A Bayesian Inference based Model Interpolation and Extrapolation

• Published in: SAE International journal of materials and manufacturing Vol. 5; no. 2; pp. 357 - 364
• Main Authors: Zhan, Zhenfei, Fu, Yan, Yang, Ren-Jye, Xi, Zhimin, Shi, Lei
• Format: Journal Article
• Language: English
• Published: Warrendale SAE International 2012; SAE International, a Pennsylvania Not-for Profit
• Subjects: Bayesian analysis; Bayesian inference; Configuration management; Design; Design engineering; Design optimization; Evaluation; Extrapolation; Impact analysis; Interpolation; Mathematical extrapolation; Mathematical models; Model testing; Modeling; Musical intervals; Parameters; Predictive modeling; Response surface methodology; Statistical inference; Vehicles
• ISSN: 1946-3979; 1946-3987; 1946-3987
• DOI: 10.4271/2012-01-0223

Model validation is a process to assess the validity and predictive capabilities of a computer model by comparing simulation results with test data for its intended use of the model. One of the key difficulties for model validation is to evaluate the quality of a computer model at different test configurations in design space, and interpolate or extrapolate the evaluation results to untested new design configurations. In this paper, an integrated model interpolation and extrapolation framework based on Bayesian inference and Response Surface Models (RSM) is proposed to validate the designs both within and outside of the original design space. Bayesian inference is first applied to quantify the distributions' hyper-parameters of the bias between test and CAE data in the validation domain. Then, the hyper-parameters are extrapolated from the design configurations to untested new design. They are then followed by the prediction interval of responses at the new design points. A vehicle design of front impact example is used to demonstrate the proposed methodology.