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An efficient method combining polynomial-chaos kriging and adaptive radial-based importance sampling for reliability analysis
Abstract This paper develops an efficient algorithm that combines polynomial-chaos kriging (PCK) and adaptive radial-based importance sampling (ARBIS) for reliability analysis. The key idea of ARBIS is to adaptively determine a sphere with the center at the origin and radius equal to the smallest distance of the failure domain to the origin, also known as the optimal -sphere, and only those samples outside the optimal -sphere have a possibility of failure and thus need to evaluate the limit-state function to judge their states (safe or failure). In the proposed algorithm, both the PCK model and -sphere are updated adaptively. In each iteration of determining the optimal -sphere, the PCK model is updated sequentially based on an active learning function, which is used to select the most informative sample from the samples between the last and current -spheres. Once the stopping criterion is met, the learning process of PCK in this iteration terminates, and the obtained PCK model is then used to determine the next -sphere. The updating iteration of the -sphere proceeds until the optimal sphere is found. Five representative examples are revisited, in which the results demonstrate the high accuracy and efficiency of the proposed PCK-ARBIS algorithm.
An efficient method combining polynomial-chaos kriging and adaptive radial-based importance sampling for reliability analysis
Abstract This paper develops an efficient algorithm that combines polynomial-chaos kriging (PCK) and adaptive radial-based importance sampling (ARBIS) for reliability analysis. The key idea of ARBIS is to adaptively determine a sphere with the center at the origin and radius equal to the smallest distance of the failure domain to the origin, also known as the optimal -sphere, and only those samples outside the optimal -sphere have a possibility of failure and thus need to evaluate the limit-state function to judge their states (safe or failure). In the proposed algorithm, both the PCK model and -sphere are updated adaptively. In each iteration of determining the optimal -sphere, the PCK model is updated sequentially based on an active learning function, which is used to select the most informative sample from the samples between the last and current -spheres. Once the stopping criterion is met, the learning process of PCK in this iteration terminates, and the obtained PCK model is then used to determine the next -sphere. The updating iteration of the -sphere proceeds until the optimal sphere is found. Five representative examples are revisited, in which the results demonstrate the high accuracy and efficiency of the proposed PCK-ARBIS algorithm.
An efficient method combining polynomial-chaos kriging and adaptive radial-based importance sampling for reliability analysis
Pan, Qiu-Jing (Autor:in) / Zhang, Rui-Feng (Autor:in) / Ye, Xin-Yu (Autor:in) / Li, Zheng-Wei (Autor:in)
29.08.2021
Aufsatz (Zeitschrift)
Elektronische Ressource
Englisch
Reliability analysis , Polynomial-chaos kriging , Radial-based importance sampling , <math xmlns="http://www.w3.org/1998/Math/MathML"><mrow><mi>β</mi></mrow></math>-sphere , Active learning , AK , Adaptive kriging , ANN , Artificial neutral network , ARBIS , Adaptive radial-based importance sampling , ASVM , Adaptive support vector machine , CoV , Coefficient of variation , CSRSM , Collocation-based stochastic response surface method , DoEs , Design of experiments , FORM/SORM , First/Second-order reliability method , GSS , Generalized subset simulation , IS , Importance sampling , LAR , Least angle regression , LHS , Latin hypercube sampling , LOO , Leave-one-out , LS , Line sampling , MCS , Monte-Carlo simulation , MPP , Most probable point , PCE , Polynomial chaos expansion , PCK , PDF , Probability density function , RBIS , RVM , Relevant Vector Machine , SPCE , Sparse polynomial chaos expansion , SR , Surface response , SS , Subset simulation , SVM , Support vector machine
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Adaptive radial-based importance sampling method for structural reliability
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