Bayesian calibration of computer models based on Takagi–Sugeno fuzzy models

Abstract Computer models have been playing a vital role in scientific and engineering problems. However, before using the models, we usually need to calibrate them by utilizing some experimental data from real tests. When calibrating computer models, it is necessary to consider the model structure error/discrepancy and formulate a realistic prior for the model discrepancy function. In this paper, we use a novel approach, i.e., a Takagi–Sugeno (T–S) fuzzy model, to formulate the model discrepancy function, which can be described as a collection of 0-order T–S type fuzzy if-then rules. The premises of the fuzzy rules are determined based on fuzzy c-means (FCM) clustering, while the consequence parameters are estimated simultaneously with the calibration parameters. The advantages of this modeling approach can be summarized as: (1) strong ability to exploit expert knowledge, (2) low computational costs, and (3) easy to interpret. Further, based on the T–S fuzzy model prior for the model discrepancy function, we construct the Bayesian model for the calibration problem and design a sampler which combines Gibbs and Metropolis–Hastings steps, forming the framework of Bayesian calibration method based on Takagi–Sugeno fuzzy model (BC-TS). To our best knowledge, it is the first attempt to bring a fuzzy model into the Bayesian model calibration. The issue of identifiability is also addressed with the help of Fisher information matrix and analysis results show that the proposed BC-TS method has a good identifiability property . Finally, the effectiveness of the proposed BC-TS is verified by a numerical example and a practical example, i.e., the Sandia 2014 verification and validation (V&V) challenge problem.