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Author: Eric Nels Fugleberg Publisher: ISBN: Category : Languages : en Pages : 87
Book Description
Inverse problems and inverse uncertainty quantification (UQ) are challenging issues when dealing with complex and highly non-linear functions. Methods have been developed to decrease the computational burden by using the Gaussian Process (GP) emulator model framework to approximate the input-output relation of a deterministic computer code. The GP emulator can then be used in place of the computer code to perform Bayesian calibration techniques to determine uncertain parameter distribution. The performance of a GP emulator is largely dependent on the quality of the points in its training set; the best emulator exactly replicates the output of the computer code. The uncertain parameter posterior sample space is not known a priori, resulting in GP training sets covering as much of the prior sample space as possible in hopes of covering the posterior space well enough. This work improves the performance of the simple GP emulator using an active learning methodology to select additional training points which cover the posterior sample space of the unknown parameters. Furthermore, the effect of the covariance function on the performance of the GP is investigated with recommendations made for future GP emulator applications.
Author: Eric Nels Fugleberg Publisher: ISBN: Category : Languages : en Pages : 87
Book Description
Inverse problems and inverse uncertainty quantification (UQ) are challenging issues when dealing with complex and highly non-linear functions. Methods have been developed to decrease the computational burden by using the Gaussian Process (GP) emulator model framework to approximate the input-output relation of a deterministic computer code. The GP emulator can then be used in place of the computer code to perform Bayesian calibration techniques to determine uncertain parameter distribution. The performance of a GP emulator is largely dependent on the quality of the points in its training set; the best emulator exactly replicates the output of the computer code. The uncertain parameter posterior sample space is not known a priori, resulting in GP training sets covering as much of the prior sample space as possible in hopes of covering the posterior space well enough. This work improves the performance of the simple GP emulator using an active learning methodology to select additional training points which cover the posterior sample space of the unknown parameters. Furthermore, the effect of the covariance function on the performance of the GP is investigated with recommendations made for future GP emulator applications.
Author: Jan Peter Hessling Publisher: BoD – Books on Demand ISBN: 9535132792 Category : Computers Languages : en Pages : 228
Book Description
Uncertainty quantification may appear daunting for practitioners due to its inherent complexity but can be intriguing and rewarding for anyone with mathematical ambitions and genuine concern for modeling quality. Uncertainty quantification is what remains to be done when too much credibility has been invested in deterministic analyses and unwarranted assumptions. Model calibration describes the inverse operation targeting optimal prediction and refers to inference of best uncertain model estimates from experimental calibration data. The limited applicability of most state-of-the-art approaches to many of the large and complex calculations made today makes uncertainty quantification and model calibration major topics open for debate, with rapidly growing interest from both science and technology, addressing subtle questions such as credible predictions of climate heating.
Author: Emmanuel Boafo Publisher: ISBN: Category : Languages : en Pages : 0
Book Description
There is an increasing interest in computational reactor safety analysis to systematically replace the conservative calculations by best estimate calculations augmented by quantitative uncertainty analysis methods. This has been necessitated by recent regulatory requirements that have permitted the use of such methods in reactor safety analysis. Stochastic uncertainty quantification methods have shown great promise, as they are better suited to capture the complexities in real engineering problems. This study proposes a framework for performing uncertainty quantification based on the stochastic approach, which can be applied to enhance safety analysis. Additionally, risk level has increased with the degradation of Nuclear Power Plant (NPP) equipment and instrumentation. In order to achieve NPP safety, it is important to continuously evaluate risk for all potential hazards and fault propagation scenarios and map protection layers to fault / failure / hazard propagation scenarios to be able to evaluate and verify safety level during NPP operation. In this study, the Fault Semantic Network (FSN) methodology is proposed. This involved the development of static and dynamic fault semantic network (FSN) to model possible fault propagation scenarios and the interrelationships among associated process variables. The proposed method was demonstrated by its application to two selected case studies. The use of FSN is essential for fault detection, understanding fault propagation scenarios and to aid in the prevention of catastrophic events. Two transient scenarios were simulated with a best estimate thermal hydraulic code, CATHENA. Stochastic uncertainty quantification and sensitivity analyses were performed using the OPENCOSSAN software which is based on the Monte Carlo method. The effect of uncertainty in input parameters were investigated by analyzing the probability distribution of output parameters. The first four moments (mean, variance, skewness and kurtosis) of the output parameters were computed and analyzed. The uncertainty in output pressure was 0.61% and 0.57% was found for the mass flow rate in the Edward's blowdown transient. An uncertainty of 0.087% was obtained for output pressure and 0.048% for fuel pin temperature in the RD-14 test case. These results are expected to be useful for providing insight into safety margins related to safety analysis and verification.
Author: Publisher: ISBN: Category : Languages : en Pages : 17
Book Description
System codes for simulation of safety performance of nuclear plants may contain parameters whose values are not known very accurately. New information from tests or operating experience is incorporated into safety codes by a process known as calibration, which reduces uncertainty in the output of the code and thereby improves its support for decision-making. The work reported here implements several improvements on classic calibration techniques afforded by modern analysis techniques. The key innovation has come from development of code surrogate model (or code emulator) construction and prediction algorithms. Use of a fast emulator makes the calibration processes used here with Markov Chain Monte Carlo (MCMC) sampling feasible. This study uses Gaussian Process (GP) based emulators, which have been used previously to emulate computer codes in the nuclear field. The present work describes the formulation of an emulator that incorporates GPs into a factor analysis-type or pattern recognition-type model. This "function factorization" Gaussian Process (FFGP) model allows overcoming limitations present in standard GP emulators, thereby improving both accuracy and speed of the emulator-based calibration process. Calibration of a friction-factor example using a Method of Manufactured Solution is performed to illustrate key properties of the FFGP based process.
Author: Publisher: ISBN: Category : Languages : en Pages :
Book Description
Statistical tools of uncertainty quantification can be used to assess the information content of measured observables with respect to present-day theoretical models, to estimate model errors and thereby improve predictive capability, to extrapolate beyond the regions reached by experiment, and to provide meaningful input to applications and planned measurements. To showcase new opportunities offered by such tools, we make a rigorous analysis of theoretical statistical uncertainties in nuclear density functional theory using Bayesian inference methods. By considering the recent mass measurements from the Canadian Penning Trap at Argonne National Laboratory, we demonstrate how the Bayesian analysis and a direct least-squares optimization, combined with high-performance computing, can be used to assess the information content of the new data with respect to a model based on the Skyrme energy density functional approach. Employing the posterior probability distribution computed with a Gaussian process emulator, we apply the Bayesian framework to propagate theoretical statistical uncertainties in predictions of nuclear masses, two-neutron dripline, and fission barriers. Overall, we find that the new mass measurements do not impose a constraint that is strong enough to lead to significant changes in the model parameters. Furthermore, the example discussed in this study sets the stage for quantifying and maximizing the impact of new measurements with respect to current modeling and guiding future experimental efforts, thus enhancing the experiment-theory cycle in the scientific method.
Author: Jakub Bijak Publisher: Springer Nature ISBN: 303083039X Category : Social Science Languages : en Pages : 277
Book Description
This open access book presents a ground-breaking approach to developing micro-foundations for demography and migration studies. It offers a unique and novel methodology for creating empirically grounded agent-based models of international migration – one of the most uncertain population processes and a top-priority policy area. The book discusses in detail the process of building a simulation model of migration, based on a population of intelligent, cognitive agents, their networks and institutions, all interacting with one another. The proposed model-based approach integrates behavioural and social theory with formal modelling, by embedding the interdisciplinary modelling process within a wider inductive framework based on the Bayesian statistical reasoning. Principles of uncertainty quantification are used to devise innovative computer-based simulations, and to learn about modelling the simulated individuals and the way they make decisions. The identified knowledge gaps are subsequently filled with information from dedicated laboratory experiments on cognitive aspects of human decision-making under uncertainty. In this way, the models are built iteratively, from the bottom up, filling an important epistemological gap in migration studies, and social sciences more broadly.
Author: Eric Nels Fugleberg
Author: Eric Nels Fugleberg
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Author: Jan Peter Hessling
Author: Pradeep Ramuhalli
Author: Emmanuel Boafo
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Author: Roger Ghanem
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Author: Jakub Bijak