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<p>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 thirty-dimensional benchmark, the proposed method achieved a <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(60.39\%\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>60.39</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> mean reduction, while Gaussian process-based approaches failed to locate the global optimum. In the motor design problem, the method reduced cogging torque by <InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(91.89\%\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mn>91.89</mn> <mo>%</mo> </mrow> </math></EquationSource> </InlineEquation> with only 6702 finite element evaluations, confirming its computational efficiency for high-dimensional, strongly nonlinear engineering problems.</p>

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

  • 期刊论文

  • 发表日期：

    2026年6月17日

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  • Hyunho Jang,
  • Dongjin Lee

摘要

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 thirty-dimensional benchmark, the proposed method achieved a \(60.39\%\) 60.39 % mean reduction, while Gaussian process-based approaches failed to locate the global optimum. In the motor design problem, the method reduced cogging torque by \(91.89\%\) 91.89 % with only 6702 finite element evaluations, confirming its computational efficiency for high-dimensional, strongly nonlinear engineering problems.