Uncertainty quantification methods for evolutionary optimization under uncertainty

Abstract This paper presents a surrogate model-based computationally efficient optimization scheme for design problems with multiple, probabilistic objectives estimated through stochastic simulation. It examines the extension of the previously developed MODU-AIM (Multi-Objective Design under Uncertainty with Augmented Input Metamodels) algorithm, which performs well for bi-objective problem but encounters scalability difficulties for applications with more than two objectives. Computational efficiency is achieved by using a single surrogate model, adaptively refined within an iterative optimization setting, to simultaneously support the uncertainty quantification and the design optimization, and the MODU-AIM extension is established by replacing the originally used epsilon-constraint optimizer with a multi-objective evolutionary algorithm (MOEA). This requires various modifications to accommodate MOEA’s unique traits. For uncertainty quantification, a clustering-based importance sampling density selection is introduced to mitigate MOEA’s lack of direct control on Pareto solution density. To address the potentially large solution set of MOEAs, both the termination criterion of the iterative optimization scheme and the design of experiment (DoE) strategy for refinement of the surrogate model are modified, leveraging efficient performance comparison indicators. The importance of each objective in the different parts of the Pareto front is further integrated in the DoE to improve the adaptive selection of experiments.

Download Full-text

Global Optimization Under Uncertainty and Uncertainty Quantification Applied to Tractor-Trailer Base Flaps

Journal of Verification Validation and Uncertainty Quantification ◽

10.1115/1.4033289 ◽

2016 ◽

Vol 1 (2) ◽

Cited By ~ 1

Author(s):

Jacob A. Freeman ◽

Christopher J. Roy

Keyword(s):

Global Optimization ◽

Wind Speed ◽

Uncertainty Quantification ◽

Numerical Approximation ◽

Epistemic Uncertainty ◽

Optimization Under Uncertainty ◽

Optimized Design ◽

Predictive Uncertainty ◽

Model Form ◽

Design Variables

Using a global optimization evolutionary algorithm (EA), propagating aleatory and epistemic uncertainty within the optimization loop, and using computational fluid dynamics (CFD), this study determines a design for a 3D tractor-trailer base (back-end) drag reduction device that reduces the wind-averaged drag coefficient by 41% at 57 mph (92 km/h). Because it is optimized under uncertainty, this design is relatively insensitive to uncertain wind speed and direction and uncertain deflection angles due to mounting accuracy and static aeroelastic loading. The model includes five design variables with generous constraints, and this study additionally includes the uncertain effects on drag prediction due to truck speed and elevation, steady Reynolds-averaged Navier–Stokes (RANS) approximation, and numerical approximation. This study uses the Design Analysis Kit for Optimization and Terascale Applications (DAKOTA) optimization and uncertainty quantification (UQ) framework to interface the RANS flow solver, grid generator, and optimization algorithm. The computational model is a simplified full-scale tractor-trailer with flow at highway speed. For the optimized design, the estimate of total predictive uncertainty is +15/−42%; 8–10% of this uncertainty comes from model form (computation versus experiment); 3–7% from model input (wind speed and direction, flap angle, and truck speed); and +0.0/−28.5% from numerical approximation (due to the relatively coarse, 6 × 106 cell grid). Relative comparison of designs to the no-flaps baseline should have considerably less uncertainty because numerical error and input variation are nearly eliminated and model form differences are reduced. The total predictive uncertainty is also presented in the form of a probability box, which may be used to decide how to improve the model and reduce uncertainty.

Download Full-text