A hybrid reliability algorithm using PSO-optimized Kriging model and adaptive importance sampling

Abstract

Abstract. This paper aims to reduce the computational cost of reliability analysis. A new hybrid algorithm is proposed based on PSO-optimized Kriging model and adaptive importance sampling method. Firstly, the particle swarm optimization algorithm (PSO) is used to optimize the parameters of Kriging model. A typical function is fitted to validate improvement by comparing results of PSO-optimized Kriging model with those of the original Kriging model. Secondly, a hybrid algorithm for reliability analysis combined optimized Kriging model and adaptive importance sampling is proposed. Two cases from literatures are given to validate the efficiency and correctness. The proposed method is proved to be more efficient due to its application of small number of sample points according to comparison results. IntroductionIn recent years, the first-order reliability method (FORM) or the second-order reliability method (SORM) 5-6 is often applied to calculating the reliability, but the accuracy of the estimated reliability is very low because FORM and SORM are based on Taylor expansion, which ignores higher order terms. It is well known that the Monte Carlo simulation (MCS) is a widely accepted and robust method, but it is impossible to calculate the reliability with a great many samples in a short time. Especially, in case that the performance function is a complicated and time-consuming process.To reduce computations of the expensive performance function, the Kriging surrogate model been used to deal with this issue for many years. Romero [4], the first researcher applied Kriging on structural reliability problems, compared Kriging with polynomial regression and finite-element interpolation by the Latin hypercube sampling method. Kaymaz [5] calculate structural reliability based on Bucher's design and central composite design, and compared Kriging model method with classic response surface method. Choi [6] proposed an Bayesian reliability algorithm based on the Kriging dimension reduction method. Echard [7] proposed an active learning function for updating the design of experiment (DoE) base on Kriging, and compared it with other metamodels [8]. Dubourg [9] developed a hybrid algorithm based on Kriging model to solve reliability-based design optimization (RBDO). Zhang [10] used Kriging model for geotechnical reliability ansys. Balesdent [11] developed an adaptive importance sampling method based on Kriging when event probability estimation is rare. Tong [12] proposed a hybrid adaptive method by combining subset simulation and Kriging. In recent years, most studies concentrate more on how to apply Kriging model develped by Lophaven [13] to the structural reliability. However, study finds the solution of Kriging model developed by Lophaven is greatly affected by the given initial value  , and the pattern search method by Lophaven may lead

An active learning reliability algorithm using DMSSA‐optimized Kriging model and parallel infilling strategy

“…Tong and Gong used particle swarm optimization algorithm (PSO) to obtain the hyperparameter and effectively avoid the problem of trapping local optimal solution. 11 Li et al used genetic algorithm (GA) to optimize the hyperparameter and combined IS method to calculate the structural reliability. 12 Wei et al introduced the particle swarm optimization-simulated annealing (PSOSA) to explore the hyperparameter to improve the convergence efficiency.…”

“…Optimizing the hyperparameter θ and introducing the active learning infilling strategy both play crucial roles in improving the prediction ability of Kriging model. Tong and Gong used particle swarm optimization algorithm (PSO) to obtain the hyperparameter and effectively avoid the problem of trapping local optimal solution 11 . Li et al.…”