Structural reliability calculation active learning method based on Monte Carlo MC-dropout neural network

Abstract

The invention discloses a structural reliability active learning method based on a Monte Carlo dropout neural network, and solves the problem that a large amount of time-consuming finite elements still need to be called to analyze and calculate a limit state function when a high-dimensional strong non-linear problem is processed in an existing method. And an active learning process in each iteration is guided by utilizing a predicted mean value and a standard deviation. New samples which are close to a limit state curved surface and have significant uncertainty are identified and selected to be used for updating the proxy model, so that the precision and reliability of the model are gradually improved. In addition, the integration technology of the MC-dropout neural network is adopted to estimate the failure probability, and the analysis accuracy is further improved. In order to ensure effective proceeding of the active learning process, two convergence criteria are also introduced to judge when to terminate the learning process. The method is also suitable for structural reliability analysis.

Description

Technical Field

[0001] The present invention relates to the technical field of reliability analysis based on machine learning, and in particular to an active learning method for structural reliability calculation based on a Monte Carlo dropout neural network. Background Art

[0002] Structural reliability assessment is crucial to preventing safety accidents, ensuring the safety of life and property, and maintaining social stability. Structural reliability is an indicator to measure structural reliability.

[0003] In the prior art, structural reliability theory has made significant progress, and the theoretical framework has been increasingly improved. Approximate methods such as the first reliability method and the second reliability method, random simulation methods such as importance sampling and subset simulation, and proxy model methods such as response surface model, Kriging model and neural network model have been proposed one after another and have been widely studied and applied. Among them, the first reliability method (FORM) and the second reliability method (SORM) are gradient-based approximate methods. They reduce the computational complexity by simplifying the problem, making reliability analysis more efficient, but may lose accuracy due to over-simplification. Random simulation methods such as importance sampling and subset simulation are used to directly estimate reliability through simulation tests. Importance sampling reduces the number of samples required by changing the probability distribution of random variables, thereby improving the efficiency of simulation. Subset simulation efficiently estimates the reliability of low-probability events by gradually narrowing the search space. These methods reduce the number of samples by reducing the sampling variance, but for high-dimensional and nonlinear problems, the computational cost of these methods is still very high. Response surface models, Kriging models, and neural network models are surrogate model methods that reduce the computational cost of each analysis by building an approximation (a proxy) of the original model. Response surface models use polynomials or other simple functions to approximate the true response and are suitable for problems with relatively smooth response surfaces. Kriging models are based on spatial statistics and can provide uncertainty estimates for predictions. Neural network models can handle nonlinear problems by learning complex relationships between inputs and outputs. The advantage of these surrogate model methods is that they can significantly reduce computational time, especially when combined with computationally expensive models such as finite element analysis. However, their accuracy is highly dependent on the quality of the surrogate model, and for high-dimensional, nonlinear problems, a large amount of data is still required to train the model.

[0004] The limit state functions of large engineering structures are complex, and the amount of numerical simulation is large. Although the surrogate model method can effectively improve the computational efficiency of structural reliability analysis, the surrogate model method in the existing technology still faces challenges when dealing with high-dimensional and nonlinear reliability problems. Therefore, studying new theories and methods for reliability analysis of large engineering structures has important scientific value and practical significance. Summary of the invention

[0005] In order to solve the problem of high-dimensional and strongly nonlinear reliability analysis in the prior art, the method adopted by the present invention still requires a large number of time-consuming finite element analysis calculations of limit state functions, making it very difficult to perform reliability analysis on these problems.

[0006] To solve the above technical problems, the present invention is achieved through the following technical solutions:

[0007] Solution 1: The present invention proposes an active learning method for calculating structural reliability based on a Monte Carlo MC-dropout neural network. The active learning method for calculating structural reliability includes the following steps:

[0008] Step 1: Use the MC-dropout neural network as a proxy model to obtain the Monte Carlo sample prediction value And at the same time get the Monte Carlo sample prediction value The corresponding standard deviation

[0009] Step 2: Filter out the Monte Carlo sample prediction values ​​described in step 1 from the Monte Carlo samples The smallest top 10% of sample points are selected as candidate samples S candidate ;

[0010] Step 3: From the candidate sample S described in step 2 candidate Select the sample with the smallest value of the learning function U(x) to update the experimental design;

[0011] Step 4: Ensemble learning trains multiple MC-dropout neural networks and obtains multiple estimated failure probabilities to Calculate the mean Estimate the failure probability as an integrated function and calculate the standard deviation As a measure of uncertainty in the integrated failure probability;

[0012] Step 5: Based on the integrated failure probability and its corresponding relative standard deviation When the value drops below the critical value, it is judged whether the active learning method of structural reliability has converged, and if the method has not converged, it returns to step 1;

[0013] Step 6: Repeat the above steps until the method converges, that is, the active learning method for structural reliability calculation based on Monte Carlo MC-dropout neural network is realized.

[0014] Further, a preferred implementation is provided, in step 1, the Monte Carlo sample prediction value is obtained by using the proxy model based on the MC-dropout neural network At the same time, we get the standard deviation of the predicted value The method is:

[0015]

[0016] Among them, T is the number of forward propagation of MC-dropout neural network, y t Predict values ​​for each forward pass.

[0017] Further, a preferred implementation is provided, in step 2, the Monte Carlo sample prediction value described in step 1 is selected from the Monte Carlo samples The smallest top 10% of sample points are selected as candidate samples S candidate The method is:

[0018]

[0019] Further, a preferred implementation is provided, in which the formula for selecting the learning function U(x) in step 3 is:

[0020]

[0021] Further, a preferred implementation is provided, in step 5, according to the integrated failure probability Stability and its corresponding relative standard deviation The method convergence is judged to be below the critical value, and the relative error of the failure probability estimated by three consecutive rounds of integration is also judged to be less than the critical value. steps.

[0022] Solution 2: A computer-readable storage medium storing a computer program. When the computer program is executed by a processor, the steps of an active learning method for structural reliability calculation based on a Monte Carlo MC-dropout neural network described in any one of Solution 1 are implemented.

[0023] Solution three, a computer device, including a memory and a processor, wherein the memory stores a computer program. When the processor runs the computer program stored in the memory, the processor executes an active learning method for structural reliability calculation based on a Monte Carlo MC-dropout neural network as described in any one of Solution one.

[0024] Solution 4: A computer program product, as a computer program, when the computer program is executed, implements the active learning method for structural reliability calculation based on Monte Carlo MC-dropout neural network described in Solution 1.

[0025] The present invention is beneficial in that:

[0026] The present invention aims at the problem of high-dimensional structural reliability analysis, reduces the reliance on finite element analysis, and significantly reduces the calculation cost and time.

[0027] The present invention can handle higher-dimensional and more complex nonlinear problems, thereby improving the applicability of the analysis.

[0028] The present invention uses the MC-dropout neural network as a proxy model, and uses a weighted sampling method to uniformly sample from the Monte Carlo samples to obtain an initial experimental design, uses only a small number of samples to train the MC-dropout neural network, and uses the trained MC-dropout neural network to obtain the predicted value and corresponding standard deviation of the Monte Carlo samples;

[0029] The present invention uses the predicted value and standard deviation obtained by the MC-dropout neural network to screen candidate samples, calculates the learning function of all Monte Carlo samples, uses the learning function to guide the active learning process, selects a large number of new samples near the limit state surface and with significant uncertainty to update the proxy model, and uses a small number of samples to construct a relatively accurate proxy model to predict the failure probability.

[0030] The present invention utilizes ensemble learning technology to train multiple MC-dropout networks to estimate failure probability, and considers the standard deviation of the failure probability estimated by multiple MC-dropout networks as one of the convergence indicators to further improve the accuracy of failure probability estimation.

[0031] The results of the embodiments of the present invention show that the present invention can reduce the number of required finite element analyses by up to 80%.

[0032] In summary, the present invention utilizes the approximation ability of neural networks to high-dimensional nonlinear functions, and carries out structural reliability analysis methods and application research based on MC-dropout neural networks, providing technical support for the design and maintenance of large-scale engineering structures.

[0033] The present invention is also applicable to the field of machine learning civil engineering structure health monitoring. BRIEF DESCRIPTION OF THE DRAWINGS

[0034] Figure 1 A schematic diagram of a comparison between an MC-dropout neural network in an active learning method for structural reliability calculation based on a Monte Carlo MC-dropout neural network described in Implementation Example 1 and a neural network in the prior art.

[0035] Figure 1 In the figure, (a) is a schematic diagram of a standard neural network, and (b) is a schematic diagram of a MC-dropout neural network.

[0036] Figure 2It is a flow chart of an active learning method for structural reliability calculation based on Monte Carlo MC-dropout neural network described in implementation mode 1.

[0037] Figure 3 This is a schematic diagram of a three-dimensional finite element model in an active learning method for structural reliability calculation based on a Monte Carlo MC-dropout neural network as described in Implementation Example 9.

[0038] Figure 4 This is a schematic diagram of point selection results in an active learning method for structural reliability calculation based on a Monte Carlo MC-dropout neural network as described in Implementation Example 9.

[0039] Figure 5 Schematic diagram of the failure probability convergence process in an active learning method for structural reliability calculation based on a Monte Carlo MC-dropout neural network described in Implementation Method 1. DETAILED DESCRIPTION

[0040] In order to make the purpose, technical solutions and advantages of the implementation methods of the present application clearer, the technical solutions in the implementation methods of the present application will be clearly and completely described below in conjunction with the drawings in the implementation methods of the present application. Obviously, the described implementation methods are only part of the implementation methods of the present application, not all of the implementation methods.

[0041] Embodiment 1: This embodiment provides an active learning method for calculating structural reliability based on a Monte Carlo MC-dropout neural network. The active learning method for calculating structural reliability includes the following steps:

[0042] Step 1: Use the MC-dropout neural network as a proxy model to obtain the Monte Carlo sample prediction value And at the same time get the Monte Carlo sample prediction value The corresponding standard deviation

[0043] Step 2: Filter out the Monte Carlo sample prediction values ​​described in step 1 from the Monte Carlo samples The smallest top 10% of sample points are selected as candidate samples S candidate ;

[0044] Step 3: From the candidate sample S described in step 2 candidate Select the sample with the smallest value of the learning function U(x) to update the experimental design;

[0045] Step 4: Ensemble learning trains multiple MC-dropout neural networks and obtains multiple estimated failure probabilities to Calculate the mean Estimate the failure probability as an integrated function and calculate the standard deviation As a measure of uncertainty in the integrated failure probability;

[0046] Step 5: Based on the integrated failure probability and its corresponding relative standard deviation When the value drops below the critical value, it is judged whether the active learning method for calculating structural reliability has converged, and if the method has not converged, it returns to step 1;

[0047] Step 6: Repeat the above steps until the method converges, that is, the active learning method for structural reliability calculation based on Monte Carlo MC-dropout neural network is realized.

[0048] Implementation method 2: This implementation method is a further limitation of the active learning method for calculating structural reliability based on the Monte Carlo MC-dropout neural network described in implementation method 1. In step 1, the Monte Carlo sample prediction value is obtained based on the proxy model of the MC-dropout neural network. At the same time, we get the standard deviation of the predicted value The method is:

[0049]

[0050] Among them, T is the number of forward propagation of MC-dropout neural network, y t Predict values ​​for each forward pass.

[0051] Implementation method 3: This implementation method is a further limitation of the active learning method for calculating structural reliability based on the Monte Carlo MC-dropout neural network described in implementation method 1. In step 2, the Monte Carlo sample prediction value described in step 1 is selected from the Monte Carlo samples. The smallest top 10% of sample points are selected as candidate samples S candidate The method is:

[0052]

[0053] Implementation method 4: This implementation method is a further limitation of the active learning method for calculating structural reliability based on the Monte Carlo MC-dropout neural network described in implementation method 1. The formula for selecting the learning function U(x) in step 3 is:

[0054]

[0055] Implementation mode 5: This implementation mode further limits the active learning method for calculating structural reliability based on the Monte Carlo MC-dropout neural network described in implementation mode 1. In step 5, according to the integrated failure probability Stability and its corresponding relative standard deviation The method convergence is judged to be below the critical value, and the relative error of the failure probability estimated by three consecutive rounds of integration is also judged to be less than the critical value. steps.

[0056] Embodiment 6: A computer-readable storage medium stores a computer program, and when the computer program is executed by a processor, the steps of the method described in any one of embodiments 1 to 5 are implemented.

[0057] Embodiment 7: A computer device includes a memory and a processor, wherein the memory stores a computer program, and when the processor runs the computer program stored in the memory, the processor executes the method described in any one of embodiments 1 to 5.

[0058] Embodiment 8: A computer program product, as a computer program, implements the method described in embodiment 1 when the computer program is executed.

[0059] Embodiment 9: This embodiment provides an example, which is used to explain the above embodiments 1 to 8. The specific example is as follows:

[0060] See also Figures 1 to 5 The present embodiment is described. The purpose of the present embodiment is to propose an active learning method for structural reliability calculation based on MC-dropout neural network, so as to be applied to structural reliability analysis of civil engineering structures.

[0061] The core of this implementation is an active learning method for structural reliability calculation based on MC-dropout neural network. This method is mainly divided into two steps. The first step is to use MC-dropout neural network as a proxy model, and use it to obtain the predicted mean and predicted standard deviation to guide the active learning process in each iteration, identify and select new samples that are close to the limit state surface and have significant uncertainty, and use them to update the proxy model, thereby gradually improving the accuracy and reliability of the model. In the second step, the integration technology of MC-dropout neural network is used to estimate the failure probability, which further improves the accuracy of the analysis.

[0062] The steps in implementation mode 1 are specifically as follows:

[0063] Step 1: Sample N according to the probability distribution of high-dimensional random variables MC Monte Carlo samples S MC , set the number of steps τ = 1;

[0064] Step 2: According to the probability distribution of high-dimensional random variables, use the weighted sampling method to uniformly sample N0 samples from the candidate samples as the initial experimental design.

[0065] Step 3: Use training samples to train the MC-dropout neural network

[0066] Step 4: Forward propagate the trained MC-dropout neural network 100 times to obtain the Monte Carlo sample prediction value and the corresponding standard deviation

[0067] Step 5: Predict values ​​based on Monte Carlo samples The first 10% of samples with the smallest predicted values ​​are selected as candidate samples.

[0068] Step 6: Calculate the candidate sample learning function value And select the point where the learning function value is the smallest.

[0069] Step 7: Use ensemble learning to train multiple MC-dropout neural networks and obtain multiple estimated failure probabilities Calculate the mean of the ensemble estimated failure probabilities And calculate the integrated failure probability standard deviation

[0070] Step 8: Determine whether the method has converged. One of the convergence indicators is to determine the relative standard deviation. The second convergence index is to judge whether the relative error of the failure probability of three consecutive rounds of integrated estimation is less than the critical value

[0071]

[0072] Step 9: Use the samples selected in step 6 to update the experimental design and increase the number of rounds τ = τ + 1.

[0073] Among them, the predicted value of the proxy model based on the MC-dropout neural network in step 1 and the standard deviation corresponding to the predicted value are:

[0074]

[0075]

[0076] The point selection strategy based on the learning function is:

[0077] Step 2 is to select the top 10% of samples with smaller predicted values ​​in the Monte Carlo samples as candidate samples:

[0078]

[0079] The third step is to sample from candidate samples using the learning function:

[0080] The learning function formula is:

[0081]

[0082] The predicted distribution of the selected sample points is shown in the figure. The predicted value of the selected sample point is close to 0, and the standard deviation is large, and the uncertainty is large, which means that the probability of the neural network predicting the sample point incorrectly is large, and the selected sample point has a greater impact on the prediction accuracy of the neural network.

[0083] This implementation is based on PYTHON, and the code language is PYTORCH. The hyper parameters of each layer of the proxy model based on the MC-dropout neural network are shown in Table 1.

[0084] Table 1

[0085] Hyperparameters Number of hidden layers 2 Number of hidden units 100 Dropout rate 0.5 Activation Function ReLU Learning Rate 0.001

[0086] In this embodiment, the Python-based program is applied to the reliability analysis of the actual long-span bridge finite element analysis model. This application verifies the feasibility and practicality of the present invention. The following specific examples illustrate the effects of the present invention.

[0087] According to the design data of the cable-stayed bridge structure system, a 1:1 3D finite element model was established using the finite element analysis software ANSYS. Figure 3 As shown, it can be seen that this is a steel box girder cable-stayed bridge with a span arrangement of (48m+204m+460m+204m+48m). The steel box girder of the cable-stayed bridge structure system is divided into five parts by the bridge tower and the bridge pier, among which the middle span with the largest span is 460m. The finite element model takes into account all the load-bearing components in the cable-stayed bridge structure system. According to the functions and design forms of various components, different unit types are used to simulate them when establishing the finite element model, and are listed in Table 2.

[0088] Table 2

[0089] Component Type quantity Material Type Unit Type Bridge pier 8 Concrete Beam-44 Bridge Tower 2 Concrete Beam-44 Steel box girder 87 Steel Shell-63 Cable 144 Steel Link-10

[0090] A total of 470,698 units and 397,219 nodes were created for the entire model. The finite element model of the cable-stayed bridge structure is fixed to the ground through the piers and towers, and the constant loads of the components in the structural system are considered in the form of gravity acceleration. In this example, the limit state function is that the vertical displacement of the center of the main span does not exceed the critical value, which is defined as:

[0091] g(x)=1.15-δ(x)

[0092] Where δ(x) (unit: meter) is the vertical displacement and x is the random variable taken into account. The vertical displacement is determined by a three-dimensional finite element model established using ANSYS software. The random variable x includes the elastic modulus and cross-sectional area of ​​the cable, as well as the uniformly distributed load. Since the bridge model is symmetrical, the cables at symmetrical positions and under the same conditions are assumed to have the same elastic modulus and cross-sectional area. The random variable dimension is 35, including the elastic modulus and cross-sectional area of ​​17 different types of cables and 1 uniformly distributed load. The detailed distribution parameters of the random variables are shown in Table 3.

[0093] Table 3

[0094]

[0095]

[0096] The failure probability convergence curve of the method described in this embodiment is as follows: Figure 5 As shown in Figure 2, the neural network method based on Latin hypercube sampling requires more than 2200 samples to converge to an estimated failure probability with similar prediction accuracy, while the proposed method only requires 204 samples. This method is able to achieve a relatively accurate estimate of the failure probability using a limited number of samples.

[0097] For the purposes of the present specification, "computer-readable medium" may be any device that can contain, store, communicate, propagate or transmit a program for use with an instruction execution system, device or equipment or in conjunction with these instruction execution systems, devices or equipment. More specific examples of computer-readable media (non-exhaustive list) include the following: an electrical connection with one or N wirings (electronic device), a portable computer disk box (magnetic device), a random access memory (RAM), a read-only memory (ROM), an erasable and editable read-only memory (EPROM or flash memory), an optical fiber device, and a portable compact disk read-only memory (CDROM). In addition, the computer-readable medium may even be paper or other suitable medium on which the program may be printed, because the program may be obtained electronically, for example, by optically scanning the paper or other medium, followed by editing, interpreting or processing in other suitable ways as necessary, and then stored in a computer memory. It should be understood that the various parts of the present invention may be implemented in hardware, software, firmware or a combination thereof. In the above embodiments, the N steps or methods may be implemented in software or firmware stored in a memory and executed by a suitable instruction execution system. For example, if implemented in hardware, as in another embodiment, it can be implemented using any one of the following technologies known in the art or a combination thereof: a discrete logic circuit having a logic gate circuit for implementing a logic function on a data signal, a dedicated integrated circuit having a suitable combination of logic gate circuits, a programmable gate array (PGA), a field programmable gate array (FPGA), etc.

[0098] Those skilled in the art will appreciate that the above are only preferred embodiments of the present invention, and the various embodiments of the present disclosure and / or the features described in the claims may be combined or combined in various ways, even if such combinations or combinations are not explicitly described in the present disclosure. It is not intended to limit the present invention. Although the present invention has been described in detail with reference to the aforementioned embodiments, those skilled in the art may still modify the technical solutions described in the aforementioned embodiments, or perform equivalent substitutions on some of the technical features therein. Any modifications, equivalent substitutions, improvements, etc. made within the spirit and principles of the present invention shall be included in the protection scope of the present invention.

[0099] Although preferred embodiments of the present invention have been described, additional changes and modifications may be made to these embodiments by those skilled in the art once the basic inventive concepts are known. Therefore, the appended claims are intended to be interpreted as including the preferred embodiments and all changes and modifications that fall within the scope of the present invention. Obviously, those skilled in the art may make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalents, the present invention is also intended to include these modifications and variations.

Claims

1. An active learning method for structural reliability calculation based on Monte Carlo MC-dropout neural network, characterized in that: The active learning method for calculating structural reliability comprises the following steps: Step 1: Use the MC-dropout neural network as a proxy model to obtain the Monte Carlo sample prediction value And at the same time get the Monte Carlo sample prediction value The corresponding standard deviation Step 2: Filter out the Monte Carlo sample prediction values ​​described in step 1 from the Monte Carlo samples The smallest top 10% of sample points are selected as candidate samples S candidate ; Step 3: From the candidate sample S described in step 2 candidate Select the sample with the smallest value of the learning function U(x) to update the experimental design; Step 4: Ensemble learning trains multiple MC-dropout neural networks and obtains multiple estimated failure probabilities to Calculate the mean Estimate the failure probability as an integrated function and calculate the standard deviation As a measure of uncertainty in the integrated failure probability; Step 5: Based on the integrated failure probability and its corresponding relative standard deviation When the value drops below the critical value, it is judged whether the active learning method for calculating structural reliability has converged, and if the method has not converged, it returns to step 1; Step 6: Repeat the above steps until the method converges, that is, the active learning method for structural reliability calculation based on Monte Carlo MC-dropout neural network is realized.

2. The active learning method for structural reliability calculation based on Monte Carlo MC-dropout neural network according to claim 1 is characterized in that: In step 1, the proxy model based on the MC-dropout neural network obtains the Monte Carlo sample prediction value At the same time, we get the standard deviation of the predicted value The method is: Among them, T is the number of forward propagation of MC-dropout neural network, y t Predict values ​​for each forward pass.

3. The active learning method for structural reliability calculation based on Monte Carlo MC-dropout neural network according to claim 1 is characterized in that: In step 2, the Monte Carlo sample prediction value described in step 1 is selected from the Monte Carlo sample. The smallest top 10% of sample points are selected as candidate samples S candidate The method is:

4. The active learning method for structural reliability calculation based on Monte Carlo MC-dropout neural network according to claim 1 is characterized in that: The formula for selecting the learning function U(x) in step 3 is:

5. The active learning method for structural reliability calculation based on Monte Carlo MC-dropout neural network according to claim 1 is characterized in that: In step 5, based on the integrated failure probability Stability and its corresponding relative standard deviation The method convergence is judged to be below the critical value, and the relative error of the failure probability estimated by three consecutive rounds of integration is also judged to be less than the critical value. steps.

6. A computer storage medium for storing a computer program, characterized in that: When the computer program is read by a computer, the computer executes the method according to any one of claims 1 to 5.

7. A computer device comprising a processor and a storage medium, characterized in that A computer program is stored in the memory. When the processor runs the computer program stored in the memory, the processor executes the method according to any one of claims 1 to 5.

8. A computer program product, in which a computer program is embedded, characterized in that When the computer program is read, the method according to any one of claims 1 to 5 is implemented.

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