[en] This report includes contents of the project for the following purposes. The first purpose of this project is to accelerate the calculation of the system analysis code to reduce a computing burden. The second purpose is to clarify the prediction mechanism of the developed models for overcoming the ‘black box’ limit. The main research topic is the dramatic increase of the calculation speed of the system analysis code via an AI solver calculating the governing equations, and via AI models predicting the CHF wall temperature and the critical flow which requires long computing time. Also, the ‘black box’ limit will be solved and consequently the developed AI model will have better reliability via the XAI methodology. For the final goal, the AI system analysis code based on XAI will obtain the license for nuclear design and safety regulations

[en] Statistical approaches to uncertainty quantification and sensitivity analysis are very important in estimating the safety margins for an engineering design application. This paper presents a system analysis and optimization toolkit developed by Korea Atomic Energy Research Institute (KAERI), which includes multiple packages of the sensitivity analysis and uncertainty quantification algorithms. In order to reduce the computing demand, multiple compute resources including multiprocessor computers and a network of workstations are simultaneously used. A Graphical User Interface (GUI) was also developed within the parallel computing framework for users to readily employ the toolkit for an engineering design and optimization problem. The goal of this work is to develop a GUI framework for engineering design and scientific analysis problems by implementing multiple packages of system analysis methods in the parallel computing toolkit. This was done by building an interface between an engineering simulation code and the system analysis software packages. The methods and strategies in the framework were designed to exploit parallel computing resources such as those found in a desktop multiprocessor workstation or a network of workstations. Available approaches in the framework include statistical and mathematical algorithms for use in science and engineering design problems. Currently the toolkit has 6 modules of the system analysis methodologies: deterministic and probabilistic approaches of data assimilation, uncertainty propagation, Chi-square linearity test, sensitivity analysis, and FFTBM

[en] Highlights: • We developed an interface between an engineering simulation code and statistical analysis software. • Multiple packages of the sensitivity analysis, uncertainty quantification, and parameter estimation algorithms are implemented in the framework. • Parallel computing algorithms are also implemented in the framework to solve multiple computational problems simultaneously. - Abstract: This paper introduces a statistical data analysis toolkit, PAPIRUS, designed to perform the model calibration, uncertainty propagation, Chi-square linearity test, and sensitivity analysis for both linear and nonlinear problems. The PAPIRUS was developed by implementing multiple packages of methodologies, and building an interface between an engineering simulation code and the statistical analysis algorithms. A parallel computing framework is implemented in the PAPIRUS with multiple computing resources and proper communications between the server and the clients of each processor. It was shown that even though a large amount of data is considered for the engineering calculation, the distributions of the model parameters and the calculation results can be quantified accurately with significant reductions in computational effort. A general description about the PAPIRUS with a graphical user interface is presented in Section 2. Sections 2.1–2.5 present the methodologies of data assimilation, uncertainty propagation, Chi-square linearity test, and sensitivity analysis implemented in the toolkit with some results obtained by each module of the software. Parallel computing algorithms adopted in the framework to solve multiple computational problems simultaneously are also summarized in the paper

[en] In this work, the model calibration was done to reduce the simulation code's input parameters' uncertainties, and subsequently simulation code's prediction uncertainties of design constraining responses. Each parameter/physical Model's fidelity was identified as well to determine major sources of the modeling uncertainty. This analysis is important in deciding where additional efforts should be given to improve our simulation model. The goal of this work is to develop higher fidelity model by completing experiments and doing uncertainty quantification. Thermal hydraulic parameters were adjusted for both mildly nonlinear and highly nonlinear systems, and their a posterior parameter uncertainties were propagated through the simulation model to predict a posterior uncertainties of the key system attributes. To solve both highly nonlinear as well as mildly nonlinear problem, both deterministic and probabilistic methods were used to complete uncertainty quantification. To accomplish this, the Bayesian approach modified by regularization is used for the mildly nonlinear problem to incorporate available information in quantifying uncertainties. The a priori information considered are the parameters and the experimental data together with their uncertainties. The results indicate that substantial reductions in uncertainties on the system responses can be achieved using experimental data to obtain a posterior input parameters' uncertainty distributions. The MCMC method was used for the highly nonlinear transient. Due to the computational burden, this method would not be applicable if there are many parameters, but it can provide the best solution since the algorithm does not approximate the responses while the deterministic approach assumes linearity of the responses with regard to dependencies on the parameters. Using MCMC non-Gaussian a posterior distributions of the parameters with reduced uncertainties were obtained due to the nonlinearity of the system sensitivity equations

[en] There are several Design Extension Condition (DEC) events of PGSFR such as unprotected transient overpower (UTOP), unprotected loss of flow (ULOF), unprotected loss of heat sink (ULOHS), large partial subassembly blockage, large Steam Generator Tube Rupture (SGTR), large sodium leak and Station Black Out (SBO) as summarized in table I. It should be noted that DEC events are the accidents having probability of occurrence ranging from 10"-"8 to 10"-"6. In this research, ULOF accident was selected after determining the Phenomena Identification and Ranking Table (PIRT). Based on the development of PIRT, the sensitivity analysis was performed to confirm the relative importance of the parameters. In this research, the sensitivity analysis for the ULOF of the PGSFR was performed. For 23 parameters the ACLP strain coefficient, core radial expansion coefficient, Doppler reactivity, coastdown curve, and core inlet form loss were dominant in the ULOF. Alternately, the GP strain coefficient, fuel density reactivity, RV expansion reactivity coefficient, heat capacity of reactor vessel material, wall roughness of IHX shell side, and spacer grid form loss did not affect the PGSFR system for the ULOF. The core inlet form loss should address additional sensitivity analysis

[en] In this research, uncertainty analyses for multiple safety parameters were performed for Unprotected Loss of Flow (ULOF) for the Prototype Gen-IV Sodium-cooled Fast Reactor (PGSFR) by using the PArallel Computing Platform IntegRated for Uncertainty and Sensitivity analysis (PAPIRUS). The objective of the global uncertainty analysis is to evaluate all safety parameters of the system in the combined phase space formed by the parameters and dependent variables. The uncertainty propagation was performed by mapping the uncertainty bands of the model parameters through the MARS-LMR to determine the distributions for the fuel centerline, cladding, and coolant temperatures. The Best Estimate Plus Uncertainty (BEPU) analysis adopted for uncertainty quantification of the code predictions has been performed through a statistical approach where the Figure of Merit (FOM) is evaluated multiple times by using several combinations of parameters that are randomly generated according to their distributions. The statistical approach of uncertainty quantification is known to be very powerful for estimating response distributions, but sometimes inapplicable owing to demanding calculation requirements. In this research, Wilks’ formula was used to estimate the 95% probability value of the FOM from a limited number of code calculations. This paper also introduces the application of data assimilation in best-estimate modeling to improve the prediction of the reactor system performance by refining various sources of uncertainties through model calibration technique. An inverse problem was formulated based upon Bayes theorem and solved to estimate the posteriori distributions of parameters. (author)

[en] This paper introduces Markov chain Monte Carlo simulation methodology for data assimilation to calculate the estimated uncertainty of the physical model using a posteriori distribution of parameters derived based on Bayes' theorem. The probabilistic method provides the best solution for nonlinear problems, but it is usually not applicable to a multi physics multi scale system that has multiple parameters and responses. It is thus desired to develop an uncertainty quantification method for the complex thermal hydraulic system to perform an efficient calculation. This paper proposes uncertainty quantification methodology for the computationally demanding system to develop computational tool that calculates the physical model's uncertainty for nonlinear problems with tremendous reduction in the computing demand for thermal hydraulic system calculation. This is done by utilizing surrogate model with an appropriate link between the surrogate and the high fidelity model. It was shown that even though the surrogate models provide poor approximation of the responses, the distributions of the parameters can be quantified accurately with significant reductions in computational effort. (authors)

[en] When the reactor power excursion due to a reactivity initiated accident occurs, the temperature of the fuel pellet increases very rapidly and may even excess the melting temperature of the pellet. Once the pellet temperature reaches the melting temperature, the phase change from solid to liquid occurs at the melting temperature. Such a melting process model may not be required for the analysis of the design basis accidents (DBAs) but is essential for the analysis of the design extension conditions (DECs). An additional processing model for the SPACE code is required to simulate the melting process in the reactor components during a transient for the analysis of the DEC scenarios. The phase change model based on the enthalpy change has been developed and validated through the comparison with the analytical solution of Stefan’s problem. Although the calculation results were dependent on the number of mesh points, overall behavior of the results showed a good agreement with that of the analytical solutions for the temperature and melting front location during a transient. Therefore, the phase change model developed by this project can be applied to melting analysis of the major reactor components such as a reactor pressure vessel as well as fuel rod. In addition, to extent the applicable range of this model.

[en] In this research, uncertainty analyses for multiple safety parameters were performed for Unprotected Loss of Flow (ULOF) for the Prototype Gen-IV Sodium-cooled Fast Reactor (PGSFR) by using the PArallel Computing Platform IntegRated for Uncertainty and Sensitivity analysis (PAPIRUS). The objective of the global uncertainty analysis is to evaluate all safety parameters of the system in the combined phase space formed by the parameters and dependent variables. The uncertainty propagation was performed by mapping the uncertainty bands of the model parameters through the MARS-LMR to determine the distributions for the fuel centerline, cladding, and coolant temperatures. The Best Estimate Plus Uncertainty (BEPU) analysis adopted for uncertainty quantification of the code predictions has been performed through a statistical approach where the Figure of Merit (FOM) is evaluated multiple times by using several combinations of parameters that are randomly generated according to their distributions. The statistical approach of uncertainty quantification is known to be very powerful for estimating response distributions, but sometimes inapplicable owing to demanding calculation requirements. In this research, Wilks'formula was used to estimate the 95% probability value of the FOM from a limited number of code calculations. This paper also introduces the application of data assimilation in best-estimate modeling to improve the prediction of the reactor system performance by refining various sources of uncertainties through model calibration technique. An inverse problem was formulated based upon Bayes theorem and solved to estimate the posteriori distributions of parameters. (author)

[en] This paper introduces data assimilation (calibration) methodology for an engineering system to improve the prediction of the system behavior. Bayesian based model calibration technique, which incorporates measured data and computed information, was employed to update a priori information to obtain a more accurate posterior parameter density. Given flooding experimental data and a priori distributions of the parameters, a posteriori distributions can be obtained by calibrating system models based on Bayes' theorem to achieve better agreement between measured and predicted response values. The mathematical approach that is used to complete this analysis depends upon whether the system responses are or are not linearly dependent upon the parameters. A linearity test showed that there exist nonlinear behaviors, hence probabilistic methods were used to complete data assimilation on parameters and to propagate parameter uncertainties through simulation code. (author)