(x) (11)

[0117] Where f(x) represents the input value after the activation function, x is the input value of the convolutional layer, and y is the result of element-by-element addition.

[0118] Finally, the present invention designs a new weighted regression loss function which can be expressed as follows:

[0119]

[0120] Where β is a non-negative trade-off parameter set to 0.01 in the present invention, y is the observed value, is the mean of all observations, is the predicted value and n is the number of observations.

[0121] Step 10: Using the data collected in step 8, randomly select 70% as training samples and build a convolutional residual network model to train the data.

[0122] Step 11: Model parameter setting and optimization. For the proposed convolutional residual network, the Adam optimization method is used, and the number of iterations is set to 300. The parameters that need to be adjusted in the model are mainly: the convolution kernel size of the residual unit and the number of neurons in the fully connected layer. The convolution kernel size is used to determine the length of the sequence involved in the convolution calculation, while the number of neurons in the one-dimensional convolutional residual network is used to learn the depth of the network and feature extraction. The selection of the above two hyperparameters will affect the overall performance of the model. Therefore, in order to obtain the best prediction needs, a trial and error experiment was carried out. The size of the residual block convolution kernel is set to 1×1, the number of convolution kernels is set in the range of [64-320], and the step size is set to 64.

[0123] Step 12: Use mean absolute error (MAE) and root mean square error (RMSE) to evaluate the quality of the model and compare it with the experimental results.

[0124]

[0125] Step 13: After the one-dimensional convolutional residual network model training is completed, you can enter Figure 1 In this phase, when a new set of experimental structural responses (OMA modal data in this study) is obtained, When the finite element model is updated, the updated target parameters Assigned to this model;

[0126]

[0127] Step 14: Follow step 13 to get the updated finite element model as shown below: Figure 5 As shown, the first 6-order calculated frequencies of the initial finite element model and the first 6-order calculated frequencies of the modified bridge finite element model are further compared with the first 6-order measured frequencies, and the results are shown in Table 4.

[0128] Table 4 Corrected frequency and error

[0129]

[0130] Note: Error = (measured frequency / corrected calculated frequency - 1) × 100%.

[0131] It can be seen from Table 4 that the calculated frequency of the corrected bridge finite element model is very close to the true frequency, indicating that the bridge finite element model correction method based on a deep learning inverse proxy algorithm provided by the present invention can effectively correct the bridge finite element model.

[0132] The above is only a preferred specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any changes or substitutions that can be easily thought of by a person skilled in the art within the technical scope disclosed by the present invention should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A bridge finite element model correction method based on deep learning, characterized by: Here are the steps: Step 1: According to the as-built drawing information of the bridge, establish the initial single-tower span finite element model of the bridge; Step 2: Identify the true frequency of the bridge based on the measured vibration response data; Step 3: Take the longitudinal spring stiffness of the main beam, main tower, support and the transverse spring stiffness of the support in the single-tower span finite element model as the parameters to be corrected; Step 4: Use the sensitivity method to select the parameters to be corrected of the finite element and define the target structural parameters M of the finite element model that needs to be updated; The target structure is: main beam concrete elastic modulus, main beam concrete density, main tower concrete elastic modulus, main tower concrete density, transverse spring stiffness, longitudinal spring stiffness; Step 5: Based on the target structure in step 4, define the parameter correction range of the target structure; Step 6: Based on the parameter correction range set in step 5, generate S Each vector contains a set of values ​​randomly selected within their respective boundaries and assigned to the target parameter; the vector representation is as follows: Step 7: For each s sample, y s Parameters are assigned to the finite element model and the number N of structural responses is calculated and collected; the vector representation is as follows: X S =[x s1 ,x s2 ,…,x sN ] Step 8. Collect all vectors X s and s , forming the feature matrix: Target matrix: Step 9: Using the data collected in step 8, randomly select 70% as training samples, build a convolutional residual network model to train the data, and use the remaining 30% as prediction samples; Step 10: The training samples are subjected to a one-dimensional convolution layer, batch normalization, and global pooling layer for local feature extraction, and then output through a swish activation function; Construct three fully connected layers in the direct connection layer, set one fully connected layer in the skip layer, and output the features of the direct connection layer and the skip layer after fusion through the Addition layer; The fused features are processed through a fully connected layer and a regression loss function to complete the training of the one-dimensional convolutional residual network; Step 11: Use the remaining 30% of the prediction samples to make predictions using the model trained in step 10, and use the mean absolute error and root mean square error as evaluation indicators to evaluate the accuracy of the model; Step 12: based on the prediction results of the parameters to be corrected by the one-dimensional convolutional residual network model in step 11, update the single tower span finite element model; Step 13: Calculate the error between the modal frequency of the updated and corrected single-tower span finite element model and the modal frequency identified by the actual bridge tower sensor. If the error is closer to 0 than before correction, it is determined that the bridge finite element model is effectively corrected.

2. The bridge finite element model correction method based on deep learning according to claim 1 is characterized in that: In step 4, the sensitivity method is used to select the parameters to be corrected in the finite element. The sensitivity k of each parameter is calculated by the following formula: Where Δf is the frequency change rate, and Δω is the parameter change rate.

3. The bridge finite element model correction method based on deep learning according to claim 1 is characterized in that: The lower and upper limit expressions of the parameters to be corrected in step 5 are as follows: in and are vectors of lower and upper bounds on the structural parameters, respectively.

4. The bridge finite element model correction method based on deep learning according to claim 1 is characterized in that: In step 9, a convolutional residual network model is constructed, and local representation of features is extracted through one-dimensional convolutional layers, batch normalization, and global pooling, and then output through the swish activation function; The one-dimensional convolution layer operation can be expressed as: Where Y[i] is the value of the output feature map at position i, W[j] is the jth element in the convolution kernel, X[i+j] is the value of the input feature map at position i+j, and K is the size of the convolution kernel; The batch normalization operation includes three steps: calculating the mean and variance, standardization, scaling, and offset; (1.1), the mean and variance are calculated as follows: Where x represents the input data, usually the output of a layer of the neural network, m is the number of samples in the current batch, μ is the mean of the current batch, which is used to standardize the input, and σ 2 is the variance of the current batch, used to standardize the input; (1.2), the standardization operation is expressed as follows: is the standardized output, ò is a small constant to avoid zero values ​​when calculating the variance; (1.3), scaling and offset operations are expressed as follows: Among them, γ and β are learnable parameters, the scaling parameter is used to adjust the scale of the standardized value, and the offset parameter is used to adjust the center position of the standardized value; For a feature map F, the formula for global average pooling can be expressed as: Where H and W are the height and width of the feature map, respectively, and G is the global feature of the output; The Swish activation function is a nonlinear activation function, and the formula is defined as follows: σ(x) is the Sigmoid function, which is used to map the input value x to between 0 and 1; Swish(x) is the output of the Swish activation function, which represents the nonlinear transformation of the input value x; The Addition layer is used to add the output of the convolutional layer to the previous input, which can be expressed as follows: y=x+f(x) Where f(x) represents the input value after the activation function, x is the input value of the convolutional layer, and y is the result of the corresponding addition of the elements; The weighted regression loss function can be expressed as follows: Where β is a non-negative trade-off parameter set to 0.01 in the present invention, y is the observed value, is the mean of all observations, is the predicted value and n is the number of observations.

5. The bridge finite element model correction method based on deep learning according to claim 1 is characterized in that: Based on the one-dimensional convolutional residual network model completed in step 11, the single tower span finite element model is updated through the experimental structural response state data; a new set of experimental structural responses is obtained When the finite element model is updated, the updated target parameters Assigned to this model, the expression is as follows;

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