Time-Variant Reliability-Based Optimization with Double-Loop Kriging Surrogates

Time-variant reliability (TvR) analysis allows capturing the time-dependence of the probability of failure and the uncertainty of the deterioration process. The assessment of TR of existing structures subjected to degradation is an important task for taking decisions on inspection, maintenance and repair actions. The Time-variant Reliability-Based Design Optimization (TvRBDO) approach aims at searching the optimal design that minimizes the structural cost and to ensure a target reliability level during the operational life. However, for engineering problems, the TvRBDO problems may become computationally prohibitive when complex simulation models are involved (ie. Finite element method). This work proposes a surrogate-assisted double-loop approach for TvRBDO, where the outer-loop optimizes the objective function and the inner loop calculates the time-dependent reliability constraints. The time-dependent reliability of the inner loop is calculated by Monte Carlo simulations at discreted time intervals. To reduce the number of function evaluations, an inner Kriging is used to predict the response of limit state functions. The so-called single-loop Kriging surrogate method (SILK) developed by Hu and Mahadevan is adopted to calculate the time-variant reliability. The reliability results of the inner-loop are then used to train an outer-loop Kriging, and Expected Feasible Function (EFF) is used to improve its accuracy. After the outer-loop Kriging is trained, TvRBDO is conducted based on it, and the program stops when the difference between two optimum is less then allowance error. Two examples are used to validate this method.