<p><i>We study the use of Hessian interaction terms to quickly identify design variables that can reduce system performance variability. As a first step, we quantify the uncertainty and compute the variance decomposition to determine contributing noise variables of an initial design. Minimizing uncertainty through probabilistic optimization becomes computationally difficult, whether by including distribution parameters as an objective function or through robust design of experiments. Instead, we consider a second step of determining the more easily computed Hessian interaction matrix terms of the variance-contributing noise variables and the variables of any proposed design change. We relate the Hessian term coefficients to reduction in Sobol indices and response variance. Design variable changes with large Hessian terms against noise variables are thereby identified quickly as the design changes that can reduce variability. Furthermore, the Jacobian terms of these design changes can indicate which design variables can shift the mean response, to maintain a desired nominal performance target. Using a combination of easily computed Hessian and Jacobian terms, design changes can be proposed to reduce variability while maintaining a targeted nominal. Through this combination, a third step is necessary in order to re-compute the uncertainty and variance decomposition at the Hessian and yield a more robust design configuration. This workflow can therefore make use of UQ/SA methods and find design changes that improve robustness with a minimal 4 runs per design change. An example is shown on a Stirling engine design where the top three variance-contributing tolerances are identified: two design changes identified through Hessian terms, and a new design found with 29% less variance. </i></p>

Uncertainty Quantification and Reduction Using Sensitivity Analysis and Hessian Derivatives

Paper Proceedings: https://asmedigitalcollection.asme.org/IDETC-CIE/IDETC-CIE2021/volume/85369

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