Reliability analysis method of non-gaussian cross-correlation random field based on considering parameters of cnn

Abstract

The application relates to the field of geotechnical engineering reliability analysis, and specifically discloses a reliability analysis method of a parameter non-Gaussian mutual correlation random field based on CNN, which comprises the following steps: determining the edge distribution and Copula function of soil parameters; establishing a finite element model and deriving unit information; utilizing parameter non-Gaussian mutual correlation random field discretization; obtaining a geotechnical structure response value through stability analysis; drawing and preprocessing a random field image; constructing a proxy model between the random field image and the geotechnical structure response value; and analyzing the reliability of the geotechnical structure. The application simultaneously considers the mutual correlation and spatial variability of soil parameters, guarantees the accuracy of the analysis result, constructs the proxy model between the random field image and the geotechnical structure response value, inputs the random field image to obtain the response value, reduces the number of finite element analysis, significantly improves the efficiency of the reliability analysis, and has important significance for quickly and accurately evaluating the stability of the geotechnical body in engineering practice.

Description

Technical Field

[0001] This application relates to the field of reliability analysis technology in geotechnical engineering, and in particular to a reliability analysis method based on CNN that considers parametric non-Gaussian cross-correlation random fields. Background Technology

[0002] In geotechnical engineering practice, stability analysis of geotechnical structures has always been a crucial step. Since structural reliability is influenced by various factors, including soil physical and mechanical parameters, geological structure, and environmental conditions, accurate reliability analysis is key to ensuring the safe operation of the project. However, traditional reliability analysis methods often rely on the assumption that parameters follow a Gaussian correlation, neglecting the non-Gaussian nature of these parameters. This assumption can lead to biased analysis results.

[0003] Meanwhile, the Finite Element Method (FEM) is widely used in numerical analysis of structural reliability, and combining FEM with random field theory is a current research hotspot. However, FEM requires significant time and computational resources, especially when considering the spatial variability of parameters (i.e., combining with random field theory). Therefore, improving computational efficiency while ensuring the accuracy and precision of reliability analysis has become a major requirement in the field of reliability analysis.

[0004] In recent years, scholars have developed various surrogate models to reduce the computational burden of reliability analysis, such as polynomial chaotic expansion, response surface methodology, and machine learning methods. Among them, the Convolutional Neural Networks (CNN) method has achieved remarkable success in the fields of image processing and recognition. Its ability to extract features from images and construct complex mapping relationships provides a new approach to reliability analysis. By building a CNN model, a surrogate model can be established between random field images and the response values ​​of soil and rock structures (or other reliability analysis indicators of soil and rock structures), achieving the effect of obtaining response values ​​simply by inputting a random field image, thus reducing the number of finite element analyses. Summary of the Invention

[0005] To improve analysis efficiency and provide strong support for rapid and accurate assessment of geotechnical engineering reliability in engineering practice, this application provides a CNN-based reliability analysis method for non-Gaussian cross-correlation random fields considering parameters. This method utilizes convolutional neural networks to construct a surrogate model between random field images and response values ​​of geotechnical structures, taking into account non-Gaussian cross-correlation and spatial variability among parameters.

[0006] This application provides a reliability analysis method for parameterized non-Gaussian cross-correlation random fields based on CNNs, which employs the following technical solution:

[0007] A reliability analysis method for parameterized non-Gaussian cross-correlation random fields based on CNNs includes the following steps:

[0008] Determine the marginal distribution of soil parameters and the Copula function;

[0009] Establish a finite element model and derive the node and element information of the finite element model;

[0010] Random fields are discretized using non-Gaussian cross-correlation of parameters to generate cross-correlated random fields;

[0011] Stability analysis was performed on a finite element model based on a cross-correlation random field using analytical tools to obtain the response values ​​of the soil and rock structure.

[0012] Based on the node and element information of the finite element model and the cross-correlation random field results, a random field image is plotted and preprocessed.

[0013] Construct a proxy model between the preprocessed random field image and the response values ​​of the soil and rock structure;

[0014] The reliability analysis of the soil and rock structure was performed using the surrogate model, and the results of the reliability analysis were obtained.

[0015] Furthermore, the method for determining the marginal distribution of soil parameters and the Copula function includes: calculating the statistical information of soil parameters based on measured data, and using the AIC criterion or BIC criterion to determine the optimal fitting marginal distribution and optimal Copula function of the statistical information of soil parameters.

[0016] Furthermore, the method for establishing a finite element model and deriving the node and element information of the finite element model includes: establishing a finite element model of the research object using ABAQUS based on the geometric dimensions of the research object, and obtaining various types of node and element information from the inp file, including the number and coordinates.

[0017] Furthermore, methods for generating cross-correlated random fields by discretizing random fields using non-Gaussian cross-correlation parameters include:

[0018] The autocorrelation matrix is ​​obtained by discretizing the autocorrelation random field of soil parameters based on Cholesky decomposition.

[0019] The autocorrelation matrix is ​​decomposed to obtain a lower triangular matrix;

[0020] The autocorrelation random field of parameters is obtained from the lower triangular matrix;

[0021] Based on the non-Gaussian cross-correlation random field coupling of Copula, the coupling of autocorrelation random fields is completed, and cross-correlation random fields are generated.

[0022] Furthermore, methods for obtaining the response values ​​of geotechnical structures by performing stability analysis on finite element models based on cross-correlation random fields using analytical tools include:

[0023] Using MATLAB statements that conform to the inp file format, a set of each finite element element and its corresponding material properties are created. The material parameter values ​​of each finite element element are assigned to the material properties of each finite element element, resulting in a non-Gaussian cross-correlated random field embedded finite element model.

[0024] Using Python to call ABAQUS, the modified inp file is automatically submitted to ABAQUS;

[0025] Stability analysis was performed using the strength reduction method in ABAQUS, and the calculation results were automatically output using Python.

[0026] Furthermore, methods for plotting random field images include:

[0027] Based on the node and element information of the finite element model and the cross-correlation random field results, the random field image is plotted using the patch function of MATLAB to obtain the preliminary image of the random field, namely the RGB image of the random field.

[0028] Furthermore, preprocessing methods for random field images include:

[0029] Convert a 3-channel RGB image to a single-channel grayscale image;

[0030] The single-channel grayscale image is converted into an H×W×1 double variable using the im2double() function; where W is the image width and H is the image height.

[0031] Suppose we consider m random variables, and we want to merge m H×W×1 double variables into a single H×W×m double variable;

[0032] After N iterations of random field discretization and analysis, in MATLAB, the random field image of N sets of two parameters is represented as a 4-D double variable of type H×W×m×N.

[0033] Furthermore, methods for constructing a surrogate model between the preprocessed random field image and the response values ​​of the soil and rock structure include:

[0034] A convolutional neural network model is constructed, and the hyperparameters of the convolutional neural network are optimized using Bayesian methods, trained, and tested to obtain the surrogate model.

[0035] The processed 4-D double variables are input into the surrogate model, and the geotechnical structure response values ​​are output.

[0036] This application also provides a reliability analysis system based on CNN for parametric non-Gaussian cross-correlation random fields, including:

[0037] The optimal fitting marginal distribution and Copula function selection module calculates soil parameter statistics based on measured data to determine the optimal fitting marginal distribution and optimal Copula function for soil parameters.

[0038] The finite element model building module builds a finite element model based on the geometric dimensions of the research object and exports node and element information;

[0039] The cross-correlation random field generation module uses non-Gaussian cross-correlation parameters to discretize random fields and generate cross-correlation random fields.

[0040] The stability analysis module uses analysis tools to perform stability analysis on a finite element model based on a cross-correlation random field, and obtains the response values ​​of the soil and rock structure.

[0041] The random field image rendering and preprocessing module renders and preprocesses random field images based on the node and element information of the finite element model and the cross-correlation random field results.

[0042] The model training module uses random field images and data obtained from corresponding stability analysis as samples to train the model;

[0043] The reliability analysis module uses a surrogate model to perform reliability analysis on soil and rock structures and obtain the reliability analysis results.

[0044] This application also provides a computer program product, including a computer program that, when executed by a processor, implements a reliability analysis method for a CNN-based parametric non-Gaussian cross-correlation random field.

[0045] In summary, this application includes at least one of the following beneficial technical effects:

[0046] 1. The method proposed in this application overcomes the limitations of the assumption of Gaussian cross-correlation of parameters in traditional reliability analysis. By introducing Copula function and random field theory, it more accurately describes the actual distribution and correlation of soil parameters, thereby improving the reliability of the analysis results.

[0047] 2. This method significantly improves the efficiency of reliability analysis. Finite element analysis is a commonly used stability analysis method, but its large computational load and long processing time are major limitations. The computational load increases significantly when considering parameter space variability. To address the shortcomings of existing technologies, this application utilizes a convolutional neural network to construct a surrogate model between random field images and geotechnical structure response values. Only a certain number of samples are needed to train the convolutional neural network model to achieve the effect of inputting a random field image and obtaining response values. Furthermore, thanks to the powerful image feature extraction and complex network construction capabilities of convolutional neural networks, this method achieves high accuracy. Therefore, while improving computational efficiency, it also ensures the accuracy of the analysis results, meeting the needs of rapid evaluation in engineering practice.

[0048] 3. This application only takes slope reliability analysis as an example, but in fact, the method of this application can also be extended to the reliability analysis of other geotechnical structures, such as foundations, pile foundations, retaining walls, etc. Therefore, the method provided by this application is highly practical and can provide strong support for the reliability analysis of geotechnical masses, and has broad application prospects. Attached Figure Description

[0049] Figure 1 This is a flowchart of the method provided in the embodiments of this application;

[0050] Figure 2 This is a technical roadmap of the method provided in the embodiments of this application;

[0051] Figure 3 It is a finite element model of a slope;

[0052] Figure 4 These are random field RGB images and grayscale images in the embodiments of this application;

[0053] Figure 5 This is a schematic diagram illustrating the change process of the objective function in the Bayesian optimization of the hyperparameters of the convolutional neural network model in the embodiments of this application;

[0054] Figure 6 This is a schematic diagram of the training process of the convolutional neural network model in the embodiments of this application;

[0055] Figure 7 This is a comparison chart of the training set prediction results in the embodiments of this application;

[0056] Figure 8 This is a relative error diagram of the model training set in the embodiments of this application;

[0057] Figure 9 This is a comparison chart of the prediction results of the test set in the embodiments of this application;

[0058] Figure 10 This is a relative error diagram of the model test set in the embodiments of this application;

[0059] Figure 11 This is a graph showing the ratio of model predictions to actual values ​​in the embodiments of this application. Detailed Implementation

[0060] The following is in conjunction with the appendix Figure 1-11 This application will be described in further detail.

[0061] This application, taking slope reliability analysis as an example, discloses a reliability analysis method based on CNN that considers non-Gaussian cross-correlation random fields. (Refer to...) Figure 1 and Figure 2 The reliability analysis method for non-Gaussian cross-correlated random fields based on CNNs includes the following steps:

[0062] S100. Determine the edge distribution of soil parameters and the Copula function, specifically including the following steps:

[0063] S110. There are two methods for determining the marginal distribution of soil parameters: 1. Assume the marginal distribution and statistical information of soil parameters based on engineering experience; 2. Calculate the statistical information of soil parameters based on measured data, and use the AIC criterion (Akaike Information Criterion) or the BIC criterion (Bayesian Information Criterion) to determine the optimal fitting marginal distribution and optimal Copula function of the statistical information of soil parameters.

[0064] In this embodiment, the marginal distribution and statistical information of the parameters are determined based on measured data. Measured soil parameter data for a certain site are used, as shown in Table 1.

[0065] Table 1. Soil cohesion c and internal friction angle at a certain site measured data

[0066]

[0067]

[0068] In this embodiment, the AIC criterion is used, which means that the marginal distribution with the smallest AIC value is the best-fit marginal distribution. The formula for calculating the AIC value is as follows:

[0069]

[0070] In the formula, f(·) is the probability density function of the marginal distribution, p and q are the characteristic parameters of the marginal distribution function, and k m Where N is the number of characteristic parameters, and N is the number of sets of measured data, x (d)k This represents the d-th measured value of the k-th soil parameter.

[0071] S120. Based on measured data, the optimal Copula function is determined using the AIC criterion. The Copula function that minimizes the AIC value is the optimal fit Copula function for the soil parameters. The formula for calculating AIC is as follows:

[0072]

[0073]

[0074]

[0075] In the formula, u (d)k This indicates that the d-th group of measured values ​​for the k-th soil parameter has been converted from data in the original space to values ​​in the standard uniform space. rank(·) represents x. (d)k In the measured data {x} sorted in ascending order (1)k ,x (2)k ,...,x (N)k In the}, the rank, c(·,·;θ) is the probability density function of the Copula function, the subscripts i and j represent the i-th and j-th soil parameters, and θ is the characteristic parameter of the Copula function. i,i+1 These are the Copula function characteristic parameters for the i-th and (i+1)-th soil parameters. Represents θ i,i+1 The estimated value, k c This represents the number of characteristic parameters of the Copula function.

[0076] According to the AIC criterion, the AIC values ​​for three edge distributions and four Copula functions were calculated, and the AIC calculation results are shown in Table 2. Table 2 shows that the optimal fitting edge distribution for cohesion c is the Weibull distribution, while the internal friction angle... The optimal fitting marginal distribution is a truncated normal distribution, and the optimal Copula for both is the Plackett Copula.

[0077] Table 2. AIC values ​​of various marginal distributions and Copula functions

[0078]

[0079] S200. Establish a finite element model and export the node and element information of the finite element model. This includes the following steps:

[0080] S210. Based on the geometric dimensions of the research object, a finite element model of the research object is established using ABAQUS;

[0081] In this embodiment, the research object is a two-dimensional slope with a height of 15m and a width of 30m. The finite element model has 1210 elements, each with a side length of 0.5m. The bottom of the slope is fully consolidated, and vertical movement is allowed only on the left and right sides. The slope considers cohesion c and internal friction angle. Two random variables, the weight of the slope soil γ = -18 kN / m 3 Finite element model such as Figure 3 As shown.

[0082] S220, and retrieve various information about nodes and elements from the inp file, including their numbers and coordinates.

[0083] S300. Discretize random fields using non-Gaussian cross-correlation parameters to generate cross-correlated random fields. This includes the following steps:

[0084] S310. Discretize the autocorrelation random field of soil parameters based on Cholesky decomposition to obtain the autocorrelation matrix C;

[0085] The autocorrelation of a parameter is affected by the autocorrelation function (ACF) and the fluctuation range (SOF). There are many types of ACF. In this embodiment, a single exponential autocorrelation function is used, which can be expressed as:

[0086]

[0087] Where, τ xij =|x i -x j |,τ yij =|y i -y j | represents the relative distance between the i-th and j-th units in the x and y directions, respectively; δ x and δ y These represent the fluctuation ranges in the x and y directions, respectively.

[0088] By calculating the value of the autocorrelation function, the autocorrelation matrix C is obtained, which is expressed as:

[0089]

[0090] Where n is the number of elements in the finite element model.

[0091] S320. Decompose the autocorrelation matrix C to obtain the lower triangular matrix L, satisfying:

[0092] L·L T =C

[0093] S330. The autocorrelation random field Z with parameters obtained from the lower triangular matrix L. IN , is represented as:

[0094] Z IN =L·ξ

[0095] Where ξ is an n×1 standard normal random vector.

[0096] Following the above steps, an autocorrelation random field for the variables can be established. This application only considers c and The two variables can be used to obtain the autocorrelation random field.

[0097] S340. Based on Copula, non-Gaussian cross-correlation random field coupling is used to complete the autocorrelation random field Z. IN The coupling generates a cross-correlated random field Z. CNN The details are as follows:

[0098] In this application, only the cohesion c and the internal friction angle are considered. Using Copula theory, the joint distribution of two variables can be expressed as:

[0099]

[0100] In the formula, u = F1(c) and c and The marginal cumulative distribution function (CDF) is denoted as C(u,v; θ), which is the cumulative distribution function of a two-dimensional Copula.

[0101] Table 3 lists several commonly used Copula probability density functions (PDF), h-functions, and h-functions. -1 - The function and the corresponding range of values ​​for θ; θ is a Copula parameter used to quantify the correlation between variables, which can be obtained by converting the Pearson correlation coefficient ρ or the Kendall rank correlation coefficient τ. In this application, the Kendall rank correlation coefficient τ is used to convert θ, and the calculation formula is as follows:

[0102]

[0103] Based on c and The joint distribution function can be used to obtain c and The joint probability density function is:

[0104]

[0105] In the formula, f1(c) and c and The marginal probability density function; the probability density function of the two-dimensional Copula obtained by differentiating D(u,v;θ) from C(u,v;θ), the differentiation process is as follows:

[0106]

[0107] Table 3 Several commonly used binary Copula models

[0108]

[0109] Based on the above theory and the Rosenblatt transform, autocorrelation random fields can be constructed. The coupling generates cross-correlated random fields. The steps are as follows:

[0110] Z c IN =Φ -1 (F c (Z c CNN ))

[0111]

[0112] In the formula, Φ -1 (·) denotes the inverse function of the standard normal distribution CDF, F c (·)and They represent c and The marginal CDF, F(·|·) denotes the conditional CDF of the Copula. Transforming the above equation, we can obtain c and Cross-correlated random fields The expression:

[0113]

[0114]

[0115] In the formula, F1 -1 (·) and F2 -1 (·) represent c and The inverse function of the marginal cumulative distribution function. After the transformation steps above, c and Autocorrelation random fields Coupled into cross-correlated random fields using different Copula functions Meanwhile, in this step, the discrete results of each random field are saved for use in the random field image drawing of subsequent steps.

[0116] S400. Use analysis tools to perform stability analysis on the finite element model based on cross-correlation random fields to obtain the response values ​​of the soil and rock structure. This includes the following steps:

[0117] S410. Using MATLAB to output statements conforming to the inp file format, embed the non-Gaussian cross-correlated random field generated in the above steps into the finite element model; create a set for each finite element element and its corresponding material properties, and assign the material parameter values ​​(i.e., the corresponding random field values) of each finite element element to the material properties of each finite element element to obtain the non-Gaussian cross-correlated random field embedded finite element model.

[0118] S420. Write Python statements to call ABAQUS using Python's ABAQUS interface functions, automatically submitting the modified inp file to ABAQUS for calculation. For reference, the model inp file in this embodiment is named 'Slope.inp', and the following Python statements can be used to submit the inp file:

[0119] FileName = 'Slope'

[0120] mdb.JobFromInputFile(name=FileName,inputFileName=FileName+'.inp')

[0121] mdb.jobs[FileName].submit()

[0122] mdb.jobs[FileName].waitForCompletion()

[0123] S430. Taking slope reliability analysis as an example, stability analysis is performed using the strength reduction method in ABAQUS, and the calculation results are automatically output using Python. The strength reduction method can be expressed as:

[0124]

[0125]

[0126] In the formula, Fr is the reduction factor, and c and c represents the cohesion and internal friction angle values ​​obtained after the previous reduction, respectively. m and These represent the reduced cohesive force and internal friction angle values, respectively.

[0127] In this application, ABAQUS is used for strength reduction. The reduction factor at the end of the calculation is considered the slope safety factor FS, which is the reduction factor corresponding to the last stack of the last analysis step for any set (i.e., any element) in ABAQUS. For reference, the following Python statement can be used to obtain the FS corresponding to the last stack:

[0128] o=openOdb(path=FileName+'.odb')

[0129] step = o.steps.values()[1]

[0130] lastframe=o.steps['reduce'].frames[-1]

[0131] sglele=o.rootAssembly.instances['SLOPE-1'].elementSets['SET-**']

[0132] F=lastframe.fieldOutputs['FV1'].getSubset(region=sglele).values

[0133] S500. Based on the node and element information of the finite element model and the cross-correlation random field results, plot the random field image and perform preprocessing, specifically including the following steps:

[0134] S510. Based on the node and element information of the finite element model and the cross-correlation random field results, use the MATLAB patch function to plot the random field image; for reference, the following MATLAB statements can be used to plot the random field image:

[0135] patch('Faces',Element(1:N_Element,[2:end]),'Vertices',Node(:,[2:end]),'FaceVertex CData',X(1:end)','EdgeColor','none','FaceColor','flat');

[0136] Where Element is the element information matrix of the finite element model, the first column is the element number, the second to the last column are the node numbers of the element, Node is the node information matrix of the finite element model, the first column is the node number, the second to the last column are the coordinates of the node in each direction, and X is the random field discretization result, that is, the parameter values ​​of each element arranged in the order of element number.

[0137] Taking a discrete result X from a random field as an example, X is a 1×2420 matrix. Elements 1 to 1210 of X represent the cohesion c of each element sorted by element number, and elements 1211 to 2420 of X represent the internal friction angle of each element sorted by element number. The MATLAB statement for plotting random field images can be expressed as:

[0138] patch('Faces',Element(1:1210,[2:5]),'Vertices',Node(:,[2:3]),'FaceVertexCData',X(1:1210)','EdgeColor','none','FaceColor','flat');

[0139] patch('Faces',Element(1211:2420,[2:5]),'Vertices',Node(:,[2:3]),'FaceVertexCData',X(1211,2420)','EdgeColor','none','FaceColor','flat');

[0140] Wherein, Element is the element information matrix of the finite element model, the first column is the element number, and the second to last columns are the node numbers of the element. Node is the node information matrix of the finite element model, the first column is the node number, and the second to third columns are the coordinates of the node in each direction.

[0141] After the above steps, a preliminary image of the random field is obtained, namely the RGB image of the random field. Figure 4 The results of rendering a random field RGB image and a grayscale image are shown.

[0142] S520: Convert a 3-channel RGB image to a single-channel grayscale image;

[0143] Each parameter's random field image (i.e., a single random field discretization) is a uint8 variable of size H×W×3, where W is the image width, H is the image height, and 3 is the number of channels (3 for RGB images). Subsequently, the 3-channel RGB image needs to be converted into a single-channel grayscale image H×W×1uint8, which can be achieved using the rgb2gray() function in MATLAB.

[0144] S530. Use the im2double() function to convert a single-channel grayscale image into an H×W×1 double variable;

[0145] S540. In this application, two soil parameters are considered, and two H×W×1 double variables (i.e., a random field image of two soil parameters) are merged into one H×W×2 double variable.

[0146] S550. After performing N random field discretization and analysis, in MATLAB, the random field image of N sets of two parameters is represented as a 4-D double variable of type H×W×2×N.

[0147] In this embodiment, the RGB image is represented by two 30×60×3 uint8 variables; the rgb2gray() function is used to convert the RGB image to a grayscale image, which is represented by two 30×60×1 uint8 variables in MATLAB; the im2double() function is used to convert the grayscale image to two 30×60×1 double variables, and then merges them into a single 30×60×2 double variable. Assuming there are N random field discretization results, the N random field images can be represented in MATLAB as 30×60×2×N 4-D double variables.

[0148] S600. Construct a surrogate model between the preprocessed random field image and the response values ​​of the soil and rock structure, specifically including the following steps:

[0149] S610, Building a Convolutional Neural Network Model;

[0150] The 4-D double variables obtained from the processing are used as the input to the model, and the output of the model is the response value of the geotechnical structure, which is the result of N stability analyses (for example, for slopes, it is N slope safety factors).

[0151] In this embodiment, N=1000 random field discretizations and corresponding stability analyses were performed, resulting in 1000 sets of samples. After the previous step, a 30×60×2×1000 4-D double variable is obtained, and the corresponding output is a 1000×1 matrix, representing the slope safety factor FS obtained from the 1000 sets of samples.

[0152] From input to output, the process involves convolutional layers, activation layers, pooling layers, fully connected layers, and so on. The CNN model is built according to the requirements, and the structure of each layer of the model is determined.

[0153] The convolutional neural network structure built in this embodiment consists of the following layers: input layer, convolutional layer, activation layer, pooling layer, dropout layer, fully connected layer, and output layer. The convolutional layer has a kernel size of 5×10, 20 kernels, a stride of 1, and 0 padding. The activation layer uses the ReLU function, and the pooling layer uses average pooling with a pooling window size of 2×2, a stride of 1, and 0 padding.

[0154] S620, Bayesian optimization of hyperparameters;

[0155] Select the hyperparameters that need to be optimized (such as kernel size, stride, number of kernels, pooling window size, stride, initial learning rate, and dropout rate), and use Bayesian optimization methods to optimize the hyperparameters to ensure that the model has good feature learning capabilities.

[0156] In this embodiment, the 1000 samples are divided into a training set of 700 samples and a test set of 300 samples. First, Bayesian optimization of hyperparameters is performed, selecting the initial learning rate and dropout rate as the hyperparameters to be optimized. The coefficient of determination R of the test set is then set. 2 The negative number is used as the objective function, and Bayesian optimization is performed using the bayesopt package in MALTAB. The change process of the objective function during the iteration is as follows: Figure 5 As shown in the figure. Ultimately, it can be determined that the objective function reaches its minimum when the initial learning rate is 0.024 and the dropout rate is 17.33%.

[0157] S630, model training;

[0158] After determining the model structure and hyperparameters, the training set is input into the model for multiple iterations of training. The iteration is stopped after the maximum number of iterations is reached, and the trained model is saved.

[0159] S640, Model Testing;

[0160] Input the test set into the trained model. The results of model training and testing are as follows: Figure 6-11 As shown in Table 4, the values ​​of each evaluation index are shown in the evaluation index and training effect diagram. It can be seen from the evaluation index and the training effect diagram that the model's prediction effect is relatively accurate.

[0161] Table 4 Model Evaluation Indicators

[0162] Evaluation indicators training set test set Root Mean Square Error (RMSE) 0.000 0.000 Mean Absolute Error (MAE) 0.009 0.126 Mean Absolute Percentage Error (MAPE) 0.148 0.019 <![CDATA[Coefficient of determination (R 2 )]]> 0.974 0.954

[0163] S700. Reliability analysis of geotechnical structures is performed using a surrogate model to obtain the reliability analysis results. This includes the following steps:

[0164] Perform N m N is generated by Monte Carlo simulation. m Each random field is processed, and its random field image is plotted. The preprocessed image is then input into the convolutional neural network model trained in the previous steps to obtain the response value corresponding to each random field. Taking a slope as an example, the response value is the slope safety factor. The failure probability P is then calculated. f The formula for calculating the reliability index β is:

[0165]

[0166] β=-Φ -1 (Pf )

[0167] In the formula, I(·) is the indicator function, FS represents the slope safety factor, and Φ(·) is the cumulative distribution function of the standard normal distribution.

[0168] In this embodiment, 10,000 Monte Carlo simulations were performed, generating 10,000 sets of cross-correlated random fields. Six sets of random fields corresponded to slope safety factors less than 1, meaning the actual failure probability was 6 × 10⁻⁶. -4 When these 10,000 random field images were input into the trained convolutional neural network model, 5 of the random fields corresponded to slope safety factors less than 1, meaning the model predicted a failure probability of 5 × 10⁻⁶. -4 Such prediction results are acceptable for problems with low failure probabilities.

[0169] This application also provides a reliability analysis system based on CNN for parametric non-Gaussian cross-correlation random fields, including:

[0170] The optimal fitting marginal distribution and Copula function selection module calculates soil parameter statistics based on measured data to determine the optimal fitting marginal distribution and optimal Copula function for soil parameters.

[0171] The finite element model building module builds a finite element model based on the geometric dimensions of the research object and exports node and element information;

[0172] The cross-correlation random field generation module uses non-Gaussian cross-correlation parameters to discretize random fields and generate cross-correlation random fields.

[0173] The stability analysis module uses analysis tools to perform stability analysis on a finite element model based on a cross-correlation random field, and obtains the response values ​​of the soil and rock structure.

[0174] The random field image rendering and preprocessing module renders and preprocesses random field images based on the node and element information of the finite element model and the cross-correlation random field results.

[0175] The model training module uses random field images and data obtained from corresponding stability analysis as samples to train the model;

[0176] The reliability analysis module uses a surrogate model to perform reliability analysis on soil and rock structures and obtain the reliability analysis results.

[0177] This application also provides a computer program product, including a computer program that, when executed by a processor, implements the above-described reliability analysis method for a CNN-based non-Gaussian cross-correlation random field considering parameters.

[0178] The above embodiments are only used to illustrate the technical solutions of this application, and are not intended to limit them. Although this application has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of this application.

Claims

1. A reliability analysis method for parametric non-Gaussian cross-correlation random fields based on CNN, characterized in that: Includes the following steps: Determine the marginal distribution of soil parameters and the Copula function; Establish a finite element model and derive the node and element information of the finite element model; Random fields are discretized using non-Gaussian cross-correlation of parameters to generate cross-correlated random fields; Stability analysis was performed on a finite element model based on a cross-correlation random field using analytical tools to obtain the response values ​​of the soil and rock structure. Based on the node and element information of the finite element model and the cross-correlation random field results, a random field image is plotted and preprocessed. Construct a proxy model between the preprocessed random field image and the response values ​​of the soil and rock structure; The reliability analysis of the soil and rock structure was performed using the surrogate model, and the results of the reliability analysis were obtained.

2. The reliability analysis method for a CNN-based non-Gaussian cross-correlation random field considering parameters, as described in claim 1, is characterized in that: The method for determining the marginal distribution and Copula function of soil parameters includes: calculating the statistical information of soil parameters based on measured data, and using the AIC criterion or BIC criterion to determine the optimal fitting marginal distribution and optimal Copula function of the statistical information of soil parameters.

3. The reliability analysis method for a CNN-based non-Gaussian cross-correlation random field considering parameters, as described in claim 1, is characterized in that: The method for establishing a finite element model and deriving the node and element information of the finite element model includes: establishing a finite element model of the research object using ABAQUS based on the geometric dimensions of the research object, and obtaining various types of node and element information from the inp file, including the number and coordinates.

4. The reliability analysis method for a CNN-based non-Gaussian cross-correlation random field considering parameters, as described in claim 1, is characterized in that: Methods for generating cross-correlated random fields by discretizing random fields using non-Gaussian cross-correlation parameters include: The autocorrelation matrix is ​​obtained by discretizing the autocorrelation random field of soil parameters based on Cholesky decomposition. The autocorrelation matrix is ​​decomposed to obtain a lower triangular matrix; The autocorrelation random field of parameters is obtained from the lower triangular matrix; Based on the non-Gaussian cross-correlation random field coupling of Copula, the coupling of autocorrelation random fields is completed, and cross-correlation random fields are generated.

5. The reliability analysis method for a CNN-based non-Gaussian cross-correlation random field considering parameters, as described in claim 1, is characterized in that: Methods for obtaining the response values ​​of geotechnical structures by performing stability analysis on finite element models based on cross-correlation random fields using analytical tools include: Using MATLAB statements that conform to the inp file format, a set of each finite element element and its corresponding material properties are created. The material parameter values ​​of each finite element element are assigned to the material properties of each finite element element, resulting in a non-Gaussian cross-correlated random field embedded finite element model. Using Python to call ABAQUS, the modified inp file is automatically submitted to ABAQUS; Stability analysis was performed using the strength reduction method in ABAQUS, and the calculation results were automatically output using Python.

6. The reliability analysis method for a CNN-based non-Gaussian cross-correlation random field considering parameters, as described in claim 1, is characterized in that: Methods for plotting random field images include: Based on the node and element information of the finite element model and the cross-correlation random field results, the random field image is plotted using the patch function of MATLAB to obtain the preliminary image of the random field, namely the RGB image of the random field.

7. The reliability analysis method for a CNN-based non-Gaussian cross-correlation random field considering parameters, as described in claim 6, is characterized in that: Preprocessing methods for random field images include: Convert a 3-channel RGB image to a single-channel grayscale image; The single-channel grayscale image is converted into an H×W×1 double variable using the im2double() function; where W is the image width and H is the image height. Suppose we consider m random variables, and we want to merge m H×W×1 double variables into a single H×W×m double variable; After N iterations of random field discretization and analysis, in MATLAB, the random field image of N sets of two parameters is represented as a 4-D double variable of type H×W×m×N.

8. The reliability analysis method for a CNN-based non-Gaussian cross-correlation random field considering parameters, as described in claim 1, is characterized in that: Methods for constructing a surrogate model between preprocessed random field images and soil structure response values ​​include: A convolutional neural network model is constructed, and the hyperparameters of the convolutional neural network are optimized using Bayesian methods, trained, and tested to obtain the surrogate model. The processed 4-D double variables are input into the surrogate model, and the geotechnical structure response values ​​are output.

9. A reliability analysis system for parametric non-Gaussian cross-correlation random fields based on CNN, characterized in that: include: The optimal fitting marginal distribution and Copula function selection module calculates soil parameter statistics based on measured data to determine the optimal fitting marginal distribution and optimal Copula function for soil parameters. The finite element model building module builds a finite element model based on the geometric dimensions of the research object and exports node and element information; The cross-correlation random field generation module uses non-Gaussian cross-correlation parameters to discretize random fields and generate cross-correlation random fields. The stability analysis module uses analysis tools to perform stability analysis on a finite element model based on a cross-correlation random field, and obtains the response values ​​of the soil and rock structure. The random field image rendering and preprocessing module renders and preprocesses random field images based on the node and element information of the finite element model and the cross-correlation random field results. The model training module uses random field images and data obtained from corresponding stability analysis as samples to train the model; The reliability analysis module uses a surrogate model to perform reliability analysis on soil and rock structures and obtain the reliability analysis results.

10. A computer program product, comprising a computer program, characterized in that, When the computer program is executed by the processor, it implements the reliability analysis method for a CNN-based non-Gaussian cross-correlation random field considering any one of claims 1-8.

Images