An efficient surrogate model method considering the candidate sample pool reduction by safety optimal hypersphere for random-interval mixed reliability analysis

Under the random and interval mixed uncertainties, the structural safety level is measured by the upper and lower bounds of failure probability (B-FP). To accurately estimate the B-FP, an efficient Kriging surrogate model method is proposed in this paper, and the candidate sample pool (CSP) reduction strategy is proposed based on the safety optimal hypersphere (SOH). SOH is centered at coordinate origin with radius of reliability index and a stepwise strategy of searching the SOH is proposed in this paper. The state of random sample inside the SOH can be identified as safety directly. Based on the SOH, the efficiency of training the Kriging model for estimating the B-FP can be greatly improved by the following proposed strategies: (1) The Kriging model is adaptively updated in the random CSP subsets generated in the stepwise process of searching the SOH to save more training time. (2) By the employment of SOH, both the random CSP size and the combination CSP size of random and interval inputs are reduced. (3) The adaptive Kriging model is used to iteratively solve the reliability index by the dichotomy. The presented examples demonstrate the superior efficiency of the proposed method over the existing methods under the acceptable accuracy.