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

Multifidelity Modeling of Ultrasonic Testing Simulations with Cokriging

Multifidelity methods are introduced to the nondestructive evaluation (NDE) of measurement systems. In particular, Cokriging interpolation metamodels of physics-based ultrasonic testing (UT) simulation responses are utilized to accelerate the uncertainty propagation in model-assisted NDE. The proposed approach is applied to a benchmark test case of UT simulations and compared with the current state-of-the-art techniques. The results show that Cokriging captures the physics of the problem well and is able to reduce the computational burden by over one order of magnitude compared to the state of the art. To the best of the author\u27s knowledge, this the first time multifidelity methods are applied to model-assisted NDE problems

Efficient Yield Estimation of Multiband Patch Antennas by Polynomial Chaos-Based Kriging

Yield estimation of antenna systems is important to check their robustness with respect to the uncertain sources. Since direct Monte Carlo sampling of accurate physics-based models can be computationally intensive, this work proposes the use of the polynomial chaos–Kriging (PC-Kriging) metamodeling method for fast yield estimation of multiband patch antennas. PC-Kriging integrates the polynomial chaos expansion (PCE) as the trend function of Kriging metamodel since the PCE is good at capturing the function tendency and Kriging is good at matching the observations at training points. The PC-Kriging method is demonstrated on two analytical cases and two multiband patch antenna cases and is compared with the PCE and Kriging metamodeling methods. In the analytical cases, PC-Kriging reduces the computational cost by over 40% compared with PCE and over 94% compared with Kriging. In the antenna cases, PC-Kriging reduces the computational cost by over 60% compared with Kriging and over 90% compared with PCE. In all cases, the savings are obtained without compromising the accuracy

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