Research On Reliability Analysis Method Of Structural System Based On Kriging Model

In the practical engineering,the failure of structural system often leads to serious consequence,such as endangering human life,causing huge economic losses and social panic,etc.Therefore,it is necessary to study the reliability of structural system.For reducing the failure probability of structural system,modern engineering structures are usually designed to be high reliable.That is to say the reliability estimation refers to the problem of structural system reliability with small failure probability.In addition,complicated load environment,use of new materials and so on increase the degree of non-linearity of structural analysis,resulting in the performance function with high non-linearity.Therefore,the result given by gradientbased methods is not accurate enough,especially for the problem with multiple failure regions.Simulation-based methods need huge computational resources.The smaller the failure probability,the higher the computational cost.In the recent decades,the reliability methods based on adaptive metamodel have attached a lot of attention.In this paper,based on adaptive Kriging model,combined with importance sampling and modified subset simulation,two effective algorithms are proposed for calculating small probability failure problems.After that two stage Kriging model algorithm is proposed to identify the dominant failure modes and estimate the failure probability of system.Finally,combining stress-strength interference theory and nonlinear finite element method,a new method structural system reliability analysis is given.The main research contents of this paper are as follows:(1)AK-MCS-IS algorithm is proposed which corresponds to adaptive Kriging-based Monte Carlo simulations and importance sampling.The strategy is to replace the initial population with two or more populations with small sampling size and the next best point is identified by the iterative approach based on a point not in the original populations.Another stopping condition is given that the probability of failure estimated by the Kriging model changes slightly in three adjacent populations.(2)Combing adaptive Kriging model and modified subset simulation,AK-MSS algorithm is proposed.The original population is replaced by the equivalent population generated by MSS algorithm.Then the sample size in each iteration is determined by the average failure probability that is estimated by the Kriging model.(3)Two stage Kriging model algorithm is proposed to identify the dominant failure modes and estimate the system failure probability.After that,the algorithm that combines the proposed method of small failure probability is given to estimate the system reliability with different failure probability levels.(4)According to the theory of stress-strength interference and method of nonlinear finite element,the performance function expressions and values of each failure mode are given.Then,based on the two-stage Kriging model algorithm,the dominant failure mode is identified and the failure probability of the structural system is calculated.Then the calculation method of the parallel structural system is studied through two examples,and based on this,the reliability method of the series-parallel structural system is given.Finally,the correctness of the algorithm is verified by three cases,and the influence of random variable dimensions on the performance of the algorithm is discussed.