用贝叶斯优化提升高精度制造中极低故障率设计的可靠性
Maximizing Reliability with Bayesian Optimization
- 基于汤普森采样和知识梯度，结合重要性采样应对极端小故障概率
- 在 $10^{-6}$ 到 $10^{-8}$ 的极低故障率下仍保持高效优化性能
- 适合对可靠性要求极高的工程设计场景，如航空航天与芯片制造
贝叶斯优化（BO）是一种高效的黑箱优化方法，适用于昂贵且难以评估的优化问题。在制造业中，一个关键挑战是最大化设计的可靠性，即最小化因随机扰动导致的故障概率，这类问题常涉及极低的故障率（$P_ ext{fail} = 10^{-6}-10^{-8}$）。本文提出两种基于汤普森采样和知识梯度的贝叶斯优化方法，后者近似于最小化故障概率对数的一步贝叶斯最优策略。两种方法均引入重要性采样技术，以聚焦于极小故障概率区域。实验表明，所提方法在极端与非极端故障率条件下均优于现有方法。
原文摘要 · Abstract (English)
Bayesian optimization (BO) is a popular, sample-efficient technique for expensive, black-box optimization. One such problem arising in manufacturing is that of maximizing the reliability, or equivalently minimizing the probability of a failure, of a design which is subject to random perturbations - a problem that can involve extremely rare failures ($P_\mathrm{fail} = 10^{-6}-10^{-8}$). In this work, we propose two BO methods based on Thompson sampling and knowledge gradient, the latter approximating the one-step Bayes-optimal policy for minimizing the logarithm of the failure probability. Both methods incorporate importance sampling to target extremely small failure probabilities. Empirical results show the proposed methods outperform existing methods in both extreme and non-extreme regimes.
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