Title: Integrated Bayesian probabilistic approach to improve predictive modelling

Authors: Xiaofei Guan; Xiaomo Jiang; Yucheng Tang; Xueyu Cheng; Yong Yuan

Addresses: School of Mathematical Sciences, Tongji University, Shanghai 200092, China ' Department of Geotechnical Engineering, Tongji University, Shanghai 200092, China ' Department of Mechanical Engineering, Shanghai Jiaotong University, Shanghai 200240 China ' Clayton State University, Morrow, Georgia 30260, USA ' Department of Geotechnical Engineering, Tongji University, Shanghai 200092, China

Abstract: This paper presents an integrated Bayesian probabilistic methodology to calibrate parameters of a predictive model and quantitatively evaluate its validity and predictive capacity with non-normality data, considering uncertainties. Bayes network is developed to graphically represent the relationships of all model variables. Bayesian regression theory associated with Markov Chain Monte Carlo simulation and Gibbs sampling is presented to calibrate model parameters to improve model accuracy. The Bayesian method is compared to maximum likelihood and nonlinear optimisation approaches. A generic procedure is presented to integrate the model calibration and quantitative validation. Anderson-Darling goodness-of-fit test and Box-Cox transformation are employed respectively to perform normality hypothesis test of difference data and normality conversion. The confidence of calibrated model is quantified via Bayesian inference method. The integrated methodology and procedure is demonstrated with a nonlinear analytical model for pressure loss prediction in a gas turbine and five sets of different measurement data.

Keywords: Bayesian statistics; Bayes network; hypothesis testing; model calibration; model validation.

DOI: 10.1504/IJRS.2017.089702

International Journal of Reliability and Safety, 2017 Vol.11 No.3/4, pp.153 - 181

Available online: 31 Jan 2018

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