Variable-fidelity optimization of microwave filters using co-kriging and trust regions

In this paper, a variable-fidelity optimization methodology for simulation-driven design optimization of filters is presented. We exploit electromagnetic (EM) simulations of different accuracy. Densely sampled but cheap low-fidelity EM data is utilized to create a fast kriging interpolation model (the surrogate), subsequently used to find an optimum design of the high-fidelity EM model of the filter under consideration. The high-fidelity data accumulated during the optimization process is combined with the existing surrogate using the co-kriging technique. This allows us to improve the surrogate model accuracy while approaching the optimum. The convergence of the algorithm is ensured by embedding it into the trust region framework that adaptively adjusts the search radius based on the quality of the predictions made by the co-kriging model. Three filter design cases are given for demonstration and verification purposes

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

Efficient simulation-driven design optimization of antennas using co-kriging

We present an efficient technique for design optimization of antenna structures. Our approach exploits coarse-discretization electromagnetic (EM) simulations of the antenna of interest that are used to create its fast initial model (a surrogate) through kriging. During the design process, the predictions obtained by optimizing the surrogate are verified using high-fidelity EM simulations, and this high-fidelity data is used to enhance the surrogate through co-kriging technique that accommodates all EM simulation data into one surrogate model. The co-kriging-based optimization algorithm is simple, elegant and is capable of yielding a satisfactory design at a low cost equivalent to a few high-fidelity EM simulations of the antenna structure. To our knowledge, this is a first application of co-kriging to antenna design. An application example is provided

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

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