Regression modeling for computer model validation with functional responses

Statistical analysis of functional responses based on functional data from both computer and physical experiments has gained increasing attention due to the dynamic nature of many engineering systems. However, the complexity and huge amount of functional data bring many difficulties to apply traditional or existing methodologies. The objective of the present study is twofold: (1) prediction of functional responses based on functional data and (2) prediction of bias function for validation of a computer model that predicts functional responses. In this paper, we first develop a functional regression model with linear basis functions to analyze functional data. Then combining data from both computer and physical experiments, we use the functional analysis modeling to predict the bias function which is crucial for validating a computer model. The proposed method, following the classical nonparametric regression framework, uses a single step procedure which is easily implemented and computationally efficient. Through an application example of motor engine analysis to predict acceleration performance and gear shift events, we demonstrate our approach and compare it to using the Gaussian process modeling approach.