Abstract
SummaryIn 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.
Highlights
Optimization techniques are becoming increasingly integrated within the engineering design process when computational models of the system are available
Recourse to regular Monte Carlo is required for the current design point, but in order to determine whether Information reuse (IR) or regular MC requires more evaluations, a way of predicting how many sampled values each approach would use is required
optimization under uncertainty (OUU) using MC sampling requires a relatively large number of system evaluations so may be infeasible for computationally expensive applications, multi-fidelity methods for MC sampling can reduce the computational cost enough for it to become feasible in many cases
Summary
Optimization techniques are becoming increasingly integrated within the engineering design process when computational models of the system are available. Monte Carlo (MC) sampling, on the other hand, is a method whose convergence rate is independent of both the dimensionality and smoothness of the problem [20, 21], making it attractive for problems with a large number of uncertainties or with non-smooth behavior This convergence rate is slow, and some problems may be too computationally expensive for MC sampling; for example if only a few hundred expensive high-fidelity model evaluations can be afforded within an optimization, MC sampling is not recommended since a designer would have little confidence in the accuracy of the results. The formulation in that work applies to general low-fidelity models, but of particular benefit in the OUU setting is the use of information from previous optimization iterations, termed “information reuse” in Ref. 23 This control-variate-based approach, as presented in Ref. 23, is limited to formulations of the OUU problem where estimators of the quantities being optimized or constrained must be expressed as a sample average (e.g., estimators of the first two statistical moments, mean and variance).
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Free) 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a call
