Analysis and Validation of Wilks Nonparametric Uncertainty Method for Best-Estimate Calculations in Nuclear Safety
Authors: Cheng-Cheng Deng , Wei-Li Liu , Jun Yang , Qiao Wu 
Published: October 2017

Traditional safety analysis of nuclear power plants is usually performed by conservative methods. However, conservative methods bring some problems, for instance, the calculation results deviate much from the true physical process, and the results are uncertain to be fully conservative. In 1988, Nuclear regulatory commission (NRC) amended the Emergency Core Cooling System (ECCS) licensing rules contained in 10CFR50.46 to permit Best-Estimate Plus Uncertainty (BEPU) analysis as an alternative of conservative methods in nuclear safety analysis. Best-estimate codes are used to perform more realistic calculations, and uncertainty quantitative analysis is required as a necessary complement of best-estimate calculation. To support the revised ECCS regulation, the Code Scaling, Applicability and Uncertainty (CSAU) methodology was developed by NRC as a basic framework of uncertainty analysis. In the original CSAU methodology, response surface method is applied to perform uncertainty quantitative calculations, however, constructing appropriate response surface takes demanding computation costs. Recently, Wilks nonparametric statistical method is widely used in nuclear industry for uncertainty quantification due to its simplicity and efficiency. However, the accuracy and stability of the confidence results using Wilks method is still controversial in actual applications.
In this paper, Wilks nonparametric uncertainty method was studied through statistical theory, and then applied in the uncertainty analysis of loss of flow accident for a simple pressurized water reactor. The best-estimate code RELAP5/MOD3.4 was employed to build a model of the simple nuclear plant and carry out uncertainty calculations. In order to improve the calculation efficiency, the thermal-hydraulic code RELAP5 and the statistical code DAKOTA were bridged to perform integrated uncertainty propagating calculations, including input uncertain parametric sampling, multiple executions of code runs in batches and data extraction after calculations. And the BEPU analysis of loss of flow accident was demonstrated through the integrated uncertainty calculating platform. Thereafter, the output database of the figure of merit (Peak Cladding Temperature, PCT) was obtained for uncertainty evaluation. The statistical distribution of PCT results was fitted and its 95% quantile value was given as the reference point. Moreover, the probability density distribution and the corresponding mean and variance values of the 95/95 results of PCT using Wilks uncertainty method at different orders were presented. Thus, the accuracy and stability of the confidence results using Wilks method at different orders was analyzed and validated.
The results indicate that, with the increasing of the order, the 95/95 PCT results using Wilks uncertainty method become more accurate with less conservative degree, and also become more stable with smaller dispersal degree, which is agreeable with Wallis’ theoretical analysis. Therefore, as the computing resources permit, Wilks method at higher order is suggested to be used to carry out uncertainty quantification so as to achieve the confidence results with enough accuracy and stability. Our study will provide some theoretical statistic basis and applicable guidance for best-estimate nuclear safety analysis.