Int. J. of Reliability and Safety   »   2017 Vol.11, No.3/4



Title: Integrated Bayesian probabilistic approach to improve predictive modelling


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


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.2017.10010795


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


Submission date: 05 Apr 2017
Date of acceptance: 21 Jul 2017
Available online: 31 Jan 2018



Editors Full text accessAccess for SubscribersPurchase this articleComment on this article