مقایسه روش های تجزیه و تحلیل حساسیت جهانی و اقدامات مهم در PSA

This paper discusses application and results of global sensitivity analysis techniques to probabilistic safety assessment (PSA) models, and their comparison to importance measures. This comparison allows one to understand whether PSA elements that are important to the risk, as revealed by importance measures, are also important contributors to the model uncertainty, as revealed by global sensitivity analysis. We show that, due to epistemic dependence, uncertainty and global sensitivity analysis of PSA models must be performed at the parameter level. A difficulty arises, since standard codes produce the calculations at the basic event level. We discuss both the indirect comparison through importance measures computed for basic events, and the direct comparison performed using the differential importance measure and the Fussell–Vesely importance at the parameter level. Results are discussed for the large LLOCA sequence of the advanced test reactor PSA.

Probabilistic safety assessment (PSA) is a methodology that produces numerical estimates for a number of risk metrics for complex technological systems. The core damage frequency (CDF) and the large early release frequency (LERF) are the common risk metrics of interest in nuclear power plants (NPP). The generic risk metric can be written as a function of the frequencies of the initiating events, i.e. events that disturb the normal operation of the facility such as a power excursion and the conditional probabilities of the failure modes of structures, systems and components (SSCs) equation(1) where i=1,…,Z, is the set of the frequencies of initiating events with Z the total number of initiating events included in the PSA model and j=1,…,N, is the set of the basic event probabilities, with N, the total number of basic events in the PSA. More synthetically, qj=p(BEj), j=1,…,N. Once the logical expression of the minimal cut sets is expanded and the rare event approximation is considered, R is linear in and [4]. Since Eq. (1) relates the risk metric to the basic events, we refer to Eq. (1) as the basic event representation or basic event level of the PSA model. A ‘point estimate’ of the risk metric R can be produced by Eq. (1) using point (‘best estimate’) values of the inputs ( and in this case). We write equation(2) where we have introduced the symbol to denote the generic qj or fij=1,2,…,N, i=1,2,…,Z). One refers to R0 as to the nominal value or the risk metric, or, shortly, the nominal risk. The risk metric is often expressed as a function of more fundamental parameters. For example, the failure time of a component is usually assumed to follow an exponential distribution with a failure rate λ. In the case the component is renewed every τ units of time, then, its average (over time) unavailability is [2]: equation(3) However, more rigorously, we acknowledge that these inputs are uncertain and express this uncertainty using state-of-knowledge or epistemic probability distributions (Kaplan and Garrick, 1981) [1], [12], [13], [14], [15] and [17]. The propagation of these distributions produces the epistemic distribution of R. Epistemic or state of knowledge dependencies and conditional dependencies are not captured by the basic event expression of R. Eq. (1) needs to be replaced by its parametric representation, if we want to take them into account [4]. We denote the expression of the risk metric as a function of the PSA model parameters as: equation(4) The importance of a PSA element with respect to the risk is found applying PSA importance measures. Importance measures traditionally used are the Fussell–Vesely (FV), risk achievement worth (RAW) [8] and [26] These measures show shortcomings when applied to set of basic events ( Eq. (1)). Furthermore, RAW cannot be used to compute the importance of parameters ( Eq. (4)) [4]. The differential importance measure (DIM) proposed recently by Borgonovo and Apostolakis [4] remedies this situation. In addition, DIM is defined for both and , providing measures of the risk-significance of both basic events and parameters ( Section 2). PSA importance measures (FV, RAW and DIM) are local measures, i.e. they deal with a point value of R and of the parameters. However, to assess the relevance of a parameter with respect to the model uncertainty, the entire epistemic uncertainty in R and in the parameters should be taken into account. Global sensitivity analysis (GSA) techniques are the appropriate techniques for this task [21]. We have investigated several GSA techniques in this work. In this paper we focus on the results and performance of global sensitivity indices computed via extended fourier amplitude sensitivity test (FAST) [12], [22] and [24]. We show that, due to epistemic dependencies, the appropriate level to perform GSA is the parameter level of the PSA model. Thus, the comparison of importance measures and GSA technique results is not direct, since importance measures are produced at the basic event level by most standard PSA software tools, while GSA techniques are computed at the parameter level. We propose both an indirect approach for the comparison of FV and RAW results at the basic event level to GSA results, and a direct comparison that makes use of DIM and FV at the parameter level as measures of risk. We provide quantitative results through the use of the large loss of coolant accident (LLOCA) PSA model of the advanced test reactor (ATR) [10]. In Section 2, we present DIM, FV, and RAW and discuss their properties. In Section 3, we introduce variance-based techniques and the definition of model coefficient of determination. In Section 4, we discuss dependencies caused by epistemic uncertainty. In Section 5, we present the application and results of GSA and importance measures, and their comparison for the large LLOCA sequence of the ATR PSA model. In Section 6 a number of conclusions is offered.

We have discussed the application and results of GSA techniques to PSA models, focusing on variance-based techniques, computed through extended FAST. We have seen that the presence of epistemic uncertainty makes it necessary to perform GSA at the parameter level of the model. Application and results of the extended FAST technique for the computation of the first and total order sensitivity indices for the parameters of the reference model have been discussed. We have computed the reduction in the risk metric variance that we obtain if the parameters ranked in the first 10 positions by first order global sensitivity indices were known with certainty. We have seen that we would be able to reduce VR by two order of magnitudes. We have analyzed how uncertainty is partitioned between the two safety systems. We have found that parameters of the FIS are responsible for most of the uncertainty. We have seen that, to understand whether uncertainty drivers are also associated to risk significant element, we must compare GSA results to importance measure results. Since R is computed at the basic event level, and FV and RAW are produced for basic events by standard software codes [6] and [4], a direct comparison of importance measure and GSA results is not possible. Thus, the results of such a comparison are to be considered qualitative. However, using DIM and FV at the parameter level the comparison is direct and quantitative results can be obtained. The comparison of risk contributors and uncertainty drivers at the basic event level for model at hand has produced an intermediate value of the correlation coefficient, indicating that uncertainty drivers are not necessarily risk significant contributors. However, LLOCA, the initiating event, is ranked first by all the measures. This means that getting information to reduce the uncertainty in the initiating event frequency (LLOCA), would allow a reduction in the uncertainty of an important risk contributors, while effectively reducing our uncertainty in the CDFLLOCA. At the parameter level, we have obtained again an intermediate correlation for the rankings obtained with FV(xj) and DIM (xj) and those obtained with extended FAST. This means that parameters that are important to risk are not necessarily uncertainty drivers. The most important parameter according to this analysis at the basic event level and confirms that this parameter is the most significant in both the model uncertainty and determination of the risk. The analyst can then utilize this information to allocate resources and prioritize information and data collection for the model. In this respect, GSA techniques provide useful analytical capabilities that respond to the need of improving uncertainty analysis of PSA models.