A Multi-fidelity Model Using a Scaling Factor and a Shifting Factor

Abstract

This study developed a new algorithm for multi-fidelity (MF) models that use a scaling and shifting factor. Through this shifting factor the algorithm enhance the accuracy of the MF (multi-fidelity) model. Unlike the other previous MF model, the new model includes a shifting parameter which could improve the accuracy of the MF model. In this study we compared this Scaled and shifted MF model to a Scaled low fidelity (LF) model with two scaling parameters (Xiong, et al, 2008) through the mathematical and application test problems. These two kinds of modeling technique are based on the Gaussian process model and used to construct a surrogate model to integrate information from both LF and HF models. In the MF model with scaling and shifting factors, compared to the HF model, the LF model is shifted in the design variable direction. Hence we add a shifting parameter on order to reduce the error of the multi-fidelity model. Specifically we use the Gaussian process to build the model and propose the Least Square Method (LSM) and the Maximum Likelihood Estimation (MLE) method to estimate each parameter. For the design of experiment (DOE) part of building the MF model we chose the Optimal Latin-Hypercube Design (OLHD) to generate the sampling points for HF data and used Augmented Latin-Hypercube Design (ALHD) to generate the sampling points for the LF data. To evaluate the performance of the two approaches, we chose 18 test functions and application problems compared their RMSE values to show their differences visually. The comparison revealed a significant improvement of the new advanced approach over the previous model.