[论文解读] Machine learning-based system reliability analysis with Gaussian Process Regression

Lisang Zhou, Ziqian Luo+1 more|arXiv (Cornell University)|Mar 17, 2024

Software Reliability and Analysis Research被引用 8

一句话总结

论文针对基于高斯过程的可靠性分析发展理论结果和最优学习策略，比较Kriging相关采样与非相关采样，并提供贝叶斯序贯设计的见解。

ABSTRACT

Machine learning-based reliability analysis methods have shown great advancements for their computational efficiency and accuracy. Recently, many efficient learning strategies have been proposed to enhance the computational performance. However, few of them explores the theoretical optimal learning strategy. In this article, we propose several theorems that facilitates such exploration. Specifically, cases that considering and neglecting the correlations among the candidate design samples are well elaborated. Moreover, we prove that the well-known U learning function can be reformulated to the optimal learning function for the case neglecting the Kriging correlation. In addition, the theoretical optimal learning strategy for sequential multiple training samples enrichment is also mathematically explored through the Bayesian estimate with the corresponding lost functions. Simulation results show that the optimal learning strategy considering the Kriging correlation works better than that neglecting the Kriging correlation and other state-of-the art learning functions from the literatures in terms of the reduction of number of evaluations of performance function. However, the implementation needs to investigate very large computational resource.

研究动机与目标

• 提出理论定理以指导基于机器学习的可靠性分析中的学习策略。
• 分析有无Kriging相关性（设计样本的相关性）的情况。
• 将U学习重构为在忽略Kriging相关性下的最优函数。
• 推导基于贝叶斯的用于带损失函数的序列增强的最优学习策略。

提出的方法

• 在不同采样相关性下，形式化并证明用于ML-based可靠性分析的定理。
• 展示在忽略Kriging相关性时，将U学习函数重构为最优函数。
• 通过贝叶斯估计和损失函数推导用于序列训练样本增量的理论最优学习策略。
• 通过仿真比较策略以评估性能评估次数。

实验结果

研究问题

• RQ1 在考虑设计样本之间的Kriging相关性时，可靠性分析的最优学习策略是什么？
• RQ2 忽略Kriging相关性如何影响最优学习函数和性能？
• RQ3 在忽略Kriging相关性的前提下，U学习函数是否可以重构为最优学习函数？
• RQ4 基于贝叶斯的序列样本增量对减少评估次数的影响是什么？
• RQ5 在实际中，基于Kriging的信息策略是否优于其他最先进的学习函数？

主要发现

• 考虑Kriging相关性的最优学习策略可减少性能评估次数。
• 忽略Kriging相关性会改变学习函数，使在该假设下将U重构为最优函数成为可能。
• 带有适当损失函数的贝叶斯序列性增益为添加训练样本提供理论上最优的指导。
• 仿真结果表明，考虑Kriging的策略在评估次数减少方面优于忽略Kriging相关性及某些现有方法。
• 然而，实施需要极大计算资源。