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This paper is concerned with modeling computer experiments with multiple responses. It has been common that one may collect multiple responses from a physical or computer experiment. However, to our best knowledge, there is little work to model computer experiment with multiple responses. In this paper, we propose a modeling procedure for such computer experiment by using a multivarate kriging model, a natural extension of the ordinary kriging model. We further extend functional ANOVA of single response to multiple response and apply it for analyzing the effect of each design variable. The proposed methodology is demonstrated by an analysis of data collected from a case study concerned with the design of the engine structure to minimize the radiated noise.

To address the conflicting goals of minimal piston friction and minimal piston noise, a dynamic power cylinder model was developed to predict piston motion and side loads within the cylinder. This correlated model was the basis of a comprehensive analytical design of experiments (DOE) where both piston noise and piston friction were monitored. The results of the DOE were used to generate metamodels for piston friction and for piston noise. To insure design robustness, variability was introduced into the surrogate models via First Order Reliability Method (FORM). A Pareto curve using 99% probability was constructed and a piston robust to both noise and friction was selected.