Importance sampling method for reliability calculation of high-speed railway bridges based on deep generative network

Abstract

The present application provides an important sampling method for calculating the reliability of a high-speed railway bridge based on a deep generative network, comprising the following steps: determining the probability distribution of random parameters of the high-speed railway bridge, and randomly sampling to generate a predetermined number of training samples; building an interpretable deep generative network sampling model, and defining the loss function of the deep generative network; training the interpretable deep generative network and the monotonic neural network, and determining the threshold for Gaussian distribution sampling based on the monotonic neural network; sampling a one-dimensional Gaussian distribution, screening training samples less than the threshold, and obtaining a first input sample, sampling a multi-dimensional Gaussian distribution, and obtaining a second input sample; merging the first input sample and the second input sample into a synthetic input sample; inputting the synthetic input sample into an interpretable deep generative network model to obtain an output sample, calculating the important sampling density of the output sample based on the estimated value of the probability distribution of the random parameters, and calculating the reliability of the high-speed railway bridge based on the important sampling density.

Description

Technical Field

[0001] The present invention relates to the technical field of high-speed railway bridge reliability assessment, and in particular to an important sampling method for high-speed railway bridge reliability calculation based on a deep generative network. Background Art

[0002] During long-term service, large-span high-speed railway (HSR) bridges may be subjected to strong external loads such as wind and earthquake, which seriously threaten the driving safety of high-speed railway bridges. Conducting reliability performance evaluation of large-span HSR bridges is a key task to ensure the comfort and safety of high-speed railway driving. Since both the large-span HSR bridges themselves and external loads have strong randomness, the traditional deterministic evaluation method of large-span HSR bridges is difficult to meet engineering needs. Reliability calculation can fully consider the randomness of the large-span HSR bridges themselves and wind loads, and more accurately evaluate the reliability performance of large-span HSR bridges, which is an important means to ensure the comfort and safety of large-span HSR bridges.

[0003] The Monte Carlo simulation method is a general method for calculating the reliability of long-span high-speed railway bridges. It solves the complete probability information of bridge response by random sampling, response analysis and probability statistics. However, since the reliability calculation of long-span high-speed railway bridges generally requires a large number of finite element calculations, the traditional Monte Carlo simulation method requires a large number of samples to ensure sufficient estimation accuracy. The direct use of the Monte Carlo simulation method for the reliability calculation of long-span high-speed railway bridges has a large amount of calculation. The importance sampling method is an important means to improve the efficiency of Monte Carlo simulation. The importance sampling method reduces the number of samples required for Monte Carlo simulation by replacing the original probability density function sampling of random variables with the important sampling density function. The importance sampling method for the reliability calculation of long-span high-speed railway bridges often uses probability distribution models such as Gaussian distribution, Gaussian mixture and kernel density estimation to fit the important sampling density function. However, in order to fit the important sampling density function, the existing importance sampling method generally needs to determine the training samples of the failure area in advance. Since the failure area is unknown in advance, it is very difficult to fit the complex important sampling density. The existing important sampling density function has insufficient fitting accuracy and low sampling efficiency. Summary of the invention

[0004] The purpose of the present invention is to overcome the above-mentioned technical deficiencies and provide an important sampling method for calculating the reliability of high-speed railway bridges based on a deep generative network, so as to solve the technical problems in the prior art that it is very difficult to calculate complex important sampling densities, the existing important sampling density function has insufficient fitting accuracy and low sampling efficiency.

[0005] In order to achieve the above technical objectives, in a first aspect, the technical solution of the present invention provides an important sampling method for calculating the reliability of a high-speed railway bridge based on a deep generative network, comprising the following steps:

[0006] Determine the probability distribution of random parameters of the high-speed railway bridge, and perform random sampling according to the probability distribution of the random parameters to generate a predetermined number of training samples;

[0007] Building an interpretable deep generative network sampling model, the deep network sampling model includes: a deep generative network and a monotonic neural network, and defining a loss function of the deep generative network;

[0008] Using a small batch stochastic gradient descent method to train the interpretable deep generative network and the monotone neural network, and determining a threshold for Gaussian distribution sampling based on the monotone neural network;

[0009] Sampling the one-dimensional Gaussian distribution, screening the training samples that are smaller than the threshold, obtaining a first input sample, sampling the multidimensional Gaussian distribution, obtaining a second input sample, the dimension of the multidimensional Gaussian distribution is D-1, where D is the dimension of the random parameter;

[0010] Merging the first input sample and the second input sample into a D-dimensional synthetic input sample;

[0011] The synthetic input samples are input into the interpretable deep generative network model to obtain output samples, the important sampling density of the output samples is calculated according to the probability distribution estimate of the random parameters, and the reliability of the high-speed railway bridge is calculated according to the important sampling density using the important sampling theory.

[0012] Compared with the prior art, the beneficial effects of the present invention include:

[0013] The invention provides an important sampling method for calculating the reliability of high-speed railway bridges based on a deep generative network. The method adopts a deep generative network and a monotonic neural network to construct an interpretable deep generative network sampling model, thereby realizing efficient sampling of complex important sampling density, and thus improving the efficiency and accuracy of the reliability calculation of large-span high-speed railway bridges.

[0014] According to some embodiments of the present invention, the loss function of the deep generative network includes: a first loss function, a second loss function, a third loss function and a fourth loss function;

[0015] In order to fit the probability distribution of the random parameters, the first loss function is designed as:

[0016]

[0017] Among them G -1 (x) is the inverse transformation of the deep generative network, and the fitting probability distribution is The true probability distribution of the random parameter is q(x);

[0018] In order to narrow the fitting probability distribution The difference between the true probability distribution q(x) constrains the shape of the fitted distribution and avoids overfitting. The second loss function is defined as:

[0019]

[0020] In order to achieve the interpretability of the deep generative network and reduce the error between the monotone neural network prediction value and the sample limit state function, the third loss function is defined as:

[0021] loss3=[g(x)-M(z1)]2=[g(x)-M ( G-1(x)1 ) ] 2

[0022] Among them, G -1 (x)1 represents G -1 The first dimension of (x), g(x) is the limit state function value of the training sample, and M(z1) is the predicted value of the monotone neural network;

[0023] In order to prevent the predicted value of the monotone neural network from converging to the local optimal value, the monotone neural network is encouraged to predict the new limit state function value. The fourth loss function is defined as:

[0024]

[0025] Among them, n is the number of samples for small batch learning, The predicted value of the i-th sample.

[0026] According to some embodiments of the present invention, the random parameters include: bridge geometry, material properties and external loads, main beam elastic modulus, bridge tower elastic modulus, lane uniformly distributed load, cable steel wire cross-sectional area and cable elastic modulus.

[0027] According to some embodiments of the present invention, a mini-batch stochastic gradient descent method is used to train the interpretable deep generative network and the monotonic neural network, comprising the steps of:

[0028] Using a mini-batch stochastic gradient descent method to simultaneously train the deep generative network and the monotonic neural network;

[0029] When the prediction accuracy of the deep generative network meets the requirements, the monotone neural network is trained separately to make the monotone neural network have higher prediction accuracy.

[0030] According to some embodiments of the present invention, the dimension of the first input sample is 1 dimension, the dimension of the second input sample is 4 dimensions, and the dimension of the synthetic input sample is 5 dimensions.

[0031] According to some embodiments of the present invention, a threshold for Gaussian distribution sampling is determined according to the monotone neural network, and the threshold is calculated as follows:

[0032]

[0033] Among them, the empirical coefficient of ΔP classification error is taken as 0.05;

[0034] The calculation formula is:

[0035]

[0036] The calculation formula of M0 is:

[0037]

[0038] According to some embodiments of the present invention, the important sampling density of the output samples is calculated according to the estimated value of the probability distribution of the random parameter, and the calculation formula is as follows:

[0039]

[0040] in, is the probability distribution estimate of the random parameter.

[0041] According to some embodiments of the present invention, the reliability of the high-speed railway bridge is calculated according to the importance sampling density using the importance sampling theory, and the calculation formula is as follows:

[0042]

[0043] In a second aspect, the technical solution of the present invention provides an electronic device, comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the important sampling method for calculating the reliability of a high-speed railway bridge based on a deep generative network as described in any one of the first aspects is implemented.

[0044] In a third aspect, the technical solution of the present invention provides a computer-readable storage medium, which stores computer-executable instructions, and the computer-executable instructions are used to enable a computer to execute the important sampling method for calculating the reliability of high-speed railway bridges based on a deep generative network as described in any one of the first aspects.

[0045] The present invention does not require the preparation of training samples from the failure area in advance, and can directly use samples generated according to the original probability distribution of random parameters to train an interpretable deep generative network; then use the interpretability of the interpretable deep generative network to calculate the input sample threshold, and use the sampling ability of the deep generative network to sample from the important sampling density; finally, the reliability of large-span high-speed railway bridges can be calculated with high efficiency and high precision. Compared with existing methods, the present invention has higher sampling efficiency and reliability calculation accuracy for complex important sampling densities.

[0046] Additional aspects and advantages of the present invention will be given in part in the following description and in part will be obvious from the following description, or will be learned through practice of the present invention. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] The above and / or additional aspects and advantages of the present invention will become apparent and easily understood from the description of the embodiments in conjunction with the following drawings, wherein the abstract drawings are identical to one of the drawings in the specification:

[0048] Figure 1 A flowchart of an important sampling method for calculating reliability of a high-speed railway bridge based on a deep generative network provided by an embodiment of the present invention;

[0049] Figure 2 An interpretable deep generative network sampling model diagram of an important sampling method for calculating reliability of high-speed railway bridges based on a deep generative network provided in another embodiment of the present invention;

[0050] Figure 3 A schematic diagram of a method for determining a threshold value of an important sampling method for calculating reliability of a high-speed railway bridge based on a deep generative network provided by another embodiment of the present invention;

[0051] Figure 4 A schematic diagram of a bridge finite element model of an important sampling method for calculating reliability of a high-speed railway bridge based on a deep generative network provided by another embodiment of the present invention;

[0052] Figure 5 An input Gaussian distribution sample of an important sampling method for calculating reliability of a high-speed railway bridge based on a deep generative network provided by another embodiment of the present invention;

[0053] Figure 6 Another embodiment of the present invention provides an important sampling sample of the output random parameter distribution of an important sampling method for calculating the reliability of a high-speed railway bridge based on a deep generative network. DETAILED DESCRIPTION

[0054] In order to make the purpose, technical solution and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0055] It should be noted that, although the functional modules are divided in the system schematic diagram and the logical order is shown in the flowchart, in some cases, the steps shown or described may be performed in a different order than the module division in the system or the order in the flowchart. The terms "first", "second", etc. in the specification, claims and the above drawings are used to distinguish similar objects, and are not necessarily used to describe a specific order or sequence.

[0056] The present invention provides an important sampling method for calculating the reliability of high-speed railway bridges based on a deep generative network. It does not require the preparation of training samples from the failure area in advance. The samples generated according to the original probability distribution of random parameters can be directly used to train an interpretable deep generative network. The interpretability of the interpretable deep generative network is then used to calculate the input sample threshold, and the sampling ability of the deep generative network is used to sample from the important sampling density. Finally, the reliability of large-span high-speed railway bridges is calculated with high efficiency and high precision. Compared with the existing methods, the present invention has higher sampling efficiency and reliability calculation accuracy for complex important sampling densities.

[0057] The embodiments of the present invention are further described below in conjunction with the accompanying drawings.

[0058] Reference Figure 1 , Figure 1 A flowchart of an important sampling method for calculating the reliability of a high-speed railway bridge based on a deep generative network provided by an embodiment of the present invention; the important sampling method for calculating the reliability of a high-speed railway bridge based on a deep generative network includes but is not limited to the following steps:

[0059] Step S110, determining the probability distribution of random parameters of the high-speed railway bridge, and performing random sampling according to the probability distribution of the random parameters to generate a predetermined number of training samples;

[0060] Step S120, building an interpretable deep generative network sampling model, the deep network sampling model includes: a deep generative network and a monotone neural network, and defining a loss function of the deep generative network;

[0061] Step S130, using a small batch stochastic gradient descent method to train an interpretable deep generative network and a monotone neural network, and determining a threshold for Gaussian distribution sampling based on the monotone neural network;

[0062] Step S140, sampling the one-dimensional Gaussian distribution, screening the training samples that are smaller than the threshold, obtaining the first input sample, and sampling the multi-dimensional Gaussian distribution, obtaining the second input sample;

[0063] Step S150, merging the first input sample and the second input sample into a D-dimensional synthetic input sample;

[0064] Step S160, input the synthesized input sample into an interpretable deep generative network model to obtain the output sample, calculate the important sampling density of the output sample according to the probability distribution estimate of the random parameter, and use the important sampling theory to calculate the reliability of the high-speed railway bridge according to the important sampling density.

[0065] In one embodiment, an important sampling method for calculating the reliability of a high-speed railway bridge based on a deep generative network includes the following steps: determining the probability distribution of random parameters of the high-speed railway bridge, and performing random sampling according to the probability distribution of the random parameters to generate a predetermined number of training samples; building an interpretable deep generative network sampling model, the deep deep network sampling model includes: a deep generative network and a monotone neural network, and defining the loss function of the deep generative network; using a small batch stochastic gradient descent method to train the interpretable deep generative network and the monotone neural network, and determining the threshold for Gaussian distribution sampling according to the monotone neural network; sampling a one-dimensional Gaussian distribution, screening training samples less than the threshold, to obtain a first input sample, sampling a multidimensional Gaussian distribution, to obtain a second input sample, the dimension of the multidimensional Gaussian distribution is D-1, where D is the dimension of the random parameter; merging the first input sample and the second input sample into a D-dimensional synthetic input sample; inputting the synthetic input sample into the interpretable deep generative network model to obtain an output sample, calculating the important sampling density of the output sample according to the estimated value of the probability distribution of the random parameter, and calculating the reliability of the high-speed railway bridge according to the important sampling density using the importance sampling theory.

[0066] The important sampling method for calculating the reliability of high-speed railway bridges based on deep generative networks provided in this embodiment includes the steps of: generating training samples, building an interpretable deep generative network, defining a loss function, training an interpretable deep generative network, calculating a threshold, generating input and output samples, and calculating reliability. The present invention constructs an interpretable deep generative network sampling model through a deep generative network and a monotone neural network, and adopts four loss functions to enable the interpretable deep generative network to sample the target probability distribution while being interpretable. According to the interpretability of the interpretable deep generative network, the threshold of the input Gaussian distribution sample can be effectively calculated, and then the input Gaussian sample can be screened according to the threshold, thereby realizing the sampling of any important sampling density. The present invention can directly use the training samples generated according to the original distribution of random parameters to train the interpretable deep generative network, and realize the efficient sampling of complex important sampling density, which can effectively improve the efficiency and accuracy of the reliability calculation of large-span high-speed railway bridges.

[0067] Reference Figures 2 to 6 , Figure 2 An interpretable deep generative network sampling model diagram of an important sampling method for calculating reliability of high-speed railway bridges based on a deep generative network provided in another embodiment of the present invention;

[0068] Figure 3 A schematic diagram of a method for determining a threshold value of an important sampling method for calculating reliability of a high-speed railway bridge based on a deep generative network provided by another embodiment of the present invention; Figure 4 A schematic diagram of a bridge finite element model of an important sampling method for calculating reliability of a high-speed railway bridge based on a deep generative network provided by another embodiment of the present invention; Figure 5 An input Gaussian distribution sample of an important sampling method for calculating reliability of a high-speed railway bridge based on a deep generative network provided by another embodiment of the present invention; Figure 6 Another embodiment of the present invention provides an important sampling sample of the output random parameter distribution of an important sampling method for calculating the reliability of a high-speed railway bridge based on a deep generative network.

[0069] In one embodiment, the high-speed railway bridge reliability calculation importance sampling method based on deep generative network includes the following steps:

[0070] The reliability calculation of a certain bridge is carried out using an importance sampling method for reliability calculation of a large-span high-speed railway bridge based on an interpretable deep generative network.

[0071] (1) First, the probability distribution q(x) of random parameters of high-speed railway bridges, such as bridge geometric dimensions, material properties, and external loads, is determined. As shown in the following table, five random parameters, including the elastic modulus of the main beam, the elastic modulus of the bridge tower, the uniformly distributed load on the lane, the cross-sectional area of ​​the cable steel wire, and the elastic modulus of the cable, are considered. The specific probability distribution information is shown in the following table.

[0072]

[0073] (2) According to the probability distribution of random parameters, random sampling is performed to generate a certain number of training samples, and the limit state function value g(x) of the samples is calculated using the finite element model. Figure 4 As shown;

[0074] (3) Build an interpretable deep generative network sampling model, such as Figure 2 As shown. The deep generative network sampling model consists of two parts: a deep generative network and a monotone neural network. Its input is a Gaussian distribution sample, and its output is a random parameter distribution sample;

[0075] (4) Define the loss function of the interpretable deep generative network. In order to efficiently train the deep generative network model, four loss functions are designed. First, in order to adopt Fitting the target random parameter distribution q(x), the first loss function is designed as

[0076]

[0077] Among them G -1 (x) is the inverse transformation of the deep generative network. The second loss function is used to shrink the fitting probability distribution The difference between the true probability distribution q(x) and the distribution of the fitted distribution can also be constrained to avoid overfitting. The second loss function is defined as

[0078]

[0079] In order to achieve the interpretability of the deep generative network, the third loss function is used to reduce the error between the monotone neural network prediction value and the sample limit state function. Therefore, the third loss function is

[0080] loss3=[g(x)-M(z1)] 2 =[g(x)-M(G -1 (x)1)] 2 (3)

[0081] Among them, G -1 (x)1 represents G -1 (x), g(x) is the limit state function value of the sample, and M(z1) is the predicted value of the monotone neural network. In order to prevent the predicted value of the monotone neural network from converging to the local optimal value, a fourth loss function is designed to encourage the monotone neural network to predict the new limit state function value. The loss function is defined as

[0082]

[0083] Among them, n is the number of samples for small batch learning, The predicted value of the i-th sample;

[0084] (5) Use the mini-batch stochastic gradient descent method to train the interpretable deep generative network. First, train the deep generative network and the monotone neural network simultaneously. When the prediction accuracy of the deep generative network meets the requirements, train the monotone neural network separately to ensure that the monotone neural network has higher prediction accuracy.

[0085] (6) Determine the threshold of Gaussian distribution sampling based on the monotonic neural network. The threshold calculation formula is:

[0086]

[0087] Among them, the empirical coefficient of ΔP classification error can be taken as 0.05; It can be calculated according to the following formula

[0088]

[0089] Among them, M0 can be calculated using the following formula

[0090]

[0091] (7) Sampling the one-dimensional Gaussian distribution, filtering out samples smaller than the threshold Sample, get the input sample z1;

[0092] (8) Sampling the 4-dimensional Gaussian distribution, we get the input sample z 2-5 ;

[0093] (9) Input sample z1 and input sample z 2-5 Merge into 5-dimensional input samples z. The input samples shown in dimensions 1-2 are as follows Figure 5 As shown;

[0094] (10) Input the 5-dimensional input sample z into the interpretable deep generative network model to obtain the output sample x. The output sample shown in the 1st-2nd dimension is as follows Figure 6 As shown;

[0095] (11) Calculate the important sampling density of the sample based on the probability distribution estimate of the random parameter

[0096]

[0097] The estimated value of the probability density The following formula is used for calculation:

[0098] x o =xσ x +μ x (9)

[0099]

[0100] (12) The reliability of high-speed railway bridges is calculated using the importance sampling theory. The calculation formula is as follows:

[0101]

[0102] The reliability calculation results are shown in the following table.

[0103]

[0104] In one embodiment, an important sampling method for calculating the reliability of a high-speed railway bridge based on a deep generative network includes the following steps: determining the probability distribution of random parameters of the high-speed railway bridge, and performing random sampling according to the probability distribution of the random parameters to generate a predetermined number of training samples; building an interpretable deep generative network sampling model, the deep deep network sampling model includes: a deep generative network and a monotone neural network, and defining the loss function of the deep generative network; using a small batch stochastic gradient descent method to train the interpretable deep generative network and the monotone neural network, and determining the threshold for Gaussian distribution sampling according to the monotone neural network; sampling a one-dimensional Gaussian distribution, screening training samples less than the threshold, to obtain a first input sample, sampling a multidimensional Gaussian distribution, to obtain a second input sample, the dimension of the multidimensional Gaussian distribution is D-1, where D is the dimension of the random parameter; merging the first input sample and the second input sample into a D-dimensional synthetic input sample; inputting the synthetic input sample into the interpretable deep generative network model to obtain an output sample, calculating the important sampling density of the output sample according to the estimated value of the probability distribution of the random parameter, and calculating the reliability of the high-speed railway bridge according to the important sampling density using the importance sampling theory.

[0105] The loss functions of the deep generative network include: a first loss function, a second loss function, a third loss function and a fourth loss function;

[0106] In order to fit the probability distribution of random parameters, the first loss function is designed as:

[0107]

[0108] Among them G -1 (x) is the inverse transformation of the deep generative network, and the fitting probability distribution is The true probability distribution of the random parameter is q(x);

[0109] In order to narrow the fitting probability distribution The difference between the true probability distribution q(x) constrains the shape of the fitted distribution and avoids overfitting. The second loss function is defined as:

[0110]

[0111] In order to achieve the interpretability of the deep generative network and reduce the error between the monotonic neural network prediction value and the sample limit state function, the third loss function is defined as:

[0112] loss3=[g(x)-M(z1)]2=[g(x)-M(G-1(x)1)] 2

[0113] Among them, G -1 (x)1 represents G -1The first dimension of (x), g(x) is the limit state function value of the training sample, and M(z1) is the predicted value of the monotone neural network;

[0114] In order to avoid the prediction value of the monotone neural network from converging to the local optimal value and encourage the monotone neural network to predict the new limit state function value, the fourth loss function is defined as:

[0115]

[0116] Among them, n is the number of samples for small batch learning, The predicted value of the i-th sample.

[0117] The input of the interpretable deep generative network sampling model is a Gaussian distribution sample, and the output is a random parameter distribution sample. Among them, the deep generative network can realize probability transformation, and then obtain a random parameter distribution sample based on the input Gaussian distribution sample; the monotone neural network is coupled with the deep generative network using a third loss function, so that the output of the deep generative network is monotonically increasing with respect to the input. The high-speed railway bridge reliability calculation important sampling method based on the deep generative network provided in this embodiment has high sampling efficiency and reliability calculation accuracy for complex important sampling density.

[0118] Furthermore, the threshold of Gaussian distribution sampling is determined according to the monotone neural network, and the threshold is calculated as follows:

[0119]

[0120] Among them, the empirical coefficient of ΔP classification error is taken as 0.05;

[0121] The calculation formula is:

[0122]

[0123] The calculation formula of M0 is:

[0124]

[0125] Furthermore, the important sampling density of the output samples is calculated based on the estimated value of the probability distribution of the random parameters, and the calculation formula is as follows:

[0126]

[0127] in, is the probability distribution estimate of the random parameter.

[0128] Furthermore, the reliability of the high-speed railway bridge is calculated based on the importance sampling density using the importance sampling theory. The calculation formula is as follows:

[0129]

[0130] In one embodiment, an important sampling method for calculating the reliability of a high-speed railway bridge based on a deep generative network includes the following steps: determining the probability distribution of random parameters of the high-speed railway bridge, and performing random sampling according to the probability distribution of the random parameters to generate a predetermined number of training samples; building an interpretable deep generative network sampling model, the deep deep network sampling model includes: a deep generative network and a monotone neural network, and defining the loss function of the deep generative network; using a small batch stochastic gradient descent method to train the interpretable deep generative network and the monotone neural network, and determining the threshold for Gaussian distribution sampling according to the monotone neural network; sampling a one-dimensional Gaussian distribution, screening training samples less than the threshold, to obtain a first input sample, sampling a multidimensional Gaussian distribution, to obtain a second input sample, the dimension of the multidimensional Gaussian distribution is D-1, where D is the dimension of the random parameter; merging the first input sample and the second input sample into a D-dimensional synthetic input sample; inputting the synthetic input sample into the interpretable deep generative network model to obtain an output sample, calculating the important sampling density of the output sample according to the estimated value of the probability distribution of the random parameter, and calculating the reliability of the high-speed railway bridge according to the important sampling density using the importance sampling theory. The random parameters include: bridge geometry, material properties and external loads, main beam elastic modulus, bridge tower elastic modulus, lane uniformly distributed load, cable wire cross-sectional area and cable elastic modulus.

[0131] In one embodiment, an important sampling method for calculating the reliability of a high-speed railway bridge based on a deep generative network includes the following steps: determining the probability distribution of random parameters of the high-speed railway bridge, and performing random sampling according to the probability distribution of the random parameters to generate a predetermined number of training samples; building an interpretable deep generative network sampling model, the deep deep network sampling model includes: a deep generative network and a monotone neural network, and defining the loss function of the deep generative network; using a small batch stochastic gradient descent method to train the interpretable deep generative network and the monotone neural network, and determining the threshold for Gaussian distribution sampling according to the monotone neural network; sampling a one-dimensional Gaussian distribution, screening training samples less than the threshold, to obtain a first input sample, sampling a multidimensional Gaussian distribution, to obtain a second input sample, the dimension of the multidimensional Gaussian distribution is D-1, where D is the dimension of the random parameter; merging the first input sample and the second input sample into a D-dimensional synthetic input sample; inputting the synthetic input sample into the interpretable deep generative network model to obtain an output sample, calculating the important sampling density of the output sample according to the estimated value of the probability distribution of the random parameter, and calculating the reliability of the high-speed railway bridge according to the important sampling density using the importance sampling theory.

[0132] A small batch stochastic gradient descent method is used to train an interpretable deep generative network and a monotone neural network, including the steps of: simultaneously training the deep generative network and the monotone neural network using the small batch stochastic gradient descent method; when the prediction accuracy of the deep generative network meets the requirements, training the monotone neural network separately to make the monotone neural network have higher prediction accuracy.

[0133] In one embodiment, an important sampling method for calculating the reliability of a high-speed railway bridge based on a deep generative network includes the following steps: determining the probability distribution of random parameters of the high-speed railway bridge, and performing random sampling according to the probability distribution of the random parameters to generate a predetermined number of training samples; building an interpretable deep generative network sampling model, the deep deep network sampling model includes: a deep generative network and a monotone neural network, and defining the loss function of the deep generative network; using a small batch stochastic gradient descent method to train the interpretable deep generative network and the monotone neural network, and determining the threshold for Gaussian distribution sampling according to the monotone neural network; sampling a one-dimensional Gaussian distribution, screening training samples less than the threshold, to obtain a first input sample, sampling a multidimensional Gaussian distribution, to obtain a second input sample, the dimension of the multidimensional Gaussian distribution is D-1, where D is the dimension of the random parameter; merging the first input sample and the second input sample into a D-dimensional synthetic input sample; inputting the synthetic input sample into the interpretable deep generative network model to obtain an output sample, calculating the important sampling density of the output sample according to the estimated value of the probability distribution of the random parameter, and calculating the reliability of the high-speed railway bridge according to the important sampling density using the importance sampling theory. The dimension of the first input sample is 1 dimension, the dimension of the second input sample is 4 dimensions, and the dimension of the synthesized input sample is 5 dimensions.

[0134] The present application also provides an electronic device, comprising: a memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the important sampling method for calculating the reliability of a high-speed railway bridge based on a deep generative network as described above is implemented.

[0135] The processor and the memory may be connected via a bus or other means.

[0136] As a non-transient computer-readable storage medium, the memory can be used to store non-transient software programs and non-transient computer executable programs. In addition, the memory may include a high-speed random access memory, and may also include a non-transient memory, such as at least one disk storage device, a flash memory device, or other non-transient solid-state storage device. In some embodiments, the memory may optionally include a memory remotely disposed relative to the processor, and these remote memories may be connected to the processor via a network. Examples of the above-mentioned network include, but are not limited to, the Internet, an intranet, a local area network, a mobile communication network, and combinations thereof.

[0137] The device embodiments described above are merely illustrative, and the units described as separate components may or may not be physically separated, and may be located in one place or distributed on multiple network units. Some or all of the modules may be selected according to actual needs to achieve the purpose of the solution of this embodiment.

[0138] In addition, an embodiment of the present invention also provides a computer-readable storage medium, which stores computer-executable instructions, and the computer-executable instructions are executed by a processor or controller, for example, by a processor in the above-mentioned terminal embodiment, so that the above-mentioned processor can execute the important sampling method for calculating the reliability of high-speed railway bridges based on the deep generative network in the above-mentioned embodiment.

[0139] It will be appreciated by those skilled in the art that all or some of the steps and systems in the disclosed method above may be implemented as software, firmware, hardware and appropriate combinations thereof. Some physical components or all physical components may be implemented as software executed by a processor, such as a central processing unit, a digital signal processor or a microprocessor, or may be implemented as hardware, or may be implemented as an integrated circuit, such as an application specific integrated circuit. Such software may be distributed on a computer-readable medium, which may include a computer storage medium (or a non-transitory medium) and a communication medium (or a temporary medium). As known to those skilled in the art, the term computer storage medium includes volatile and non-volatile, removable and non-removable media implemented in any method or technology for storing information (such as computer-readable instructions, data structures, program modules or other data). Computer storage media include, but are not limited to, RAM, ROM, EEPROM, flash memory or other memory technologies, CD-ROM, digital versatile disks (DVD) or other optical disk storage, magnetic cassettes, magnetic tapes, disk storage or other magnetic storage devices, or any other medium that may be used to store desired information and may be accessed by a computer. Furthermore, it is well known to those skilled in the art that communication media typically embodies computer readable instructions, data structures, program modules, or other data in a modulated data signal such as a carrier wave or other transport mechanism, and may include any information delivery media.

[0140] The above is a specific description of the preferred implementation of the present invention, but the present invention is not limited to the above-mentioned implementation mode. Technical personnel familiar with the field can also make various equivalent deformations or substitutions without violating the spirit of the present invention. These equivalent deformations or substitutions are all included in the scope defined by the claims of the present invention.

[0141] The specific implementation of the present invention described above does not constitute a limitation on the protection scope of the present invention. Any other corresponding changes and modifications made based on the technical concept of the present invention should be included in the protection scope of the claims of the present invention.

Claims

1. An important sampling method for calculating the reliability of high-speed railway bridges based on deep generative networks, characterized in that: The following steps are involved: Determine the probability distribution of random parameters of the high-speed railway bridge, and perform random sampling according to the probability distribution of the random parameters to generate a predetermined number of training samples; the random parameters include bridge geometry, material properties, external loads, main beam elastic modulus, bridge tower elastic modulus, lane uniform load, cable steel wire cross-sectional area and cable elastic modulus; Building an interpretable deep generative network sampling model, the deep generative network sampling model includes: a deep generative network and a monotonic neural network, and defining a loss function of the deep generative network; Using a small batch stochastic gradient descent method to train the interpretable deep generative network and the monotone neural network, and determining a threshold for Gaussian distribution sampling based on the monotone neural network; Sampling the one-dimensional Gaussian distribution, screening the training samples that are smaller than the threshold, obtaining a first input sample, sampling the multidimensional Gaussian distribution, obtaining a second input sample, the dimension of the multidimensional Gaussian distribution is D-1, where D is the dimension of the random parameter; Merging the first input sample and the second input sample into a D-dimensional synthetic input sample; The synthetic input samples are input into the interpretable deep generative network model to obtain output samples, the important sampling density of the output samples is calculated according to the probability distribution estimate of the random parameters, and the reliability of the high-speed railway bridge is calculated according to the important sampling density using the important sampling theory.

2. The high-speed railway bridge reliability calculation importance sampling method based on deep generative network according to claim 1 is characterized in that: The loss function of the deep generative network includes: a first loss function, a second loss function, a third loss function and a fourth loss function; In order to fit the probability distribution of the random parameters, the first loss function is designed as: Among them, G -1 (x) is the inverse transform of the deep generative network, is the Jacobian matrix of the inverse transformation of the deep generative network, and the fitting probability distribution is The true probability distribution of the random parameter is q(x); In order to narrow the fitting probability distribution The difference between the true probability distribution q(x) constrains the shape of the fitted distribution and avoids overfitting. The second loss function is defined as: In order to achieve the interpretability of the deep generative network and reduce the error between the monotone neural network prediction value and the sample limit state function, the third loss function is defined as: loss3=[g(x)-M(z1)] 2 =[g(x)-M(G- 1 (x)1)] 2 Among them, G -1 (x)1 represents G -1 The first dimension of (x), g(x) is the limit state function value of the training sample, and M(z1) is the predicted value of the monotone neural network; In order to prevent the predicted value of the monotone neural network from converging to the local optimal value, the monotone neural network is encouraged to predict the new limit state function value. The fourth loss function is defined as: Among them, n is the number of samples for small batch learning, The predicted value of the i-th sample.

3. The high-speed railway bridge reliability calculation importance sampling method based on deep generative network according to claim 1 is characterized in that: The random parameters include: bridge geometric dimensions, material properties and external loads, main beam elastic modulus, bridge tower elastic modulus, lane uniformly distributed load, cable steel wire cross-sectional area and cable elastic modulus.

4. The high-speed railway bridge reliability calculation importance sampling method based on deep generative network according to claim 1 is characterized in that: The mini-batch stochastic gradient descent method is used to train the interpretable deep generative network and the monotone neural network, comprising the steps of: Using a mini-batch stochastic gradient descent method to simultaneously train the deep generative network and the monotonic neural network; When the prediction accuracy of the deep generative network meets the requirements, the monotone neural network is trained separately to make the monotone neural network have higher prediction accuracy.

5. The high-speed railway bridge reliability calculation importance sampling method based on deep generative network according to claim 1 is characterized in that: The dimension of the first input sample is 1 dimension, the dimension of the second input sample is 4 dimensions, and the dimension of the synthetic input sample is 5 dimensions.

6. The high-speed railway bridge reliability calculation importance sampling method based on deep generative network according to claim 2 is characterized in that: The threshold of Gaussian distribution sampling is determined according to the monotone neural network, and the calculation formula of the threshold is: Among them, the empirical coefficient of ΔP classification error is taken as 0.05; The calculation formula is: The calculation formula of M0 is: Among them, g0 is the zero value of the standardized bridge limit state function, g(x o ) is the limit state function zero value is 0, μ g is the average value of the limit state function of the training samples, σ g is the standard deviation of the limit state function value of the training samples.

7. The high-speed railway bridge reliability calculation importance sampling method based on deep generative network according to claim 6 is characterized in that: The important sampling density of the output samples is calculated according to the estimated value of the probability distribution of the random parameters, and the calculation formula is as follows: in, is the probability distribution estimate of the random parameter, I is the indicator function, and the function value is 1 when the inequality in the brackets holds, otherwise it is 0.

8. The high-speed railway bridge reliability calculation importance sampling method based on deep generative network according to claim 7 is characterized in that: The reliability of the high-speed railway bridge is calculated using the importance sampling theory according to the importance sampling density. The calculation formula is as follows:

9. An electronic device, characterized in that: include: A memory, a processor, and a computer program stored in the memory and executable on the processor, wherein when the processor executes the computer program, the important sampling method for calculating the reliability of a high-speed railway bridge based on a deep generative network as described in any one of claims 1 to 8 is implemented.

10. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores computer-executable instructions, and the computer-executable instructions are used to enable a computer to execute the important sampling method for calculating the reliability of a high-speed railway bridge based on a deep generative network as described in any one of claims 1 to 8.

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