Reliability Analysis Method Based On Self-learning HMC-Kriging

There are many uncertainties in the practical engineering,and the reliability evaluation is an urgent problem to solve.Importance sampling(IS)is one of the effective methods to evaluate the structural reliability.The determination of importance sampling function is the key,which directly determines the efficiency and accuracy of the importance sampling method.Moreover,the adaptive importance sampling method can avoid searching the most probable point(MPP).The Markov chain importance sampling method(MCMC-IS)is one of the commonly used adaptive importance sampling methods.MCMC-IS can treat the problems of multiple MPPs and highly non-linear failure surface,however,which needs high computational cost and is not suitable for the practical engineering.Using the surrogate model is an effective way to improve the efficiency of reliability evaluation.Kriging based adaptive import sampling method(KAIS)for MCMC-IS uses MCMC method to get samples in the optimal importance sampling density function,then initialize Kriging surrogate model with the sample points extracted already,finally train Kriging surrogate model with the U-Learning criterion to replace the function to solve the failure probability.KAIS method provides a theoretical basis for the framework of Kriging with MCMC-IS,however,a lot of computational cost is needed in the process of the pre-sampling due to the independence between MCMC sampling and Kriging model training.In this paper,KAIS is improved by using the hybrid Monte Carlo(HMC),and a selflearning HMC-Kriging reliability analysis method is proposed.Compared with the traditional MCMC sampling method,HMC uses the gradient information of random samples,with higher sample acceptance rate and convergence speed,which can avoid the problem of random walk.Moreover,HMC-Kriging method updates Kriging model while using HMC sampling to extract sample center and replace the real function for sampling,and employs U learning function to find dangerous points to update Kriging model.The above process is repeated until the convergence conditions are met,which can avoid the waste of computing resources caused by pre-sampling process.In addition,the step size of HMC sampling is adjusted so that the proposed method can be used to solve the problem of multiple MPPs in multiple failure domains.The proposed method are tested by some problems of low failure probability,high nonlinearity and multi-MPPs,with more efficient and accurate results compared with several popular methods.Then,the time-independent HMC-Kriging framework is extended to the timedependent reliability analysis,combined with the random process transformation method.The time-dependent importance sampling formula is derived.The results of numerical examples show that the HMC-Kriging for time-dependent reliability analysis also works well in the stationary stochastic Gaussian process.