Novel model calibration method via non-probabilistic interval characterization and Bayesian theory

• Published in: Reliability engineering & system safety Vol. 183; pp. 84 - 92
• Main Authors: Wang, Chong, Matthies, Hermann G.
• Format: Journal Article
• Language: English
• Published: Barking Elsevier Ltd 01-03-2019; Elsevier BV
• Subjects: Bayesian analysis; Bayesian theory; Calibration; Computer applications; Feasibility studies; Interval sampling method; Kennedy and O'Hagan model; Mathematical models; Model calibration; Non-probabilistic interval characterization; Parameter uncertainty; Probabilistic methods; Probability; Probability theory; Reliability engineering; Sampling; Technology assessment; Unbiased interval quantification; Uncertainty; Uncertainty analysis; Unbiased interval quantification; Interval sampling method; Model calibration; Bayesian theory; Non-probabilistic interval characterization; Kennedy and O'Hagan model
• ISSN: 0951-8320; 1879-0836
• DOI: 10.1016/j.ress.2018.11.005

•A combined interval-Bayesian framework is constructed for model calibration.•Interval parameters via Bayesian update give a faithful uncertainty representation.•An unbiased estimation is presented for interval quantification with limited data.•An interval sampling method is developed for interval response prediction.
For many uncertainty-based engineering practices, the information or experimental data used to construct the uncertainty analysis model are often deficient, thus rendering traditional probabilistic methods ineffective. In this context, this paper proposes a novel model calibration method that combines non-probabilistic interval technology with Bayesian analysis theory. First, based on both the mean value and the standard deviation of the available sample data, a new interval quantification method is introduced to approximately describe the bounds of the uncertain input parameters. Then, via the well-known Kennedy and O'Hagan model and Bayesian theory, an interval parameter calibration framework is constructed that can be used to increase the agreement between experimental response measurements and computational response results. To improve the execution time of the uncertain response prediction with respect to interval parameters, an efficient interval sampling method is proposed that utilizes interval endpoints and extreme points. Finally, the feasibility of the proposed method is demonstrated using the renowned Sandia thermal challenge problem.