A Two-Level Kriging-Based Approach with Active Learning for Solving Time-Variant Risk Optimization Problems

• Published in: Reliability engineering & system safety 2020-11, Vol.203, p.107033, Article 107033
• Main Authors: Kroetz, H.M., Moustapha, M., Beck, A.T., Sudret, B.
• Format: Article
• Language: English
• Subjects: Adaptive Kriging; Computation; Computer applications; Extreme values; Iterative methods; Life cycle costs; Limit states; Load resistance; Methodology; Model accuracy; Monte Carlo simulation; Objective function; Optimization; Random loads; Reliability analysis; Reliability engineering; Risk; Risk-Based Optimization; Statistics; Time-Dependent Reliability
• ISSN: 0951-8320; 1879-0836
• DOI: 10.1016/j.ress.2020.107033

•Adaptive surrogate models for solution of time-variant risk optimization problems;•Efficient Global Optimization (EGO) and Efficient Global Reliability Analysis (EGRA) combined;•One surrogate for objective function, one for limit state;•Stochastic processes explicitly modelled as time series;•Load-path dependent reliability problems addressed; Several methods have been proposed in the literature to solve reliability-based optimization problems, where failure probabilities are design constraints. However, few methods address the problem of life-cycle cost or risk optimization, where failure probabilities are part of the objective function. Moreover, few papers in the literature address time-variant reliability problems in life-cycle cost or risk optimization formulations; in particular, because most often computationally expensive Monte Carlo simulation is required. This paper proposes a numerical framework for solving general risk optimization problems involving time-variant reliability analysis. To alleviate the computational burden of Monte Carlo simulation, two adaptive coupled surrogate models are used: the first one to approximate the objective function, and the second one to approximate the quasi-static limit state function. An iterative procedure is implemented for choosing additional support points to increase the accuracy of the surrogate models. Three application problems are used to illustrate the proposed approach. Two examples involve random load and random resistance degradation processes. The third problem is related to load-path dependent failures. This subject had not yet been addressed in the context of risk-based optimization. It is shown herein that accurate solutions are obtained, with extremely limited numbers of objective function and limit state functions calls.