Reliability calculation method and system for cracking of concrete face of rock-fill dam

Abstract

The invention provides a rock-fill dam concrete panel cracking reliability calculation method and system, and the method comprises the steps: determining test parameters based on obtained physical parameters of a rock-fill material used by a rock-fill dam; duncan E-B model parameters are determined based on the test parameters, factor sensitivity analysis is conducted on the Duncan E-B model parameters based on an orthogonal test method, and sensitivity parameters are determined; carrying out random field characterization on the sensitivity parameters by using a normal random field, and discretizing random field data by using a Cholesky decomposition method to obtain a sample set and a test set of a training agent model; based on a Kriging model constructed by the sample set, performing optimization iteration through MPSO and a learning function to obtain an optimal agent model, and evaluating the optimal agent model; inputting the test set into the optimal agent model to calculate to obtain a predicted value and an evaluation index, establishing a structural performance function, and calculating to obtain the panel cracking reliability by adopting an important sampling subset simulation method; according to the method, the accuracy of the cracking reliability is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of reliability calculation of face rockfill dams, and in particular to a method and system for calculating the cracking reliability of concrete face panels of a face rockfill dam. Background Art

[0002] In recent years, concrete panels have been increasingly used for dams in engineering applications due to the panel rockfill dam's many advantages, including simple structure, convenient construction, strong adaptability to adverse climate, terrain and geological conditions, short construction period, high construction efficiency, low project cost and good stability. More and more concrete panel rockfill dams have been built using concrete panels, with a total of more than 400. In a panel rockfill dam, cracking of the panel rockfill dam is mainly caused by factors such as uneven settlement and deformation of the dam body. The factors affecting the uneven settlement and deformation of the dam body are mainly the rheological properties of the dam construction materials, the pre-settlement period of the dam body, the compaction quality of the rockfill body, the water storage process of the dam, the topographic and geological conditions, etc. The panel is the first anti-seepage structure of the panel rockfill dam, and its integrity is crucial to the anti-seepage safety of the dam. If the panel cracks, it will cause different degrees of impact on the dam according to the degree of cracking, the range of cracks and the depth. In mild cases, it will cause reservoir water to penetrate into the dam and increase the seepage of the dam body; in severe cases, it will cause the rockfill body to become unstable and cause the risk of dam collapse. Furthermore, in the construction process of the panel rockfill dam, the reliability analysis of the concrete panel is often carried out to determine whether the concrete panel is cracked.

[0003] Currently, reliability analysis of concrete panels is often performed by constructing a proxy model. The proxy model is combined with the spatial variability of rockfill material parameters to calculate the cracking reliability of the concrete panels. During this calculation process, the key soil parameters are discretized through the random field, usually resulting in a high-dimensional random field variable matrix. The distribution of data points in the high-dimensional space formed by the high-dimensional random field variable matrix becomes extremely sparse, making it impossible for the proxy model to capture the interaction of enough data points in the high-dimensional space during the processing process. As a result, the proxy model will fall into a local minimum during the processing process, resulting in large errors in the calculated cracking reliability, which in turn affects construction decisions. Summary of the Invention

[0004] In order to solve the problem that in the existing concrete panel reliability calculation process, the processing of key soil parameters will obtain a high-dimensional random field variable matrix, causing the proxy model to fall into a local minimum during the processing process, resulting in large errors in the calculated cracking reliability, the present invention provides a method and system for calculating the cracking reliability of a pile of rockfill dam concrete panels.

[0005] To achieve the above object, the present invention provides the following technical solutions: The present invention proposes a reliability calculation method for cracking of a rockfill dam concrete face plate, comprising the following steps: Determine the test parameters based on the obtained physical parameters of the rockfill material used in the rockfill dam; The parameters of the Duncan Zhang EB model are determined based on the experimental parameters, and the sensitivity parameters are determined by performing factor sensitivity analysis on the parameters of the Duncan Zhang EB model based on the orthogonal experimental method; The sensitivity parameters are characterized by a normal random field, and the random field data are discretized using the Cholesky decomposition method to obtain the sample set and test set for training the proxy model. Based on the Kriging model constructed by the sample set, the optimal surrogate model is obtained through optimization iteration through MPSO and learning function, and the optimal surrogate model is evaluated; The test set is input into the optimal surrogate model to calculate the predicted value and evaluation index to establish the structural performance function, and the panel cracking reliability is calculated using the importance sampling subset simulation method.

[0006] Preferably, determining the test parameters based on the acquired physical parameters of the rockfill material used in the rockfill dam includes: Obtain specimen confining pressure The value of the internal friction angle decreasing when one logarithmic period is increased and the initial internal friction angle , based on the value of the reduction of the internal friction angle during the logarithmic period , initial internal friction angle and specimen confining pressure Calculate the internal friction angle of the material ; Obtaining the material cohesion of rockfill materials , through material cohesion and the internal friction angle of the material Calculate the deviatoric stress at the time of rockfill failure; Obtain the tangent modulus base of the rockfill material , Unit atmospheric pressure in the area where the rockfill dam is located , axial pressure of rockfill dam , Tangent modulus index of rockfill material used in rockfill dam ; Based on axial pressure and specimen confining pressure Calculate the asymptotic value of the deviatoric stress , based on axial pressure , specimen confining pressure , asymptotic value and deviatoric stress are calculated to obtain material failure ratio, stress level and initial tangent modulus respectively; Get the bulk modulus number , based on the bulk modulus number , unit atmospheric pressure , specimen confining pressure and bulk modulus index The tangent bulk modulus is calculated.

[0007] Preferably, Determining the Duncan Zhang EB model parameters based on the experimental parameters, performing factor sensitivity analysis on the Duncan Zhang EB model parameters based on the orthogonal test method, and determining the sensitivity parameters include: The experimental parameters were analyzed to determine the parameters of the Duncan Zhang EB model; The Duncan Zhang EB model parameter setting variation is carried out by orthogonal test. , multiple experimental data sets are constructed; The experimental data set is processed based on the constructed three-dimensional finite element calculation model to obtain the finite element calculation results; The range and variance analysis methods were used to compare and analyze the finite element calculation results and determine the sensitivity parameters.

[0008] Preferably, the comparative analysis of the finite element calculation results using range and variance analysis methods to determine the sensitivity parameters includes: The range and variance analysis methods were used to compare and analyze the finite element calculation results, and the statistical parameters of the influence of each data point in the test data set on the stress sensitivity of the panel were obtained; Calculate the difference between the statistical maximum and the statistical minimum of the statistical parameter to obtain the range value; The sensitivity parameter is determined based on the range value.

[0009] Preferably, the sensitivity parameters are characterized by a normal random field to obtain random field data, and the random field data are discretized using the Cholesky decomposition method to obtain a sample set and a test set for training the proxy model, including: Calculate the relative distance and autocorrelation distance between the coordinates of any two unit center points in the three-dimensional space constructed by the sensitivity parameters, and use the exponential autocorrelation function based on the relative distance and autocorrelation distance to represent the spatial variability of the random variable and obtain the autocorrelation coefficient matrix; The random field data is decomposed using the Cholesky decomposition method to obtain the non-Gaussian random field of random variables. Dataset; Non-Gaussian random fields for random variables The data set is subjected to finite element calculation to obtain variable finite element data, and the stress value in the variable finite element data is extracted to obtain the finite element stress value; the non-Gaussian random field is sorted out. and finite element stress values ​​to obtain the sample set and test set for training the proxy model.

[0010] Preferably, the Kriging surrogate model constructed based on the sample set is optimized and iterated through MPSO and learning function to obtain the optimal surrogate model, and the optimal surrogate model is evaluated, including: Define the Kriging proxy module and build the Kriging initial model based on the sample set; The sample set is input into the Kriging initial model for training to obtain the Kriging training model, that is, the random field discrete data and finite element stress values ​​of the random variables in the sample set are input into the Kriging initial model for iterative training until the Kriging initial model converges to obtain the Kriging training model; Particle swarm optimization (MPSO) algorithm based on hybridization to find the optimal correlation parameters , get the Kriging optimization proxy model; The Kriging optimization surrogate model is iteratively trained based on the optimization dataset through the learning function to obtain the optimal surrogate model.

[0011] Preferably, The Kriging proxy module is defined to construct a Kriging initial model based on a random field discrete data set, including: Use piecewise inverse regression analysis method to reduce the dimension of random field discrete data set and obtain projection vector; Use the inverse regression analysis method to find the mapping relationship between the variable sample and the low-dimensional response vector through the projection vector; Based on the projection vector, the initial mapping relationship between the defined variable sample and the low-dimensional response vector is transformed into a dimension reduction transformation to obtain a second mapping relationship; The variable samples in the non-Gaussian random field are used to calculate the corresponding low-dimensional response vector through mapping relationship 2, and the Kriging initial model is constructed based on the random field discrete data set and the corresponding low-dimensional response vector.

[0012] Preferably, the hybridization-based particle swarm optimization (MPSO) algorithm expands the random field discrete data to obtain an optimization data set, including: Generate a prediction population based on variable samples in random field discrete data, and initialize the position and velocity of each particle in the population in the MPSO algorithm; Obtain the particle position and particle velocity of each individual particle in the predicted population, set the position range and velocity range, calculate the particle fitness of each particle at each position within the position range based on the particle velocity, and determine the population displacement and population velocity based on the particle velocity and particle fitness value; Compare the fitness of the particles at each position, determine that the particle with the minimum fitness is the best, extract the corresponding particle speed and particle position, and obtain the optimal particle speed and optimal particle position; Based on the optimal particle speed and optimal particle position, the corresponding particle speed and particle position in the predicted population are updated to obtain the optimized predicted population. The hybridization probability is preset, and particles are selected from the optimized predicted population based on the hybridization probability and input into the hybridization pool. Randomly hybridize any two particles to produce the same number of offspring particles. Based on the speed and position of the particle and the speed calculation, the speed and position of the offspring particle are obtained. Based on the speed and position of the offspring particle, the fitness of the offspring particle is calculated to determine the optimal prediction population and obtain the optimization data set.

[0013] Preferably, Based on the test set input into the optimal surrogate model, the predicted value and evaluation index are calculated to establish the structural performance function. The panel cracking reliability is calculated using the importance sampling subset simulation method, including: Establish structure function function according to evaluation index , input the test set into the optimal surrogate model to calculate the predicted value, and determine the failure area based on the predicted value; The failure area is divided into multiple failure sub-areas, and sample points are extracted from each failure sub-area using the importance sampling technique to obtain multiple failure sample sets; Define the conditional failure probability, extract failure sample points from multiple failure sample sets, and generate the first failure sample point that is independent and identically distributed and obeys the joint probability density function; The first failure sample point calculates the failure response through the established mapping relationship, and sorts the failure responses in descending order to extract the first failure sample point. The value is used as the critical value of the intermediate failure event ; Judgment critical value Is it less than 0? If the critical value If it is less than 0, the second failure sample point that falls into the failure domain within the intermediate failure event is counted. , and based on the second failure sample point The initial failure probability is calculated by the number of the first failure sample points; If the critical value If it is not less than 0, the third failure sample point that does not fall into the failure domain within the intermediate failure event is counted , calculate the third failure sample point Corresponding to the mean of the failure response, a new density function is constructed, and re-sampling is performed to generate the fourth failure sample point that is independent and identically distributed and obeys the new density function; The fourth failure sample point is calculated by the established mapping relationship to obtain the optimized failure response, and the optimized failure responses are sorted in descending order to extract the first The critical value of the intermediate failure event is calculated and the initial failure probability is recalculated; All initial failure probabilities are counted, the mean of all initial failure probabilities is calculated, the final failure probability is obtained, and the panel cracking reliability is obtained.

[0014] The present invention proposes a reliability calculation system for cracking of a rockfill dam concrete face plate, which is used in the above-mentioned reliability calculation method for cracking of a rockfill dam concrete face plate, comprising: A test parameter acquisition module is configured to determine test parameters based on the acquired physical parameters of the rockfill material used in the rockfill dam; A sensitivity analysis module is configured to determine the parameters of the Duncan Zhang EB model based on the experimental parameters, and to perform factor sensitivity analysis on the parameters of the Duncan Zhang EB model based on the orthogonal experimental method to determine the sensitivity parameters; The discrete processing module is configured to use a normal random field to perform random field characterization on the sensitivity parameter to obtain random field data, and discretize the random field data using a Cholesky decomposition method to obtain a random field discrete data set; The model training module is configured to use the Kriging model constructed based on the sample set to iterate and optimize the optimal surrogate model through MPSO and the learning function, and to evaluate the optimal surrogate model; The cracking reliability calculation module is configured to calculate the predicted value and the evaluation index based on the test set input to the optimal surrogate model to establish a structural function, and calculate the panel cracking reliability using the importance sampling subset simulation method; The output module is configured to output panel cracking reliability.

[0015] Compared with the prior art, the present invention has the following beneficial technical effects: The present invention proposes a method for calculating the cracking reliability of rockfill dam concrete panels. The method uses an orthogonal test method to efficiently process the determined Duncan-Zhang EB model parameters, significantly reducing the parameter combination explosion effect, and generating a multidimensional test data set while retaining the influencing characteristics of key parameters. Through normal random field representation and Cholesky decomposition discretization processing, the continuous random field is converted into computable discrete data while maintaining the spatial correlation of variables, and the high-dimensional variable matrix is ​​converted into a low-dimensional vector. Finally, based on the global approximation capability of the optimized Kriging surrogate model and combined with the important sampling subset simulation method, the failure area sampling is focused, which not only avoids the failure risk of traditional surrogate models in the local minimum trap, but also significantly improves the reliability calculation accuracy through efficient exploration of probability space. Through multi-stage dimensionality reduction processing and hybrid modeling strategy, the method realizes the optimization of the entire process from parameter sensitivity analysis to failure probability calculation, overcomes the limitations of traditional methods in high-dimensional nonlinear problems, and improves the accuracy of the calculated cracking reliability.

[0016] Furthermore, this method uses logarithmic periodic loading tests to accurately quantify the nonlinear attenuation law of the internal friction angle with confining pressure based on the physical parameters of the rockfill material. Combined with the spatial distribution characteristics of the cohesion parameters, a deviatoric stress evolution model reflecting the true failure characteristics of the material is constructed. Through the dual-parameter characterization method of the tangent modulus base and exponent, combined with the joint action mechanism of axial pressure and confining pressure, a dynamic calculation framework for the initial tangent modulus considering stress path dependence is established, which effectively overcomes the subjectivity of the modulus value in the traditional model. The volume deformation constraint condition related to the bulk modulus number and atmospheric pressure is introduced to realize the multi-factor coupled calculation of the tangent bulk modulus, significantly improving the accuracy of volume strain prediction. This method solves the problem of proxy model failure caused by high-dimensional random field variables through multi-parameter collaborative optimization and in-depth exploration of physical mechanisms. It also achieves accurate identification of cracking failure modes through parameter sensitivity analysis and multi-field coupling simulation.

[0017] Furthermore, this method quantitatively assesses the sensitivity of rockfill material parameters to the stress response of the faceplate, constructing a dynamically adaptive parameter reduction system. Using extreme values ​​as key screening indicators, this method accurately identifies the core parameters that dominate cracking behavior by comparing the fluctuation amplitudes of statistical parameters. This effectively eliminates the spatial dimensional interference of redundant variables on reliability calculations. While retaining the influencing mechanisms of key mechanical properties, it significantly reduces the complexity of random field variables, improves the training efficiency of the surrogate model, and achieves precise allocation of computing resources by focusing on highly sensitive parameters, making the identification of cracking failure modes more efficient and accurate. Compared with traditional full-parameter modeling methods, this strategy significantly reduces the dimension of the variable matrix while maintaining model prediction accuracy, avoiding the local convergence problem of the surrogate model caused by high-dimensional random fields.

[0018] Furthermore, this method utilizes the linear regression and steady-state Gaussian process characteristics of the Kriging initial model to accurately capture the spatial correlation of random field variables, introduces a hybridization mechanism through the MPSO algorithm, and embeds a global search strategy in the prediction population initialization stage, effectively overcoming the local convergence problem of traditional optimization algorithms in complex high-dimensional spaces. During the population iteration process, by dynamically adjusting the particle speed and position, combined with the gene recombination operation in the hybridization pool, the diversity of the search space is maintained and the optimal solution is efficiently located. Through the fitness evaluation of the offspring particles and the elite retention strategy, the approximation accuracy of the proxy model to the failure boundary is significantly improved. The iterative sampling mechanism centered on optimizing the mean of random variables realizes the intelligent expansion of random field discrete data. The model convergence is accelerated by constructing a learning function sample library, and ultimately a balance is achieved between global optimization and local refined search. Through multi-stage collaborative optimization, this method solves the problem of proxy model failure caused by high-dimensional random field variables and significantly improves the reliability of failure area prediction.

[0019] Furthermore, this method uses a three-dimensional exponential autocorrelation function to accurately quantify the spatial variability of rockfill parameters, and combines it with Cholesky decomposition to achieve random field discretization, which not only retains the autocorrelation characteristics between variables but also avoids the computational complexity of directly processing high-dimensional covariance matrices. For non-Gaussian random fields, an innovative strategy combining Latin hypercube sampling and piecewise inverse regression analysis is used to achieve intelligent dimensionality reduction of the variable space while maintaining the coverage of the sample space. The synergistic effect of projection vector calculation and principal component analysis effectively extracts the key features of the dominant failure mode, overcoming the model overfitting problem caused by feature redundancy in traditional methods. In particular, the eigenvalue threshold screening mechanism further reduces the variable dimension while ensuring information integrity, providing high-quality low-dimensional input for surrogate model training. Through multi-stage coupled modeling and adaptive dimensionality reduction, this method significantly improves the efficiency of reliability calculation, significantly enhances the accuracy of failure area prediction and the robustness of the calculation process.

[0020] Furthermore, this method subdivides the failure area into multiple sub-areas and combines the importance sampling technique to focus on areas with high failure probability density, significantly improving sampling efficiency and solving the waste of computational resources caused by uniform sampling in traditional Monte Carlo methods. By defining the conditional failure probability and generating failure sample points that obey the joint probability density distribution, a refined reconstruction of the failure response distribution is achieved. In particular, the critical failure points are accurately located through descending sorting and threshold screening strategies, effectively reducing the sample size requirement. When the critical value does not meet the convergence condition, a new density function is constructed for iterative sampling. By optimizing the failure response distribution, the true failure boundary is gradually approached, significantly enhancing the ability to capture low-probability failure events. Through the synergistic effect of failure sub-area division and dynamic sampling strategy, this method not only overcomes the dimensionality curse problem of high-dimensional random field modeling, but also achieves a balance between computational accuracy and efficiency through adaptive critical value adjustment, significantly improving the prediction accuracy and evaluation efficiency of panel cracking failure probability. BRIEF DESCRIPTION OF THE DRAWINGS

[0021] Figure 1 The present invention provides a flow chart of a reliability calculation method for cracking of a rockfill dam concrete face panel. DETAILED DESCRIPTION

[0022] Hereinafter, only certain exemplary embodiments are briefly described. As will be appreciated by those skilled in the art, the described embodiments may be modified in various ways without departing from the spirit or scope of the present invention. Therefore, the drawings and description are to be considered as illustrative in nature and not restrictive.

[0023] The terms "first" and "second" are used for descriptive purposes only and should not be construed as indicating or implying relative importance or implicitly specifying the number of the technical features being referred to. Thus, a feature specified as "first" or "second" may explicitly or implicitly include one or more of such features. In the description of the present invention, "plurality" means two or more, unless otherwise specifically defined.

[0024] The embodiments of the present invention are described in detail below with reference to the accompanying drawings.

[0025] This paper proposes a method for calculating the cracking reliability of rockfill dam concrete face panels. Figure 1 As shown, the following steps are included: Step 1: Based on the obtained physical parameters of the rockfill material used in the rockfill dam, determine the test parameters; wherein the test parameters include: material internal friction angle , deviatoric stress , material damage ratio , stress level , initial tangent modulus , tangent modulus and tangent bulk modulus ; Specifically, step 1.1, apply specimen confining pressure to the rockfill material used in the rockfill dam. , obtain the specimen confining pressure The value of the internal friction angle decreasing when one logarithmic period is increased and the initial internal friction angle , based on the value of the reduction of the internal friction angle during the logarithmic period , initial internal friction angle and specimen confining pressure Calculate the internal friction angle of the material ; Material internal friction angle The calculation process is:

[0026] in, is the initial internal friction angle, Specimen confining pressure The value of the internal friction angle decreases when one logarithmic period is increased. is the specimen confining pressure, is the unit atmospheric pressure.

[0027] Step 1.2: Obtain the material cohesion of the rockfill material used in the rockfill dam , through material cohesion and the internal friction angle of the material Calculate the deviatoric stress at the time of rockfill failure; Deviatoric stress during rockfill failure The calculation process is:

[0028] in, For material cohesion, is the internal friction angle of the material.

[0029] Step 1.3: Obtain the tangent modulus base of the rockfill material used in the rockfill dam , Unit atmospheric pressure in the area where the rockfill dam is located , axial pressure of rockfill dam , Tangent modulus index of rockfill material used in rockfill dam ; Based on axial pressure and specimen confining pressure Calculate the asymptotic value of the deviatoric stress , axial pressure , specimen confining pressure The material failure ratio is calculated by the asymptotic value of the deviatoric stress and the deviatoric stress at the time of rockfill failure. , stress level and initial tangent modulus ; Material damage ratio The calculation process is:

[0030] in, is the axial pressure, is the specimen confining pressure, is the deviatoric stress at the time of rockfill failure, is the asymptotic value of the deviatoric stress; Stress level The calculation process is:

[0031] in, is the axial pressure, is the specimen confining pressure, is the deviatoric stress at the time of rockfill failure, For material cohesion, is the internal friction angle of the material.

[0032] Initial tangent modulus The calculation process is:

[0033] in, is the specimen confining pressure, is the unit atmospheric pressure, the tangent modulus base , tangent modulus index ; The material damage ratio obtained by calculation , stress level and initial tangent modulus Calculate the tangent modulus ; Tangent modulus The calculation process is:

[0034] in, is the initial tangent modulus; is the material damage ratio; is the stress level, is the specimen confining pressure, is the unit atmospheric pressure, the tangent modulus base , tangent modulus index , For material cohesion, is the internal friction angle of the material.

[0035] Step 1.4, obtain the bulk modulus , based on the bulk modulus number , unit atmospheric pressure , specimen confining pressure and bulk modulus index Calculate the tangent bulk modulus ; The calculation process of tangent bulk modulus is:

[0036] Step 2: Determine the parameters of the Duncan Zhang EB model based on the experimental parameters, perform factor sensitivity analysis on the parameters of the Duncan Zhang EB model based on the orthogonal experimental method, and determine the sensitivity parameters.

[0037] Specifically, in step 2.1, the internal friction angle of the material , deviatoric stress , material damage ratio , stress level , initial tangent modulus , tangent modulus and tangent bulk modulus The experimental analysis was carried out to determine the parameters of the Duncan-Zhang EB model, among which the parameters of the Duncan-Zhang EB model include the internal friction angle of the material , tangent modulus cardinality , material damage ratio , tangent modulus index , material cohesion , bulk modulus , bulk modulus index and tangent bulk modulus ; The parameters of Duncan Zhang EB model are set by orthogonal test. , that is, the internal friction angle of the material , tangent modulus cardinality , material damage ratio , tangent modulus index , material cohesion , bulk modulus , bulk modulus index and tangent bulk modulus The variation values ​​are set to -0.2, -0.1, 0.0, 0.1, and 0.2 respectively to construct multiple test data sets; negative values ​​are obtained by subtracting corresponding values ​​from the original data, and positive values ​​are obtained by adding corresponding values ​​to the original data.

[0038] Step 2.2: Process the test data set based on the constructed three-dimensional finite element calculation model to obtain the finite element calculation results; Specifically, a data map of the concrete face rockfill dam project was obtained, and a three-dimensional finite element calculation model was established using the finite element analysis software (ABAQUS). The multiple test data sets constructed in step 2.1 were input into the three-dimensional finite element calculation model respectively. The rockfill parameters of the three-dimensional finite element calculation model were changed while keeping other parameters unchanged, and the finite element calculation results were obtained.

[0039] Step 2.3, use range and variance analysis methods to compare and analyze the finite element calculation results to determine the sensitivity parameters; Specifically, the range and variance analysis methods are used to compare and analyze the finite element calculation results, and the statistical parameters of the influence of each data point in the test data set on the stress sensitivity of the panel are obtained, that is, the test index value of each orthogonal test method is obtained. , calculate the average test result of the finite element calculation results corresponding to each data point in the test data set , based on the average value of test results and test index values Statistical parameters of the average value of the test results at multiple levels are obtained ; The average value of the test results The statistical process is:

[0040] in, is the rockfill parameter exist The average value of the experimental results under the level; is the rockfill parameter exist the number of trials at the level; For the Test index value; is the average value of all test results.

[0041] Calculate the difference between the statistical maximum and minimum values ​​of the statistical parameters to obtain the range value , if the extreme value The larger the value, the greater the impact of the horizontal change of the rockfill body parameters of the three-dimensional finite element calculation model on the test index, that is, the sensitivity of the rockfill body parameters of the three-dimensional finite element calculation model is large, and the rockfill body parameters are retained; If the extreme value If the value is small, it indicates that the influence of the horizontal change of the rockfill body parameters of the three-dimensional finite element calculation model on the test index is small, that is, the sensitivity of the rockfill body parameters of the three-dimensional finite element calculation model is small, and the rockfill body parameters are eliminated; the retained rockfill body parameters are statistically analyzed to determine the sensitivity parameters; Range The calculation process is:

[0042] in, is the extreme value, is the statistical maximum value, is the statistical minimum value.

[0043] Step 3: Use normal random field to characterize the sensitivity parameters to obtain random field data, and use Cholesky decomposition method to discretize the random field data to obtain the sample set and test set for training the proxy model; Specifically, step 3.1 is to obtain the three-dimensional model in the three-dimensional finite element calculation model, extract the coordinates of the unit center points corresponding to the rockfill body in the three-dimensional model, calculate the relative distance and autocorrelation distance of the coordinates of any two unit centers in the three-dimensional space in three directions, and express the spatial variability of the random variable with an exponential autocorrelation function based on the relative distance and autocorrelation distance of the coordinates of any two unit centers in three directions to obtain the autocorrelation coefficient matrix. , that is, random field data is obtained; among them, .

[0044] The representation process is:

[0045] in: 、 、 Any two points in space i andj Between , , The relative distances in three directions, and , , ; 、 、 Represent the autocorrelation distances in three directions respectively.

[0046] Step 3.2, use Cholesky decomposition method to decompose the random field data to obtain the non-Gaussian random field of random variables Data set; that is, using Cholesky decomposition method to autocorrelation coefficient matrix Decompose, that is , and obtain the lower triangular matrix , for the lower triangle After standardization, the Latin hypercube sampling method is used to obtain the standard Gaussian random field F ; Lower Triangular Matrix The standardization process is:

[0047] in, is the lower triangular matrix, is the autocorrelation coefficient matrix.

[0048] The standard Gaussian random field is obtained using the Latin hypercube sampling method. Specifically: Determine the total number of samples of a random variable ; and divide the random variable into equal probabilities independent randomly distributed areas, and the divided randomly distributed areas can be completely covered by the sampling points, that is, , and there are ; from A sample is drawn from each of the independent random distribution areas, and only one parameter sample is drawn from each independent random distribution area, and we get parameter samples, The parameter samples are randomly combined to obtain a random variable sample combination set, that is, the random field variable data is obtained, and the standard Gaussian random field is obtained by calculating the random field variable data. , at this time, the positions of samples in each random distribution area are random; For standard Gaussian random Perform equal probability transformation to obtain a non-Gaussian random field , through non-Gaussian random fields Construct a non-Gaussian random field Dataset; Non-Gaussian random fields The equal probability transformation process is:

[0049] in, is the inverse function of the marginal distribution of the non-Gaussian distribution, is the cumulative distribution function of the standard normal distribution.

[0050] Step 3.3, for the non-Gaussian random field of random variables The data set is subjected to finite element calculation to obtain variable finite element data, and the stress value in the variable finite element data is extracted to obtain the finite element stress value; the non-Gaussian random field is sorted out. and finite element stress values ​​to obtain the sample set and test set for training the proxy model.

[0051] Step 4: Construct a Kriging proxy model based on the sample set, optimize and iterate through MPSO and learning function to obtain the optimal proxy model, and evaluate the optimal proxy model.

[0052] Step 4.1, define the Kriging proxy module and build the Kriging initial model based on the sample set; Step 4.1.1, use the piecewise inverse regression analysis method to analyze the non-Gaussian random field in the random field discrete data set. Perform dimensionality reduction to obtain the projection vector ; Specifically, step 4.1.1.1, based on the non-Gaussian random field Perform evaluation processing to obtain the projection vector ; Step 4.1.1.2, statistics of non-Gaussian random fields All variable samples in and extract multiple variable samples Constructing a training sample set, and standardizing the training sample set to obtain a standard training sample set; Step 4.1.1.3, calculate the corresponding sample response based on the standard training sample set , all sample responses Divide into multiple non-overlapping groups, that is, M 1, M 2,…, M H ; Calculate the group response mean and conditional expected value of the group as well as r Order weighted covariance matrix; Step 4.1.1.4, based on the group response mean and conditional expected value Perform principal component analysis to determine the eigenvalues ​​and eigenvectors corresponding to the covariance matrix; Step 4.1.1.3, sort the eigenvalues ​​in descending order to obtain the eigenvalue sequence, select multiple eigenvalues ​​in the eigenvalue sequence whose eigenvalues ​​are greater than the preset threshold, and extract the eigenvectors corresponding to the multiple eigenvalues ​​to obtain the projection vector .

[0053] Step 4.1.2, by projecting the vector Use inverse regression analysis to find variable samples and low-dimensional response vectors The mapping relationship g ( x ); Define variable samples and low-dimensional response vectors The initial mapping relationship is:

[0054] in, is the vector of standard normal random variables of variable samples; is the low-dimensional response vector; Step 4.1.3, based on the projection vector For the defined variable samples and low-dimensional response vector The initial mapping relationship is transformed into a dimensionality reduction transformation, and the mapping relationship is obtained. g ( );

[0055] in, is the standard normal random variable vector of the projection vector, is the mapping variable after dimensionality reduction, disturbance term; Step 4.1.4, non-Gaussian random field The variable samples in the mapping relationship are g ( ) calculates the corresponding low-dimensional response vector based on the non-Gaussian random field The variable samples and the corresponding low-dimensional response vector are used to construct the Kriging initial model, where the Kriging initial model includes a linear regression submodule and a steady-state Gaussian submodule. The expression of the Kriging initial model is:

[0056] in, is a polynomial function of the variable sample, is the number of items; is the coefficient of the regression term, is the number of coefficients, is the covariance, a steady-state Gaussian process that obeys the normal distribution, .

[0057] because, ,but

[0058] Therefore, the Kriging initial model can be further expressed as:

[0059] Defining covariance for:

[0060] in, is the variance of the Gaussian process; is the correlation function between two variable samples; Related functions The Gaussian correlation function is generally used:

[0061] in, is the correlation parameter, is a variable sample in the random field discrete data The corresponding low-dimensional response vector A quantity, For variable samples The corresponding low-dimensional response vector A portion.

[0062] Correlation parameters Used to describe the smoothness of the Kriging initial model between two variable sample points, which can be obtained by maximum likelihood estimation. The likelihood estimation function as follows:

[0063] in, is the correlation coefficient matrix of variable samples; is the estimate of the variance The correlation coefficient matrix is ​​obtained by using the variable samples in the random field discrete data Input to the relevant function The correlation function matrix is ​​constructed in:

[0064] The polynomial parameters of the Kriging initial model are calculated using the least squares method for the correlation function matrix. , the coefficient of the regression term in random field discrete data for:

[0065] in, For variable samples The corresponding low-dimensional response vector; The estimate of the variance in random field discrete data is:

[0066] Arbitrary determination of prediction points on the 3D finite element model , determine the prediction point and variable samples in random field discrete data The correlation vector between for:

[0067] Based on the correlation vector And combine the Kriging initial model to determine the calculation of any prediction point The proxy model at is:

[0068] in, For variable samples The corresponding low-dimensional response vector; is the coefficient of the regression term in the random field discrete data, Correlation vector The inner product of are polynomial parameters, is the correlation coefficient matrix of the variable samples The inverse matrix of .

[0069] Step 4.2: Input the sample set into the Kriging initial model to train and obtain the Kriging training model. That is, input the random field discrete data and finite element stress values ​​of the random variables in the sample set into the Kriging initial model for iterative training until the Kriging initial model converges to obtain the Kriging training model. Step 4.3, hybridization-based particle swarm MPSO algorithm to find the optimal correlation parameters of the Kriging training model , get the Kriging optimization proxy model; Step 4.3.1, generate a prediction population based on the variable samples in the sample set random field discrete data, and initialize the position and velocity of each particle in the population in the MPSO algorithm; Step 4.3.2: Obtain the particle position and particle velocity of each individual particle in the predicted population, set the position range and velocity range, calculate the particle fitness of each particle at each position within the position range based on the particle velocity, and determine the predicted population parameter values, namely, population displacement and population velocity, based on the particle velocity and particle fitness values; Step 4.3.3, compare the particle fitness at each position, determine the particle with the minimum fitness as the optimal, extract the corresponding particle speed and particle position, and obtain the optimal particle speed and optimal particle position; Step 4.3.4: Based on the optimal particle velocity and optimal particle position, the corresponding particle velocity and particle position in the predicted population are updated to obtain the optimized predicted population. A hybridization probability is preset, and particles are selected from the optimized predicted population based on the hybridization probability and input into the hybridization pool. Randomly hybridize any two particles to produce the same number of progeny particles. Step 4.3.5, based on the speed and position of the particle, the speed and position of the offspring particle are calculated, and the fitness of the offspring particle is calculated based on the speed and position of the offspring particle. The fitness of the offspring particle is compared with the fitness of the particle. If the fitness of the offspring particle is small, the offspring particle speed and position are used to replace the speed and displacement of the particles in the optimized prediction population to obtain the optimal prediction population. The optimal prediction population is used to find the optimal correlation parameters in the Kriging training model through the MPSO algorithm. ; By the optimal correlation parameter Update the Kriging training model to obtain the Kriging optimization proxy model; The calculation expression of the displacement of the daughter particles is:

[0070] in, is the displacement of the daughter particles, is the hybridization probability, usually ranging from 0.1 to 0.5, is the displacement of a particle that generates a daughter particle, The displacement of another particle that generates a daughter particle.

[0071] The calculation expression of the offspring particle velocity is:

[0072] in, is the velocity of the daughter particles, is the velocity of a particle that generates daughter particles, The velocity of another particle that generates a daughter particle.

[0073] Step 4.4, iteratively train the Kriging optimization surrogate model through the learning function to obtain the optimal surrogate model; Step 4.4.1: Center the random variables in the sample set at their mean and use MC extraction. The sample points are used as the learning sample library of the learning function, and the learning sample library is input into the U learning function to determine whether it meets the convergence criterion of the U learning function. If it meets the convergence criterion, it is added to the sample set, and the sample set is expanded and updated to obtain the updated sample set. S ={ S ; X U}.

[0074] Step 4.4.2: Input the updated sample set into the Kriging optimization agent model for iterative training, and calculate the certainty coefficient after each training. and root mean square error , if the coefficient of certainty ≥0.9 and root mean square error RMSE When it approaches 0, it means that the accuracy of the proxy model meets the requirements, and the iteration is stopped. The Kriging optimization proxy model after iteration is retained to obtain the optimal proxy model. Determination coefficient The calculation process is:

[0075] in, is the true value of the test sample, is the predicted value of the surrogate model, is the average value of the test samples, n is the number of data in the test data set; Root mean square error The calculation process is:

[0076] in, is the true value of the test sample, is the predicted value of the surrogate model, n is the number of data in the test data set; Step 5: Based on the test set input into the optimal surrogate model, the predicted value and evaluation index are calculated to establish the structural performance function, and the panel cracking reliability is calculated using the importance sampling subset simulation method; Step 5.1: Establish structure function according to evaluation index , the test set is input into the optimal proxy model to calculate the predicted value, that is, the maximum tensile stress. The maximum tensile stress criterion is used to evaluate whether the panel will crack and determine the failure area; The structure function is:

[0077] in, is the tensile strength of concrete, is the tensile stress in the concrete panel.

[0078] Step 5.2: Divide the failure area into multiple failure sub-areas. Use the importance sampling technique to extract sample points from each failure sub-area to obtain multiple failure sample sets. Step 5.3, define the conditional failure probability P 0=0.1, use MC to extract failure sample points from multiple failure sample sets and generate The first failure sample points are independent and identically distributed and obey the joint probability density function .

[0079] Step 5.4, first failure sample point Through the mapping relationship g ( ) calculates the failure response and sorts the failure response in descending order, extracts the first The value is used as the critical value of the intermediate failure event , ).

[0080] Step 5.5, determine the critical value Is it less than 0? If the critical value If it is less than 0, the second failure sample point that falls into the failure domain within the intermediate failure event is counted. , the initial failure probability is If the critical value If it is not less than 0, the third failure sample point that does not fall into the failure domain within the intermediate failure event is counted , calculate the third failure sample point Corresponding to the mean of the failure response, a new density function is constructed and resampled using MC to generate The fourth failure sample points are independent and identically distributed and obey the new density function; Step 5.6, the fourth failure sample point is mapped through the relationship g ( ) calculates the optimized failure response, sorts the optimized failure response in descending order, and extracts the first The critical value of the intermediate failure event , , repeat step 5.4.

[0081] Step 5.7: Repeat steps 5.2 to 5.6 until the critical value is reached. If it is less than 0, all initial failure probabilities are counted, the mean of all initial failure probabilities is calculated, and the final failure probability is obtained, and the panel cracking reliability is calculated.

[0082] The present invention proposes a cracking reliability calculation system for rockfill dam concrete panels, which is applied to the above-mentioned cracking reliability calculation method for rockfill dam concrete panels. The system includes a test parameter acquisition module, a sensitivity analysis module, a discrete processing module, a model training and region determination module, a cracking reliability calculation module, and an output module. in, A test parameter acquisition module is configured to determine test parameters based on the acquired physical parameters of the rockfill material used in the rockfill dam; A sensitivity analysis module is configured to determine the parameters of the Duncan Zhang EB model based on the experimental parameters, and to perform factor sensitivity analysis on the parameters of the Duncan Zhang EB model based on the orthogonal experimental method to determine the sensitivity parameters; The discrete processing module is configured to use a normal random field to perform random field characterization on the sensitivity parameter to obtain random field data, and discretize the random field data using a Cholesky decomposition method to obtain a random field discrete data set; The model training module is configured to use the Kriging model constructed based on the sample set to iterate and optimize the optimal surrogate model through MPSO and the learning function, and to evaluate the optimal surrogate model; The cracking reliability calculation module is configured to calculate the predicted value and the evaluation index based on the test set input to the optimal surrogate model to establish a structural function, and calculate the panel cracking reliability using the importance sampling subset simulation method; The output module is configured to output panel cracking reliability.

[0083] The above shows and describes the basic principles and main features of the present invention and the advantages of the present invention. It is obvious to those skilled in the art that the present invention is not limited to the details of the above exemplary embodiments, and that the present invention can be implemented in other specific forms without departing from the spirit or essential characteristics of the present invention. Therefore, from all points of view, the embodiments should be regarded as illustrative and non-restrictive. The scope of the present invention is defined by the appended claims rather than the above description, and it is intended that all changes that fall within the meaning and range of equivalents of the claims are included in the present invention. Any reference signs in the claims should not be construed as limiting the claim to which they relate.

[0084] In addition, it should be understood that although this specification describes the embodiments, not every embodiment contains only one independent technical solution. This description is for clarity only. Those skilled in the art should consider the specification as a whole. The technical solutions in each embodiment can also be appropriately combined to form other embodiments that can be understood by those skilled in the art. The above content is only for the purpose of illustrating the technical concept of the present invention and cannot be used to limit the scope of protection of the present invention. Any changes made based on the technical solution in accordance with the technical concept proposed by the present invention fall within the scope of protection of the claims of the present invention.

Claims

1. A reliability calculation method for cracking of rockfill dam concrete face panels, characterized in that: The following steps are involved: Determine the test parameters based on the obtained physical parameters of the rockfill material used in the rockfill dam; The parameters of the Duncan Zhang EB model are determined based on the experimental parameters, and the sensitivity parameters are determined by performing factor sensitivity analysis on the parameters of the Duncan Zhang EB model based on the orthogonal experimental method; The sensitivity parameters are characterized by a normal random field, and the random field data are discretized using the Cholesky decomposition method to obtain the sample set and test set for training the proxy model. Based on the Kriging model constructed by the sample set, the optimal surrogate model is obtained through optimization iteration through MPSO and learning function, and the optimal surrogate model is evaluated; The test set is input into the optimal surrogate model to calculate the predicted value and evaluation index to establish the structural performance function, and the panel cracking reliability is calculated using the importance sampling subset simulation method.

2. The reliability calculation method for cracking of rockfill dam concrete panels according to claim 1 is characterized in that: The test parameters are determined based on the obtained physical parameters of the rockfill material used in the rockfill dam, including: Obtain specimen confining pressure The value of the internal friction angle decreasing when one logarithmic period is increased and the initial internal friction angle , based on the value of the reduction of the internal friction angle during the logarithmic period , initial internal friction angle and specimen confining pressure Calculate the internal friction angle of the material ; Obtaining the material cohesion of rockfill materials , through material cohesion and the internal friction angle of the material Calculate the deviatoric stress at the time of rockfill failure; Obtain the tangent modulus base of the rockfill material , Unit atmospheric pressure in the area where the rockfill dam is located , axial pressure of rockfill dam , Tangent modulus index of rockfill material used in rockfill dam ; Based on axial pressure and specimen confining pressure Calculate the asymptotic value of the deviatoric stress , based on axial pressure , specimen confining pressure , asymptotic value and deviatoric stress are calculated to obtain material failure ratio, stress level and initial tangent modulus respectively; Get the bulk modulus number , based on the bulk modulus number , unit atmospheric pressure , specimen confining pressure and bulk modulus index The tangent bulk modulus is calculated.

3. The reliability calculation method for cracking of rockfill dam concrete panels according to claim 1 is characterized in that: Determining the Duncan Zhang EB model parameters based on the experimental parameters, performing factor sensitivity analysis on the Duncan Zhang EB model parameters based on the orthogonal test method, and determining the sensitivity parameters include: The experimental parameters were analyzed to determine the parameters of the Duncan Zhang EB model; The Duncan Zhang EB model parameter setting variation is carried out by orthogonal test. , multiple experimental data sets are constructed; The experimental data set is processed based on the constructed three-dimensional finite element calculation model to obtain the finite element calculation results; The range and variance analysis methods were used to compare and analyze the finite element calculation results and determine the sensitivity parameters.

4. The reliability calculation method for cracking of rockfill dam concrete panels according to claim 3 is characterized in that: The range and variance analysis methods are used to compare and analyze the finite element calculation results to determine the sensitivity parameters, including: The range and variance analysis methods were used to compare and analyze the finite element calculation results, and the statistical parameters of the influence of each data point in the test data set on the stress sensitivity of the panel were obtained; Calculate the difference between the statistical maximum and the statistical minimum of the statistical parameter to obtain the range value; The sensitivity parameter is determined based on the range value.

5. The reliability calculation method for cracking of rockfill dam concrete panels according to claim 1 is characterized in that: The sensitivity parameters are characterized by a normal random field, and the random field data are discretized using the Cholesky decomposition method to obtain the sample set and test set for training the proxy model, including: Calculate the relative distance and autocorrelation distance between the coordinates of any two unit center points in the three-dimensional space constructed by the sensitivity parameters, and use the exponential autocorrelation function based on the relative distance and autocorrelation distance to represent the spatial variability of the random variable and obtain the autocorrelation coefficient matrix; The random field data is decomposed using the Cholesky decomposition method to obtain the non-Gaussian random field of random variables. Dataset; Non-Gaussian random fields for random variables The data set is subjected to finite element calculation to obtain variable finite element data, and the stress value in the variable finite element data is extracted to obtain the finite element stress value; the non-Gaussian random field is sorted out. and finite element stress values ​​to obtain the sample set and test set for training the proxy model.

6. The reliability calculation method for cracking of rockfill dam concrete panels according to claim 1 is characterized in that: The Kriging surrogate model constructed based on the sample set is optimized and iterated through MPSO and learning function to obtain the optimal surrogate model, and the optimal surrogate model is evaluated, including: Define the Kriging proxy module and build the Kriging initial model based on the sample set; The sample set is input into the Kriging initial model for training to obtain the Kriging training model, that is, the random field discrete data and finite element stress values ​​of the random variables in the sample set are input into the Kriging initial model for iterative training until the Kriging initial model converges to obtain the Kriging training model; Particle swarm optimization (MPSO) algorithm based on hybridization to find the optimal correlation parameters of Kriging training model , get the Kriging optimization proxy model; The Kriging optimization surrogate model is iteratively trained based on the optimization dataset through the learning function to obtain the optimal surrogate model.

7. The reliability calculation method for cracking of rockfill dam concrete face panels according to claim 6 is characterized in that: The Kriging proxy module is defined to construct a Kriging initial model based on a random field discrete data set, including: Use piecewise inverse regression analysis method to reduce the dimension of random field discrete data set and obtain projection vector; Use the inverse regression analysis method to find the mapping relationship between the variable sample and the low-dimensional response vector through the projection vector; Based on the projection vector, the initial mapping relationship between the defined variable sample and the low-dimensional response vector is transformed into a dimension reduction transformation to obtain a second mapping relationship; The variable samples in the non-Gaussian random field are used to calculate the corresponding low-dimensional response vector through mapping relationship 2, and the Kriging initial model is constructed based on the random field discrete data set and the corresponding low-dimensional response vector.

8. The reliability calculation method for cracking of rockfill dam concrete panels according to claim 6 is characterized in that: The hybridization-based particle swarm optimization (MPSO) algorithm expands the random field discrete data to obtain the optimal data set, including: Generate a prediction population based on variable samples in random field discrete data, and initialize the position and velocity of each particle in the population in the MPSO algorithm; Obtain the particle position and particle velocity of each individual particle in the predicted population, set the position range and velocity range, calculate the particle fitness of each particle at each position within the position range based on the particle velocity, and determine the population displacement and population velocity based on the particle velocity and particle fitness value; Compare the fitness of the particles at each position, determine that the particle with the minimum fitness is the best, extract the corresponding particle speed and particle position, and obtain the optimal particle speed and optimal particle position; Based on the optimal particle speed and optimal particle position, the corresponding particle speed and particle position in the predicted population are updated to obtain the optimized predicted population. The hybridization probability is preset, and particles are selected from the optimized predicted population based on the hybridization probability and input into the hybridization pool. Randomly hybridize any two particles to produce the same number of offspring particles. The offspring particle speed and position are calculated based on the particle speed and position. The offspring particle fitness is calculated based on the offspring particle speed and position to determine the optimal prediction population. The optimal prediction population is used to find the optimal correlation parameters in the Kriging training model through the MPSO algorithm. ; By the optimal correlation parameter Update the Kriging training model to obtain the Kriging optimization proxy model.

9. The reliability calculation method for cracking of rockfill dam concrete panels according to claim 1 is characterized in that: Based on the test set input into the optimal surrogate model, the predicted value and evaluation index are calculated to establish the structural performance function. The panel cracking reliability is calculated using the importance sampling subset simulation method, including: Establish structure function function based on evaluation index , input the test set into the optimal surrogate model to calculate the predicted value, and determine the failure area based on the predicted value; The failure area is divided into multiple failure sub-areas, and sample points are extracted from each failure sub-area using the importance sampling technique to obtain multiple failure sample sets; Define the conditional failure probability, extract failure sample points from multiple failure sample sets, and generate the first failure sample point that is independent and identically distributed and obeys the joint probability density function; The first failure sample point calculates the failure response through the established mapping relationship, and sorts the failure responses in descending order to extract the first failure sample point. The value is used as the critical value of the intermediate failure event ; Judgment critical value Is it less than 0? If the critical value If it is less than 0, the second failure sample point that falls into the failure domain within the intermediate failure event is counted. , and based on the second failure sample point The initial failure probability is calculated by the number of the first failure sample points; If the critical value If it is not less than 0, the third failure sample point that does not fall into the failure domain within the intermediate failure event is counted , calculate the third failure sample point Corresponding to the mean of the failure response, a new density function is constructed, and re-sampling is performed to generate the fourth failure sample point that is independent and identically distributed and obeys the new density function; The fourth failure sample point is calculated by the established mapping relationship to obtain the optimized failure response, and the optimized failure responses are sorted in descending order to extract the first The critical value of the intermediate failure event is calculated and the initial failure probability is recalculated; All initial failure probabilities are counted, the mean of all initial failure probabilities is calculated, the final failure probability is obtained, and the panel cracking reliability is obtained.

10. A reliability calculation system for cracking of a rockfill dam concrete face plate, used in the reliability calculation method for cracking of a rockfill dam concrete face plate according to any one of claims 1 to 9, characterized in that: include: A test parameter acquisition module is configured to determine test parameters based on the acquired physical parameters of the rockfill material used in the rockfill dam; A sensitivity analysis module is configured to determine the parameters of the Duncan Zhang EB model based on the experimental parameters, and to perform factor sensitivity analysis on the parameters of the Duncan Zhang EB model based on the orthogonal experimental method to determine the sensitivity parameters; The discrete processing module is configured to use a normal random field to perform random field characterization on the sensitivity parameter to obtain random field data, and discretize the random field data using a Cholesky decomposition method to obtain a random field discrete data set; The model training module is configured to use the Kriging model constructed based on the sample set to iterate and optimize the optimal surrogate model through MPSO and the learning function, and to evaluate the optimal surrogate model; The cracking reliability calculation module is configured to calculate the predicted value and the evaluation index based on the test set input to the optimal surrogate model to establish a structural function, and calculate the panel cracking reliability using the importance sampling subset simulation method; The output module is configured to output panel cracking reliability.

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