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

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.