Metamorphic Relations Identification on Chebyshev Rational Approximation Method in the Nuclide Depletion Calculation Program

The Chebyshev rational approximation method (CRAM) is an essential numerical solution algorithm for the burnup equation. Since the high complexity of nuclide depletion calculation, especially the existence of short-lived nuclide and closed cycle in the transition chains, outputs of the program are almost impossible to predict accurately. Therefore, the traditional testing methods are inapplicable, even invalid. Metamorphic testing (MT) is a promising method to solve such a typical testing oracle problem. However, the absence of metamorphic relations (MRs) severely hinders its application. According to the nuclear software development process, we established a nuclear MR hierarchical model (MRHM) for guiding MR identification and classification. MRHM divides MRs into three layers: physics, algorithm, and code. After in-depth analysis, we carried out a group of MRs from the burnup equation and CRAM and classified them according to MRHM. We adopted these MRs in MT of the Nuclide Inventory Tool (NUIT), which is a program that has implemented CRAM. These MRs represent the natural properties of CRAM, and other CRAM programs indeed used them. Moreover, the MRHM will extend to more nuclear science software.