Robust Design Optimization of Expensive Stochastic Simulators Under Lack-of-Knowledge

Koen van Mierlo, Augustin Persoons, M. Faes, D. Moens
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Abstract

Robust design optimisation of stochastic black-box functions is a challenging task in engineering practice. Crashworthiness optimisation qualifies as such problem especially with regards to the high computational costs. Moreover, in early design phases, there may be significant uncertainty about the numerical model parameters. Therefore, this paper proposes an adaptive surrogate-based strategy for robust design optimisation of noise-contaminated models under lack-of-knowledge uncertainty. This approach is a significant extension to the Robustness under Lack-of-Knowledge method (RULOK) previously introduced by the authors, which was limited to noise-free models. In this work it is proposed to use a Gaussian Process as a regression model based on a noisy kernel. The learning process is adapted to account for noise variance either imposed and known or empirically learned as part of the learning process. The method is demonstrated on three analytical benchmarks and one engineering crashworthiness optimisation problem. In the case studies, multiple ways of determining the noise kernel are investigated: (1) based on a coefficient of variation, (2) calibration in the Gaussian Process model, (3) based on engineering judgement, including a study of the sensitivity of the result with respect to these parameters. The results highlight that the proposed method is able to efficiently identify a robust design point even with extremely limited or biased prior knowledge about the noise.
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缺乏知识条件下昂贵随机模拟器的稳健设计优化
随机黑盒函数的稳健设计优化是工程实践中一个具有挑战性的课题。耐撞性优化就是这样一个问题,特别是考虑到高计算成本。此外,在早期设计阶段,数值模型参数可能存在很大的不确定性。因此,本文提出了一种基于自适应代理的无知识不确定性噪声污染模型鲁棒设计优化策略。该方法是对作者先前介绍的鲁棒性知识缺乏方法(RULOK)的重要扩展,该方法仅限于无噪声模型。在这项工作中,提出使用高斯过程作为基于噪声核的回归模型。学习过程适应于考虑作为学习过程的一部分强加的和已知的或经验学习的噪声方差。通过三个分析基准和一个工程耐撞优化问题对该方法进行了验证。在案例研究中,研究了确定噪声核的多种方法:(1)基于变异系数,(2)高斯过程模型的校准,(3)基于工程判断,包括研究结果相对于这些参数的灵敏度。结果表明,即使对噪声的先验知识非常有限或有偏差,所提出的方法也能有效地识别出稳健的设计点。
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CiteScore
5.20
自引率
13.60%
发文量
34
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