Sensitivity analysis of a complex, proposed geologic waste disposal system using the Fourier Amplitude Sensitivity Test method

The Fourier Amplitude Sensitivity Test (FAST) method has been used to perform a sensitivity analysis of a computer model developed for conducting total system performance assessment of the proposed high-level nuclear waste repository at Yucca Mountain, Nevada, USA. The computer model has a large number of random input parameters with assigned probability density functions, which may or may not be uniform, for representing data uncertainty. The FAST method, which was previously applied to models with parameters represented by the uniform probability distribution function only, has been modified to be applied to models with nonuniform probability distribution functions. Using an example problem with a small input parameter set, several aspects of the FAST method, such as the effects of integer frequency sets and random phase shifts in the functional transformations, and the number of discrete sampling points (equivalent to the number of model executions) on the ranking of the input parameters have been investigated. Because the number of input parameters of the computer model under investigation is too large to be handled by the FAST method, less important input parameters were first screened out using the Morris method. The FAST method was then used to rank the remaining parameters. The validity of the parameter ranking by the FAST method was verified using the conditional complementary cumulative distribution function (CCDF) of the output. The CCDF results revealed that the introduction of random phase shifts into the functional transformations, proposed by previous investigators to disrupt the repetitiveness of search curves, does not necessarily improve the sensitivity analysis results because it destroys the orthogonality of the trigonometric functions, which is required for Fourier analysis.     

Random balance designs for the estimation of first order global sensitivity indices

We present two methods for the estimation of main effects in global sensitivity analysis. The methods adopt Satterthwaite's application of random balance designs in regression problems, and extend it to sensitivity analysis of model output for non-linear, non-additive models. Finite as well as infinite ranges for model input factors are allowed. The methods are easier to implement than any other method available for global sensitivity analysis, and reduce significantly the computational cost of the analysis. We test their performance on different test cases, including an international benchmark on safety assessment for nuclear waste disposal originally carried out by OECD/NEA.     

A new uncertainty importance measure

Uncertainty in parameters is present in many risk assessment problems and leads to uncertainty in model predictions. In this work, we introduce a global sensitivity indicator which looks at the influence of input uncertainty on the entire output distribution without reference to a specific moment of the output (moment independence) and which can be defined also in the presence of correlations among the parameters. We discuss its mathematical properties and highlight the differences between the present indicator, variance-based uncertainty importance measures and a moment independent sensitivity indicator previously introduced in the literature. Numerical results are discussed with application to the probabilistic risk assessment model on which Iman [A matrix-based approach to uncertainty and sensitivity analysis for fault trees. Risk Anal 1987;7(1):22–33] first introduced uncertainty importance measures.     

Assignment of probability distributions for parameters in the 1996 performance assessment for the Waste Isolation Pilot Plant. Part 1: description of process

A managed process was used to consistently and traceably develop probability distributions for parameters representing epistemic uncertainty in four preliminary and the final 1996 performance assessment (PA) for the Waste Isolation Pilot Plant. Between 67 probability density functions (PDFs) in the 1989 PA and 236 PDFs in the 1996 PA were assigned by a parameter development team, using a process described in a companion paper. In the five iterative PAs conducted, the most commonly used distributions were the uniform PDF and piecewise-uniform PDF (also referred to as a piecewise-linear cumulative distribution function (CDF)). Other distributions used included the truncated normal, truncated Student-t, and triangular PDFs. In a few instances, a discrete delta (piecewise-uniform CDF), beta, and exponential PDF were also used. The PDFs produced for the 24 most important parameters observed in the five iterative PAs are presented. As background, the list of 194 parameters documented in the first 1989 PA through the 1471 parameters documented in the 1996 compliance PA are also provided.     

Summary discussion of the 1996 performance assessment for the Waste Isolation Pilot Plant

The Waste Isolation Pilot Plant (WIPP) is under development by the US Department of Energy (DOE) for the geologic disposal of transuranic waste. The construction of complementary cumulative distribution functions (CCDFs) for total radionuclide release from the WIPP to the accessible environment is described. The resultant CCDFs (i) combine releases due to cuttings and cavings, spallings, direct brine release, and long-term transport in flowing groundwater; (ii) fall substantially to the left of the boundary line specified by the US Environmental Protection Agency's (EPA's) standard 40 CFR 191 for the geologic disposal of radioactive waste; and (iii) constitute an important component of the DOE's successful Compliance Certification Application to the EPA for the WIPP. Insights and perspectives gained in the performance assessment (PA) that led to these CCDFs are described, including the importance of: (i) an iterative approach to PA; (ii) uncertainty and sensitivity analysis; (iii) a clear conceptual model for the analysis; (iv) the separation of stochastic (i.e. aleatory) and subjective (i.e. epistemic) uncertainty; (v) quality assurance procedures; (vi) early involvement of peer reviewers, regulators, and stakeholders; (vii) avoidance of conservative assumptions; and (viii) adequate documentation.     

Seismic PSA method for multiple nuclear power plants in a site

The maximum number of nuclear power plants in a site is eight and about 50% of power plants are built in sites with three or more plants in the world. Such nuclear sites have potential risks of simultaneous multiple plant damages especially at external events. Seismic probabilistic safety assessment method (Level-1 PSA) for multi-unit sites with up to 9 units has been developed. The models include Fault-tree linked Monte Carlo computation, taking into consideration multivariate correlations of components and systems from partial to complete, inside and across units. The models were programmed as a computer program CORAL reef. Sample analysis and sensitivity studies were performed to verify the models and algorithms and to understand some of risk insights and risk metrics, such as site core damage frequency (CDF per site-year) for multiple reactor plants. This study will contribute to realistic state of art seismic PSA, taking consideration of multiple reactor power plants, and to enhancement of seismic safety.     

Implementation and evaluation of nonparametric regression procedures for sensitivity analysis of computationally demanding models

The analysis of many physical and engineering problems involves running complex computational models (simulation models, computer codes). With problems of this type, it is important to understand the relationships between the input variables (whose values are often imprecisely known) and the output. The goal of sensitivity analysis (SA) is to study this relationship and identify the most significant factors or variables affecting the results of the model. In this presentation, an improvement on existing methods for SA of complex computer models is described for use when the model is too computationally expensive for a standard Monte-Carlo analysis. In these situations, a meta-model or surrogate model can be used to estimate the necessary sensitivity index for each input. A sensitivity index is a measure of the variance in the response that is due to the uncertainty in an input. Most existing approaches to this problem either do not work well with a large number of input variables and/or they ignore the error involved in estimating a sensitivity index. Here, a new approach to sensitivity index estimation using meta-models and bootstrap confidence intervals is described that provides solutions to these drawbacks. Further, an efficient yet effective approach to incorporate this methodology into an actual SA is presented. Several simulated and real examples illustrate the utility of this approach. This framework can be extended to uncertainty analysis as well.     

Test case of the long term preliminary performance assessment for the L&IL radioactive waste repository Baita Bihor, Romania

The paper presents the assessment methodology developed in the framework of the long-term preliminary performance assessment of Baita Bihor Romanian national low-level and intermediate-level radioactive waste repository. Conservative assumptions, input parameters and tools used in this approach reflect limitations imposed by the current assessment capability, as well as limited knowledge and understanding of the disposal system. The resultant dose rates are presented and analysed. Conclusions are drawn relating to the safety of the repository.     

A new computational method of a moment-independent uncertainty importance measure

For a risk assessment model, the uncertainty in input parameters is propagated through the model and leads to the uncertainty in the model output. The study of how the uncertainty in the output of a model can be apportioned to the uncertainty in the model inputs is the job of sensitivity analysis. Saltelli [Sensitivity analysis for importance assessment. Risk Analysis 2002;22(3):579-90] pointed out that a good sensitivity indicator should be global, quantitative and model free. Borgonovo [A new uncertainty importance measure. Reliability Engineering and System Safety 2007;92(6):771-84] further extended these three requirements by adding the fourth feature, moment-independence, and proposed a new sensitivity measure, δ_i. It evaluates the influence of the input uncertainty on the entire output distribution without reference to any specific moment of the model output. In this paper, a new computational method of δ_i is proposed. It is conceptually simple and easier to implement. The feasibility of this new method is proved by applying it to two examples.     

Sensitivity of the stochastic response of structures coupled with vibrating barriers

The sensitivity of the stochastic response of linear behaving structures controlled by the novel Vibrating Barrier (ViBa) device is scrutinized. The Vibrating Barrier (ViBa) is a massive structure, hosted in the soil, calibrated for protecting structures by exploiting the structure–soil–structure interaction effect. Therefore the paper addresses the study of the sensitivity of soil–structure coupled systems in which the soil is modelled as a linear elastic medium with hysteretic damping. In order to accomplish efficient sensitivity analyses, a reduced model is determined by means of the Craig–Bampton procedure. Moreover, a lumped parameter model is used for converting the hysteretic damping soil model rigorously valid in the frequency domain to the approximately equivalent viscous damping model in order to perform conventional time-history analysis. The sensitivity is evaluated by determining a semi-analytical method based on the dynamic modification approach for the case of multi-variate stochastic input process. The ground motion is modelled as non-stationary zero-mean Gaussian random process defined by a given evolutionary Power Spectral Density function. The paper presents the sensitivity of the response statistics of a model of an industrial building, passively controlled by the ViBa, to relevant design parameters. Comparisons with pertinent Monte Carlo Simulation will show the effectiveness of the proposed approach.     

Application of sensitivity analysis in extension,inflation, and torsion of residually stressed circular cylindrical tubes

This paper deals with applying two main sensitivity analysis (SA) methods, namely, the Sobol method and the Fourier Amplitude Sensitivity Test (FAST) method on the problem of mixed extension, inflation, and torsion of a circular cylindrical tube in the presence of residual stress. The mechanical side of the problem was previously proposed by Merodio & Ogden (2016). The input parameters in the form of the initial cylinder geometry, the amount of the residual stress, the azimuthal stretch, the axial elongation, and the torsional strain are distributed according to three probability distribution methods, namely the uniform, the gamma, and the normal distribution. In the present work, through applying Sobol and FAST methods, the most influential factors among input parameters on the output variable have been determined. The assessment of our results is then determined by the computation of bias and standard deviation of Sobol and FAST indices for each input parameter in the model.     

Probabilistic dose calculations and sensitivity analyses using analytic models

Newly developed analytic models mimic numerical models for radionuclide transport and dose calculations for a deep repository for spent nuclear fuel, reducing computation times more than three orders of magnitude. In this paper, the analytic models are used to extend preliminary probabilistic dose calculations reported in a recent performance assessment for a deep repository in Sweden. It is demonstrated that the analytic models are useful for gaining insights into the probabilistic properties of the system concerning, e.g. the importance of input variable correlations and various properties of input distributions. Regarding sensitivity analyses, the analytic model is used for screening out nuclides which do not influence the calculation end-point, for demonstrating monotonicity and for developing tailored regression models with non-linear expressions.     

Phase differential angular rate sensor-concept and analysis

This paper proposes and analyzes a new differential phase angular rate (AR) sensor employing a vibrating beam mass structure that traces an elliptical path when subject to rotation due to Coriolis force. Two sensing elements are strategically located to sense a combination of drive and Coriolis vibration to create a phase differential representative of the input rotation rate. A general model is developed, describing the device operation. The main advantages of the phase detection scheme are explored, including removing the need to maintain constant drive amplitude, independence of sensing element gain factor, and advantageous response shapes. A ratio of device parameters is defined and shown to dictate the device response shape. This ratio can be varied to give an optimally linear phase difference output over a set input range, a high sensitivity around zero input rate, or a response shape not seen before, that can give maximum sensitivity around an offset from the zero-rate input. This may be exploited in an array configuration for a highly accurate device over a wide input range. A worked example shows how the developed equations can be used as design tools to achieve a desired response with low sensitivity to variation in device parameters.     

Conversion of a mainframe simulation for maintenance performance to a PC environment

This paper presents a brief review of a mainframe version of a computer code for simulating maintenance crew performance crew and introduces advantages realized with the recent implementation of a personal computer (PC) version. The basic computer model—the maintenance personnel performance simulation (MAPPS)—has been developed and validated by the US nuclear Regulatory Commission (NRC) in order to improve maintenance practices and procedures at nuclear power plants. The simulation model is stochastically based, and users are able to model 2 to 15 person crews. Maintenance crew performance is varied as a function of task, environment, and personnel factors. MAPPS produces human error probabilities (HEPs) suitable for use in probabilistic risk assessments. These HEPs are also a potentially important source of information for risk management data bases such as the NRC sponsored Nuclear Computerized Library for Assessing Reactor Reliability (NUCLARR).     

Response surfaces and sensitivity analyses for an environmental model of dose calculations

A parametric sensitivity analysis is carried out on GASCON, a radiological impact software describing the radionuclides transfer to the man following a chronic gas release of a nuclear facility. An effective dose received by age group can thus be calculated according to a specific radionuclide and to the duration of the release. In this study, we are concerned by 18 output variables, each depending of approximately 50 uncertain input parameters. First, the generation of 1000 Monte-Carlo simulations allows us to calculate correlation coefficients between input parameters and output variables, which give a first overview of important factors. Response surfaces are then constructed in polynomial form, and used to predict system responses at reduced computation time cost; this response surface will be very useful for global sensitivity analysis where thousands of runs are required. Using the response surfaces, we calculate the total sensitivity indices of Sobol by the Monte-Carlo method. We demonstrate the application of this method to one site of study and to one reference group near the nuclear research Center of Cadarache (France), for two radionuclides: iodine 129 and uranium 238. It is thus shown that the most influential parameters are all related to the food chain of the goat's milk, in decreasing order of importance: dose coefficient “effective ingestion”, goat's milk ration of the individuals of the reference group, grass ration of the goat, dry deposition velocity and transfer factor to the goat's milk.     

The development and application of the accident dynamic simulator for dynamic probabilistic risk assessment of nuclear power plants

This paper describes the principal modelling concepts, practical aspects, and an application of the Accident Dynamic Simulator (ADS) developed for full scale dynamic probabilistic risk assessment (DPRA) of nuclear power plants. Full scale refers not only to the size of the models, but also to the number of potential sequences which should be studied. Plant thermal-hydraulics behaviour, safety systems response, and operator interactions are explicitly accounted for as integrated active parts in the development of accident scenarios. ADS uses discrete dynamic event trees (D-DET) as the main accident scenario modelling approach, and introduces computational techniques to minimize the computer memory requirement and expedite the simulation. An operator model (including procedure-based behaviour and several types of omission and commission errors) and a thermal-hydraulic model with a PC run time more than 300 times faster than real accident time are among the main modules of ADS. To demonstrate the capabilities of ADS, a dynamic PRA of the Steam Generator Tube Rupture event of a US nuclear power plant is analyzed.     

Development of the DQFM method to consider the effect of correlation of component failures in seismic PSA of nuclear power plant

This paper presents a new calculation method for considering the effect of correlation of component failures in seismic probabilistic safety assessment (PSA) of nuclear power plants (NPPs) by direct quantification of Fault Tree (FT) using the Monte Carlo simulation (DQFM) and discusses the effect of correlation on core damage frequency (CDF).In the DQFM method, occurrence probability of a top event is calculated as follows: (1) Response and capacity of each component are generated according to their probability distribution. In this step, the response and capacity can be made correlated according to a set of arbitrarily given correlation data. (2) For each component whether the component is failed or not is judged by comparing the response and the capacity. (3) The status of each component, failure or success, is assigned as either TRUE or FALSE in a Truth Table, which represents the logical structure of the FT to judge the occurrence of the top event. After this trial is iterated sufficient times, the occurrence probability of the top event is obtained as the ratio of the occurrence number of the top event to the number of total iterations.The DQFM method has the following features compared with the minimal cut set (MCS) method used in the well known Seismic Safety Margins Research Program (SSMRP). While the MCS method gives the upper bound approximation for occurrence probability of an union of MCSs, the DQFM method gives more exact results than the upper bound approximation. Further, the DQFM method considers the effect of correlation on the union and intersection of component failures while the MCS method considers only the effect on the latter. The importance of these features in seismic PSA of NPPs are demonstrated by an example calculation and a calculation of CDF in a seismic PSA.The effect of correlation on CDF was evaluated by the DQFM method and was compared with that evaluated in the application study of the SSMRP methodology. In the application study, Bohn et al. showed that correlation had a significant effect on CDF and may vary it by up to an order. However, in the results calculated by the DQFM method correlation varied CDF by at most 2 or 3 times compared with CDF for a case where no correlation was assumed. Although some factors should further be examined, this implied that the MCS method may have overestimated the effect of correlation on CDF and the effect of correlation on CDF may not be so significant as that evaluated in the SSMRP.