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

Isolation by Distance Between Spouses and its Effect on Boys’ Maturational Timing

Heterosis is thought to be an important contributor to human growth and development. Marital distance (distance between parental birthplaces) is commonly considered as a factor favoring the occurrence of heterosis and can be used as a proximate measure of its level. It has already been shown that marital distance appears to be an independent and important factor influencing the height of offspring. However, there is no study showing this effect on maturational timing in boys. The aim of the study was to assess the effect of marital radius on age at peak height velocity in boys, controlling for midparental height and the socioeconomic status of family. Longitudinal, annual height measurements on 740 boys from 11 to 15 years of age from Ostrowiec Świętokrzyski, Poland, were analyzed along with sociodemographic data from their parents. Midparental height was calculated as the average of the reported heights of the parents. The SITAR model was applied to the longitudinal data of height in order to assess the age at peak height velocity (APHV). As the measurements were incomplete, the APHV was successfully estimated in only 298 boys. Multiple Linear regression showed the small, but significant effect of Marital distance on the maturation rate of boys (standardized beta=-0.14; p<0.05). According to the ‘‘isolation by distance’’ hypothesis, a greater distance between parental birthplaces may increase heterozygosity, potentially promoting heterosis. We propose that these conditions may result in reduced metabolic costs of growth among heterozygous individuals, and hence a lowered velocity of growth