Mechanical structure reliability evaluation method based on iTLBO-SCN proxy model

Abstract

The invention relates to a mechanical structure reliability evaluation method based on an iTLBO-SCN proxy model. The method mainly comprises the following steps: (1) establishing a performance function model and a reliability evaluation model of a mechanical structure; (2) quantifying uncertainty of geometry, size and load parameters; (3) Latin hypercube sampling of random parameters; (4) carrying out structural finite element simulation based on a Latin hypercube sample; (5) carrying out Monte Carlo sampling on random parameters; (6) establishing a hyper-parameter optimization model of the SCN; (7) constructing an iTLBO-SCN proxy model; (8) predicting the Monte Carlo sample based on the proxy model; and (9) realizing structural reliability evaluation based on a prediction result. The method has the beneficial effects that the improved teaching and learning optimization algorithm is provided for agent model hyper-parameter optimization, so that the generalization of the agent model is improved, the SCN agent model which does not need to pre-determine a network structure and can be quickly trained is established, and the reliability evaluation efficiency of the mechanical structure is improved.

Description

Technical field

[0001] The present invention belongs to the field of mechanical structure reliability design and analysis, and in particular relates to a mechanical structure reliability evaluation method based on an iTLBO-SCN agent model. Background Art

[0002] Influenced by factors such as fluctuations in machining process quality, the random distribution of internal material defects, and the randomness of environmental loads, mechanical structures often exhibit uncertainty in load parameters, material performance parameters, and geometric dimensions. As uncertainty propagates, performance output parameters also exhibit dispersion, rendering theoretical designs that meet expected functional requirements unfeasible in actual engineering applications, leading to structural failure and product malfunction. Structural failure can significantly reduce overall product efficiency, resulting in significant economic losses and even serious safety hazards. Therefore, structural reliability assessment is crucial for optimizing structural design and maintaining safe product operation.

[0003] Generally, structural performance outputs are difficult to quantify analytically. Finite element simulation methods are often used for structural performance evaluation, combined with Monte Carlo simulations for structural reliability assessment. Although these methods offer high evaluation accuracy, Monte Carlo simulations require repeated invocations of finite element simulations to evaluate performance outputs under different random inputs, resulting in lengthy computational times and resource consumption. Consequently, these methods are less feasible for practical engineering applications. Surrogate models can achieve rapid and effective predictions for given inputs, significantly improving the computational efficiency of structural reliability assessments. In recent years, surrogate models based on artificial neural networks have gained popularity due to their powerful ability to approximate complex nonlinearities. Back propagation neural networks (BPNNs) are one of the most commonly used neural network architectures, but they suffer from the drawbacks of being prone to local optima and slow training speeds. If BPNNs are used as surrogate models, their inefficient model training will limit their modeling efficiency. Furthermore, BPNNs generally require manual specification of the network structure, such as the number of hidden neurons, and rely heavily on empirical knowledge.

[0004] Compared to traditional BPNNs, stochastic configuration networks (SCNs) randomly assign weights and biases to neurons in the hidden layer through a supervised mechanism, eliminating the need for iterative updates of node parameters and enabling rapid neural network training. Furthermore, SCNs adaptively determine the number of neurons in the hidden layer based on training errors, eliminating the need for manual pre-determination of the network structure. However, it is important to note that the generalization performance of SCNs is closely related to the setting of hyperparameters. To achieve good performance in surrogate models, these hyperparameters require careful tuning. Grid search and manual tuning are currently common hyperparameter tuning methods, but they suffer from low search efficiency. Automatic hyperparameter determination based on optimization algorithms offers greater flexibility. In summary, building on existing research, this study proposes a stochastic configuration network (SCN) as a surrogate model for hyperparameter optimization. A hyperparameter optimization model for SCNs is established, and an improved teaching-and-learning optimization algorithm is applied to solve the SCN hyperparameter optimization model. This surrogate model enables rapid approximate prediction of the performance parameters of interest, thereby improving the computational efficiency of structural reliability assessment. Summary of the Invention

[0005] To improve the computational efficiency of mechanical structure reliability assessment, the present invention provides a mechanical structure reliability assessment method based on a stochastic configuration network (SCN) surrogate model using an improved teaching-learning-based optimization (iTLBO) algorithm. This method uses the improved teaching-learning optimization algorithm to heuristically optimize the hyperparameters of the SCN model, constructing an SCN surrogate model with optimal hyperparameters as a substitute for expensive finite element simulations. This method then performs structural reliability simulations, thereby reducing computational costs. This method can be used to guide structural reliability design and has strong practical engineering application value.

[0006] The present invention proposes a mechanical structure reliability assessment method based on the iTLBO-SCN proxy model, comprising the following steps:

[0007] Step 1: Identify the failure modes and corresponding failure criteria of the mechanical structure, establish the corresponding functional model and reliability evaluation model based on Monte Carlo simulation;

[0008] Specifically, the performance function model is shown in formula (1):

[0009] g(x)=f(x)-f′ (1)

[0010] Where f(x) represents the performance parameter of the mechanical structure when the input is x, f′ represents the fault criterion, and g(x) represents the performance function;

[0011] The reliability assessment model based on Monte Carlo simulation is as follows:

[0012]

[0013] in, represents the reliability estimated by Monte Carlo simulation method, n M is the number of Monte Carlo samples, n g(x)＞0 Indicates n M The number of samples whose performance function is greater than zero in a Monte Carlo sample is the number of safe samples;

[0014] Step 2: Sort out the uncertain design variables of the structure and establish a probabilistic uncertainty representation model for each design variable to quantify its random uncertainty;

[0015] Specifically, three types of parameters are considered, namely load parameters, material parameters and size parameters. The load parameters include N L design variables, material parameters include N M design variables, the dimensional parameters include N d design variables, totaling M=N L +N M +N d design variables, and further establish probability distribution models to quantify the random uncertainty of each design variable;

[0016] Step 3: Based on the probability distribution uncertainty representation model of each design variable, Latin hypercube sampling is performed to generate n L samples, thereby constructing the Latin hypercube sample matrix L of the design variables, where the number of rows of the matrix L represents the number of Latin hypercube samples, the i-th row represents the i-th group of Latin hypercube samples composed of each design variable, the number of columns of the matrix L represents the number of design variables, and the j-th column represents the Latin hypercube sample of the j-th design variable. The matrix L and its i-th row and j-th column are shown as follows:

[0017]

[0018] x i =[x i,1 … x i,j … x i,M ] (4)

[0019] x j =[x 1,j … x i,j … xnL,j ] T (5)

[0020] Where M represents the number of design variables, x i represents the i-th group of Monte Carlo samples, x j represents the Latin hypercube sample of the j-th variable;

[0021] Step 4: Based on the Latin hypercube sample matrix L, perform finite element simulation of the mechanical structure according to the samples corresponding to each row, and add the obtained simulation results as a new column to the matrix L, thereby updating the matrix L to the matrix L′ shown in the following formula:

[0022]

[0023] Among them, x i,M+1 represents the simulation results of the i-th group of Latin hypercube samples;

[0024] Step 5: Based on the probabilistic uncertainty representation model of the design variables, Monte Carlo sampling is performed on each design variable to generate n M samples, thereby constructing the Monte Carlo sample matrix D of the design variables, where the number of rows of the matrix D represents the number of Monte Carlo samples, the i-th row represents the i-th group of Monte Carlo samples composed of each design variable, the number of columns of the matrix D represents the number of design variables, and the j-th column represents the Monte Carlo sample of the j-th design variable. The matrix D and its i-th row and j-th column are shown as follows:

[0025]

[0026] Step 6: Based on the sample information in the matrix L′, a hyperparameter optimization model of the Stochastic Configuration Network (SCN) is established;

[0027] Step 61: Substitute n in the matrix L′ described in step 4 L The group samples are randomly divided into training set and test set in the ratio of 8:2;

[0028] Step 62: Divide the training set into k folds randomly and equally

[0029] Step 63: Based on the k-fold cross-validation error of the SCN model on the training set, a hyperparameter optimization model of the Stochastic Configuration Network (SCN) is established. Specifically, the optimization variables in the optimization model are the hyperparameters to be optimized, the optimization target is the k-fold cross-validation error of the SCN, and the constraints are the value ranges of the optimization variables. The established hyperparameter optimization model is shown in the following formula:

[0030]

[0031] Where θ=(θ1,θ2,…,θ d ) represents the hyperparameter vector to be optimized, i.e., the optimization variable, and d represents the number of hyperparameters to be optimized. It represents the k-fold cross validation error of the SCN configured with the hyperparameter θ on the training set expressed as RMSE, as shown in the following formula:

[0032]

[0033] Among them, l (i) (θ) represents the validation error of the i-th fold expressed as RMSE;

[0034] Step 7: Combining the random mapping strategy and the adversarial learning strategy, an improved teaching and learning optimization algorithm is proposed to solve the hyperparameter optimization model of the stochastic configuration network established in step 5 above, thereby constructing an improved Teaching Learning based Optimization-Stochastic Configuration Network (iTLBO-SCN) agent model based on the improved teaching and learning optimization algorithm;

[0035] Step 71: Use the logistic mapping strategy to initialize the class group to promote more diverse exploration behaviors. Each student corresponds to a set of hyperparameter values.

[0036] Based on the logical mapping strategy shown in the following formula, a chaotic sequence consisting of N samples is generated for each of the d dimensions:

[0037] z j+1 = r·z j ·(1-z j ) (12)

[0038] Among them, j represents the serial number, z j ∈(0,1), r∈(0,4] are control parameters;

[0039] Further combining the value range of each dimension, the chaotic sequence is mapped to generate an initial candidate class consisting of N individuals based on the following formula:

[0040]

[0041] Among them, ub i is the upper bound of the value of the i-th dimension, lb i is the lower bound of the value of the i-th dimension, x j,i represents the i-th dimension of the j-th individual, represents the jth sample in the chaotic sequence corresponding to the i-th dimension, i = 1, 2, ..., d, j = 1, 2, ..., N;

[0042] Step 72: Generate opposing individuals for all students in the current initial candidate class as the initial opposing class;

[0043] Step 73: Evaluate the fitness of each student in the initial candidate class and its counterpart class, and determine the N individuals with the highest fitness in the original candidate class and the counterpart class as the final initial population for subsequent optimization iterations. The fitness of each student is the root mean square error (RMSE) of the five-fold cross-validation of the SCN model on the training set under the corresponding hyperparameter combination. The smaller the RMSE, the better the fitness.

[0044] Step 74: Perform group update according to the TLBO group update rule, as follows:

[0045] The individual with the highest fitness in the class is regarded as the teacher, and the jth student in the kth iteration is recorded as The average score of all students is recorded as Teachers are recorded as

[0046] During the teaching phase, each student is updated based on the following formula:

[0047]

[0048] in, represents the candidate solution generated after updating the jth student in the teaching phase, j = 1, 2, ..., N, i = 1, 2, ..., d, rand(·) is a random number in the range [0, 1], T F is the teaching factor determined based on the following formula:

[0049] T F =round[1+rand(0,1)] (15)

[0050] Will and The solution with higher fitness is taken as the jth new solution and recorded as is passed on to the learning phase;

[0051] During the learning phase, each student in the class x j ,j=1,2,…,N Randomly select another student x in the class j′ ,j′=1,2,…,N,j′≠j as a reference, and update the status by analyzing the difference between itself and the student:

[0052]

[0053] Where rand(·) represents a random number in the range [0,1];

[0054] At the same time, retain and The solution with higher fitness is taken as the jth new solution;

[0055] Step 75: Determine the critical value CR and generate a random number ra. If ra < CR, use the adversarial learning method to further update the population based on the current population.

[0056] Specifically, generate the opposite individuals of all individuals in the current class and retain the top N individuals with the highest fitness among all individuals and their opposite individuals. If the jth individual in the current class is recorded as x j =(x j,1 ,x j,2 ,…,x j,d ), then its opposite individual It can be calculated by the following formula:

[0057]

[0058] Where j = 1, 2, ..., N, i = 1, 2, ..., d, N represents the number of individuals in the class, d represents the variable dimension of the individual, DLB i and DUB i They represent the dynamic lower bound and dynamic upper bound of the i-th dimension, respectively, as shown in the following formula:

[0059] DLB i =min(x j,i ),j=1,…,N (18)

[0060] DUB i =max(x j,i ),j=1,…,N (19)

[0061] If the value of the generated opposition individual in the i-th dimension exceeds the specified value range, it will become an infeasible solution and needs to be randomly generated again based on the following formula:

[0062]

[0063] Step 76: Iterate steps 74 and 75 until a given number of iterations is met;

[0064] Step 77: Determine the individual with the highest fitness in the class, whose corresponding information is the optimal hyperparameter combination, and mark the corresponding SCN model as the optimal SCN model;

[0065] Step 8: Based on the iTLBO-SCN agent model established above, the n in the Monte Carlo sample matrix D M The finite element output prediction is performed on each group of samples one by one to obtain the corresponding n M The corresponding prediction result is added as a new column to the last column of the matrix D, thereby updating the matrix D to the matrix D′ shown in the following formula;

[0066]

[0067] Step 9: Based on the prediction results in the matrix D′ described in step 8, calculate the performance function value of each Monte Carlo sample and record it as the performance function vector g i ,i=1,2,…,n M , and further evaluate the reliability of the structure based on the reliability model;

[0068] Step 91: Evaluate the performance function of each Monte Carlo sample based on the established surrogate model, as shown in the following formula:

[0069]

[0070] in, represents the performance evaluation result of the surrogate model for the i-th Monte Carlo sample, f′ represents the fault criterion, Indicates the corresponding functional evaluation result;

[0071] Step 92: According to the reliability evaluation model based on Monte Carlo simulation established in step 1, the reliability of the mechanical structure is evaluated as shown in the following formula:

[0072]

[0073] in, Indicates the reliability of the estimate, n M is the number of Monte Carlo samples, Indicates n M The number of samples whose performance function prediction results in a Monte Carlo sample are greater than zero is the number of safe samples;

[0074] Compared with the prior art, the advantages of the present invention are:

[0075] The present invention provides a mechanical structure reliability assessment method based on the iTLBO-SCN proxy model. By establishing a proxy model of computationally expensive functional functions, the computational efficiency of structural reliability assessment is significantly improved. Specifically, to enhance the global optimization capability of the standard teaching-learning optimization algorithm, an improved teaching-learning optimization algorithm is proposed by combining a logical mapping strategy and an adversarial learning strategy. Furthermore, based on the input and output data of random finite element simulation, the improved teaching-learning optimization algorithm is combined to optimize the hyperparameters of the SCN proxy model. Based on the optimized hyperparameters, an SCN proxy model for finite element simulation is established. The proxy model is further used to perform high-precision and rapid predictions of Monte Carlo samples, thereby achieving structural reliability assessment. Compared with traditional structural reliability assessment methods based on Monte Carlo simulation, the present invention can significantly reduce the number of calls to computationally expensive finite element simulations, saving computing resources and improving computational efficiency. The established SCN proxy model randomly assigns the weights and biases of hidden neurons in the hidden layer through a supervision mechanism, avoiding the need for iterative updates of hidden neuron parameters in the BPNN, enabling rapid training of the neural network, and thus improving the modeling efficiency of the proxy model. At the same time, SCN can adaptively determine the number of neurons in the hidden layer based on training errors, eliminating the need for manual pre-determination of the network structure and reducing reliance on expert experience. Furthermore, the proposed automatic hyperparameter determination method based on iTLBO offers greater flexibility and tuning efficiency than grid search and manual adjustment methods, thereby ensuring good generalization performance of the surrogate model. BRIEF DESCRIPTION OF THE DRAWINGS

[0076] Figure 1 This is a flow chart of a mechanical structure reliability assessment method based on the iTLBO-SCN agent model of the present invention;

[0077] Figure 2 Schematic diagram of fitness evaluation represented by RMSE of five-fold cross validation in an embodiment of the present invention; DETAILED DESCRIPTION

[0078] The present invention will be further described with reference to the accompanying drawings.

[0079] Step 1: Identify the failure modes and corresponding failure criteria of the mechanical structure, and establish the corresponding functional model and reliability assessment model;

[0080] Specifically, the performance function model is shown in the following formula:

[0081] g(x)=f(x)-f′ (24)

[0082] Where f(x) represents the performance parameter of the mechanical structure when the input is x, f′ represents the fault criterion, and g(x) represents the performance function;

[0083] The reliability evaluation model is as follows:

[0084]

[0085] Among them, R represents the reliability of the mechanical structure, P(g(x)>0) represents the probability that the performance function takes a value greater than zero, and p x (x) is the joint probability density function of each design variable;

[0086] Since the relationship between the performance parameters and design parameters of a mechanical structure is often implicit, finite element simulation is often required for evaluation and solution, which makes the integral region implicitly defined. Therefore, the above integral is difficult to solve analytically. To facilitate the solution, the above reliability model is converted into a reliability model based on Monte Carlo simulation, as shown below:

[0087]

[0088] in, represents the reliability estimated by Monte Carlo simulation method, n M is the number of Monte Carlo samples, n g(x)＞0 Indicates n M The number of samples whose performance function is greater than zero in a Monte Carlo sample is the number of safe samples;

[0089] Step 2: Sort out the uncertain design variables of the structure and establish a probabilistic uncertainty representation model for each design variable to quantify its random uncertainty;

[0090] Specifically, three types of parameters are considered, namely load parameters, material parameters and size parameters. The load parameters include N L design variables, material parameters include N M design variables, the dimensional parameters include N d design variables, totaling M=N L +N M +N d design variables, and further establish probability distribution models to quantify the random uncertainty of each design variable;

[0091] Step 3: Based on the probability distribution uncertainty representation model of each design variable, Latin hypercube sampling is performed to generate n L samples, thereby constructing the Latin hypercube sample matrix L of the design variables, where the number of rows of the matrix L represents the number of Latin hypercube samples, the i-th row represents the i-th group of Latin hypercube samples composed of each design variable, the number of columns of the matrix L represents the number of design variables, and the j-th column represents the Latin hypercube sample of the j-th design variable. The matrix L and its i-th row and j-th column are shown as follows:

[0092]

[0093] x i =[x i,1 … x i,j … x i ,M] (28)

[0094] x j =[x 1,j … x i,j … x nL,j ] T (29)

[0095] Where M represents the number of design variables, x i represents the i-th group of Monte Carlo samples, x j represents the Latin hypercube sample of the j-th variable;

[0096] Step 4: Based on the Latin hypercube sample matrix L, perform finite element simulation of the mechanical structure according to the samples corresponding to each row, and add the obtained simulation results as a new column to the matrix L, thereby updating the matrix L to the matrix L′ shown in the following formula:

[0097]

[0098] Among them, x i,M+1 represents the simulation results of the i-th group of Latin hypercube samples;

[0099] Step 5: Based on the probabilistic uncertainty representation model of the design variables, Monte Carlo sampling is performed on each design variable to generate n M samples, thereby constructing the Monte Carlo sample matrix D of the design variables, where the number of rows of the matrix D represents the number of Monte Carlo samples, the i-th row represents the i-th group of Monte Carlo samples composed of each design variable, the number of columns of the matrix D represents the number of design variables, and the j-th column represents the Monte Carlo sample of the j-th design variable. The matrix D and its i-th row and j-th column are shown as follows:

[0100]

[0101]

[0102] Step 6: Based on the sample information in the matrix L′, a hyperparameter optimization model of the Stochastic Configuration Network (SCN) is established;

[0103] Step 61: Substitute n in the matrix L′ described in step 4 L The group samples are randomly divided into training set and test set in the ratio of 8:2;

[0104] Step 62: Divide the training set into k folds randomly and equally

[0105] Step 63: Based on the k-fold cross-validation error of the SCN model on the training set, a hyperparameter optimization model of the Stochastic Configuration Network (SCN) is established. Specifically, the optimization variables in the optimization model are the hyperparameters to be optimized, the optimization target is the k-fold cross-validation error of the SCN, and the constraints are the value ranges of the optimization variables. The established hyperparameter optimization model is shown in the following formula:

[0106]

[0107] Where θ=(θ1,θ2,…,θ d ) represents the hyperparameter vector to be optimized, i.e., the optimization variable, and d represents the number of hyperparameters to be optimized. It represents the k-fold cross validation error of the SCN configured with the hyperparameter θ on the training set expressed as RMSE, as shown in the following formula:

[0108]

[0109] Among them, l (i) (θ) represents the validation error of the i-th fold expressed as RMSE;

[0110] Step 7: Combining the random mapping strategy and the adversarial learning strategy, an improved teaching and learning optimization algorithm is proposed to solve the hyperparameter optimization model of the stochastic configuration network established in step 5 above, thereby constructing an improved Teaching Learning based Optimization-Stochastic Configuration Network (iTLBO-SCN) agent model based on the improved teaching and learning optimization algorithm;

[0111] Step 71: Use the logistic mapping strategy to initialize the class group to promote more diverse exploration behaviors. Each student corresponds to a set of hyperparameter values.

[0112] Based on the logical mapping strategy shown in the following formula, a chaotic sequence consisting of N samples is generated for each of the d dimensions:

[0113] z j+1 = r·z j ·(1-z j ) (36)

[0114] Among them, j represents the serial number, z j∈(0,1), r∈(0,4] are control parameters;

[0115] Further combining the value range of each dimension, the chaotic sequence is mapped to generate an initial candidate class consisting of N individuals based on the following formula:

[0116]

[0117] Among them, ub i is the upper bound of the value of the i-th dimension, lb i is the lower bound of the value of the i-th dimension, x j,i represents the i-th dimension of the j-th individual, represents the jth sample in the chaotic sequence corresponding to the i-th dimension, i = 1, 2, ..., d, j = 1, 2, ..., N;

[0118] Step 72: Generate opposing individuals for all students in the current initial candidate class as the initial opposing class;

[0119] Step 73: Evaluate the fitness of each student in the candidate class and its opposition class, and use the N individuals with the highest fitness in the candidate class and the opposition class as the initial class for subsequent population updates. The fitness of each student is the root mean square error (RMSE) of the five-fold cross-validation of the SCN model on the training set under the corresponding hyperparameter combination. The smaller the RMSE, the better the fitness.

[0120] Step 74: Perform group update according to the TLBO group update rule, as follows:

[0121] The individual with the highest fitness in the class is regarded as the teacher, and the jth student in the kth iteration is recorded as The average score of all students is recorded as Teachers are recorded as

[0122] During the teaching phase, each student is updated based on the following formula:

[0123]

[0124] in, represents the candidate solution generated after updating the jth student in the teaching phase, j = 1, 2, ..., N, i = 1, 2, ..., d, rand(·) is a random number in the range [0, 1], T F is the teaching factor determined based on the following formula:

[0125] T F =round[1+rand(0,1)] (39)

[0126] Will and The solution with higher fitness is taken as the jth new solution and recorded as is passed on to the learning phase;

[0127] During the learning phase, each student in the class x j ,j=1,2,…,N Randomly select another student x in the class j′ ,j′=1,2,…,N,j′≠j as a reference, and update the status by analyzing the difference between itself and the student:

[0128]

[0129] Where rand(·) represents a random number in the range [0,1];

[0130] At the same time, retain and The solution with higher fitness is taken as the jth new solution;

[0131] Step 75: Determine the critical value CR and generate a random number ra. If ra < CR, use the adversarial learning method to further update the population based on the current population.

[0132] Specifically, generate the opposite individuals of all individuals in the current class and retain the top N individuals with the highest fitness among all individuals and their opposite individuals. If the jth individual in the current class is recorded as x j =(x j,1 ,x j,2 ,…,x j,d ), then its opposite individual It can be calculated by the following formula:

[0133]

[0134] Where j = 1, 2, ..., N, i = 1, 2, ..., d, N represents the number of individuals in the class, d represents the variable dimension of the individual, DLB i and DUB i They represent the dynamic lower bound and dynamic upper bound of the i-th dimension, respectively, as shown in the following formula:

[0135] DLB i =min(x j,i ),j=1,…,N (42)

[0136] DUB i =max(x j,i ),j=1,…,N (43)

[0137] If the value of the generated opposition individual in the i-th dimension exceeds the specified value range, it will become an infeasible solution and needs to be randomly generated again based on the following formula:

[0138]

[0139] Step 76: Iterate steps 74 and 75 until a given number of iterations is met;

[0140] Step 77: Determine the individual with the highest fitness in the class, whose corresponding information is the optimal hyperparameter combination, and mark the corresponding SCN model as the optimal SCN model;

[0141] Step 8: Based on the iTLBO-SCN agent model established above, the n in the Monte Carlo sample matrix D M The finite element output prediction is performed on each group of samples one by one to obtain the corresponding n M The corresponding prediction result is added as a new column to the last column of the matrix D, thereby updating the matrix D to the matrix D′ shown in the following formula;

[0142]

[0143] Step 9: Based on the prediction results in the matrix D′ described in step 8, calculate the performance function value of each Monte Carlo sample and record it as the performance function vector g i ,i=1,2,…,n M , and further evaluate the reliability of the structure based on the reliability model;

[0144] Step 91: Evaluate the performance function of each Monte Carlo sample based on the established surrogate model, as shown in the following formula:

[0145]

[0146] in, represents the performance evaluation result of the surrogate model for the i-th Monte Carlo sample, f′ represents the fault criterion, Indicates the corresponding functional evaluation result;

[0147] Step 92: According to the reliability evaluation model based on Monte Carlo simulation established in step 1, the reliability of the mechanical structure is evaluated as shown in the following formula:

[0148]

[0149] in, Indicates the reliability of the estimate, n M is the number of Monte Carlo samples, Indicates n MThe number of samples whose performance function prediction results in a Monte Carlo sample are greater than zero is the number of safe samples;

[0150] Specific implementation case 1:

[0151] A flexible material mechanical structure that bears tensile load is taken as the analysis object, where the geometric model of the mechanical structure is a rectangular plate with a circular hole in the middle. Figure 1 The method flow shown in the figure applies a mechanical structure reliability assessment method based on the iTLBO-SCN agent model proposed by the present invention to analyze the reliability level of the structure. This implementation case mainly includes the following contents:

[0152] Step 1: According to the failure mode of the structure, clarify the corresponding failure criteria, and establish the corresponding functional model and reliability assessment model;

[0153] Specifically, when the maximum stress of the rectangular plate exceeds the given allowable stress threshold, it is considered that the structural strength failure occurs, and the performance function model is established as shown in the following formula:

[0154] g(x)=σ max (x)-σ′ (48)

[0155] Among them, σ max (x) represents the maximum stress of the structure when the input is x, σ′ represents the failure criterion based on the allowable stress, and g(x) represents the performance function;

[0156] Based on the aforementioned performance function model, the reliability evaluation model is established according to the Monte Carlo method as shown below:

[0157]

[0158] in, represents the reliability estimated by the Monte Carlo method, n M is the number of Monte Carlo samples, n g(x)＞0 Indicates n M The number of samples whose performance function is greater than zero in a Monte Carlo sample is the number of safe samples;

[0159] Step 2: Sort out the load parameter design variables, material parameter design variables, and size parameter design variables of the rectangular plate, and establish a probabilistic uncertainty characterization model for each design variable to quantify its random uncertainty;

[0160] Specifically, the three types of parameters considered include a total of five design variables. The load parameter involves one design variable: the pressure load on the rectangular plate. The material parameter involves one design variable: the elastic modulus. The dimensional parameters include three design variables: the plate's length, width, and inner hole diameter.

[0161] Furthermore, the normal probability distribution is used to quantify the uncertainty of each random variable. The probability density function of the normal distribution is shown as follows:

[0162]

[0163] Specifically, for material parameters, their nominal values ​​were used as the means of the corresponding normal distributions, and the standard deviations of the corresponding normal distributions were determined using a coefficient of variation of 0.05. For dimensional parameters, their nominal values ​​were used as the means of the corresponding normal distributions, and the standard deviations of the corresponding normal distributions were determined using a coefficient of variation of 0.01. For the pressure loads on the rectangular plates, their nominal values ​​were used as the means of the corresponding normal distributions, and the standard deviations of the corresponding normal distributions were determined using a coefficient of variation of 0.05. In summary, the distribution parameters of the uncertainty characterization models for the five random variables established are shown in Table 1.

[0164] Table 1 Distribution parameters of the random variable uncertainty characterization model

[0165]

[0166]

[0167] Step 3: Based on the probability distribution uncertainty characterization model of each design variable, Latin hypercube sampling is performed to generate 1000 sets of samples, thereby constructing the Latin hypercube sample matrix L of the design variables, where the number of rows in the matrix L represents the number of Latin hypercube samples, the number of columns in the matrix L represents the number of design variables, each column in the matrix L represents the Latin hypercube sample of a given design variable, and each row in the matrix L represents a set of Latin hypercube samples composed of various design variables;

[0168] Step 4: According to the Latin hypercube sample matrix L, perform structural finite element simulation for each group of samples, add the corresponding simulation results as a new column to the last column of the matrix L, and update the matrix L to the matrix L′;

[0169] Step 5: Based on the probability uncertainty representation model of the design variables, Monte Carlo sampling is performed on each design variable to generate 10 6 samples, thereby constructing the Monte Carlo sample matrix D of the design variables, where the number of rows of the matrix D represents the number of Monte Carlo samples, the number of columns of the matrix D represents the number of design variables, each column in the matrix represents a Monte Carlo sample of a given design variable, and each row in the matrix represents a group of Monte Carlo samples composed of various design variables;

[0170] Step 6: Based on the sample information in the matrix L′, a hyperparameter optimization model of the Stochastic Configuration Network (SCN) is established;

[0171] First, the 1000 groups of samples in the matrix L′ described in step 4 are randomly divided into training and test sets in a ratio of 8:2. Second, the training set is randomly divided into 5 equal folds. Then, based on the k-fold cross-validation error of the SCN model on the training set, a hyperparameter optimization model for the Stochastic Configuration Network (SCN) is established.

[0172] Specifically, the optimization variables in the optimization model are the hyperparameters to be optimized, the optimization target is the k-fold cross-validation error of SCN, and the constraints are the value ranges of each optimization variable. The established hyperparameter optimization model is shown in the following formula:

[0173]

[0174] Where θ=(θ1,θ2,…,θ d ) represents the hyperparameter vector to be optimized, i.e., the optimization variable. The hyperparameters to be optimized for the SCN model and their value ranges are shown in Table 2. It represents the k-fold cross validation error of the SCN configured with the hyperparameter θ on the training set expressed as RMSE, as shown in the following formula:

[0175]

[0176] Among them, l (i) (θ) represents the validation error of the i-th fold expressed as RMSE;

[0177] Table 2 Hyperparameters to be optimized in the SCN model and their corresponding value ranges

[0178]

[0179] Step 7: Based on the input and output information of the stochastic finite element simulation in the matrix L′, an improved Teaching Learning based Optimization-Stochastic Configuration Network (iTLBO-SCN) agent model is constructed;

[0180] Step 71: Use the logistic mapping strategy to initialize the class group, and each student corresponds to a set of hyperparameter values;

[0181] Based on the logical mapping strategy shown in the following formula, a chaotic sequence consisting of 30 samples is generated for each of the d dimensions:

[0182] z j+1 = r·z j ·(1-z j ) (53)

[0183] Among them, j represents the serial number, z j ∈(0,1), r∈(0,4] are control parameters;

[0184] Further combining the value ranges of each dimension, the chaotic sequence is mapped to generate an initial candidate class consisting of 30 individuals based on the following formula:

[0185]

[0186] Among them, ub i is the upper bound of the value of the i-th dimension, lb i is the lower bound of the value of the i-th dimension, x j,i represents the i-th dimension of the j-th individual, represents the jth sample in the chaotic sequence corresponding to the i-th dimension, i = 1, 2, ..., d, j = 1, 2, ..., N;

[0187] Step 72: Generate opposing individuals for all students in the current initial candidate class as the initial opposing class;

[0188] Step 73: Evaluate the fitness of each student in the initial candidate class and its opposition class. The N individuals with the highest fitness in the candidate class and the opposition class are used as the initial class for subsequent population updates. The fitness of each student is the root mean square error (RMSE) of the five-fold cross-validation of the SCN model on the training set under the corresponding hyperparameter combination. The smaller the RMSE, the better the fitness.

[0189] Step 74: Perform group update according to the TLBO group update rule, as follows:

[0190] The individual with the highest fitness in the class is regarded as the teacher, and the jth student in the kth iteration is recorded as The average score of all students is recorded as Teachers are recorded as

[0191] During the teaching phase, each student is updated based on the following formula:

[0192]

[0193] in, represents the candidate solution generated after updating the jth student in the teaching phase, j = 1, 2, ..., N, i = 1, 2, ..., d, rand(·) is a random number in the range [0, 1], T F is the teaching factor determined based on the following formula:

[0194] T F =round[1+rand(0,1)] (56)

[0195] Will and The solution with higher fitness is taken as the jth new solution and recorded as is passed on to the learning phase;

[0196] During the learning phase, each student in the class x j ,j=1,2,…,N Randomly select another student x in the class j′ ,j′=1,2,…,N,j′≠j as a reference, and update the status by analyzing the difference between itself and the student:

[0197]

[0198] Where rand(·) represents a random number in the range [0,1];

[0199] At the same time, retain and The solution with higher fitness is taken as the jth new solution;

[0200] Step 75: Determine the critical value CR and generate a random number ra. If ra < CR, use the adversarial learning method to further update the population based on the current population.

[0201] Specifically, generate the opposite individuals of all individuals in the current class and retain the top N individuals with the highest fitness among all individuals and their opposite individuals. If the jth individual in the current class is recorded as x j =(x j,1 ,x j,2 ,…,x j,d ), then its opposite individual It can be calculated by the following formula:

[0202]

[0203] Where j = 1, 2, ..., N, i = 1, 2, ..., d, N represents the number of individuals in the class, d represents the variable dimension of the individual, DLB i and DUB i They represent the dynamic lower bound and dynamic upper bound of the i-th dimension, respectively, as shown in the following formula:

[0204] DLB i =min(x j,i ),j=1,…,N (59)

[0205] DUB i =max(x j,i ),j=1,…,N (60)

[0206] If the value of the generated opposition individual in the i-th dimension exceeds the specified value range, it will become an infeasible solution and needs to be randomly generated again based on the following formula:

[0207]

[0208] Step 76: Iterate steps 74 and 75 until 60 iterations are completed;

[0209] Step 77: Determine the individual with the highest fitness in the class, and its corresponding information is the optimal hyperparameter combination. Specifically, the optimal hyperparameter value combination obtained by using the improved teaching and learning optimization algorithm is shown in Table 3;

[0210] Table 3 Hyperparameter combination optimization results of SCN model

[0211]

[0212] The root mean square error (RMSE) and mean absolute percentage error (MAPE) of the iTLBO-SCN proxy model on the test set are calculated to evaluate the effectiveness of the iTLBO-SCN proxy model. The calculation expressions of RMSE and MAPE are as follows:

[0213]

[0214] Among them, n t is the total number of samples in the test set, y i is the observed value of the i-th sample, is the predicted value of the i-th sample, is the average of all sample observations.

[0215] The performance evaluation results of the established iTLBO-SCN proxy model on the training set and test set are shown in Table 4, which shows that the established iTLBO-SCN model has a high level of accuracy;

[0216] Table 4 Performance of the iTLBO-SCN proxy model on the test set

[0217]

[0218] Step 8: Based on the iTLBO-SCN agent model established above, the 10 6 The finite element output prediction of each group of samples is performed one by one to obtain the corresponding 10 6 The corresponding prediction result is added as a new column to the last column of the matrix D, thereby updating the matrix D to the matrix D′;

[0219] Step 9: Based on the prediction results in the matrix D′ described in step 7, calculate the performance function of each Monte Carlo sample and record it as the performance function vector g i ,i=1,2,…,n M , and further evaluate the reliability of the structure based on the reliability model;

[0220] Specifically, the performance function of each Monte Carlo sample is evaluated based on the established surrogate model as follows:

[0221]

[0222] in, represents the predicted Von Mises stress of the surrogate model for the i-th Monte Carlo sample, and f′ represents the allowable Von Mises stress, i.e., the failure criterion. Here, f′=290Pa. Indicates the corresponding functional evaluation result;

[0223] Furthermore, the reliability of the flexible material structure is calculated according to the reliability evaluation model established in step 1:

[0224]

[0225] in, Indicates the reliability of the estimate, n M is the number of Monte Carlo samples, Indicates n M The number of samples whose performance function prediction results in a Monte Carlo sample are greater than zero is the number of safe samples;

[0226] Specific implementation case 2:

[0227] Taking the stepped shaft under compression load in a mechanical transmission mechanism as the analysis object, based on Figure 1 The method flow shown in the figure applies a structural reliability assessment method based on the iTLBO-SCN proxy model proposed in this invention to analyze the reliability level of the stepped shaft structure. This implementation case mainly includes the following contents:

[0228] Step 1: According to the failure mode of the structure, clarify the corresponding failure criteria, and establish the corresponding functional model and reliability assessment model;

[0229] Specifically, when the buckling load factor of the stepped shaft is less than the design load multiplication factor, structural failure occurs, and the functional model is established as shown in the following formula:

[0230] g(x)=λ cr (x)-λ d (66)

[0231] Among them, λ cr (x) represents the buckling load factor of the stepped shaft structure when the input is x, λ d represents the multiplication factor of the design load, g(x) represents the performance function;

[0232] Based on the aforementioned performance function model, the reliability evaluation model is established according to the Monte Carlo method as shown below:

[0233]

[0234] in, represents the reliability estimated by the Monte Carlo method, n M is the number of Monte Carlo samples, n g(x)＞0 Indicates n M The number of samples whose performance function is greater than zero in a Monte Carlo sample is the number of safe samples;

[0235] Step 2: Sort out the load parameter design variables, material parameter design variables, and dimensional parameter design variables of the stepped shaft, and establish a probabilistic uncertainty characterization model for each design variable to quantify its random uncertainty;

[0236] Specifically, the three types of parameters considered include a total of 10 design variables. The load parameters involve two design variables: the two loads borne by the stepped shaft, acting in opposite directions. The material parameters involve two design variables: the elastic modulus and Poisson's ratio. The dimensional parameters include six design variables: the stepped shaft's major diameter length, major diameter, minor diameter, minor diameter, axis centerline offset distance, and offset angle.

[0237] Furthermore, the uniform distribution is used to quantify the uncertainty of the two random variables, the axis offset distance and the offset angle, and the normal distribution is used to quantify the uncertainty of the remaining eight random variables. The probability density function of the normal distribution is shown as follows:

[0238]

[0239] Specifically, the distribution parameters of the uncertainty characterization model of the 10 random variables established are shown in Table 5.

[0240] Table 5 Distribution parameters of the step axis random variable uncertainty characterization model

[0241]

[0242]

[0243] Step 3: Based on the probability distribution uncertainty characterization model of each design variable, Latin hypercube sampling is performed to generate 1000 sets of samples, thereby constructing the Latin hypercube sample matrix L of the design variables, where the number of rows in the matrix L represents the number of Latin hypercube samples, the number of columns in the matrix L represents the number of design variables, each column in the matrix L represents the Latin hypercube sample of a given design variable, and each row in the matrix L represents a set of Latin hypercube samples composed of various design variables;

[0244] Step 4: According to the Latin hypercube sample matrix L, perform structural finite element simulation for each group of samples, add the corresponding simulation results as a new column to the last column of the matrix L, and update the matrix L to the matrix L′;

[0245] Step 5: Based on the probability uncertainty representation model of the design variables, Monte Carlo sampling is performed on each design variable to generate 10 6 samples, thereby constructing the Monte Carlo sample matrix D of the design variables, where the number of rows of the matrix D represents the number of Monte Carlo samples, the number of columns of the matrix D represents the number of design variables, each column in the matrix represents a Monte Carlo sample of a given design variable, and each row in the matrix represents a group of Monte Carlo samples composed of various design variables;

[0246] Step 6: Based on the sample information in the matrix L′, a hyperparameter optimization model of the Stochastic Configuration Network (SCN) is established;

[0247] First, the 1000 groups of samples in the matrix L′ described in step 4 are randomly divided into training and test sets in a ratio of 8:2. Second, the training set is randomly divided into 5 equal folds. Then, based on the k-fold cross-validation error of the SCN model on the training set, a hyperparameter optimization model for the Stochastic Configuration Network (SCN) is established.

[0248] Specifically, the optimization variables in the optimization model are the hyperparameters to be optimized, the optimization target is the k-fold cross-validation error of SCN, and the constraints are the value ranges of each optimization variable. The established hyperparameter optimization model is shown in the following formula:

[0249]

[0250] Where θ=(θ1,θ2,…,θd ) represents the hyperparameter vector to be optimized, i.e., the optimization variable. The hyperparameters to be optimized for the SCN model and their value ranges are shown in Table 6. It represents the k-fold cross validation error of the SCN configured with the hyperparameter θ on the training set expressed as RMSE, as shown in the following formula:

[0251]

[0252] Among them, l (i) (θ) represents the validation error of the i-th fold expressed as RMSE;

[0253] Table 6 Hyperparameters to be optimized in the SCN model and their corresponding value ranges

[0254]

[0255] Step 7: Based on the input and output information of the stochastic finite element simulation in the matrix L′, an improved Teaching Learning based Optimization-Stochastic Configuration Network (iTLBO-SCN) agent model is constructed;

[0256] Step 71: Use the logistic mapping strategy to initialize the class group, and each student corresponds to a set of hyperparameter values;

[0257] Based on the logical mapping strategy shown in the following formula, a chaotic sequence consisting of 30 samples is generated for each of the d dimensions:

[0258] z j+1 = r·z j ·(1-z j ) (71)

[0259] Among them, j represents the serial number, z j ∈(0,1), r∈(0,4] are control parameters;

[0260] Further combining the value ranges of each dimension, the chaotic sequence is mapped to generate an initial candidate class consisting of 30 individuals based on the following formula:

[0261]

[0262] Among them, ub i is the upper bound of the value of the i-th dimension, lb i is the lower bound of the value of the i-th dimension, x j,i represents the i-th dimension of the j-th individual, represents the jth sample in the chaotic sequence corresponding to the i-th dimension, i = 1, 2, ..., d, j = 1, 2, ..., N;

[0263] Step 72: Generate opposing individuals for all students in the current initial candidate class as the initial opposing class;

[0264] Step 73: Evaluate the fitness of each student in the initial candidate class and its opposing class. The N individuals with the highest fitness in the initial candidate class and its opposing class are used as the initial class for subsequent population updates. The fitness of each student is the root mean square error (RMSE) of the five-fold cross-validation of the SCN model on the training set under the corresponding hyperparameter combination. The smaller the RMSE, the better the fitness.

[0265] Step 74: Perform group update according to the TLBO group update rule, as follows:

[0266] The individual with the highest fitness in the class is regarded as the teacher, and the jth student in the kth iteration is recorded as The average score of all students is recorded as Teachers are recorded as

[0267] During the teaching phase, each student is updated based on the following formula:

[0268]

[0269] in, represents the candidate solution generated after updating the jth student in the teaching phase, j = 1, 2, ..., N, i = 1, 2, ..., d, rand(·) is a random number in the range [0, 1], T F is the teaching factor determined based on the following formula:

[0270] T F =round[1+rand(0,1)] (74)

[0271] Will and The solution with higher fitness is taken as the jth new solution and recorded as is passed on to the learning phase;

[0272] During the learning phase, each student in the class x j ,j=1,2,…,N Randomly select another student x in the class j′ ,j′=1,2,…,N,j′≠j as a reference, and update the status by analyzing the difference between itself and the student:

[0273]

[0274] Where rand(·) represents a random number in the range [0,1];

[0275] At the same time, retain and The solution with higher fitness is taken as the jth new solution;

[0276] Step 75: Determine the critical value CR and generate a random number ra. If ra < CR, use the adversarial learning method to further update the population based on the current population.

[0277] Specifically, generate the opposite individuals of all individuals in the current class and retain the top N individuals with the highest fitness among all individuals and their opposite individuals. If the jth individual in the current class is recorded as x j =(x j,1 ,x j,2 ,…,x j,d ), then its opposite individual It can be calculated by the following formula:

[0278]

[0279] Where j = 1, 2, ..., N, i = 1, 2, ..., d, N represents the number of individuals in the class, d represents the variable dimension of the individual, DLB i and DUB i They represent the dynamic lower bound and dynamic upper bound of the i-th dimension, respectively, as shown in the following formula:

[0280] DLB i =min(x j,i ),j=1,…,N (77)

[0281] DUB i =max(x j,i ),j=1,…,N (78)

[0282] If the value of the generated opposition individual in the i-th dimension exceeds the specified value range, it will become an infeasible solution and needs to be randomly generated again based on the following formula:

[0283]

[0284] Step 76: Iterate steps 74 and 75 until 60 iterations are completed;

[0285] Step 77: Determine the individual with the highest fitness in the class, and its corresponding information is the optimal hyperparameter combination. Specifically, the optimal hyperparameter value combination obtained by using the improved teaching and learning optimization algorithm is shown in Table 7;

[0286] Table 7 Hyperparameter combination optimization results of SCN model

[0287]

[0288] The root mean square error (RMSE) and mean absolute percentage error (MAPE) of the iTLBO-SCN proxy model on the test set are calculated to evaluate the effectiveness of the iTLBO-SCN proxy model. The calculation expressions of RMSE and MAPE are as follows:

[0289]

[0290] Among them, n t is the total number of samples in the test set, y i is the observed value of the i-th sample, is the predicted value of the i-th sample, is the average of all sample observations.

[0291] The performance evaluation results of the established iTLBO-SCN proxy model on the training set and test set are shown in Table 8, which shows that the established iTLBO-SCN model has a high level of accuracy;

[0292] Table 8 Performance of the iTLBO-SCN proxy model on the test set

[0293]

[0294] Step 8: Based on the iTLBO-SCN agent model established above, the 10 6 The finite element output prediction of each group of samples is performed one by one to obtain the corresponding 10 6 The corresponding prediction result is added as a new column to the last column of the matrix D, thereby updating the matrix D to the matrix D′;

[0295] Step 9: Based on the prediction results in the matrix D′ described in step 8, calculate the performance function of each Monte Carlo sample and record it as the performance function vector g i ,i=1,2,…,n M , and further evaluate the reliability of the structure based on the reliability model;

[0296] Specifically, the performance function of each Monte Carlo sample is evaluated based on the established surrogate model as follows:

[0297]

[0298] in, represents the buckling load factor evaluation result of the surrogate model for the i-th Monte Carlo sample, λd Represents the design load multiplication factor, here we take λ d =18, Indicates the corresponding functional evaluation result;

[0299] Furthermore, according to the reliability evaluation model established in step 1, the reliability of the gear pair with respect to the contact fatigue failure mode is calculated:

[0300]

[0301] in, Indicates the reliability of the estimate, n M is the number of Monte Carlo samples, Indicates n M The number of samples in a Monte Carlo sample whose performance function prediction result is greater than zero is the number of safe samples.

Claims

1. A mechanical structure reliability assessment method based on the iTLBO-SCN agent model, characterized by: The following steps are involved: Step 1: Identify the failure mode and failure criteria of the mechanical structure and establish the functional model shown below: g(x)=f(x)-f′ (1) Where f(x) represents the performance parameter of the mechanical structure when the input is x, f′ represents the fault criterion, and g(x) represents the performance function; Furthermore, a reliability assessment model based on Monte Carlo simulation is established as follows: in, is the reliability estimate obtained by Monte Carlo simulation method, n M is the number of Monte Carlo samples, n g(x)＞0 Indicates n M The number of samples whose performance function is greater than zero in a Monte Carlo sample is the number of safe samples; Step 2: Sort out the load parameter design variables, material parameter design variables, and dimensional parameter design variables of the mechanical structure, totaling M, and establish a probabilistic uncertainty representation model for each design variable to quantify its random uncertainty; Step 3: Based on the probabilistic uncertainty representation model of each design variable, Latin hypercube sampling is performed to generate n L samples, thereby constructing the Latin hypercube sample matrix L of the design variables, where the number of rows of the matrix L represents the number of Latin hypercube samples, the i-th row represents the i-th group of Latin hypercube samples composed of each design variable, the number of columns of the matrix L represents the number of design variables, and the j-th column represents the Latin hypercube sample of the j-th design variable. The matrix L and its i-th row and j-th column are shown as follows: x i =[x i,1 …x i,j …x i,M ] (4) Where M represents the number of design variables, x i represents the i-th group of Monte Carlo samples, x j represents the Latin hypercube sample of the j-th variable; Step 4: Based on the Latin hypercube sample matrix L, perform structural finite element simulation according to the samples corresponding to each row, and add the obtained simulation results as a new column to the matrix L, thereby updating the matrix L to the matrix L′ shown in the following formula: Among them, x i,M+1 represents the simulation results of the i-th group of Latin hypercube samples; Step 5: Based on the probabilistic uncertainty representation model of the design variables, perform Monte Carlo sampling on each design variable to generate n M samples, thereby constructing the Monte Carlo sample matrix D of the design variables, where the number of rows of the matrix D represents the number of Monte Carlo samples, the i-th row represents the i-th group of Monte Carlo samples composed of each design variable, the number of columns of the matrix D represents the number of design variables, and the j-th column represents the Monte Carlo sample of the j-th design variable. The matrix D and its i-th row and j-th column are shown as follows: Step 6: Based on the sample information in the matrix L′, establish a hyperparameter optimization model of the Stochastic Configuration Network (SCN); Step 7: Combining the random mapping strategy and the adversarial learning strategy, an improved teaching and learning optimization algorithm is proposed to solve the hyperparameter optimization model of the stochastic configuration network established in step 5 above, thereby constructing an improved Teaching Learning based Optimization-Stochastic Configuration Network (iTLBO-SCN) agent model based on the improved teaching and learning optimization algorithm; Step 8: Use the iTLBO-SCN proxy model established in step 7 to make output predictions for each group of Monte Carlo samples described in step 5. Add the obtained prediction results as a new column to the last column of matrix D, so that matrix D is updated to matrix D′, where matrix D′ is shown as follows: Step 9: Based on the prediction results in the matrix D′ described in step 8, the performance function value of each Monte Carlo sample is calculated based on the performance function model established in step 1, and the corresponding calculation results are recorded as the performance function vector g i ,i=1,2,…,n M , and further bring it into the reliability evaluation model based on Monte Carlo simulation established in step 1 to further evaluate the reliability of the mechanical structure.

2. A mechanical structure reliability assessment method based on the iTLBO-SCN agent model according to claim 1, characterized in that: The hyperparameter optimization model established in step 6: All samples in the matrix L′ described in step 4 are randomly divided into training set and test set in a ratio of 8:

2. The training set is further randomly divided into k-fold Therefore, a hyperparameter optimization model of the Stochastic Configuration Network (SCN) is established based on the k-fold cross-validation error of the sample on the training set. Specifically, the optimization variables in the optimization model are the hyperparameters to be optimized, the optimization target is the k-fold cross-validation error of SCN, and the constraints are the value ranges of each optimization variable. The established hyperparameter optimization model is shown in the following formula: Where θ=(θ1,θ2,…,θ d ) represents the hyperparameter vector to be optimized, i.e., the optimization variable, and d represents the number of hyperparameters to be optimized. It represents the k-fold cross validation error of the SCN configured with the hyperparameter θ on the training set, as shown in the following formula: in, represents the validation error of the i-th fold.

3. The mechanical structure reliability assessment method based on the iTLBO-SCN agent model according to claim 1 is characterized in that: The improved teaching and learning optimization algorithm in step 7: The improvements to the standard teaching and learning optimization algorithm are mainly reflected in the following two aspects: (1) In the class initialization phase, the following logic mapping strategy is introduced based on the standard TLBO: With j+1 =r·z j (1-z j ) (13) Among them, j represents the serial number, z j ∈(0,1), r∈(0,4] is the control parameter. When 3.5699<r≤4, the system is in a chaotic state; Based on the logical mapping strategy shown in the above formula, a chaotic sequence consisting of N samples is generated for each of the d dimensions. Further combined with the value range of each dimension, a candidate class consisting of N individuals is generated based on the following mapping: Among them, ub i is the upper bound of the value of the i-th dimension, lb i is the lower bound of the value of the i-th dimension, x j,i represents the i-th dimension of the j-th individual, represents the jth sample in the chaotic sequence of the i-th dimension, i = 1, 2, ..., d, j = 1, 2, ..., N; Furthermore, an adversarial learning strategy is introduced to generate an adversarial class for the original candidate class, and the N individuals with the highest fitness in the original candidate class and its adversarial class are determined as the final initial population for subsequent optimization iterations. (2) In the population iteration stage, based on the standard TLBO, an adversarial learning strategy is introduced with a given probability α (0 < α < 0.5) to enhance the algorithm's ability to escape from the local optimum. Specifically, the adversarial individuals of all individuals in the current class are generated, and the top N individuals with the highest fitness among all current individuals and adversarial individuals are retained. If the jth individual in the current class is denoted as x j =(x j,1 ,x j,2 ,…,x j,d ), then the opposing individual of this individual It can be calculated by the following formula: Where j = 1, 2, ..., N, i = 1, 2, ..., d, N represents the number of individuals in the class, d represents the variable dimension of the individual, DLB i and DUB i They represent the dynamic lower bound and dynamic upper bound of the i-th dimension, respectively, as shown in the following formula: DLB i =min(x j,i ),j=1,…,N (16) DUB i =max(x j,i ),j=1,…,N (17) If the value of the generated opposition individual in the i-th dimension exceeds the value range of the variable in the dimension [lb i ,ub i ], it is randomly generated based on the following formula:

4. The mechanical structure reliability assessment method based on the iTLBO-SCN agent model according to claim 1, characterized in that: The random configuration network agent model based on the improved teaching and learning optimization algorithm in step 7: (1) According to the hyperparameter model established in claim 2, the samples in the matrix L′ are divided into a training set and a test set in a ratio of 8:2, wherein the 1:M columns of the matrix L′ represent input information and the 1+M columns of the matrix L′ represent output information; (2) According to the established hyperparameter model described in claim 2, determine the hyperparameters to be optimized for the SCN and the corresponding value ranges, which are used as optimization variables and constraints; (3) Based on the chaotic mapping strategy shown in equations (14) and (15), a candidate class containing N individuals and its corresponding opposition class are initialized and generated. The N individuals with the highest fitness in the candidate class and the opposition class are used as the initial class. Each individual in the class corresponds to a set of hyperparameter values. (4) According to the hyperparameter model established in claim 2, the training set is first randomly divided into k folds Then, the SCN agent model is trained based on the hyperparameter information and training folds of the individuals in the initial class. Finally, the k-fold cross-validation error of each SCN model on the training set is used as the fitness evaluation result. The smaller the k-fold cross-validation error, the higher the fitness. (5) Update all individuals in the current class according to the TLBO optimization criterion; (6) Determine the critical value CR and generate a random number ra; (7) If ra < CR, further conduct adversarial learning based on the current class, determine the dynamic boundaries of each dimension according to the class performance, and thus generate the adversarial solutions of all solutions in the current class based on formula (16); Evaluate the fitness values ​​of the current solution and the opposite solution respectively, and retain N individuals with higher fitness among all the current solutions and their opposite solutions; (8) Iteratively executing steps (5), (6) and (7) until a preset number of iterations is met; (9) Select the individual with the best fitness in the class, and its corresponding information is the optimal hyperparameter combination.

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