Metamodels for variable importance decomposition with applications to probabilistic engineering design

It is routine in probabilistic engineering design to conduct modeling studies to determine the influence of an input variable (or a combination) on the output variable(s). The output or the response can then be fine-tuned by changing the design parameters based on this information. However, simply fine-tuning the output to the desired or target value is not adequate. Robust design principles suggest that we not only study the mean response for a given input vector but also the variance in the output attributed to noise and other unaccounted factors. Given our desire to reduce variability in any process, it is also important to understand which of the input factors affect the variability in the output the most. Given the significant computational overhead associated with most Computer Aided Engineering models, it is becoming popular to conduct such analysis through surrogate models built using a variety of metamodeling techniques. In this regard, existing literature on metamodeling and sensitivity analysis techniques provides useful insights into the various scenarios that they suit the best. However, there has been a limitation of studies that simultaneously consider the combination of metamodeling and sensitivity analysis and the environments in which they operate the best. This paper aims at contributing to reduce this limitation by basing the study on multiple metrics and using two test problems. Two test functions have been used to build metamodels, using three popular metamodeling techniques: Kriging, Radial-Basis Function (RBF) networks, and Support Vector Machines (SVMs). The metamodels are then used for sensitivity analysis, using two popular sensitivity analysis methods, Fourier Amplitude Sensitivity Test (FAST) and Sobol, to determine the influence of variance in the input variables on the variance of the output variables. The advantages and disadvantages of the different metamodeling techniques, in combination with the sensitivity analysis methods, in determining the extent to which the variabilities in the input affect the variabilities in the output are analyzed.