استفاده از روش تجزیه و تحلیل حساسیت پیشرو برای بهبود پوسته شدن کد، کاربردی بودن و متدولوژی عدم قطعیت (CSAU)

Since the code scaling, applicability, and uncertainty (CSAU) methodology was proposed about two decades ago, it has been widely used for new reactor designs and existing LWRs power uprates. In spite of these huge successes, CSAU has been criticized for the need of further improvement, focusing on two main issues – lack of objectiveness and high cost. With the effort to develop next generation safety analysis codes, new opportunities appear to take advantage of new numerical methods, better physical models, and modern uncertainty qualification methods. Forward sensitivity (FS) analysis directly solves the partial differential equations for parameter sensitivities. Moreover, our work shows that time and space steps can be treated as special sensitivity parameters so that numerical errors can be directly compared with physical uncertainties. It should be noted that FS analysis is an intrusive uncertainty quantification method that requires the user of the method to be familiar with the simulation code structure including numerical spatial and temporal integration techniques. When the FS analysis is implemented in a new advanced system analysis code, CSAU could be significantly improved by quantifying numerical errors and allowing a quantitative PIRT (Q-PIRT) to reduce subjective judgment and improve efficiency. This paper will review the issues related to the current CSAU implementations, introduce FS analysis, show a simple example to perform FS analysis, and discuss potential improvements on CSAU with FS analysis. Finally, the general research direction and requirements to use FS analysis in an advanced system analysis code will be discussed.

The code scaling, applicability, and uncertainty (CSAU) methodology was developed in late 1980s by USNRC (Nuclear Regulatory Commission) to systematically quantify reactor simulation uncertainty. This method was developed in response to the USNRC rule change to allow the use of realistic physical models to analyze the loss of coolant accident (LOCA) in a light water reactor (Boyack et al., 1990). Prior to this time, the evaluation of this accident was subject to a prescriptive set of rules set by Appendix K of the regulations which require conservative models and assumptions to be applied simultaneously, leading to very pessimistic estimates of the impact of this accident on the reactor safety. The rule change therefore promised to provide significant benefits by allowing nuclear power reactor to increase output without major plant modifications. CSAU was developed to apply realistic methods, while properly taking into account uncertainty in data, physical modeling and plant variability. The method was first demonstrated in 1996 for licensed application by Westinghouse to be structured, traceable, and practical (Young et al., 1998). Since then, best estimate plus uncertainty (BEPU) methods have been extensively used by the nuclear power industry around the world for power upratings, license renewals, and new design certifications. One example is AREVA's realistic large break LOCA (LB-LOCA) analysis methodology which received approval by USNRC in April 2003 (Martin and O’Dell, 2005). It incorporates the nonparametric statistical approach originally incorporated in the Gesellschaft fur Anlagen und Reaktorsicherheit (GRS) methodology for LOCA analysis. Another example is the Westinghouse automated statistical treatment of uncertainty method (ASTRUM) approved at the end of 2004 (Muftuoglu et al., 2004). The ASTRUM uses the same code and uncertainty distributions as the 1996 BELOCA method but uses nonparametric order statistics and more explicit treatment of more uncertainty parameters. For the same PWR plants, the calculated 95th percentile PCT (peak clad temperature) value is reduced by 126 K with the ASTRUM method, comparing with the value obtained from the 1996 BELOCA method. Almost all of demonstration applications of BEPU methods so far are for LOCA including both LB-LOCA and SB-LOCA (small break LOCA) and most of licensing applications of BEPU methods are for LBLOCA (Prosek and Mavko, 2007). Although CSAU methodology has been traditionally employed with nuclear reactor safety analysis codes like TRACE, TRAC, and RELAP5, the authors believe that it can have a more general role that applies to any simulation code employed for nuclear reactor analysis.

CSAU methodology could be significantly improved with forward sensitivity analysis implemented in a new advanced system analysis code by reducing its cost and subjective judgment. By including time step and grid size sensitivity analysis, time and space convergence studies can be performed in one run and global numerical errors can be directly compared with physical parameter uncertainties. A quantitative PIRT process can be implemented with forward sensitivity analysis. Effectively using forward sensitivity raises new requirements on system analysis code design.