通过贝叶斯神经网络增强的多项式维分解实现非线性系统的鲁棒设计优化
Robust design optimization for a nonlinear system via Bayesian neural network enhanced polynomial dimensional decomposition
AI总结：
本文提出一种结合贝叶斯神经网络和多项式维分解的鲁棒设计优化方法，通过主动学习和多点单步策略提高计算效率，有效解决高维强非线性问题。
摘要：
不确定性如制造公差导致复杂工程系统性能波动，使鲁棒设计优化（RDO）成为必要。然而，基于仿真的RDO在统计矩估计上面临高昂的计算成本，且强非线性限制了传统替代模型的精度。本研究提出了一种新的RDO方法，将贝叶斯神经网络（BNN）与多项式维分解（PDD）相结合。该方法采用基于不确定性的主动学习来增强BNN替代模型的准确性，并采用多点单步策略，将设计空间动态调整为子区域，在其中PDD从BNN预测中解析统计矩。通过数学基准和电动机形状优化的验证表明，该方法以显著较少的函数评估次数收敛到鲁棒最优解。在十维基准中，所提方法实现了99.97%的均值减少，而基于高斯过程和蒙特卡洛的方法未能找到全局最优。在电动机设计问题中，该方法仅通过6644有限元评估将齿槽转矩减少了94.75%，证实了其在高维、强非线性工程问题中的计算效率。
英文摘要：
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 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.
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