Generalized information reuse for optimization under uncertainty with non‐sample average estimators

• Published in: International journal for numerical methods in engineering 2018-09, Vol.115 (12), p.1457-1476
• Main Authors: Cook, Laurence W., Jarrett, Jerome P., Willcox, Karen E.
• Format: Article
• Language: English
• Subjects: Computer simulation; Covariance; Design engineering; Design optimization; Estimators; Iterative methods; Monte Carlo simulation; multifidelity; optimization; optimization under uncertainty; probabilistic methods; Reuse; Sampling methods; stochastic problems; Uncertainty
• ISSN: 0029-5981; 1097-0207
• DOI: 10.1002/nme.5904

Summary In optimization under uncertainty for engineering design, the behavior of the system outputs due to uncertain inputs needs to be quantified at each optimization iteration, but this can be computationally expensive. Multifidelity techniques can significantly reduce the computational cost of Monte Carlo sampling methods for quantifying the effect of uncertain inputs, but existing multifidelity techniques in this context apply only to Monte Carlo estimators that can be expressed as a sample average, such as estimators of statistical moments. Information reuse is a particular multifidelity method that treats previous optimization iterations as lower fidelity models. This work generalizes information reuse to be applicable to quantities whose estimators are not sample averages. The extension makes use of bootstrapping to estimate the error of estimators and the covariance between estimators at different fidelities. Specifically, the horsetail matching metric and quantile function are considered as quantities whose estimators are not sample averages. In an optimization under uncertainty for an acoustic horn design problem, generalized information reuse demonstrated computational savings of over 60% compared with regular Monte Carlo sampling.