Finite element model response prediction method based on Monte Carlo and deep learning

Abstract

The invention belongs to the technical field of model correction and response prediction, and particularly relates to a finite element model response prediction method based on Monte Carlo and deep learning. Structural parameters are randomly extracted by utilizing a Monte Carlo method, and firstly, a preliminary structural response is obtained by utilizing finite element simulation software; and the structure parameters and the structure response are used as input and output of a training neural network respectively, then a test response result is used as an additional network training sample to optimize a response prediction network and a model correction network, and finally the neural network meeting the precision requirement is obtained to be used for accurately predicting the response of the structure. The final response prediction network and the model correction network obtained by the method can obtain the relatively accurate response prediction network and the model correction network under the common optimization of finite element simulation analysis and test response, and some uncertain factors in a structure model are considered by using a deep learning method, so that the accuracy of the structure model is improved. The response result is more accurate; the method provided by the invention has wide application prospects in the aspects of structural model correction and response prediction.

Description

Technical Field

[0001] The present invention belongs to the technical field of model correction and response prediction, and specifically relates to a finite element model correction and response prediction method based on Monte Carlo and deep learning methods. Background Art

[0002] Establishing an accurate structural finite element calculation and analysis model that can reflect the current actual situation is a necessary premise and basis for health monitoring, damage assessment, performance evaluation and maintenance of existing structures, especially large structures, to ensure their safe operation. However, the structural finite element model directly established by the design scheme has made considerable mechanical simplifications to the real structure. Under normal circumstances, there is often a certain difference between the calculation results of the finite element model and the experimental test data. At this time, it is necessary to correct the finite element model so that it can (or in a certain sense) truly reflect the current situation of the actual structure. Usually, the finite element model correction is to modify certain uncertain parameters used when establishing the initial theoretical model within a certain range, including the boundary conditions of the theoretical model, the constitutive relationship of the material, and the connection properties of the structural components, so that the response results calculated by the theoretical model are as consistent as possible with the actual structure.

[0003] Traditional deterministic finite element model correction has been widely used in bridges, aerospace and other fields. This type of method assumes that the finite element model parameters are deterministic values, and indirectly estimates the values ​​of the structural parameters through the response of the structure, so that the finite element model response results are as consistent as possible with the test results. However, there are a large number of uncertain factors in actual engineering problems, such as model simplification, changes in elastic modulus due to structural wear, and measurement errors in test data. This uncertainty can be described by probabilistic statistics.

[0004] Stochastic finite element model correction takes a group of structures whose structural parameters obey a certain distribution as the research object, and estimates the statistical characteristics of the structural parameters by analyzing the response statistical characteristics of a group of structures. It is the inverse problem of finite element model correction.

[0005] In addition, deep learning technology has achieved remarkable results in the fields of computer vision, speech recognition, and natural language processing in recent years. Its essence is to use algorithms to analyze data, learn the inherent laws and representation levels of sample data, learn a model from the data, establish a nonlinear mapping relationship between sample data and its label, and then use this model to make predictions for new sample data.

[0006] The Monte Carlo method is a statistical method that solves mathematical problems through random sampling. Its basic idea is to use random numbers to solve deterministic problems. Especially when dealing with numerical solution problems in "high-dimensional space", random sampling methods such as uniform sampling or importance sampling can be used to generate random sample points. It is a very effective and mature solution in the field of numerical solution. Moreover, the Monte Carlo method is very suitable for parallel computing, and parallelization can be used to improve computing efficiency and shorten computing time. Random sampling and statistical analysis can greatly reduce computing time. However, this method has not yet been used in the field of deep learning, especially in the field of finite element model correction and response prediction based on deep learning methods. This requires a lot of computing time and consumes a lot of computing resources in model training using conventional deep learning methods, and it is impossible to quickly and effectively perform model correction and response prediction. Therefore, the solution that combines Monte Carlo and deep learning methods for model correction and response prediction has outstanding advantages. Summary of the invention

[0007] The purpose of this invention is to avoid the inadequacy of model response prediction caused by a large number of uncertain factors in existing engineering problems, and to propose a finite element model modification and response prediction method based on Monte Carlo and deep learning methods.

[0008] The technical solution of the present invention is a method for finite element model correction and response prediction based on Monte Carlo and deep learning methods. The overall design idea is to use the Monte Carlo method to randomly extract structural parameters, and first use finite element simulation software to obtain a preliminary structural response; then use the structural parameters and structural response as the input and output of the training neural network respectively, and then use the experimental response results as additional network training samples to optimize the response prediction network and the model correction network, and finally obtain a neural network that meets the accuracy requirements for accurately predicting the response of the structure.

[0009] Based on the above design concept, the present invention specifically proposes a method for finite element model correction and response prediction based on Monte Carlo and deep learning methods, and the specific steps are as follows:

[0010] Step S1, obtaining training data;

[0011] Step S2, constructing a response prediction network and a model correction network;

[0012] Step S3, model correction and network verification;

[0013] Step S4: Network optimization.

[0014] Furthermore, in step S1, the structure is first discretized into k regions, and for each region there are n parameters θ that need to be corrected in(1<i<k), i is the i-th parameter among n parameters that need to be corrected; assuming that different parameters conform to a certain mathematical random distribution function, for a certain area that needs to be corrected, the Monte Carlo method is used to sample different parameters y times to obtain y groups of different structural parameter combination samples; each group of structural parameter samples is brought into the finite element simulation software for calculation to obtain m structural displacement response and strain response results under the corresponding parameter samples; the column vector composed of the y groups of structural parameter samples and the column vector composed of the structural response samples are used as the sample database of the deep neural network.

[0015] Furthermore, in step S2, the method for constructing a response prediction network is: using the structural parameters obtained in step S1 as the input of the deep learning neural network model to learn the mapping relationship between the structural parameters and the structural response; through the deep learning neural network model, the mapping relationship between the simulation structural parameters and the structural response can be established, that is, a response prediction network is established.

[0016] Furthermore, in step S2, the process of constructing a model correction network is: using the structural response obtained in step S1 as the input of the deep learning neural network model to learn the mapping relationship between the structural response and the structural parameters; through the deep learning neural network model, the mapping relationship between the simulated structural response and the structural parameters can be established, that is, a model correction network is established.

[0017] Furthermore, in step S3, the model correction and network verification process is: using the structural response (displacement and strain) data obtained from the experimental measurement as the input of the model correction neural network trained in step S2, and outputting the predicted structural parameters; using the predicted structural parameters to perform finite element simulation analysis, and obtaining the difference between the finite element simulation structural response (displacement and strain) under the predicted structural parameters and the experimental response (displacement and strain); if the difference between the two meets the accuracy requirements, the training is terminated, and the final response prediction network and the final model correction network are obtained.

[0018] Furthermore, the network optimization process in step S4 is: when the response difference does not meet the accuracy requirement, the predicted structural parameters and the finite element simulation structural response under the predicted structural parameters are used as additional training samples; then, the network training is repeated in step S2 using these additional samples to obtain a new response prediction network and a new model correction network; then, the model correction network in step S3 is replaced by the new model correction network to perform network verification; this step is repeatedly performed until the difference between the test response (displacement and strain) and the finite element simulation response (displacement and strain) meets the accuracy requirement; that is, the final response prediction network and the final model correction network are obtained.

[0019] Furthermore, in the above-mentioned method for finite element model modification and response prediction, the structural parameters of step S1 include all parameters in the structure that may affect the structural response result.

[0020] Furthermore, in the above-mentioned method of finite element model correction and response prediction, the neural network in step S2 is a deep learning neural network.

[0021] Beneficial effects of the present invention: The present invention utilizes the Monte Carlo method to randomly extract structural parameters, firstly uses finite element simulation software to obtain preliminary structural responses; then utilizes structural parameters and structural responses as input and output of the neural network respectively, establishes the response prediction network and model correction network of the structure; then utilizes the test response results as additional network training samples to optimize the response prediction network and model correction network, and finally obtains a neural network that meets the accuracy requirements. The final response prediction network and model correction network obtained by the present invention can obtain a relatively accurate response prediction network and model correction network under the joint optimization of finite element simulation analysis and test response, and utilizes deep learning methods to take into account certain uncertain factors in the structural model, so that the response results are more accurate.

[0022] The invention has a simple principle and obvious effect, and provides a new idea for the engineering application of structural model correction and response prediction in the future, and has broad application prospects in structural model correction and response prediction. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 A schematic diagram of obtaining training data for the present invention;

[0024] Figure 2 A schematic diagram of the present invention using training data to train a response prediction network;

[0025] Figure 3 A schematic diagram of the present invention using training data to train a model to correct the network;

[0026] Figure 4 This is a schematic diagram of the present invention using test response data to optimize the model correction network and the response prediction network. DETAILED DESCRIPTION

[0027] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments 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.

[0028] See attached Figures 1 to 4, as shown in the figure, the method of finite element model modification and response prediction based on Monte Carlo and deep learning methods, the specific steps are as follows:

[0029] Step 1: Get training data;

[0030] like Figure 1 As shown, the structure is first discretized into k regions, and for each region there are n parameters θ that need to be corrected in (1<i<k), i is the i-th parameter among the n parameters that need to be corrected. Assume that different parameters conform to a certain mathematical random distribution function. Here are three types of normal distribution, uniform distribution and exponential distribution, but the random distribution functions mentioned in the present invention are not limited to the above. For a certain area that needs to be corrected, the Monte Carlo method is used to sample different parameters y times to obtain y groups of different structural parameter combination samples. Each group of structural parameter samples is brought into the finite element simulation software for calculation to obtain m structural displacement response and strain response results under the corresponding parameter sample. The column vector composed of y groups of structural parameter samples and the column vector composed of structural response samples are used as the sample database of the deep neural network.

[0031] Step 2: Construct response prediction network and model correction network.

[0032] The structural parameters obtained in step 1 are used as the input of the deep learning neural network model to learn the mapping relationship between the structural parameters and the structural response (displacement and strain). Through the deep learning neural network model, the mapping relationship between the simulation structural parameters and the structural response can be established, that is, a response prediction network can be established.

[0033] The structural response obtained in step 1 is used as the input of the deep learning neural network model to learn the mapping relationship between the structural response and the structural parameters. Through the deep learning neural network model, the mapping relationship between the simulated structural response and the structural parameters can be established, that is, a model correction network can be established.

[0034] Step 3: Model modification and network verification.

[0035] The structural response (displacement and strain) data obtained from the test measurement is used as the input of the model correction neural network trained in step 2, and the predicted structural parameters are output. The predicted structural parameters are used for finite element simulation analysis to obtain the difference between the finite element simulation structural response (displacement and strain) and the experimental response (displacement and strain) under the predicted structural parameters. If the difference between the two meets the accuracy requirements, the training is completed, and the final response prediction network and the final model correction network are obtained.

[0036] Step 4: Network optimization.

[0037] When the response difference in step three does not meet the accuracy requirements, the predicted structural parameters and the finite element simulation structural responses under the predicted structural parameters are used as additional training samples. Then, use these additional samples to repeat step two for network training to obtain a new response prediction network and a new model correction network. Then, the new model correction network replaces the model correction network in step three for network verification. Repeat this step until the difference between the test response (displacement and strain) and the finite element simulation response (displacement and strain) meets the accuracy requirements. That is, the final response prediction network and the final model correction network are obtained.

[0038] Embodiment 1. The embodiments described below with reference to the accompanying drawings are exemplary and are intended to further explain the present invention, but should not be construed as limiting the present invention. In this specific implementation case;

[0039] Finite element model modification:

[0040] The structural finite element model modification process can be expressed in terms of mathematical optimization concepts as follows: finding appropriate key mechanical performance parameters of the structural finite element model within a certain (reasonable) range, so that the difference between the structural response calculated based on the modified structural finite element model and the structural response of the actual structural test is minimized. The structural finite element model modification process can be transformed into solving the following mathematical optimization problem:

[0041]

[0042] Where X is the key mechanical performance parameter set of the structural finite element model to be corrected; X u , X i is the upper and lower limits of the structural finite element model parameter set X (reasonable range of structural parameter values), which is the constraint condition of the optimization problem. F(X) is the index function vector that reflects the difference between the structural response calculated according to the structural finite element model and the measured structural response, which is the objective function of the optimization problem and can generally be expressed as:

[0043] F(X)=F(FEM(P,X)-TEST) (2)

[0044] Where TEST is the measured response of the structural static load test, FEM(P, X) is the structural response calculated by the structural finite element model corresponding to TEST, which can be obtained through structural finite element calculation and analysis, and P is the load of the structural test. When F(X) is a single function, it is a single-objective optimization problem, and when F(X) is a function vector set, it is a multi-objective optimization problem.

[0045] Monte Carlo method:

[0046] The Monte Carlo method, also known as the statistical simulation method or the statistical test method, is a numerical simulation method that takes probability phenomena as the research object and uses the sampling survey method to obtain statistical values ​​to infer unknown characteristic quantities. In computational simulation, the random characteristics of the system can be simulated by constructing a probability model that is similar to the system performance and conducting random experiments on the computer.

[0047] The basic steps to solve practical problems using the Monte Carlo method are:

[0048] (1) According to the characteristics of the actual problem, a simple and easy-to-implement probability statistical model is constructed so that the solution is exactly the probability distribution or mathematical expectation of the problem;

[0049] (2) Provide sampling methods for various random variables with different distributions in the model;

[0050] (3) Statistically process the simulation results and provide statistical estimates and precision estimates of the solutions to the problem.

[0051] like Figures 1 to 4 As shown, the present invention includes structural model, random distribution function, structural parameters, structural response, deep learning neural network, finite element simulation analysis, response prediction network, model correction network, test response data, predicted structural parameters, predicted structural response, accuracy requirements, final response prediction network, and final model correction network.

[0052] The specific implementation process is as follows Figures 1 to 4 First, as Figure 1 As shown, the structural model is discretized into k regions, and for each region there are n parameters θ that need to be corrected in (1<i<k). Assuming different parameters θ in A random distribution function that conforms to a certain mathematical distribution, here listed are normal distribution, uniform distribution and exponential distribution, but the random distribution function mentioned in the present invention is not limited to the above. For a region i that needs to be corrected, for the structural parameter θ in the region in The Monte Carlo method is used to sample different parameters y times to obtain y groups of different structural parameter combination samples. Each group of structural parameter samples is brought into the finite element simulation software for finite element simulation analysis to obtain m response results under the corresponding parameter sample. Here, the structural response selected for display is the structural displacement response. and strain response This is only for illustration, and the structural response types protected by the present invention are not limited thereto. The column vectors composed of the y groups of structural parameter samples and the column vectors composed of the structural response samples are used as the sample database of the deep learning neural network.

[0053] like Figure 2As shown in the figure, y groups of structural parameter samples are used as the input of the deep learning neural network, and y groups of structural response samples are used as the output of the deep learning neural network. By learning the mapping relationship between structural parameters and structural responses, the network is trained to establish a response prediction network. Figure 3 As shown, y groups of structural response samples are used as the input of the deep learning neural network, and y groups of structural parameter samples are used as the output of the deep learning neural network. By learning the mapping relationship between structural response and structural parameters, the network is trained to establish a model correction network.

[0054] like Figure 4 As shown, the measured test response data is used as the input of the trained model correction network, and the predicted structural parameters are output. The predicted structural parameters are used for finite element simulation analysis to obtain the difference between the finite element simulation structural response (displacement and strain) under the predicted structural parameters and the test response (displacement and strain). If the difference between the two meets the accuracy requirements, the training is completed, and the final response prediction network and the final model correction network are obtained. If the response difference does not meet the accuracy requirements, the predicted structural parameters and the finite element simulation structural response under the predicted structural parameters are used as additional training samples. Then, these additional samples are used to perform deep learning neural network training again to obtain a new response prediction network and a new model correction network. Then, the measured test response data is used as the input of the new model correction network again, and the predicted structural parameters are output, and the network verification is performed again. Repeat this step until the difference between the test response (displacement and strain) and the finite element simulation response (displacement and strain) meets the accuracy requirements. That is, the final response prediction network and the final model correction network are obtained.

[0055] The above is only a specific embodiment of the present invention, and the present invention is described in detail. The unexplained part is a conventional technology. However, the protection scope of the present invention is not limited to this. Any changes or substitutions that can be easily thought of by any technician familiar with the technical field within the technical scope disclosed by the present invention should be included in the protection scope of the present invention. The protection scope of the present invention shall be based on the protection scope of the claims.

Claims

1. A finite element model response prediction method based on Monte Carlo and deep learning; characterized in that, The method uses the Monte Carlo method to randomly extract structural parameters, and first uses finite element simulation software to obtain preliminary structural responses; then uses the structural parameters and structural responses as input and output of training the neural network respectively, and then uses the test response results as additional network training samples to optimize the response prediction network and the model correction network, and finally obtains a neural network that meets the accuracy requirements for accurately predicting the response of the structure.

2. The finite element model response prediction method based on Monte Carlo and deep learning as claimed in claim 1; characterized in that: The finite element model response prediction method comprises the following steps: Step S1, obtaining training data; Step S2, constructing a response prediction network and a model correction network; Step S3, model correction and network verification; Step S4: Network optimization.

3. The finite element model response prediction method based on Monte Carlo and deep learning as claimed in claim 2; characterized in that: In step S1, the structure is first discretized into k regions, and for each region there are n parameters θ that need to be corrected in (1<i<k), i is the i-th parameter among n parameters that need to be corrected; assuming that different parameters conform to a certain mathematical random distribution function, for a certain area that needs to be corrected, the Monte Carlo method is used to sample different parameters y times to obtain y groups of different structural parameter combination samples; each group of structural parameter samples is brought into the finite element simulation software for calculation to obtain m structural displacement response and strain response results under the corresponding parameter samples; the column vector composed of the y groups of structural parameter samples and the column vector composed of the structural response samples are used as the sample database of the deep neural network.

4. The finite element model response prediction method based on Monte Carlo and deep learning as claimed in claim 3; characterized in that: In step S2, the response prediction network is constructed by: using the structural parameters obtained in step S1 as the input of the deep learning neural network model to learn the mapping relationship between the structural parameters and the structural response; through the deep learning neural network model, a mapping relationship between the simulation structural parameters and the structural response is established, that is, a response prediction network is established.

5. The finite element model response prediction method based on Monte Carlo and deep learning as claimed in claim 4; characterized in that: In step S2, the process of constructing a model correction network is: using the structural response obtained in step S1 as the input of the deep learning neural network model to learn the mapping relationship between the structural response and the structural parameters; through the deep learning neural network model, the mapping relationship between the simulated structural response and the structural parameters can be established, that is, the model correction network is established.

6. The finite element model response prediction method based on Monte Carlo and deep learning as claimed in claim 5; characterized in that: In step S3, the model correction and network verification process is: using the structural response data obtained by experimental measurement as the input of the model correction neural network trained in step S2, and outputting the predicted structural parameters; using the predicted structural parameters to perform finite element simulation analysis to obtain the difference between the finite element simulation structural response under the predicted structural parameters and the experimental response; If the difference between the two meets the accuracy requirement, the training ends and the final response prediction network and the final model correction network are obtained.

7. The finite element model response prediction method based on Monte Carlo and deep learning as claimed in claim 5; characterized in that: The network optimization process in step S4 is: when the response difference does not meet the accuracy requirement, the predicted structural parameters and the finite element simulation structural response under the predicted structural parameters are used as additional training samples; then, the network training is repeated in step S2 using these additional samples to obtain a new response prediction network and a new model correction network; then, the model correction network in step S3 is replaced by the new model correction network to perform network verification; this step is repeatedly performed until the difference between the test response and the finite element simulation response meets the accuracy requirement; that is, the final response prediction network and the final model correction network are obtained.

8. The finite element model response prediction method based on Monte Carlo and deep learning as claimed in claim 2; characterized in that: The structural parameters in step S1 include all parameters in the structure that may affect the structural response result.

9. The finite element model response prediction method based on Monte Carlo and deep learning as claimed in claim 2; characterized in that: The neural network in step S2 is a deep learning neural network.

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