Reliability optimization method and system for multi-failure domain structures based on adaptive clustering

Abstract

The present invention discloses a multi-failure domain structural reliability optimization method and system based on adaptive clustering. The method comprises: based on engineering structure data, performing a first-stage training of a Kriging proxy model by an active learning method to construct a first-stage Kriging proxy model; based on an adaptive clustering algorithm, performing failure domain identification on the first-stage Kriging proxy model to construct an important sampling density; based on the important sampling density, performing a second-stage training of the first-stage Kriging proxy model by an active learning method to output a second-stage Kriging proxy model; and calculating the failure probability of the engineering structure based on the second-stage Kriging proxy model to obtain an engineering structure reliability calculation result. The present invention can accurately identify the potential sub-failure domains of the engineering structure, thereby improving the calculation efficiency of the failure probability of the engineering structure. As a multi-failure domain structural reliability optimization method and system based on adaptive clustering, the present invention can be widely used in the field of structural reliability optimization technology.

Description

Technical Field

[0001] The present invention relates to the technical field of structural reliability optimization, and in particular to a multi-failure domain structural reliability optimization method and system based on adaptive clustering. Background Art

[0002] Structural reliability analysis quantifies the uncertainties inherent in engineering structures and the loads they bear. This is crucial for accurately assessing structural safety, preventing structural failure, and ensuring the safety of life and property. Structural reliability is a quantitative measure of structural reliability. Structural reliability is typically characterized by failure probability, and the primary goal of structural reliability calculations is to determine the failure probability of a structure. Despite significant progress in structural reliability analysis theory and computational methods, calculating failure probability remains challenging. First, structural performance functions (SPFs) are typically expressed using models such as finite element models, resulting in a very high computational load for each call. Second, engineering structures typically have large safety margins, making structural failure a rare event. Consequently, structural reliability calculations typically require numerous simulations (and, consequently, numerous calls to SPFs), significantly increasing the computational load. The computational load required for structural reliability analysis is governed by the number of SPF calls. The fundamental challenge of structural reliability analysis is to develop efficient computational methods that can obtain sufficiently accurate failure probabilities while minimizing the number of SPF calls.

[0003] Existing structural reliability calculation methods primarily include approximate analytical methods, numerical simulation methods, and surrogate model methods. Approximate analytical methods primarily include the first-order reliability method (FORM) and the second-order reliability method (SORM). These methods offer high computational efficiency but suffer from large errors for strongly nonlinear problems. Numerical simulation methods primarily include Monte Carlo simulation and various improved methods, such as importance sampling (IS), subset simulation (SS), line sampling (LS), and directional sampling (DS). However, due to the large number of samples required for simulation, the computational complexity is high. Surrogate model methods employ a computationally efficient surrogate model to replace the actual structural performance function, significantly reducing the computational complexity. Common surrogate models include response surface model (RSM), artificial neural network (ANN), support vector machine (SVM), and kriging model. The main drawback of surrogate model methods is the inability to quantify the approximation error introduced by the surrogate model, resulting in biased estimates of failure probability. Active learning methods combine the high accuracy of numerical simulation methods with the computational efficiency of surrogate models. The core of this approach lies in using active learning to train proxy models, significantly reducing the number of structural function calls required for proxy model training, and thus significantly reducing the computational effort required for training. However, since the failure probability of large, complex engineering structures is typically low, the sample pool used by active learning methods to train the proxy models is too large, resulting in a prohibitively high computational effort for the proxy model training itself. Furthermore, engineering structures often have multiple failure domains, and accurately identifying and quantifying the contribution of each failure domain to the failure probability remains an unresolved issue. Summary of the Invention

[0004] In order to solve the above technical problems, the purpose of the present invention is to provide a multi-failure domain structural reliability optimization method and system based on adaptive clustering, which can accurately identify the potential sub-failure domains of engineering structures and thereby improve the calculation efficiency of the failure probability of engineering structures.

[0005] The first technical solution adopted by the present invention is: a multi-failure domain structural reliability optimization method based on adaptive clustering, comprising the following steps:

[0006] Based on the engineering structure data, the Kriging surrogate model is trained in the first stage through the active learning method to construct the first stage Kriging surrogate model;

[0007] Based on the adaptive clustering algorithm, the failure domain of the first-stage Kriging surrogate model is identified and the important sampling density is constructed;

[0008] Based on the importance sampling density, the first-stage Kriging proxy model is trained in the second stage through active learning method, and the second-stage Kriging proxy model is output;

[0009] The failure probability of the engineering structure is calculated based on the second-stage Kriging surrogate model, and the reliability calculation results of the engineering structure are obtained.

[0010] Furthermore, the step of performing the first-stage training of the Kriging proxy model by the active learning method based on the engineering structure data and constructing the first-stage Kriging proxy model specifically includes:

[0011] Acquire engineering structure data and generate an initial experimental design and an initial sample pool within a preset standard deviation range of a standard normal space based on a Latin hypercube sampling method, wherein the initial experimental design includes corresponding structural responses;

[0012] Based on the initial experimental design, a Kriging surrogate model was constructed using a preset software toolbox;

[0013] Based on the initial sample pool, the first best learning sample is obtained by active learning function identification, and the structural response of the first best learning sample is calculated by structure function function;

[0014] The structural response of the first best learning sample is expanded to the initial experimental design, and the Kriging surrogate model is iteratively updated based on the expanded experimental design until the preset stopping condition is met, and the first-stage Kriging surrogate model is output.

[0015] Furthermore, the expression of the active learning function is specifically as follows:

[0016] ;

[0017] In the above formula, represents the first best learning sample, represents the active learning function, represents the initial sample pool, represents the sample in the initial experimental design, and Represents the Kriging surrogate model The mean and standard deviation of the sample points.

[0018] Furthermore, the expression of the preset stop condition is specifically as follows:

[0019] ;

[0020] In the above formula, represents the stopping condition index based on the stability of the failure domain, represents the stopping condition indicator based on the change of the sample response sign between two adjacent iterations, 、 represents the critical threshold, Indicates the The number of failed samples in a round of active learning iteration, Indicates the The number of failed samples in a round of active learning iteration, represents the sample size, Indicates the The Kriging agent model obtained by rounds of active learning training, Indicates the The Kriging agent model obtained by rounds of active learning training, Indicates the samples.

[0021] Furthermore, the step of identifying the failure domain of the first-stage Kriging surrogate model based on the adaptive clustering algorithm and constructing the important sampling density specifically includes:

[0022] Generate samples in the failure domain corresponding to the first-stage Kriging surrogate model through the Markov chain Monte Carlo method;

[0023] The samples in the failure domain are divided and clustered by an adaptive clustering algorithm to obtain the best clustering result;

[0024] The best clustering result is fitted by Gaussian mixture density function to obtain the important sampling density.

[0025] Furthermore, the step of dividing and clustering the samples in the failure domain by using an adaptive clustering algorithm to obtain the best clustering result specifically includes:

[0026] Determine the range of candidate cluster numbers;

[0027] Based on the range of candidate cluster numbers, K-means clustering is performed on the samples in the failure domain to obtain preliminary clustering results;

[0028] The DI value is calculated for the preliminary clustering results to obtain the Dunn validity index;

[0029] The DI value corresponding to the maximum Dunn effectiveness index is selected as the optimal number of clusters;

[0030] The clustering results corresponding to the optimal number of clusters are obtained as the basis for dividing the potential failure domain. The samples in the failure domain are divided to obtain the best clustering results.

[0031] Furthermore, the expression of the Dunn effectiveness index is as follows:

[0032] ;

[0033] In the above formula, Indicates DI value, represents the range of candidate cluster numbers, 、 represents the clustering results, Represents clustering and The collection distance, Represents clustering results diameter.

[0034] Furthermore, the step of performing a second-stage training on the first-stage Kriging proxy model by an active learning method based on the importance sampling density and outputting the second-stage Kriging proxy model specifically includes:

[0035] Combining the first-stage Kriging surrogate model with the initial experimental design, the second-stage initial Kriging surrogate model is constructed;

[0036] Generate important sampling samples based on the important sampling density, and calculate the responses corresponding to the important sampling samples based on the initial Kriging proxy model in the second stage to obtain the second best learning sample;

[0037] The initial Kriging surrogate model of the second stage is judged according to the preset stopping conditions;

[0038] If the initial Kriging surrogate model in the second stage does not meet the preset stopping condition, the structural response corresponding to the second best learning sample is calculated, and the second best learning sample and the corresponding structural response are expanded to the initial experimental design to update the initial Kriging surrogate model in the second stage;

[0039] If the second-stage initial Kriging surrogate model meets the preset stopping conditions, the failure probability is calculated based on the current second-stage initial Kriging surrogate model to obtain the coefficient of variation;

[0040] If the coefficient of variation does not meet the preset target coefficient of variation, another set of important sampling samples is generated based on the importance sampling density, and the existing important sampling sample pool is expanded. The second-stage initial Kriging surrogate model is trained by active learning based on the expanded important sampling sample pool until the second-stage initial Kriging surrogate model meets the preset stopping condition. The failure probability and the corresponding coefficient of variation are calculated, and whether the preset target coefficient of variation is met is re-judged;

[0041] Until the coefficient of variation meets the preset target coefficient of variation, the second stage Kriging proxy model is output.

[0042] Furthermore, the calculation expression of the coefficient of variation is specifically as follows:

[0043] ;

[0044] In the above formula, represents the importance sampling estimate of the failure probability, represents the coefficient of variation of the failure probability estimate, represents the variance of the failure probability estimate.

[0045] The second technical solution adopted by the present invention is: a multi-failure domain structural reliability optimization system based on adaptive clustering, comprising:

[0046] The first module is used to perform the first-stage training of the Kriging surrogate model based on the engineering structure data through the active learning method to construct the first-stage Kriging surrogate model;

[0047] The second module is used to identify the failure domain of the first-stage Kriging surrogate model based on the adaptive clustering algorithm and construct the important sampling density;

[0048] The third module is used to perform the second-stage training of the first-stage Kriging proxy model through an active learning method based on the importance sampling density, and output the second-stage Kriging proxy model;

[0049] The fourth module is used to calculate the failure probability of the engineering structure based on the second-stage Kriging proxy model to obtain the reliability calculation results of the engineering structure.

[0050] The beneficial effects of the method and system of the present invention are as follows: the present invention uses engineering structure data to perform a first-stage training on a Kriging proxy model through an active learning method, constructs a first-stage Kriging proxy model, so that the model can better approximate the main shape of the failure domain, further identifies the failure domain of the first-stage Kriging proxy model based on an adaptive clustering algorithm, constructs an important sampling density, uses an adaptive clustering algorithm to automatically identify multiple potential sub-failure domains, and then constructs a GMM as an important sampling density function, and then based on the important sampling density, performs a second-stage training on the first-stage Kriging proxy model through an active learning method, outputs a second-stage Kriging proxy model, generates a large number of important sampling samples based on the constructed GMM important sampling density function, combines the AK-IS second stage with an active learning method to train the Kriging model, and efficiently calculates the failure probability. Finally, based on the second-stage Kriging proxy model, the failure probability of the engineering structure is calculated to obtain the engineering structure reliability calculation result, which can accurately identify the potential sub-failure domains of the engineering structure, thereby improving the calculation efficiency of the failure probability of the engineering structure. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 It is a flowchart of the steps of the multi-failure domain structure reliability optimization method based on adaptive clustering of the present invention;

[0052] Figure 2 It is a structural block diagram of the multi-failure domain structural reliability optimization system based on adaptive clustering of the present invention;

[0053] Figure 3 1 is a schematic diagram of the steps of an active learning method for calculating reliability of a multi-failure domain structure based on adaptive clustering provided by a specific embodiment of the present invention;

[0054] Figure 4 This is a schematic diagram of the results of the first specific embodiment of the present invention;

[0055] Figure 5 It is a result diagram of the second specific embodiment of the present invention. DETAILED DESCRIPTION

[0056] The present invention will be further described in detail below with reference to the accompanying drawings and specific embodiments. The step numbers in the following embodiments are provided for ease of description only and do not limit the order of the steps. The order of execution of the steps in the embodiments can be adaptively adjusted according to the understanding of those skilled in the art.

[0057] First, it's important to note that large, complex engineering structures, such as super-tall buildings, long-span structures, long-span bridges, reservoirs, dams, and nuclear power plants, are characterized by high investment, large size, complex construction, and critical social service functions. These structures are subject to numerous random uncertainties during their design, construction, and operation, including but not limited to material mechanical properties, geometric parameters, and loads. Under the influence of these random factors, the structural response also exhibits a high degree of randomness. Structural reliability analysis is an effective means of analyzing and evaluating the safety and reliability of engineering structures under the influence of these various random factors.

[0058] This embodiment of the present invention is primarily based on the active learning surrogate model importance sampling (AK-IS) method. AK-IS offers high solution efficiency for problems with small failure probabilities. However, its reliance on a FORM-based search for design points limits its applicability to problems with multiple failure domains. Therefore, this embodiment of the present invention proposes an active learning method for reliability calculation of multi-failure-domain structures based on adaptive clustering (AC-AK-IS). This method uses adaptive clustering to automatically identify multiple potential failure domains, providing an effective means for reliability analysis of multi-failure-domain structures.

[0059] The main goal of structural reliability calculation is to calculate the failure probability, which can be expressed as:

[0060] ;

[0061] In the above formula, is a basic random variable The joint Gaussian probability density function of is the structure function, then is the failure domain, is the characteristic function of the failure domain, if ,but ,otherwise .

[0062] Therefore, the basic concept of the AC-AK-IS embodiment of the present invention is to first use active learning to train a first-stage Kriging proxy model. Next, an adaptive clustering algorithm is used to automatically identify multiple potential failure domains. A Gaussian mixture density (GMM) is constructed based on the identified failure domains. This GMM is used as the importance sampling density. Finally, a large number of important sampling samples are extracted as a sample pool, and active learning is used to train a second-stage Kriging proxy model. Based on this second-stage Kriging proxy model, failure probabilities can be rapidly calculated.

[0063] Reference Figure 1 and Figure 3 The present invention provides a multi-failure domain structural reliability optimization method based on adaptive clustering, which includes the following steps:

[0064] S100, based on the engineering structure data, the Kriging proxy model is trained in the first stage by an active learning method to construct a first stage Kriging proxy model;

[0065] Based on the sample pool generated by Latin Hypercube Sampling (LHS), an active learning method is used to train the first-stage Kriging model to capture the global behavior of the structure-functional function, which facilitates the subsequent automatic identification of potential multiple failure domains using adaptive clustering.

[0066] Specifically, engineering structure data is obtained and an initial experimental design and an initial sample pool are generated within a preset standard deviation range of a standard normal space based on a Latin hypercube sampling method, wherein the initial experimental design includes a corresponding structural response; based on the initial experimental design, a Kriging proxy model is constructed through a preset software toolbox; based on the initial sample pool, a first optimal learning sample is obtained through active learning function identification, and the structural response of the first optimal learning sample is calculated through a structural function function; the structural response of the first optimal learning sample is expanded to the initial experimental design, and the Kriging proxy model is iteratively updated based on the expanded experimental design until a preset stopping condition is met, and a first-stage Kriging proxy model is output.

[0067] In this embodiment, we first use LHS in the standard normal space. Generates data within the range of times the standard deviation An initial design of experiments (DoE) for 10 samples, including inputs to the initial DoE: And the corresponding structural response: ,in, ,in, Within the range of times the standard deviation is the cutoff coefficient. Based on the initial experimental design, the first stage Kriging model is constructed and recorded as . Then in the same area ( Standard deviations) using LHS to generate a large number of samples, recorded as the initial sample pool ,in is the sample size. Active learning method is used in Get the best learning samples Calculate the structure function in The response at the location is extracted and expanded into the DoE. The Kriging model is further updated based on the expanded DoE. The above steps are repeated until the stopping condition is met. The stopping condition can be expressed as:

[0068] ;

[0069] The first equation in the above formula describes the stability of the failure domain and can be further written as:

[0070] ;

[0071] In the above formula, For the The second stopping condition characterizes the LHS sample pool The ratio of the response sign changes between two consecutive iterations can be written as:

[0072] ;

[0073] In the above formula, For the The Kriging model obtained by rounds of active learning training, Represents XOR operation, two critical thresholds and When the stopping condition is met in two consecutive iterations, the accuracy of the trained Kriging model is considered to meet the requirements and the active learning process is terminated.

[0074] This embodiment uses LHS samples, which have better spatial coverage. Therefore, only a small number of samples are needed to train a highly accurate Kriging model. In addition, active learning fully utilizes current information to obtain the next training sample, significantly reducing the number of samples required for Kriging model training and further improving computational efficiency.

[0075] In some specific embodiments, the initial DoE is generated in the standard normal space using LHS: And the initial sample pool: .calculate The corresponding structural response.

[0076] Training the first stage Kriging model :Based on the current DoE, the Kriging model is constructed using the MATLAB toolbox DACE . Using active learning function Identifying the best learning samples , the expression of the active learning function is as follows:

[0077] ;

[0078] In the above formula, is the active learning function, expressed as:

[0079] ;

[0080] In the above formula, and Kriging model The mean and standard deviation of the sample points. Check whether the stopping condition (two critical thresholds) is met. and If the stopping condition is met, the Kriging model is considered to be sufficiently accurate. Otherwise, the best learning sample is calculated. The corresponding structural response ,Will Expanding to DoE, repeat the steps to train the first stage Kriging model until the stopping condition is met.

[0081] S200, based on the adaptive clustering algorithm, the failure domain of the first-stage Kriging proxy model is identified and the important sampling density is constructed;

[0082] Based on the first stage Kriging model , generated using Markov Chain Monte Carlo (MCMC) The samples in the corresponding failure domain are then automatically identified using an adaptive clustering algorithm. Finally, a Gaussian mixture density is fitted to the identified failure domain and used as the important sampling density of the AK-IS.

[0083] Specifically, the Markov Chain Monte Carlo method is used to generate samples in the failure domain corresponding to the first-stage Kriging proxy model. The samples in the failure domain are divided and clustered using an adaptive clustering algorithm to obtain the optimal clustering result. The optimal clustering result is fitted with a Gaussian mixture density function to obtain the important sampling density.

[0084] More specifically, the range of candidate cluster numbers is determined; based on the range of candidate cluster numbers, K-means clustering is performed on the samples in the failure domain to obtain preliminary clustering results; DI values ​​are calculated on the preliminary clustering results to obtain the Dunn effectiveness index; the DI value corresponding to the maximum Dunn effectiveness index is selected as the optimal number of clusters; the clustering results corresponding to the optimal number of clusters are obtained as the basis for dividing the potential failure domain, and the samples in the failure domain are divided to obtain the best clustering results.

[0085] In this embodiment, first, MCMC is used to generate samples in the failure domain.

[0086] In some specific embodiments, The corresponding failure domain is denoted as . Using MCMC to generate The sample family within is denoted as ,in Progressive compliance failure domain Upper truncated normal distribution: , where Failure Domain The MCMC is implemented using the component-based Metropolis–Hastings algorithm.

[0087] The MCMC seed is the sample with a negative response in the current DoE. Starting from the seed, multiple Markov chains are generated simultaneously to enhance the exploration of the failure domain. The MCMC suggestion distribution is a uniform distribution with the center at the current sample point and the distribution interval as 2 times the standard deviation ( In addition, burn-in and thinning techniques are used to reduce the correlation of MCMC samples. During the MCMC sample generation phase, only the Kriging model is used to calculate the structural response, so the computational effort is minimal.

[0088] Next, identify the failure domain.

[0089] In some specific embodiments, an adaptive clustering algorithm is used to cluster the failure domains Samples within Divide into several groups. It can be considered that each group of samples obtained by clustering represents a potential failure domain. The adaptive clustering algorithm mainly uses K-means clustering and Dunn clustering effectiveness indicators.

[0090] First, determine the candidate interval of cluster number as ,in for and pair K-means clustering is performed from small to large until the number of clusters corresponding to the first empty cluster appears, whichever is the larger. Divided into clusters, among which Calculate each The best clustering is the one that maximizes the Dunn index. , as shown below:

[0091] ;

[0092] In the above formula, is the optimal number of clusters, for The Dunn index corresponding to each cluster.

[0093] Given clusters, each cluster is denoted as , then the Dunn index is:

[0094] ;

[0095] In the above formula, For clustering The diameter is written as:

[0096] ;

[0097] In the above formula, For clustering the center, for and The Euclidean distance of For clustering The sample size, For clustering and The set distance is recorded as:

[0098] ;

[0099] The optimal number of clusters is used as the number of potential failure domains, and the corresponding cluster can be used as the representative of each failure domain.

[0100] Furthermore, GMM is used to construct the importance sampling density.

[0101] In some specific embodiments, based on the failure domain Internal sample family The best clustering of , GMM can be fitted and used as the importance sampling density. Let is the best clustered sample family, then GMM can be expressed as:

[0102] ;

[0103] In the above formula, is the standardized weight, and The sample size is proportional to , and For each sample family The fitted The mean and covariance matrix of a Gaussian distribution.

[0104] Finally, GMM is used as the important sampling density. Combined with the first-stage Kriging model and the initial DoE, the second stage of AK-IS can be carried out to efficiently calculate the failure probability.

[0105] In summary, MCMC is used to generate failure samples within the failure domain of the surrogate model, and the MCMC algorithm is used to generate the failure domain of the surrogate model. The sample in The MCMC suggestion distribution is centered around the current sample. The combustion period length and slice length of MCMC are respectively and .

[0106] Adaptive clustering, using adaptive clustering algorithm to obtain sample families The best clustering of Divided into clusters, denoted as .

[0107] Construct importance sampling density based on clustering results Construct a GMM. This GMM is used as the important sampling density in the second stage of AK-IS.

[0108] S300, based on the importance sampling density, performing a second-stage training on the first-stage Kriging proxy model through an active learning method, and outputting a second-stage Kriging proxy model;

[0109] Specifically, the first-stage Kriging proxy model and the initial experimental design are combined to construct the second-stage initial Kriging proxy model; important sampling samples are generated based on the important sampling density, and the responses corresponding to the important sampling samples are calculated based on the second-stage initial Kriging proxy model to obtain the second best learning sample; the second-stage initial Kriging proxy model is judged according to the preset stopping condition; if the second-stage initial Kriging proxy model does not meet the preset stopping condition, the structural response corresponding to the second best learning sample is calculated, and the second best learning sample and the corresponding structural response are expanded to the initial experimental design, and the second-stage initial Kriging proxy model is updated; if the second-stage initial Kriging proxy model does not meet the preset stopping condition, the structural response corresponding to the second best learning sample is calculated, and the second best learning sample and the corresponding structural response are expanded to the initial experimental design, and the second-stage initial Kriging proxy model is updated; If the initial Kriging proxy model meets the preset stopping conditions, the failure probability is calculated based on the current second-stage initial Kriging proxy model to obtain the coefficient of variation. If the coefficient of variation does not meet the preset target coefficient of variation, another set of important sampling samples is generated based on the important sampling density, and the existing important sampling sample pool is expanded. The second-stage initial Kriging proxy model is trained by active learning based on the expanded important sampling sample pool until the second-stage initial Kriging proxy model meets the preset stopping conditions, the failure probability and the corresponding coefficient of variation are calculated, and it is re-determined whether the preset target coefficient of variation is met. Until the coefficient of variation meets the preset target coefficient of variation, the second-stage Kriging proxy model is output.

[0110] In the embodiment of the present invention, the second stage initial Kriging model is constructed, and the first stage Kriging model is respectively and DoE are used as the initial Kriging model and DoE of this stage. The second stage Kriging model is recorded as .

[0111] Search for the best learning samples , use the obtained GMM as the important sampling density to generate important sampling samples . Call the current Kriging model calculate The responses of all samples in the range are recorded as and . Use the same learning function to determine the best learning sample It should be noted that the candidate sample pool is , the proxy model is .

[0112] Determine whether convergence is based on the current proxy model and important sampling pool , to determine whether the preset stop condition is met. Note the two critical thresholds in this stage and If the stopping condition is met, jump to step 1 based on the best learning sample. Otherwise, the method jumps to the step Calculate the coefficient of variation of the failure probability estimate and continues to perform active learning.

[0113] Based on the best learning sample Expand DoE and calculate the best learning sample The corresponding structural response ,Will Expand to the current DoE. The method jumps to the step of constructing the second-stage initial Kriging model and updating the Kriging model.

[0114] Calculate the coefficient of variation of the failure probability estimate using the current Kriging model Calculate the failure probability and its coefficient of variation as shown below:

[0115] ;

[0116] In the above formula, is the important sampling estimate of the failure probability, which is expressed as:

[0117] ;

[0118] The second stage agent model Corresponding failure domain The characteristic function of is the GMM importance sampling density.

[0119] is the variance of the failure probability estimator, which is expressed as:

[0120] ;

[0121] Check whether it is satisfied , where is the target coefficient of variation specified in advance. If , the failure probability estimate is considered to be sufficiently accurate and the method stops. Otherwise, another set of important sampling samples is generated and expanded to , the method jumps to search for the best learning sample Step 2, a new round of active learning begins until the proxy model meets the target accuracy.

[0122] S400. Calculate the failure probability of the engineering structure based on the second-stage Kriging proxy model to obtain a reliability calculation result of the engineering structure.

[0123] In summary, the method proposed in the embodiments of the present invention uses active learning to train a Kriging proxy model to approximate the true structural performance function. This significantly reduces the sample size required for proxy model training (and the corresponding number of actual engineering structure analyses), and the proxy model itself exhibits high computational efficiency. Based on the trained Kriging proxy model, active learning and importance sampling are used to calculate the structural failure probability, further improving the computational efficiency of reliability analysis. Ultimately, the resulting Kriging proxy model of the structural performance function and its failure probability provide technical support for the design, optimization, and safety assessment of engineering structures.

[0124] Further, combined with the Figure 4 And attached Figure 5 The embodiment of the present invention is described. First, the parameters are described. For the first stage Kriging model, the truncation coefficient of the LHS sampling area is , that is, the sampling area is The initial DoE and LHS sample pool capacities are and The threshold of the stopping condition is 0.001, that is, For the adaptive clustering stage, the MCMC sample family capacity is , the combustion period length and slice length are and For the second stage of AK-IS, the importance sampling sample family capacity is , the threshold of the stopping condition is 0.0001, that is, The target coefficient of variation of the failure probability estimate is taken as . Use the structure function function call times , Failure probability estimation , coefficient of variation Cov and relative error To compare the performance of the proposed AC-AK-IS with existing methods. Specific embodiment one:

[0126] This embodiment is a series system with four failure domains, and the structure function is as follows:

[0127] ;

[0128] In the above formula, are all standard normal random variables.

[0129] Typical process is Figure 4 As shown. Figure 4 As shown in (a): The newly added DoEs of the Kriging model active learning in the first stage are mainly concentrated near the limit state surface. Figure 4As shown in (b): The samples and optimal clustering results within the failure domain of the surrogate model generated by MCMC, indicating that the adaptive clustering algorithm can effectively identify the sub-failure domain. Figure 4 As shown in (c) in the figure: The GMM constructed based on the identified sub-failure domain is a multimodal probability density function. Figure 4 (d) shows the important sampling sample pool and the final trained Kriging model.

[0130] The calculation results are shown in Table 1. It can be seen that the proposed AC-AK-IS method outperforms the simulation methods (MCS, DS and IS), Meta-IS and MetaAK-IS2, and can use a smaller number of structural function calls. Obtain similar or higher accuracy failure probability estimates. While slightly larger than AK-SS and ALK-KDE-IS, the failure probability estimate has a smaller coefficient of variation (Cov), indicating a higher accuracy of the failure probability estimate. Since AK-MCS+U and AK-MCS+EFF do not provide Cov, the performance of AC-AK-IS cannot be compared with these two methods. Overall, AC-AK-IS performs slightly worse than Meta-IS-AK. However, it should be noted that AC-AK-IS explicitly identifies sub-failure domains, providing an effective way to quantify the contribution of each sub-failure domain to overall failure.

[0131] Table 1 Reliability calculation results of specific embodiment 1

[0132]

[0133] Specific embodiment 2: This embodiment is a system with two failure domains, and the structure function function is as follows:

[0134] ;

[0135] In the above formula, are independent standard normal random variables. Parameters Take 3, 4, and 5 respectively, and the corresponding failure probability order of magnitude is down to .

[0136] Figure 5 Give The typical calculation process of . Figure 5 (a) in the figure is the first-stage Kriging model. Figure 5 (b) in the figure shows that the adaptive clustering algorithm can accurately identify two sub-failure domains. Figure 5 (c) in the figure is the GMM probability density function obtained by fitting. Figure 5 (d) in the figure shows the important sampling samples and the final trained Kriging model.

[0137] As shown in Table 2, the reliability computer results are given. It can be seen that the performance of the proposed AC-AK-IS significantly exceeds that of MCS, Au&Beck, and Meta-IS, and the number of function calls required is Significantly reduced. Although AC-AK-IS requires The failure probability variation coefficient Cov of AC-AK-IS is close to MetaAK-IS2 and ALK-KDE-IS, but AC-AK-IS has a smaller failure probability variation coefficient Cov, indicating that its calculation accuracy is higher. In addition, as the failure probability decreases in magnitude, the required It does not increase significantly, demonstrating robustness to changes in the order of magnitude of the failure probability.

[0138] Table 2 Reliability calculation results of specific embodiment 2

[0139]

[0140] In summary, the embodiment of the present invention firstly trains the first-stage active learning Kriging model based on the LHS sample pool, and the model can better approximate the main shape of the failure domain. Secondly, an adaptive clustering algorithm is used to automatically identify multiple potential sub-failure domains, and then construct the GMM as the important sampling density function. Finally, a large number of important sampling samples are generated based on the constructed GMM important sampling density function, and the active learning method is used to train the Kriging model in combination with the second stage of AK-IS to efficiently calculate the failure probability. The proposed method AC-AK-IS combines the important sampling method and the active learning Kriging model based on adaptive clustering, which can provide an effective means for structural reliability analysis with multiple failure domains and small failure probabilities.

[0141] Combined with specific examples, it is shown that: (1) the proposed method can accurately identify potential sub-failure domains; (2) compared with existing methods, it can generally improve computational efficiency; (3) it can provide an effective means to quantify the contribution of each sub-failure domain to structural failure.

[0142] Reference Figure 2 , a multi-failure domain structural reliability optimization system based on adaptive clustering, including:

[0143] The first module 201 is used to perform a first-stage training on the Kriging proxy model by an active learning method based on the engineering structure data to construct a first-stage Kriging proxy model;

[0144] The second module 202 is used to identify the failure domain of the first-stage Kriging proxy model based on the adaptive clustering algorithm and construct the important sampling density;

[0145] The third module 203 is configured to perform a second-stage training on the first-stage Kriging proxy model by an active learning method based on the importance sampling density, and output the second-stage Kriging proxy model;

[0146] The fourth module 204 is used to calculate the failure probability of the engineering structure based on the second-stage Kriging proxy model to obtain the engineering structure reliability calculation result.

[0147] The contents of the above method embodiments are all applicable to the present system embodiments. The functions specifically implemented by the present system embodiments are the same as those of the above method embodiments, and the beneficial effects achieved are also the same as those achieved by the above method embodiments.

[0148] The above is a specific description of the preferred implementation of the present invention, but the invention is not limited to the embodiments. Those skilled in the art can make various equivalent modifications or substitutions without violating the spirit of the present invention. These equivalent modifications or substitutions are all included in the scope defined by the claims of this application.

Claims

1. A multi-failure domain structural reliability optimization method based on adaptive clustering, characterized by: The following steps are involved: Based on the engineering structure data, the Kriging surrogate model is trained in the first stage through the active learning method to construct the first stage Kriging surrogate model; Generate samples in the failure domain corresponding to the first-stage Kriging surrogate model through the Markov chain Monte Carlo method; Determine the range of candidate cluster numbers; Based on the range of candidate cluster numbers, K-means clustering is performed on the samples in the failure domain to obtain preliminary clustering results; The DI value is calculated for the preliminary clustering results to obtain the Dunn validity index; The DI value corresponding to the maximum Dunn effectiveness index is selected as the optimal number of clusters; Obtain the clustering result corresponding to the optimal number of clusters as the basis for dividing the potential failure domain, divide the samples in the failure domain, and obtain the best clustering result; The best clustering result is fitted by Gaussian mixture density function to obtain the important sampling density; Combining the first-stage Kriging surrogate model with the initial experimental design, the second-stage initial Kriging surrogate model is constructed; Generate important sampling samples based on the important sampling density, and calculate the responses corresponding to the important sampling samples based on the initial Kriging proxy model in the second stage to obtain the second best learning sample; The initial Kriging surrogate model of the second stage is judged according to the preset stopping conditions; If the initial Kriging surrogate model in the second stage does not meet the preset stopping condition, the structural response corresponding to the second best learning sample is calculated, and the second best learning sample and the corresponding structural response are expanded to the initial experimental design to update the initial Kriging surrogate model in the second stage; If the second-stage initial Kriging surrogate model meets the preset stopping conditions, the failure probability is calculated based on the current second-stage initial Kriging surrogate model to obtain the coefficient of variation; If the coefficient of variation does not meet the preset target coefficient of variation, another set of important sampling samples is generated based on the importance sampling density, and the existing important sampling sample pool is expanded. The second-stage initial Kriging surrogate model is trained by active learning based on the expanded important sampling sample pool until the second-stage initial Kriging surrogate model meets the preset stopping condition. The failure probability and the corresponding coefficient of variation are calculated, and whether the preset target coefficient of variation is met is re-judged; Until the coefficient of variation meets the preset target coefficient of variation, the second stage Kriging proxy model is output; The failure probability of the engineering structure is calculated based on the second-stage Kriging surrogate model, and the reliability calculation results of the engineering structure are obtained.

2. The multi-failure domain structural reliability optimization method based on adaptive clustering according to claim 1 is characterized in that: The step of performing the first-stage training of the Kriging proxy model by the active learning method based on the engineering structure data and constructing the first-stage Kriging proxy model specifically includes: Acquire engineering structure data and generate an initial experimental design and an initial sample pool within a preset standard deviation range of a standard normal space based on a Latin hypercube sampling method, wherein the initial experimental design includes corresponding structural responses; Based on the initial experimental design, a Kriging surrogate model was constructed using a preset software toolbox; Based on the initial sample pool, the first best learning sample is obtained by active learning function identification, and the structural response of the first best learning sample is calculated by structure function function; The structural response of the first best learning sample is expanded to the initial experimental design, and the Kriging surrogate model is iteratively updated based on the expanded experimental design until the preset stopping condition is met, and the first-stage Kriging surrogate model is output.

3. The multi-failure domain structural reliability optimization method based on adaptive clustering according to claim 2 is characterized in that: The expression of the active learning function is specifically as follows: ； In the above formula, represents the first best learning sample, represents the active learning function, represents the initial sample pool, represents the sample in the initial experimental design, and Represents the Kriging surrogate model The mean and standard deviation of the sample points.

4. The multi-failure domain structural reliability optimization method based on adaptive clustering according to claim 3 is characterized in that: The expression of the preset stop condition is specifically as follows: ； In the above formula, represents the stopping condition index based on the stability of the failure domain, represents the stopping condition indicator based on the change of the sample response sign between two adjacent iterations, represents the critical threshold, Indicates the The number of failed samples in a round of active learning iteration, Indicates the The number of failed samples in a round of active learning iteration, represents the sample size, Indicates the The Kriging agent model obtained by rounds of active learning training, Indicates the The Kriging agent model obtained by rounds of active learning training, Indicates the samples.

5. The multi-failure domain structural reliability optimization method based on adaptive clustering according to claim 4 is characterized in that: The expression of the Dunn effectiveness index is as follows: ； In the above formula, Indicates DI value, represents the range of candidate cluster numbers, represents the clustering results, Represents clustering and The collection distance of Represents clustering results diameter.

6. The multi-failure domain structural reliability optimization method based on adaptive clustering according to claim 5 is characterized in that: The calculation expression of the coefficient of variation is specifically as follows: ； In the above formula, represents the importance sampling estimate of the failure probability, represents the coefficient of variation of the failure probability estimate, represents the variance of the failure probability estimate.

7. The multi-failure domain structural reliability optimization system based on adaptive clustering is characterized by: Includes the following modules: The first module is used to perform the first-stage training of the Kriging surrogate model based on the engineering structure data through the active learning method to construct the first-stage Kriging surrogate model; The second module is used to generate samples in the failure domain corresponding to the first-stage Kriging surrogate model through the Markov chain Monte Carlo method; Determine the range of candidate cluster numbers; Based on the range of candidate cluster numbers, K-means clustering is performed on the samples in the failure domain to obtain preliminary clustering results; The DI value is calculated for the preliminary clustering results to obtain the Dunn validity index; The DI value corresponding to the maximum Dunn effectiveness index is selected as the optimal number of clusters; Obtain the clustering result corresponding to the optimal number of clusters as the basis for dividing the potential failure domain, divide the samples in the failure domain, and obtain the best clustering result; The best clustering result is fitted by Gaussian mixture density function to obtain the important sampling density; The third module is used to combine the first-stage Kriging surrogate model with the initial experimental design to construct the second-stage initial Kriging surrogate model; Generate important sampling samples based on the important sampling density, and calculate the responses corresponding to the important sampling samples based on the initial Kriging proxy model in the second stage to obtain the second best learning sample; The initial Kriging surrogate model of the second stage is judged according to the preset stopping conditions; If the initial Kriging surrogate model in the second stage does not meet the preset stopping condition, the structural response corresponding to the second best learning sample is calculated, and the second best learning sample and the corresponding structural response are expanded to the initial experimental design to update the initial Kriging surrogate model in the second stage; If the second-stage initial Kriging surrogate model meets the preset stopping conditions, the failure probability is calculated based on the current second-stage initial Kriging surrogate model to obtain the coefficient of variation; If the coefficient of variation does not meet the preset target coefficient of variation, another set of important sampling samples is generated based on the importance sampling density, and the existing important sampling sample pool is expanded. The second-stage initial Kriging surrogate model is trained by active learning based on the expanded important sampling sample pool until the second-stage initial Kriging surrogate model meets the preset stopping condition. The failure probability and the corresponding coefficient of variation are calculated, and whether the preset target coefficient of variation is met is re-judged; Until the coefficient of variation meets the preset target coefficient of variation, the second stage Kriging proxy model is output; The fourth module is used to calculate the failure probability of the engineering structure based on the second-stage Kriging proxy model to obtain the reliability calculation results of the engineering structure.

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