Treating Uncertainties in a Nuclear Seismic Probabilistic Risk Assessment by Means of the Dempster-shafer Theory of Evidence

A Nuclear Power Plant (NPP) Seismic Probabilistic Risk Assessment (SPRA) [1] aims at estimating the probability of occurrence of different sizes of earthquakes that may affect the NPP and assesses the NPP response to such earthquakes. The results of the assessment are presented in terms of seismically induced Core Damage Frequency (CDF) and Large Early Release Frequency (LERF). SPRA is a multi-disciplinary activity combining the inputs and experience of different specialized domain disciplines, such as seismic hazard analysis, seismic fragility evaluation and system analysis, under the normative umbrella of risk analysis. All the analyses carried out in SPRA are affected by uncertainties: in general, these can be categorized as either aleatory or epistemic. Aleatory uncertainty reflects our inability to predict random observable events, whereas epistemic uncertainty represents the analyst lack of knowledge of the values of (constant) parameters (e.g. probabilities, failure rates,...) that are used in the model for a particular SPRA task. These uncertainties have to be represented coherently with the data, information and knowledge available, and propagated onto the risk measures of interest (i.e. CDF and LERF) in order to establish the level of confidence that can be placed in the decisions or conclusions taken, based on the results of the assessment. Then, the aim of analyzing the uncertainties and assessing their impact onto the SPRA results is to provide reasonable assurance that the decisions taken based on such results are robust, and would therefore not warrant reconsideration. In the traditional SPRA practice both types of uncertainty, aleatory and epistemic, are represented by probability distributions. However, the choice of a probability distribution (e.g. lognormal, gamma or beta) for representing epistemic parameter uncertainty due to imprecise and incomplete data is somewhat arbitrary and often made because of conventional reasons and simplifying assumptions [2]. On the other hand, various recent studies [3, 4] have recognized that it may be more appropriate to use a set (i.e. a family) of probability distributions to represent incomplete and imprecise information about a parameter, rather than a unique presumed probabilistic distribution. Such a family can be represented by probability boxes The analyses carried out within the Seismic Probabilistic Risk Assessments (SPRAs) of Nuclear Power Plants (NPPs) are affected by significant aleatory and epistemic uncertainties. These uncertainties have to be represented and quantified coherently with the data, information and knowledge available, to provide reasonable assurance that related decisions can be taken robustly and with confidence. The amount of data, information and knowledge available for seismic risk assessment is typically limited, so that the analysis must strongly rely on expert judgments. In this paper, a Dempster-Shafer Theory (DST) framework for handling uncertainties in NPP SPRAs is proposed and applied to an example case study. The main contributions of this paper are two: (i) applying the complete DST framework to SPRA models, showing how to build the Dempster-Shafer structures of the uncertainty parameters based on industry generic data, and (ii) embedding Bayesian updating based on plant specific data into the framework. The results of the application to a case study show that the approach is feasible and effective in (i) describing and jointly propagating aleatory and epistemic uncertainties in SPRA models and (ii) providing ‘conservative’ bounds on the safety quantities of interest (i.e. Core Damage Frequency, CDF) that reflect the (limited) state of knowledge of the experts about the system of interest.