Screening and metamodeling of computer experiments with functional outputs. Application to thermal-hydraulic computations

To perform uncertainty, sensitivity or optimization analysis on scalar variables calculated by a cpu time expensive computer code, a widely accepted methodology consists in first identifying the most influential uncertain inputs (by screening techniques), and then in replacing the cpu time expensive model by a cpu inexpensive mathematical function, called a metamodel. This paper extends this methodology to the functional output case, for instance when the model output variables are curves. The screening approach is based on the analysis of variance and principal component analysis of output curves. The functional metamodeling consists in a curve classification step, a dimension reduction step, then a classical metamodeling step. An industrial nuclear reactor application (dealing with uncertainties in the pressurized thermal shock analysis) illustrates all these steps

How to effectively compute the reliability of a thermal-hydraulic nuclear passive system

International audienceThe computation of the reliability of a thermal-hydraulic (T-H) passive system of a nuclear power plant can be obtained by (i) Monte Carlo (MC) sampling the uncertainties of the system model and parameters, (ii) computing, for each sample, the system response by a mechanistic T-H code and (iii) comparing the system response with pre-established safety thresholds, which define the success or failure of the safety function. The computational effort involved can be prohibitive because of the large number of (typically long) T-H code simulations that must be performed (one for each sample) for the statistical estimation of the probability of success or failure. The objective of this work is to provide operative guidelines to effectively handle the computation of the reliability of a nuclear passive system. Two directions of computation efficiency are considered: from one side, efficient Monte Carlo Simulation (MCS) techniques are indicated as a means to performing robust estimations with a limited number of samples: in particular, the Subset Simulation (SS) and Line Sampling (LS) methods are identified as most valuable; from the other side, fast-running, surrogate regression models (also called response surfaces or meta-models) are indicated as a valid replacement of the long-running T-H model codes: in particular, the use of bootstrapped Artificial Neural Networks (ANNs) is shown to have interesting potentials, including for uncertainty propagation.The recommendations drawn are supported by the results obtained in an illustrative application of literature

Quantitative functional failure analysis of a thermal-hydraulic passive system by means of bootstrapped Artificial Neural Networks

International audienceThe estimation of the functional failure probability of a thermal-hydraulic (T-H) passive system can be done by Monte Carlo (MC) sampling of the epistemic uncertainties affecting the system model and the numerical values of its parameters, followed by the computation of the system response by a mechanistic T-H code, for each sample. The computational effort associated to this approach can be prohibitive because a large number of lengthy T-H code simulations must be performed (one for each sample) for accurate quantification of the functional failure probability and the related statistics. In this paper, the computational burden is reduced by replacing the long-running, original T-H code by a fast-running, empirical regression model: in particular, an Artificial Neural Network (ANN) model is considered. It is constructed on the basis of a limited-size set of data representing examples of the input/output nonlinear relationships underlying the original T-H code; once the model is built, it is used for performing, in an acceptable computational time, the numerous system response calculations needed for an accurate failure probability estimation, uncertainty propagation and sensitivity analysis. The empirical approximation of the system response provided by the ANN model introduces an additional source of (model) uncertainty, which needs to be evaluated and accounted for. A bootstrapped ensemble of ANN regression models is here built for quantifying, in terms of confidence intervals, the (model) uncertainties associated with the estimates provided by the ANNs. For demonstration purposes, an application to the functional failure analysis of an emergency passive decay heat removal system in a simple steady-state model of a Gas-cooled Fast Reactor (GFR) is presented. The functional failure probability of the system is estimated together with global Sobol sensitivity indices. The bootstrapped ANN regression model built with low computational time on few (e.g., 100) data examples is shown capable of providing reliable (very near to the true values of the quantities of interest) and robust (the confidence intervals are satisfactorily narrow around the true values of the quantities of interest) point estimates

INTEGRATED DETERMINISTIC AND PROBABILISTIC SAFETY ANALYSIS: CONCEPTS, CHALLENGES, RESEARCH DIRECTIONS

International audienceIntegrated deterministic and probabilistic safety analysis (IDPSA) is conceived as a way to analyze the evolution of accident scenarios in complex dynamic systems, like nuclear, aerospace and process ones, accounting for the mutual interactions between the failure and recovery of system components, the evolving physical processes, the control and operator actions, the software and firmware. In spite of the potential offered by IDPSA, several challenges need to be effectively addressed for its development and practical deployment. In this paper, we give an overview of these and discuss the related implications in terms of research perspectives

Data Adequacy by an Extended Analytic Hierarchy Process for Inverse Uncertainty Quantification in Nuclear Safety Analysis

Data Adequacy (DA) assessment of experimental databases must be performed to control the impact of user effects on the results provided by the Thermal-Hydraulic (T-H) codes employed for the safety assessment of Nuclear Power Plants (NPPs). The activity is typically based on expert judgement, which, however, lacks a rigorous treatment of the uncertainties. With the objective to overcome this limitation, we propose a Multi-Criteria Decision Making (MCDM) approach to consider the Representativeness (R) and Completeness (C) of the databases by an Analytic Hierarchy Process (AHP) combined with Interval Analysis (IA) and Monte Carlo Simulation (MCS) to quantify the uncertainty. The approach for DA is exemplified on the databases made available to the participants of the ATRIUM (Application Tests for Realization of Inverse Uncertainty quantification and validation Methodologies in thermal hydraulics) project promoted by the WGAMA of the OECD-NEA, whose ultimate objective is the systematic application of Inverse Uncertainty Quantification (IUQ) methodologies to assess the uncertainties affecting the T-H model of an Intermediate Break Loss Of Coolant Accident (IBLOCA) of a Light Water Reactor (LWR). The outcomes of the application show that the proposed approach allows overcoming some of the limitations of expert-based approaches, reducing the reliance on subjective evaluations through the incorporation of quantitative metrics in the analysis and via the proper quantification of the uncertainty

Development of a Reactor Physics Analysis Procedure for the Plank-Based and Liquid Salt-Cooled Advanced High Temperature Reactor

Presented in this dissertation is the investigation and development of an adapted lattice physics-to-core simulator two-step procedure based on the SERPENT 2 and NESTLE neutronics codes for the rapid analysis of the Advanced High Temperature Reactor (AHTR). AHTR specific characteristics, such as its longer neutron diffusion length and double heterogeneity of TRISO fuel particles, were taken into consideration when adapting the traditional Light Water Reactor (LWR) lattice to nodal diffusion procedure to AHTR applications. The coarse energy group structure was re-optimized from the traditional LWR 2-group structure to an alternative 4-group structures to address the AHTR specific flux spectrum and neutronics characteristics. A more accurate treatment of the interface between fuel and reflector was implemented using simplified 1-D models along with the application of an Equivalence Theory based Assembly Discontinuity Factor (ADF) adjustment of the resultant few group constants. A similar ADF adjustment was also applied to treat the insertion of control blades to properly account for inter-assembly leakage. The developed two-step procedure was tested against multiple transport based high fidelity reference benchmark models and was deemed to provide reasonably accurate results, with the exception of some peripheral radial power discrepancies which have been attributed to the inadequacy of the 1-D radial reflector model to capture a 1/3 symmetric and cyclic power tilt unique to the AHTR fuel assembly design and core layout. For 2-D and 3-D full core models, eigenvalue agreement was within 130 pcm and power distribution errors within 3.5% Root Mean Squared (RMS) error. The final implementation of this two-step procedure was used to perform a representative neutronic and thermal hydraulic coupled simulation which demonstrated the ability of the developed procedure to perform 3-D full core neutronics calculations with coupling to thermal hydraulic feedback in an extremely expedient manner. This work paves the way to ultimately performing fuel cycle, core / assembly design, and safety margin assessments for the AHTR. Additionally, this procedure greatly reduces the computational expense of performing such simulations and opens the door toward AHTR design optimization