Robust design optimization for a nonlinear system via Bayesian neural network enhanced polynomial dimensional decomposition

TL;DR

This paper introduces a new robust design optimization approach combining Bayesian neural networks with polynomial dimensional decomposition, significantly reducing computational costs while accurately handling nonlinearity and uncertainties.

Contribution

The study presents a novel integration of Bayesian neural networks with polynomial dimensional decomposition for efficient, accurate robust design optimization in complex nonlinear systems.

Findings

Achieved 99.97% mean reduction in a 10D benchmark.

Reduced cogging torque by 94.75% in electric motor design.

Converged to robust solutions with fewer function evaluations.

Abstract

Uncertainties such as manufacturing tolerances cause performance variations in complex engineering systems, making robust design optimization (RDO) essential. However, simulation-based RDO faces high computational cost for statistical moment estimation, and strong nonlinearity limits the accuracy of conventional surrogate models. This study proposes a novel RDO method that integrates Bayesian neural networks (BNN) with polynomial dimensional decomposition (PDD). The method employs uncertainty-based active learning to enhance BNN surrogate accuracy and a multi-point single-step strategy that partitions the design space into dynamically adjusted subregions, within which PDD analytically estimates statistical moments from BNN predictions. Validation through a mathematical benchmark and an electric motor shape optimization demonstrates that the method converges to robust optimal solutions with significantly fewer function evaluations. In the ten-dimensional benchmark, the proposed method achieved a 99.97% mean reduction, while Gaussian process-based and Monte Carlo approaches failed to locate the global optimum. In the motor design problem, the method reduced cogging torque by 94.75% with only 6644 finite element evaluations, confirming its computational efficiency for high-dimensional, strongly nonlinear engineering problems.