Browsing by Subject "uncertainty quantification"
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Item Bayesian Estimation of Material Properties in Case of Correlated and Insufficient Data(2013-04-09) Giugno, MatteoIdentification of material properties has been highly discussed in recent times thanks to better technology availability and its application to the field of experimental mechanics. Bayesian approaches as Markov-chain Monte Carlo (MCMC) methods demonstrated to be reliable and suitable tools to process data, describing probability distributions and uncertainty bounds for investigated parameters in absence of explicit inverse analytical expressions. Though it is necessary to repeat experiments multiple times for good estimations, this might be not always feasible due to possible incurring limitations: the thesis addresses the problem of material properties estimation in presence of correlated and insufficient data, resulting in multivariate error modeling and high sample covariance matrix instability. To recover from the lack of information about the true covariance we analyze two different methodologies: first the hierarchical covariance modeling is investigated, then a method based on covariance shrinkage is employed. A numerical study comparing both approaches and employing finite element analysis within MCMC iterations will be presented, showing how the method based on covariance shrinkage is more suitable to post-process data for the range of problems under investigation.Item Continuous Model Updating and Forecasting for a Naturally Fractured Reservoir(2013-07-26) Almohammadi, HishamRecent developments in instrumentation, communication and software have enabled the integration of real-time data into the decision-making process of hydrocarbon production. Applications of real-time data integration in drilling operations and horizontal-well lateral placement are becoming industry common practice. In reservoir management, the use of real-time data has been shown to be advantageous in tasks such as improving smart-well performance and in pressure-maintenance programs. Such capabilities allow for a paradigm change in which reservoir management can be looked at as a strategy that enables a semi-continuous process of model updates and decision optimizations instead of being periodic or reactive. This is referred to as closed-loop reservoir management (CLRM). Due to the complexity of the dynamic physical processes, large sizes, and huge uncertainties associated with reservoir description, continuous model updating is a large-scale problem with a highly dimensional parameter space and high computational costs. The need for an algorithm that is both feasible for practical applications and capable of generating reliable estimates of reservoir uncertainty is a key element in CLRM. This thesis investigates the validity of Markov Chain Monte Carlo (MCMC) sampling used in a Bayesian framework as an uncertainty quantification and model-updating tool suitable for real-time applications. A 3-phase, dual-porosity, dual-permeability reservoir model is used in a synthetic experiment. Continuous probability density functions of cumulative oil production for two cases with different model updating frequencies and reservoir maturity levels are generated and compared to a case with a known geology, i.e., truth case. Results show continuously narrowing ranges for cumulative oil production, with mean values approaching the truth case as model updating advances and the reservoir becomes more mature. To deal with MCMC sampling sensitivity to increasing numbers of observed measurements, as in the case of real-time applications, a new formulation of the likelihood function is proposed. Changing the likelihood function significantly improved chain convergence, chain mixing and forecast uncertainty quantification. Further, methods to validate the sampling quality and to judge the prior model for the MCMC process in real applications are advised.Item Geomechanical Reservoir Model Calibration and Uncertainty Assessment from Microseismic Data(2015-05-04) Tarrahi, MohammadaliHydraulic stimulation of low permeability rocks in unconventional reservoirs has been observed to trigger microearthquakes (MEQs). Triggering of the MEQ events has been linked to the pore pressure, temperature, and in-situ stress variations which result in crack initiation. The resulting clouds of micro-seismic events are believed to carry information about the underlying coupled flow, geomechanics, and thermal processes and hence rock hydraulic and geomechanical property distributions. We develop a probabilistic framework called stochastic seismicity-based reservoir characterization (SSBRC) to integrate microseismic events to infer reservoir property distributions. To model the geothermal reservoir stimulation, a fully coupled thermo-poroelastic finite element method (FEM) model has been developed to handle the coupled process of heat transport, fluid flow, and rock deformation. To simulate the stimulation process, an alternate simplistic approach is also acquired based on a major hypothesis that MEQ events are triggered by an increase in pore pressure. Based on this hypothesis, the distribution of the resulting microseismicity clouds can be viewed as monitoring data that carry important information about the spatial distribution of rock permeability. We apply the ensemble Kalman filter (EnKF) to integrate the resulting continuous seismicity map to estimate hydraulic and geomechanical property distributions. We demonstrate that the standard application of the EnKF with such large correlated datasets can result in substantial loss of ensemble spread. We investigate three alternative implementation methods to mitigate this issue. We first present the methodology proposed for MEQ data integration with the EnKF, followed by a number of examples of applying SSBRC to both forward modeling methods to illustrate the uncertainty underestimation effect when the standard EnKF is applied to large-scale seismicity density map data. We then discuss the proposed methods for improving the uncertainty quantification results and illustrate the effectiveness of these methods by applying them to a number of numerical examples. We also apply and extend the proposed microseismic data integration method to unconventional reservoir with horizontal well and multistage hydraulic fractures to characterize the reservoir and induced fractures. We also investigate the effect of variogram model uncertainty in the EnKF performance and propose a modified EnKF algorithm to handle the uncertainty in variogram parameters. We also develop a computationally efficient data assimilation procedure by employing a pseudo forecast method and geological model clustering method along with EnKF. By a set of numerical experiments, we show how the proposed fast history matching method is successful in preserving the ensemble spread and expediting the integration procedure.Item New Algorithms for Uncertainty Quantification and Nonlinear Estimation of Stochastic Dynamical Systems(2012-10-19) Dutta, ParikshitRecently there has been growing interest to characterize and reduce uncertainty in stochastic dynamical systems. This drive arises out of need to manage uncertainty in complex, high dimensional physical systems. Traditional techniques of uncertainty quantification (UQ) use local linearization of dynamics and assumes Gaussian probability evolution. But several difficulties arise when these UQ models are applied to real world problems, which, generally are nonlinear in nature. Hence, to improve performance, robust algorithms, which can work efficiently in a nonlinear non-Gaussian setting are desired. The main focus of this dissertation is to develop UQ algorithms for nonlinear systems, where uncertainty evolves in a non-Gaussian manner. The algorithms developed are then applied to state estimation of real-world systems. The first part of the dissertation focuses on using polynomial chaos (PC) for uncertainty propagation, and then achieving the estimation task by the use of higher order moment updates and Bayes rule. The second part mainly deals with Frobenius-Perron (FP) operator theory, how it can be used to propagate uncertainty in dynamical systems, and then using it to estimate states by the use of Bayesian update. Finally, a method to represent the process noise in a stochastic dynamical system using a nite term Karhunen-Loeve (KL) expansion is proposed. The uncertainty in the resulting approximated system is propagated using FP operator. The performance of the PC based estimation algorithms were compared with extended Kalman filter (EKF) and unscented Kalman filter (UKF), and the FP operator based techniques were compared with particle filters, when applied to a duffing oscillator system and hypersonic reentry of a vehicle in the atmosphere of Mars. It was found that the accuracy of the PC based estimators is higher than EKF or UKF and the FP operator based estimators were computationally superior to the particle filtering algorithms.Item Physics-based Uncertainty Quantification for ZrHx Thermal Scattering Law(2013-12-06) Zheng, WeixiongThe thermal neutron scattering cross sections of ZrHx are heavily affected by the solid frequency distributions, also called ?phonon spectra?, of Zr and H in ZrHx. The phonon spectra are different for ZrHx with different x. While current reference data files, e.g. ENDF, are based on the spectra of ZrH_(2). This may induce unnegligible errors in the simulations for TRIGA reactor. We, therefore, proposed parameterized phonon spectra that can explore the effects of changing the spectra by varying the parameters. For example, we can shift the phonon positions in the spectra. The ul- timate goal of this type of work is to calibrate appropriate parameter sets to improve the simulation accuracy via comparing the simulation results and experimental data. In this thesis, a code has been developed to process the thermal scattering data for transport codes to use. Inputs of the code are basically the proposed parameters. The accuracy of the code processing Legendre moments of scatteirng was demonstrated. NJOY and MCNP were used to carry out the data processing and neutronic simulations, respectively. The phonon spectra were generated with the parameters produced in Latin Hypercube sampling designs. Quantities, like reactivity (?), fission rate density (FRD), neutron mean generation time (?), fuel temperature feedback coefficient (?Fuel), effective delayed neutron fraction (?eff ) and ex-core detector material absorption rate (Rabs), were analyzed. Analyses indicate that ?, ? and ?Fuel are sensitive to the variations of parameters. Explicit relationships were established for those quantities and the parameters. However, FRD and Rabs is insensitive to any parameters. ?eff are sensitive to the parameterized models, however, no explicit relationship could be built due to the unrecognized nonlinearities. Ongoing work will perform these analyses for the state near critical. Furthermore, time-dependent behavior could be investigated and when combined with experimental data the reasonably accurate phonon spectrum models and therefore S (?, ?) tables for the TRIGA reactor at Texas A&M University would be produced.Item Reduced Order Model and Uncertainty Quantification for Stochastic Porous Media Flows(2012-10-19) Wei, JiaIn this dissertation, we focus on the uncertainty quantification problems where the goal is to sample the porous media properties given integrated responses. We first introduce a reduced order model using the level set method to characterize the channelized features of permeability fields. The sampling process is completed under Bayesian framework. We hence study the regularity of posterior distributions with respect to the prior measures. The stochastic flow equations that contain both spatial and random components must be resolved in order to sample the porous media properties. Some type of upscaling or multiscale technique is needed when solving the flow and transport through heterogeneous porous media. We propose ensemble-level multiscale finite element method and ensemble-level preconditioner technique for solving the stochastic flow equations, when the permeability fields have certain topology features. These methods can be used to accelerate the forward computations in the sampling processes. Additionally, we develop analysis-of-variance-based mixed multiscale finite element method as well as a novel adaptive version. These methods are used to study the forward uncertainty propagation of input random fields. The computational cost is saved since the high dimensional problem is decomposed into lower dimensional problems. We also work on developing efficient advanced Markov Chain Monte Carlo methods. Algorithms are proposed based on the multi-stage Markov Chain Monte Carlo and Stochastic Approximation Monte Carlo methods. The new methods have the ability to search the whole sample space for optimizations. Analysis and detailed numerical results are presented for applications of all the above methods.