A modified Bayesian approach for model calibration with interval random observed data

초록

The traditional Bayesian approach for model calibrations is based on the random theory, while it needs a great amount of information to construct precise probability distributions of observed data. This paper presents a modified Bayesian approach, suggesting a model calibration method with limited observed information. In this approach, the observed data are described as random variables that obey certain probability distributions, while some of their distribution parameters are given variation intervals rather than precise values. Because of the existing interval parameters, a probability density distribution strip is formed in the posterior space, instead of a single distribution for each unknown model parameter as we usually obtain in the traditional Bayesian calibration. Interval analysis is then adopted for marginal posterior distribution transformation, through which effects of the interval parameters on the posterior distribution strip can be well revealed. Finally, the mean intervals and confidence intervals of the unknown model parameters, by using the interval analysis and Markov Chain Monte Carlo method, are obtained from their posterior distribution strip. As an example, in this study, a thermal model calibration problem is investigated to demonstrate the effectiveness of the present approach.

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