Development and application of objective uncertainty measures for nuclear power plant transient analysis

For the development, design and licensing of a nuclear power plant (NPP), a sound safety analysis is necessary to study the diverse physical phenomena involved in the system behaviour under a wide range of operational and transient conditions. Such studies are based on detailed computer simulations, backed by appropriate experimental information where available. With the progresses achieved in computer technology and the greater availability of experimental and plant data, the use of so-called best estimate codes for safety evaluations has been gaining increasing acceptance in the nuclear community (i.e. among regulators, policy makers and utilities). These codes predict the physical response of a NPP to a postulated (or real) transient event by using a physically more realistic, and hence less conservative, description of the system. The application of best estimate safety analysis has opened new prospects but also raised new problems that need to be addressed. Thus, it has become more crucial to assess as to how reliable code predictions are, especially when, for example, they need to be compared against safety limits that must not be crossed. It hence becomes necessary to identify and quantify the various possible sources of uncertainty that could affect the reliability of the results. Currently, such uncertainty evaluations are generally based on experts' opinion, although, when data are available, analytical methods based on parametric statistics can also be employed. In the present doctoral research, a novel methodology based on a non-parametric statistical approach has been developed for objective quantification of one of the most demanding contributors to best-estimate code uncertainties, viz. that related to the physical models which the code uses. The basis is an evaluation of the accuracy of a given physical model achieved by comparing its predictions with experimental data from an appropriate set of separate-effect tests. The discrepancies, i.e. the differences between measurements and predictions, can be considered stochastically distributed for several reasons, and thus a statistical approach can be employed. The first step which has been taken is the development of a procedure for investigating the dependence of a given physical model's accuracy on the experimental conditions. Each separate-effect test effectively provides a random sample of discrepancies between measurements and predictions, corresponding to a location in the state space defined by a certain number of independent system variables. As a consequence, the samples of "errors", achieved from analysis of the entire database, are associated to various individual points over the state space. By applying a novel multi-dimensional clustering technique, based on the non-parametric statistical Kruskal-Wallis test, it has been possible to achieve a partitioning of the state space into regions differing in terms of the quality of the physical model's predictions. The second step has been a proper quantification of the model's uncertainty, for each of the identified state space regions, by applying a newly developed, probability density function (pdf) estimator. This is a kernel-type estimator, modeled on a universal orthogonal series estimator, such that its behavior takes advantage of the good features of both estimator types and yields reasonable pdfs, even with samples of small size and not very compact distributions (as is usually the case for experimental assessment studies). The pdfs, estimated in this manner, provide a reliable basis for sampling "error values" for use in Monte-Carlo-type uncertainty propagation studies, aimed at quantifying the impact of the physical model's uncertainty on the code's output variables of interest. The effectiveness of the currently developed methodology has been demonstrated by applying it to the quantification of the uncertainty related to thermal-hydraulic (drift-flux) models implemented in the best-estimate safety analysis code RETRAN-3D. This has been done via the usage of a wide database of void-fraction experiments for saturated and subcooled conditions. Appropriate pdfs were thereby generated for quantification of the physical model's uncertainty in a 2-dimensional (pressure/mass-flux) state space, partitioned into 3 separate regions. The impact of the RETRAN-3D drift-flux model uncertainties has been assessed at three different levels of the code's application, viz. to analysis of (a) Achilles Experiment No. 2, a separate effect experiment not included in the original assessment database, (b) Omega Rod Bundle Test No. 9, an integral experiment simulating a PWR loss-of-coolant accident (LOCA), and (c) the Peach Bottom (BWR) turbine trip test, a NPP (BWR) plant transient in which the void feedback mechanism plays an important role. In all three cases, it has been shown that a more detailed, realistic and accurate representation of output uncertainty can be achieved with the proposed methodology, than is possible based on an "expert-opinion" approach. Moreover, the importance of state space partitioning has been clearly brought out, by comparing results with those obtained assuming a single pdf for the entire database. In the context of the Omega integral test analysis, it has been demonstrated that the impact of the drift-flux model's uncertainty remains important even while introducing other representative uncertainties, viz. those on a set of relevant input parameters. Furthermore, it has been confirmed that the developed methodology well retains its advantageous features during such consideration of different uncertainty sources. The Peach Bottom turbine trip study represents a valuable demonstration of the applicability of the developed methodology to NPP transient analysis. In this specific application, the novel density estimator was also employed for estimating the pdf that underlies the uncertainty in a given output sample of interest (viz. the maximum power during the transient). The results obtained in this context have been found to provide more detailed insights than can be had from the "classical" approach of simply considering tolerance limits, variance values, etc. Another feature of the turbine trip analysis has been a qualitative study of the impact of possible neutronics cross-section uncertainties on the power calculation. It has been clearly shown that, although the uncertainty in void fraction predictions has an important influence on the accuracy of this coupled transient's simulation, uncertainties in neutronics parameters and models can be crucial as well. This has pointed at the need for developing an appropriate methodology for quantifying uncertainties in neutronics calculations, so that these can be aggregated with those assessed for the thermal-hydraulic phenomena during the simulation of such multi-physics transients.


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