Reliability-based Topology Optimization using Stochastic Gradients

TL;DR

This paper introduces a stochastic gradient-based method for reliability-based topology optimization that significantly reduces computational costs while maintaining accuracy, by efficiently estimating failure probabilities and their gradients.

Contribution

It proposes a novel stochastic gradient approach that uses Bayesian updating and minimal sampling to improve efficiency in reliability-based topology optimization.

Findings

Reduces computational cost compared to traditional methods.

Accurately estimates failure probabilities with few samples.

Demonstrates effectiveness on benchmark and practical problems.

Abstract

This paper addresses the computational challenges in reliability-based topology optimization (RBTO) of structures associated with the estimation of statistics of the objective and constraints using standard sampling methods, and overcomes the accuracy issues of traditional methods that rely on approximating the limit state function. Herein, we present a stochastic gradient-based approach, where we estimate the probability of failure at every few iterations using an efficient sampling strategy. To estimate the gradients of the failure probability with respect to the design parameters, we apply Bayes' rule wherein we assume a parametric exponential model for the probability density function of the design parameters conditioned on the failure. The design parameters as well as the parameters of this probability density function are updated using a stochastic gradient descent approach requiring only a small, e.g., O(1), number of random samples per iteration, thus leading to a considerable reduction of the computational cost as compared to standard RBTO techniques. We illustrate the proposed approach with a benchmark example that has an analytical solution as well as two widely used problems in structural topology optimization. These examples illustrate the efficacy of the approach in producing reliable designs.