Advanced solution strategies for time-dependent reliability based design optimization

Abstract

Aiming at accurately and efficiently solve the Time-dependent Reliability Based Design Optimization (T-RBDO), two advanced solution strategies respectively called Time-dependent Sequential Optimization and Reliability Assessment (T-SORA) and Time-dependent Single Loop Approach (T-SLA) are established. Before constructing the T-SORA and T-SLA, a two-stage optimization is firstly established, in which the first stage makes the minimum instantaneous reliability indexes of probabilistic constraints satisfy reliability index targets and the second stage performs the time-dependent reliability indexes to match the reliability index targets. Two equivalent time-independent RBDOs are obtained based on the established two-stage optimization, and the key point is estimating the Minimum Performance Target Point (MPTP) in each stage. Two single optimization processes are constructed in T-SORA to efficiently estimate MPTPs in its two stages respectively. Two sequential single procedures are established in T-SLA to efficiently solve MPTPs and design parameter solutions in its two stages respectively, in which a new MPTP searching technique named Angle Descent Mean Value (ADMV) is proposed to approximate MPTP in each iteration. Furthermore, time-dependent reliability analysis is only required in the second stage, which will further improve the computational efficiency. Several numerical and engineering examples are introduced to show the effectiveness of the proposed T-SORA and T-SLA for solving T-RBDO.