Multifidelity optimization under uncertainty for a tailless aircraft

This paper presents a multifidelity method for optimization under uncertainty for aerospace problems. In this work, the effectiveness of the method is demonstrated for the robust optimization of a tailless aircraft that is based on the Boeing Insitu ScanEagle. Aircraft design is often affected by uncertainties in manufacturing and operating conditions. Accounting for uncertainties during optimization ensures a robust design that is more likely to meet performance requirements. Designing robust systems can be computationally prohibitive due to the numerous evaluations of expensive-to-evaluate high-fidelity numerical models required to estimate system-level statistics at each optimization iteration. This work uses a multifidelity Monte Carlo approach to estimate the mean and the variance of the system outputs for robust optimization. The method uses control variates to exploit multiple fidelities and optimally allocates resources to different fidelities to minimize the variance in the estimates for a given budget. The results for the ScanEagle application show that the proposed multifidelity method achieves substantial speed-ups as compared to a regular Monte-Carlo-based robust optimization.United States. Air Force. Office of Scientific Research. Multidisciplinary University Research Initiative (FA9550-15-1-0038

Multi-output multilevel best linear unbiased estimators via semidefinite programming

Multifidelity forward uncertainty quantification (UQ) problems often involve multiple quantities of interest and heterogeneous models (e.g., different grids, equations, dimensions, physics, surrogate and reduced-order models). While computational efficiency is key in this context, multi-output strategies in multilevel/multifidelity methods are either sub-optimal or non-existent. In this paper we extend multilevel best linear unbiased estimators (MLBLUE) to multi-output forward UQ problems and we present new semidefinite programming formulations for their optimal setup. Not only do these formulations yield the optimal number of samples required, but also the optimal selection of low-fidelity models to use. While existing MLBLUE approaches are single-output only and require a non-trivial nonlinear optimization procedure, the new multi-output formulations can be solved reliably and efficiently. We demonstrate the efficacy of the new methods and formulations in practical UQ problems with model heterogeneity.Comment: 22 pages, 5 figures, 3 table

Multifidelity approaches for uncertainty estimation in wildfire spread simulators

A variety of wildfire models are currently used for prescribed fire management, fire behaviour studies and decision support during wildfire emergencies, among other applications. All these applications are based on predictive analysis, and therefore require careful estimation of aleatoric and epistemic uncertainties such as weather conditions, vegetation properties and model parameters. However, the large computational cost of high-fidelity computaional fluid dynamics models prohibits the straightforward utilization of traditional Monte Carlo methods. Conversely, low-fidelity fire models are several orders of magnitude faster but they typically do not provide enough accuracy and they do not resolve all relevant phenomena. Multifidelity frameworks offer a viable solution to this limitation through the efficient combination of high-and low-fidelity simulations. While high-fidelity models provide the required level of accuracy, low-fidelity simulations are used to economically improve the confidence on estimated uncertainty. In this work, we assessed the suitability of multifidelity methodologies to quantify uncertainty in wildfire simulations. A collection of different multifidelity strategies, including Multilevel and Control Variates Monte Carlo, were tested and their computational efficiency compared. Fire spread was predicted in a canonical scenario using popular simulators such as the Wildland-Urban Interface Fire Dynamics Simulator (WFDS) and FARSITE. Results show that multifidelity estimators allow speedups in the order of 100× to 1000× with respect to traditional Monte Carlo