Investigation of Identification and Uncertainty Quantification Methods for Constitutive Model

Abstract

Typical input-based best estimate plus uncertainty (BEPU) analysis methods require comprehensive consideration of uncertainty from all sources. Uncertainty of the input parameters is then propagated to the output by many sampling calculations through the best estimate (BE) code. In the past, the uncertainty of the code constitutive model, which was one of the most important sources of uncertainty, was often not properly analyzed. For the purpose of quantifying the uncertainty of code constitutive models and including it into the BEPU analysis, a methodology for the identification and uncertainty quantification of key constitutive models was developed in this paper. First of all, the figure of merit (FOM) of the sensitivity analysis needed to be defined. Time series data were chosen as the target in order to better characterize the effect of the parameters on the whole transient process, and a dimension reduction was performed for the time series data using functional data analysis (FDA) method to obtain the FOMs. Then, sensitivity analysis was performed on several FOMs to get the importance ranking of the constitutive models. The sensitivity analysis approach was a two-step process, where the input model parameters were firstly screened by the Morris method, and then the screened model parameters were subjected to a quantitative sensitivity analysis by the Sobol method to obtain a parameter importance ranking. Finally, uncertainty quantification was performed for the high ranking models selected based on the sensitivity analyses. The posterior probability distributions of the parameters were calculated using the Markov chain Monte Carlo (MCMC) method based on Bayesian calibration approach. In order to validate the applicability of the above method, it was used to quantify the uncertainties of the important models based on the FLECHT-SEASET experiment, and to propagate the quantified uncertainties to the cladding temperature. In addition, the result of the sensitivity analysis of the FOM obtained by FDA analysis was compared with two traditional FOMs, which were the integral of the difference between the sampling calculation results and the experimental values, and the peak cladding temperature (PCT), respectively. The results show that it is difficult to obtain an accurate ranking of model importance when using PCT as FOM. This approach can accurately identify the key constitutive models in transient processes, and the propagation calculation results can well envelope the experimental values.

Keywords

• constitutive model
• functional data analysis
• sensitivity analysis
• bayesian calibration
• uncertainty quantification