Model bias characterization considering discrete and continuous design variables

Model bias can be normally modeled as a regression model to predict potential model errors in the design space with sufficient training data sets. Typically, only continuous design variables are considered since the regression model is mainly designed for response approximation in a continuous space. In reality, many engineering problems have discrete design variables mixed with continuous design variables. Although the regression model of the model bias can still approximate the model errors in various design/operation conditions, accuracy of the bias model degrades quickly with the increase of the discrete design variables. This paper proposes an effective model bias modeling strategy to better approximate the potential model errors in the design/operation space. The essential idea is to firstly determine an optimal base model from all combination models derived from discrete design variables, then allocate majority of the bias training samples to this base model, and build relationships between the base model and other combination models. Two engineering examples are used to demonstrate that the proposed approach possesses better bias modeling accuracy compared to the traditional regression modeling approach. Furthermore, it is shown that bias modeling combined with the baseline simulation model can possess higher model accuracy compared to the direct meta-modeling approach using the same amount of training data sets.