Analytical global sensitivity analysis and uncertainty propagation for robust design

Simulation-based robust design is playing an increasingly important role in industrial practice where design analyses involve extensive computer simulations. In simulation-based robust design, metamodels, also called response surface models, are often created to replace computationally expensive, high-fidelity, and black-box type of simulation programs. Interpretation of metamodels for the purpose of robust design becomes important. The computational expenses associated with certain types of metamodels and the random errors introduced by the data-sampling approach require the development of analytical methods, such as those for global sensitivity analysis (GSA) and uncertainty propagation (UP) to facilitate a robust-design process. In this work, generalized analytical formulations are developed for GSA and UP in robust design via the use of a variety of metamodels commonly used in engineering design applications. We show that even though the function forms of these metamodels vary significantly, they all follow the form of multivariate tensor-product basis functions for which the analytical results can be derived based on decomposed univariate integrals. The benefits of our proposed techniques are demonstrated using the robust engine piston design as an example. Even though our discussion is oriented toward simulation-based robust design, the same approach can be applied to quality engineering applications where metamodels are constructed based on physical experiments.