This master thesis examines the possibility of performing asimplified uncertainty analysis on a probabilistic safety assessment(PSA) of the Oskarshamn 3 nuclear power plant. The aim of the thesiswas divided in two parts, first to examine the uncertainty parametersof a PSA-model for Oskarshamn 3 and the second part was to developand examine a simplified method of uncertainty analysis as comparedto a more regular method of Monte Carlo-simulation. The thesis ismostly concerned with examining the core damage frequency. Theexamination of uncertainty parameters showed that many parameterswere missing from the model and thus further investigation areneeded, if a full Monte Carlo is to be performed. The simplifiedmethod for uncertainty analysis that was developed consisted ofassuming a lognormal distribution for the frequency of basic eventsand then using the minimal cutset-list to calculate an approximationto the end distribution. The simplified method was then compared tothe Monte Carlo-analysis for Oskarshamn 2 for different MCS-lists anda preliminary uncertainty analysis was performed for Oskarshamn 3.

The field of modal testing and analysis is currently facing a surge of interest in error modelling. Several errors which occur during testing campaigns are modelled analytically or numerically and propagated to various system coupling and interface reduction routines effectively. This study aims to propagate human errors, like position measurement errors and orientation measurement errors, and random noise-based errors in the measured Frequency Response Functions(FRFs) to the interface reduction algorithm called Virtual Point Transformation(VPT) and later to a substructure coupling method called Frequency-Based Substructuring(FBS). These methods form the cornerstone for Transfer Path Analsysis (TPA). Furthermore, common sources of error like sensor mass loading effect and sensor misalignment have also been investigated. Lastly, a new method to calculate the sensor positions and orientations after a measurement has been devised based on rigid body properties of the system and from the applied force characteristics. The error propagation was performed using a computationally efficient, moment method of the first order and later validated using Monte-Carlo simulations. The results show that the orientation measurement error is the most significant followed by FRF error and position measurement error. The mass loading effect is compensated using the Structural Modification Using Response Functions (SMURF) method and the sensor misalignment is corrected using coordinate transformation. The sensor positions and orientations are accurately estimated from rigid body properties and applied force characteristics; individually using matrix algebra and simultaneously using an optimization-based non-linear least squares solver. / För närvarande ser vi ett ökat intresse för felmodellering inom området modal provning och analys. Flera fel som uppstår under testserier modelleras analytiskt eller numeriskt och propageras effektivt till olika systemkopplings- och gränssnittsreduktionsrutiner. Denna studie syftar till att hantera mänskliga fel, som positionsmätningsfel och orienteringsmätfel, och slumpmässiga brusbaserade fel i de uppmätta frekvensresponsfunktionerna (FRF) till den gränssnittsreduktionsalgoritm, som kallas ”Virtual Point Transformation” (VPT), och senare till en substrukturskopplingsmetod, som kallas FBS (Frequency-Based Substructuring). Dessa metoder utgör hörnstenen för ”Transfer Path Analsysis” (TPA). Dessutom har vanliga felkällor som sensormassbelastningseffekter och felorientering av sensorer undersökts. Slutligen har en ny metod för att beräkna sensorns positioner och riktningar, efter att mätning gjorts, baserat på systemets stelkroppsegenskaper och de applicerade krafterna. Felpropageringen estimerades med en beräkningseffektiv, momentmetod av första ordningen och validerades senare med Monte-Carlo-simuleringar. Resultaten visar att orienteringsmätfelet är den mest signifikanta felkällan följt av FRF-fel och positionsmätningsfel. Massbelastningseffekten kompenseras med hjälp av ”Structural Modification Using Response Functions” (SMURF) -metoden och sensorjusteringen korrigeras med hjälp av koordinatomvandling. Sensorpositionerna och positioner och orientering beräknas exakt från stelkroppsegenskaperna och de applicerade krafterna; individuellt med matrisalgebra och samtidigt med en optimeringsbaserad icke-linjär minsta kvadratlösare.

Knowing the uncertainty of a calculated result is always important, but especially so when performing calculations for safety analysis. A traditional way of propagating the uncertainty of input parameters is Monte Carlo (MC) methods. A quicker alternative to MC, especially useful when computations are heavy, is Deterministic Sampling (DS). DS works by hand-picking a small set of samples, rather than randomizing a large set as in MC methods. The samples and its corresponding weights are chosen to represent the uncertainty one wants to propagate by encoding the first few statistical moments of the parameters' distributions. Finding a suitable ensemble for DS in not easy, however. Given a large enough set of samples, one can always calculate weights to encode the first couple of moments, but there is good reason to want an ensemble with only positive weights. How to choose the ensemble for DS so that all weights are positive is the problem investigated in this project. Several methods for generating such ensembles have been derived, and an algorithm for calculating weights while forcing them to be positive has been found. The methods and generated ensembles have been tested for use in uncertainty propagation in many different cases and the ensemble sizes have been compared. In general, encoding two or four moments in an ensemble seems to be enough to get a good result for the propagated mean value and standard deviation. Regarding size, the most favorable case is when the parameters are independent and have symmetrical distributions. In short, DS can work as a quicker alternative to MC methods in uncertainty propagation as well as in other applications.