Abstract
Efficient Robust Design Optimization (RDO) strategies coupling a parsimonious uncertainty quantification (UQ) method with a surrogate-based multi-objective genetic algorithm (SMOGA) are investigated for a test problem in computational fluid dynamics (CFD), namely the inverse robust design of an expansion nozzle. The low-order statistics (mean and variance) of the stochastic cost function are computed through either a gradient-enhanced kriging (GEK) surrogate or through the less expensive, lower fidelity, first-order method of moments (MoM). Both the continuous (non-intrusive) and discrete (intrusive) adjoint methods are evaluated for computing the gradients required for GEK and MoM. In all cases, the results are assessed against a reference kriging UQ surrogate not using gradient information. Subsequently, the GEK and MoM UQ solvers are fused together to build a multi-fidelity surrogate with adaptive infill enrichment for the SMOGA optimizer. The resulting hybrid multi-fidelity SMOGA RDO strategy ensures a good tradeoff between cost and accuracy, thus representing an efficient approach for complex RDO problems.
Highlights
In recent years, robust design optimization (RDO) [1] has received increasing interest in engineering applications, due to its ability to provide efficient designs with a stable behavior under uncertainties of a diverse nature, such as randomly fluctuating operating conditions, geometric tolerances, and model uncertainties
Afterwards, the methods are applied to a sample of nozzle geometries and used to build single or multi-fidelity surrogates used in the surrogate-based multi-objective genetic algorithm (SMOGA) RDO loop
The Bayesian kriging (BK) and gradient-enhanced kriging (GEK) uncertainty quantification (UQ) solvers were used in the same setting as Section 5.1, i.e., they are trained for each new design by using 60 and 15 samples in the uncertain space, respectively
Summary
Robust design optimization (RDO) [1] has received increasing interest in engineering applications, due to its ability to provide efficient designs with a stable behavior under uncertainties of a diverse nature, such as randomly fluctuating operating conditions, geometric tolerances, and model uncertainties. GEK surrogates can be used to reduce the number of samples for the UQ step, but GEK-based MOGA is not straightforward in the context of RDO problems, since it requires the gradient of the statistical moments of the QoI’s pdf with respect to the design variables Obtaining such a piece of information by using efficient adjoint methods is not a trivial task; on the other hand, finite difference approximations are applicable, but at the price of a considerable computational expense for high-dimensional design spaces. This is why we propose in this work a new multi-fidelity strategy for RDO that drastically reduces the required number of function calls by leveraging an inexpensive (but low-accuracy) first-order method of moments (MoM) and a Bayesian GEK [56].
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