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In this paper, we investigate the capability of the universal Kriging (UK) model for single-objective global optimization applied within an efficient global optimization (EGO) framework. We implemented this combined UK-EGO framework and studied four variants of the UK methods, that is, a UK with a first-order polynomial, a UK with a second-order polynomial, a blind Kriging (BK) implementation from the ooDACE toolbox, and a polynomial-chaos Kriging (PCK) implementation. The UK-EGO framework with automatic trend function selection derived from the BK and PCK models works by building a UK surrogate model and then performing optimizations via expected improvement criteria on the Kriging model with the lowest leave-one-out cross-validation error. Next, we studied and compared the UK-EGO variants and standard EGO using five synthetic test functions and one aerodynamic problem. Our results show that the proper choice for the trend function through automatic feature selection can improve the optimization performance of UK-EGO relative to EGO. From our results, we found that PCK-EGO was the best variant, as it had more robust performance as compared to the rest of the UK-EGO schemes; however, total-order expansion should be used to generate the candidate trend function set for high-dimensional problems. Note that, for some test functions, the UK with predetermined polynomial trend functions performed better than that of BK and PCK, indicating that the use of automatic trend function selection does not always lead to the best quality solutions. We also found that although some variants of UK are not as globally accurate as the ordinary Kriging (OK), they can still identify better-optimized solutions due to the addition of the trend function, which helps the optimizer locate the global optimum. [ABSTRACT FROM AUTHOR]

Reducing the noise level in the acoustic cavities is the important problem when treating inflight conditions of commercial planes or boats. Shape optimization of the acoustic cavity that will take into account the geometrical and material uncertainties, arising during the manufacturing process, is presented in this paper. The noise level is controlled by minimizing the energy density in the cavity, obtained through an energy method called Simplified Energy Method. Such formulation is based on our previous published work where transformation function mapping 3D cavity surface on a 2D domain was proposed. The optimization process directly relies on this function and thus avoids remeshing of the geometry. Robust optimization is performed using the nondominated sorting genetic algorithm (NSGA-II) together with the Kriging surrogate model. Influence of geometrical and material characteristics on the optimal solution is identified. [ABSTRACT FROM AUTHOR]

The many-objective optimization performance of the Kriging-surrogate-based evolutionary algorithm (EA), which maximizes expected hypervolume improvement (EHVI) for updating the Kriging model, is investigated and compared with those using expected improvement (EI) and estimation (EST) updating criteria in this paper. Numerical experiments are conducted in 3- to 15-objective DTLZ1-7 problems. In the experiments, an exact hypervolume calculating algorithm is used for the problems with less than six objectives. On the other hand, an approximate hypervolume calculating algorithm based on Monte Carlo sampling is adopted for the problems with more objectives. The results indicate that, in the nonconstrained case, EHVI is a highly competitive updating criterion for the Kriging model and EA based many-objective optimization, especially when the test problem is complex and the number of objectives or design variables is large. [ABSTRACT FROM AUTHOR]

This paper presents a comparison of the criteria for updating the Kriging surrogate models in multi-objective optimization: expected improvement (EI), expected hypervolume improvement (EHVI), estimation (EST), and those in combination (EHVI + EST). EI has been conventionally used as the criterion considering the stochastic improvement of each objective function value individually, while EHVI has recently been proposed as the criterion considering the stochastic improvement of the front of nondominated solutions in multi-objective optimization. EST is the value of each objective function estimated nonstochastically by the Kriging model without considering its uncertainties. Numerical experiments were implemented in the welded beam design problem, and empirically showed that, in an unconstrained case, EHVI maintains a balance between accuracy, spread, and uniformity in nondominated solutions for Kriging-model-based multiobjective optimization. In addition, the present experiments suggested future investigation into techniques for handling constraints with uncertainties to enhance the capability of EHVI in constrained cases. [ABSTRACT FROM AUTHOR]

Multi-objective optimization in aerodynamics plays an important role in revealing trade-offs between conflicting objectives in order to discover important knowledge and insight for better future design. Of interest here is the use of Kriging surrogate models incorporated into a sequential Bayesian optimization (BO) strategy. In this paper, we studied four variants of multi-objective BO (MOBO) techniques that are based on expected improvement (EI), that is, Euclidean-based EI (EEI), expected hypervolume improvement (EHVI), ParEGO, and expected inverted penalty boundary intersection improvement (EIPBII) to understand their capabilities on handling multi-objective aerodynamic optimization problems. Numerical tests were performed on a set consisting of six generalized Schaffer problems (GSP), five low-fidelity, and one high-fidelity airfoil design problems. Results suggest that EHVI is the only method which consistently performed well on artificial and aerodynamic problems. EEI yields the worst performance and is not suitable to deal with various problem complexities. ParEGO, although it performs modestly on GSP, surprisingly works well on the low- and high-fidelity problems. On the other hand, EIPBII encounters the opposite case, where it is one of the best performer on GSP but yields modest performance on the aerodynamic problems. In light of the results, we suggest that EHVI is a highly potential MOBO method to be applied for multi-objective aerodynamic design optimization. [ABSTRACT FROM AUTHOR]

In this paper, to reduce the computational cost of Proper Orthogonal Decomposition (POD) method in film-cooling problems, a new method based on the combination of POD method with Sparse Polynomial Chaos Expansion (PCE) and Kriging approaches is developed. In the present method, firstly, by combining compressed sensing and POD methods, the optimal basis functions are obtained via low-fidelity calculations. These basis functions are subsequently used in the trend part of the Kriging surrogate model. Then, the trend coefficients and the stochastic Gaussian part are estimated through a limited number of high-fidelity calculations. The performance of the proposed method is investigated on two challenging test cases: 1) film-cooling jet in cross-flow and 2) leading edge film cooling of a gas turbine blade with 7 and 10 uncertain variables, respectively. For the first test case, the new method reduces the computational cost by 91 % and 53.9 % with respect to the full PCE and POD methods. For the second test case, the computational cost reductions are 81 % and 37.9 % in comparison to the full PCE and POD methods, respectively. In general, the proposed method is better in terms of accuracy in comparison to combined POD and compressed sensing, especially in the cases with the lower number of low-fidelity samples. [ABSTRACT FROM AUTHOR]

Optimal non-planar wing planform geometries for a Mach 2.2 45-seat supersonic transport are generated using Kriging-based Bayesian optimisation techniques on a 22-variable, 3-objective problem for two wing-loading conditions. Sonic boom loudness, drag, and root bending moment are simultaneously minimised at a fixed lift. A Python-based framework is developed for rapid evaluation of designs in a parallel computation environment, automating conceptual geometry generation, optimised mesh griding, Euler CFD evaluation, and thermoviscous atmospheric boom propagation. An empirical turbulent skin friction coefficient is used to correct the Euler drag and an estimate of wave drag is performed. Self-organising maps and polynomial chaos expansion Shapley effects are used to explore the design variables and their associated sensitivities with respect to the design objectives. A geometric centroid-based proxy for trim is used to filter the results; feasible extreme designs and a compromise design are compared and discussed. The results indicate a trade-off between each of the three objectives due to competing design requirements, however an improvement in two of the objective functions is possible by sacrificing the remaining objective. One possible compromise solution reduces the root bending moment coefficient by 25% and the sonic boom loudness by 24% at the cost of a 5% increase in drag. [ABSTRACT FROM AUTHOR]