利用雅可比和黑森信息量化和减少不确定性

IF 1.8 Q3 ENGINEERING, MANUFACTURING
Design Science Pub Date : 2021-10-11 DOI:10.1017/dsj.2021.20
Josefina Sánchez, K. Otto
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引用次数: 1

摘要

鲁棒设计方法已经从实验技术扩展到包括抽样方法、灵敏度分析和概率优化。这种方法通常需要多次评估。我们研究了设计变量和噪声变量的响应的交叉项二阶导数,以快速识别减少响应可变性的设计变量。我们首先计算响应不确定性和方差分解,以确定初始设计的贡献噪声变量。然后,我们计算方差贡献噪声变量和设计变更变量之间的Hessian二阶导数矩阵交叉项。具有大黑森项的设计变量是那些可以减少响应变异性的设计变量。我们将Hessian系数与Sobol指数的降低和响应方差的变化联系起来。接下来,一阶导数雅可比项表明哪个设计变量可以移动平均值以保持期望的标称目标值。因此,可以提出设计变更以减少可变性,同时保持目标标称值。此工作流程通过每次设计更改最少运行四次来发现改进健壮性的更改。我们还探讨了通过复合变量实现的进一步计算减少。在斯特林发动机上展示了一个例子,其中通过16个黑森术语确定的前四个方差贡献公差和设计更改生成了方差减少20%的设计。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Uncertainty quantification and reduction using Jacobian and Hessian information
Abstract Robust design methods have expanded from experimental techniques to include sampling methods, sensitivity analysis and probabilistic optimisation. Such methods typically require many evaluations. We study design and noise variable cross-term second derivatives of a response to quickly identify design variables that reduce response variability. We first compute the response uncertainty and variance decomposition to determine contributing noise variables of an initial design. Then we compute the Hessian second-derivative matrix cross-terms between the variance-contributing noise variables and proposed design change variables. Design variable with large Hessian terms are those that can reduce response variability. We relate the Hessian coefficients to reduction in Sobol indices and response variance change. Next, the first derivative Jacobian terms indicate which design variable can shift the mean to maintain a desired nominal target value. Thereby, design changes can be proposed to reduce variability while maintaining a targeted nominal value. This workflow finds changes that improve robustness with a minimal four runs per design change. We also explore further computation reductions achieved through compounding variables. An example is shown on a Stirling engine where the top four variance-contributing tolerances and design changes identified through 16 Hessian terms generated a design with 20% less variance.
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来源期刊
Design Science
Design Science ENGINEERING, MANUFACTURING-
CiteScore
4.80
自引率
12.50%
发文量
19
审稿时长
22 weeks
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