An efficient strategy for reliability-based design optimization of linear structural dynamic systems by the cross-entropy method

Abstract

Engineering structures should be designed to minimize construction costs and maintain safety. Structural performance can be seldomly characterized deterministically, as many parameters, such as the material properties, geometric properties, environmental loads (e.g., dynamic excitations due to earthquakes and winds), are uncertain. The uncertainties can severely affect the performance of the structure, and, hence, should be explicitly accounted for during optimization. Reliability-based optimization (RBO) offers a rational framework for safe design under uncertainties by incorporating reliability measures as constraints into the optimization problem.

In this study, we consider RBO problems involving linear structural systems subjected to Gaussian process excitation. First-passage failure probability is taken as the measure of system reliability. The associated reliability estimation problem typically involves a high number of uncertain parameters and is solved by means of advanced stochastic-simulation techniques. This RBO problem is challenging to solve because of the complexity of the feasible domain shaped by multiple reliability constraints and the repeated structural response evaluations required to evaluate the reliability constraint function for each design solution generated during exploration.

We develop stochastic search algorithms for design optimization based on the cross-entropy (CE) method. The CE method is a Monte Carlo technique originally developed for rare event estimation. The method makes use of an adaptive importance sampling procedure based on the KullbackﾖLeibler divergence to efficiently sample the domain of the rare event during simulation. Based on the idea that locating the optimal solution in the feasible design space can be viewed as a rare event, the present study aims to adapt the CE-based importance sampling method to tackle the RBO problem of linear dynamical systems. Constraint handling is a crucial step in design optimization. To this end, we explore novel strategies to efficiently incorporate the dynamic reliability constraints in the generation of samples during simulation. The aim is to deliver a black-box algorithm that intelligently prioritizes the feasible solutions and, simultaneously, optimizes the objective function in a natural way.