A two-level Kriging-based approach with active learning for solving time-variant risk optimization problems

TL;DR

This paper introduces a two-level Kriging-based active learning framework to efficiently solve time-variant risk optimization problems involving reliability analysis, significantly reducing computational costs compared to traditional Monte Carlo methods.

Contribution

The paper presents a novel surrogate modeling approach with active learning for time-variant risk optimization, addressing computational challenges and including load-path dependent failure analysis.

Findings

Accurate solutions achieved with few function calls.

Effective surrogate models for objective and limit state functions.

Applicable to load degradation and load-path dependent failures.

Abstract

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.