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In this paper, we investigate the use of multiple kernel functions for assisting single-objective Kriging-based efficient global optimization (EGO). The primary objective is to improve the robustness of EGO in terms of the choice of kernel function for solving a variety of black-box optimization problems in engineering design. Specifically, three widely used kernel functions are studied, that is, Gaussian, Matérn-3/2, and Matérn-5/2 function. We investigate both model selection and ensemble techniques based on Akaike information criterion (AIC) and cross-validation error on a set of synthetic (noiseless and noisy) and non-algebraic (aerodynamic and parameter tuning) optimization problems; in addition, the use of cross-validation-based local (i.e., pointwise) ensemble is also studied. Since all the constituent surrogate models in the ensemble scheme are Kriging models, it is possible to perform EGO since the Kriging uncertainty structure is still preserved. Through analyses of empirical experiments, it is revealed that the ensemble techniques improve the robustness and performance of EGO. It is also revealed that the use of Matérn-kernels yields better results than those of the Gaussian kernel when EGO with a single kernel is considered. Furthermore, we observe that model selection methods do not yield any substantial improvement over single kernel EGO. When averaged across all types of problem (i.e., noise level, dimensionality, and synthetic/non-algebraic), the local ensemble technique achieves the best performance. [ABSTRACT FROM AUTHOR]

The presence of uncertainties is inevitable in engineering design and analysis, where failure in understanding their effects might lead to the structural or functional failure of the systems. The role of global sensitivity analysis in this aspect is to quantify and rank the effects of input random variables and their combinations to the variance of the random output. In problems where the use of expensive computer simulations is required, metamodels are widely used to speed up the process of global sensitivity analysis. In this paper, a multi-fidelity framework for global sensitivity analysis using polynomial chaos expansion (PCE) is presented. The goal is to accelerate the computation of Sobol sensitivity indices when the deterministic simulation is expensive and simulations with multiple levels of fidelity are available. This is especially useful in cases where a partial differential equation solver computer code is utilized to solve engineering problems. The multi-fidelity PCE is constructed by combining the low-fidelity and correction PCE. Following this step, the Sobol indices are computed using this combined PCE. The PCE coefficients for both low-fidelity and correction PCE are computed with spectral projection technique and sparse grid integration. In order to demonstrate the capability of the proposed method for sensitivity analysis, several simulations are conducted. On the aerodynamic example, the multi-fidelity approach is able to obtain an accurate value of Sobol indices with 36.66% computational cost compared to the standard single-fidelity PCE for a nearly similar accuracy. [ABSTRACT FROM AUTHOR]