Multi-level CFD-based Airfoil Shape Optimization With Automated Low-fidelity Model Selection

AbstractComputational fluid dynamic (CFD) models are ubiquitous in aerodynamic design. Variable-fidelity optimization algorithms have proven to be computationally efficient and therefore suitable to reduce high CPU-cost related to the design process solely based on accurate CFD models. A convenient way of constructing the variable-fidelity models is by using the high-fidelity solver, but with a varying degree of discretization and reduced number of flow solver iterations. So far, selection of the appropriate parameters has only been guided by the designer experience. In this paper, an automated low- fidelity model selection technique is presented. By defining the problem as a constrained nonlinear optimization problem, suitable grid and flow solver parameters are obtained. Our approach is compared to conventional methods of generating a family of variable-fidelity models. Comparison of the standard and the proposed approaches in the context of aerodynamic design of a transonic airfoil indicates that the automated model generation can yield significant computational savings

Scaling Properties of Multi-Fidelity Shape Optimization Algorithms

AbstractMulti fidelity optimization can be utilized for efficient design of airfoil shapes. In this paper, we investigate the scaling properties of algorithms exploiting this methodology. In particular, we study the relationship between the computational cost and the size of the design space. We focus on a specific optimization technique where, in order to reduce the design cost, the accurate high fidelity airfoil model is replaced by a cheap surrogate constructed from a low fidelity model and the shape preserving response prediction technique. In this study, we consider the design of transonic airfoils and use the compressible Euler equations in the high fidelity computational fluid dynamic (CFD) model. The low fidelity CFD model is same as the high fidelity one, but with coarser mesh resolution and reduced level of solver converge. The number of design variables varies from 3 to 11 by using NACA 4 digit airfoil shapes as well as airfoils constructed by Bézier curves. The results of the three optimization studies show that total cost increases from about 12 equivalent high fidelity model evaluations to 34. The number of high fidelity evaluations increases from 4 to 9, whereas the number of low fidelity evaluations increases more rapidly, from 600 to 2000. This indicates that, while the overall optimization cost scales more or less linearly with the dimensionality of the design space, further cost reduction can be obtained through more efficient optimization of the surrogate model

Multifidelity Modeling by Polynomial Chaos-Based Cokriging to Enable Efficient Model-Based Reliability Analysis of NDT Systems

This work proposes a novel multifidelity metamodeling approach, the polynomial chaos-based Cokriging (PC-Cokriging). The proposed approach is used for fast uncertainty propagation in a reliability analysis of nondestructive testing systems using model-assisted probability of detection (MAPOD). In particular, PC-Cokriging is a multivariate version of polynomial chaos-based Kriging (PC-Kriging), which aims at combining the advantages of the regression-based polynomial chaos expansions and the interpolation-based Kriging metamodeling methods. Following a similar process as Cokriging, the PC-Cokriging advances PC-Kriging by enabling the incorporation of multifidelity physics information. The proposed PC-Cokriging is demonstrated on two analytical functions and three ultrasonic testing MAPOD cases. The results show that PC-Cokriging outperforms the state-of-the-art metamodeling approaches when providing the same number of training points. Specifically, PC-Cokriging reduces the high-fidelity training sample cost of the Kriging and PCE metamodels by over one order of magnitude, and the PC-Kriging and conventional Cokriging multifidelity metamodeling by up to 50 % to reach the same accuracy level (defined by the root mean squared error being no greater than 1 % of the standard deviation of the testing points). The accuracy and robustness of the proposed method of the key MAPOD metrics versus various detection thresholds are investigated and satisfactory results are obtained

Sequential Domain Patching for Computationally Feasible Multi-objective Optimization of Expensive Electromagnetic Simulation Models

AbstractIn this paper, we discuss a simple and efficient technique for multi-objective design optimization of multi-parameter microwave and antenna structures. Our method exploits a stencil-based approach for identification of the Pareto front that does not rely on population-based metaheuristic algorithms, typically used for this purpose. The optimization procedure is realized in two steps. Initially, the initial Pareto-optimal set representing the best possible trade-offs between conflicting objectives is obtained using low-fidelity representation (coarsely-discretized EM model simulations) of the structure at hand. This is realized by sequential construction and relocation of small design space segments (patches) in order to create a path connecting the extreme Pareto front designs identified beforehand. In the second step, the Pareto set is refined to yield the optimal designs at the level of the high-fidelity electromagnetic (EM) model. The appropriate number of patches is determined automatically. The approach is validated by means of two multi-parameter design examples: a compact impedance transformer, and an ultra-wideband monopole antenna. Superiority of the patching method over the state-of-the-art multi-objective optimization techniques is demonstrated in terms of the computational cost of the design process

Robust Airfoil Design Optimization using Stochastic Expansions and Utility Theory

Efficient and effective robust airfoil design optimization is proposed by integrating stochastic expansions and utility theory. In this work, the stochastic expansions are generated efficiently using non-intrusive polynomial chaos (NIPC) expansions. The robust design problem is formulated using utility functions which transfer a targeted response using a prescribed mathematical function to represent the designers\u27 risk preferences. The proposed approach is demonstrated using examples of lift-constrained airfoil drag minimization in transonic viscous flow using the Mach number as an uncertain variable in the range of 0.70 to 0.75. The results are compared with the common problem formulation for robust design of the minimizing the sum of the mean and standard deviation of performance metric, as well as with single- and multi-point deterministic optimization. The approach is demonstrated on two numerical test cases, one at relatively low lift coefficient of 0.5, and the other one at a high lift of 0.824. The constraints differ between the cases as well. In both cases, the proposed approach with utility function formulation achieves the most insensitive responses compared with the standard robust problem formulation and the single- and multi-point deterministic problem formulations