Research On Two-stage Verification Model Based On Metamorphic Relation

The verification and validation of Nuclear power design and analysis programs is to ensure the correctness and reliability of numerical simulation of complex systems and reduce the risk of making wrong decisions.Verification is to evaluate whether the numerical solution method truly reflects the physical model and prove whether the programmed calculation code can correctly solve the physical model.Validation is to examine whether the numerical simulation correctly reflects the physical laws of the real world.Verification is the premise of validation.If one entered the validation process without adequate validation,it would have had a huge adverse impact on the effectiveness and efficiency of verification and validation.Testing is an important means of software quality assurance,including unit testing,integration testing and system testing.Unit testing is to examine whether the basic software units,such as functions and methods,can realize the design requirements correctly.Integration testing is to evaluate whether the functions,interfaces,performance and other design constraints of a module or subsystem assembled by units meet the requirements.System testing is to estimate whether the complete software system meets the requirements under the real working environment.The development of nuclear power software usually includes the stages of physical equation modeling,numerical method selection,program coding,etc.During software verification,it is often implicitly checked whether the program meets specific natures from the physical equations,calculation methods,and program design.If the above properties are violated,it is indicated the program has an error and cannot be passed by verification.The software test checks the nature of the program,and the verification examines the nature of the physical equations and calculation methods.Most of the verification activities use the direct comparison method,using benchmark questions,classical programs,experimental data,artificial solutions as the expected results,and comparing with the calculation results to determine the reliability of the code and the numerical precision of the solution.The burnup program describes the law of nuclide density changing with time.It is an important part of reactor physical design and plays a key role in the calculation of fuel breeding and consumption,reactivity change and so on.Because of adoption of the complex nuclides system and the existence of short half-life nuclides and closed-loop sub-chains,it is usually difficult to construct analytical or exact solutions.Moreover,the development cost of benchmark and experimental data is time consuming and costly,therefore,the number of verification examples is small.It is difficult,costly,and inadequate to use the direct comparison method for verification.The metamorphic testing is one of the indirect verification techniques,does not need constructing artificial solutions or benchmark questions,evaluates program under test whether meets specific natures to examines the correctness of such program.Moreover,it has a wide application perspective in the nuclear power field.Therefore,based on the metamorphic testing technology,this study proposes a two-stage verification model,the light-weight verification method based on metamorphic relation,the heavy-weight verification method based on metamorphic testing,and a data-driven heuristic identification method of metamorphic relations.All of these are successfully applied to the verification of the fuel depletion calculation code,namely NUIT.The main work is as follows,(1)Two-stage verification modelThe errors found in the verification can be divided into two categories:one is that the program does not correctly implement the numerical solution method,the other is that the numerical method does not accurately reflect the physical model.Further research shows that many of the type one errors can be revealed by evaluating whether the program satisfies the specific properties of the calculation method,while many of the type two errors can be found by examining whether the code satisfies the specific properties of the physical model.Therefore,in this paper,the verification is divided into light-weight and heavy-weight two stages.The former will explicitly evaluate the properties of physical models and calculation methods.After eliminating the above errors through lightweight verification,the direct comparison method is used for latter,which can significantly reduce the demand for test cases.(2)Light-weight verification based on metamorphic relationUsing the indirect comparison method,there is no need to construct a numerical solution or develop a verification example.It only uses the metamorphic relation to examine whether the program meets the specific properties of the physical model and numerical method.And the implementation algorithm is given.(3)Heavy-weight verification based on metamorphic testing For heavy-weight verification,the small number of source verification examples makes it difficult to verify the program adequately and its verification scope is limited.Using metamorphic relations,more follow-up verification examples can be derived from source examples,and adequacy and scope is improved by the metamorphic testing.And the implementation algorithm is given.(4)Data-driven heuristic identification method of metamorphic relationIn order to implement the two-stage verification,it is necessary to solve the problem of identifying the metamorphic relation.Literature research shows that there is no effective identification method at present.In this paper,a heuristic identification method based on data-driven is proposed.The intersection of code model metamorphic relation which comes from different programs with the same algorithm is used as heuristic information to analyze and deduce calculation model metamorphic relation.Similarly,the intersection of calculation model metamorphic relation which comes from different programs with the same physical equation is employed as heuristic information to analyze and infer physic model metamorphic relation.The metamorphic relation is the property in the physical model and computational model that is meaningful for verification.It has a wide applicability,which can be used to verify the same kind of programs employing the same calculation method or physical equation.(5)Two-stage verification of NUITNUIT is a point-depletion calculation program developed by Tsinghua University.The test requirements need cover calculation types,burnup equations,feed modes,refueling modes,and the core solution algorithm and calculation options.However,there are only ten source verification examples.Obviously,such number is far from meeting the above requirements.With the heuristic method,twenty-nine metamorphic relations are identified.There are 160 examples used in light-weight stage and 1128 ones used in heavy-weight stage,and 46 defects were found.The verification of NUIT is successful and effective.For nuclear power software verification,the previous research results of this paper provide a new theory,introduce a new technology,enrich the existing software testing technology system,alleviate the problem of inadequate verification examples,which is of great significance to improve the verification adequacy and prompt the quality of self-reliant software.