Browsing by Subject "Sensitivity Analysis"
Now showing 1 - 3 of 3
Results Per Page
Sort Options
Item Adjoint-Based Uncertainty Quantification and Sensitivity Analysis for Reactor Depletion Calculations(2013-08-02) Stripling, Hayes FranklinDepletion calculations for nuclear reactors model the dynamic coupling between the material composition and neutron flux and help predict reactor performance and safety characteristics. In order to be trusted as reliable predictive tools and inputs to licensing and operational decisions, the simulations must include an accurate and holistic quantification of errors and uncertainties in its outputs. Uncertainty quantification is a formidable challenge in large, realistic reactor models because of the large number of unknowns and myriad sources of uncertainty and error. We present a framework for performing efficient uncertainty quantification in depletion problems using an adjoint approach, with emphasis on high-fidelity calculations using advanced massively parallel computing architectures. This approach calls for a solution to two systems of equations: (a) the forward, engineering system that models the reactor, and (b) the adjoint system, which is mathematically related to but different from the forward system. We use the solutions of these systems to produce sensitivity and error estimates at a cost that does not grow rapidly with the number of uncertain inputs. We present the framework in a general fashion and apply it to both the source-driven and k-eigenvalue forms of the depletion equations. We describe the implementation and verification of solvers for the forward and ad- joint equations in the PDT code, and we test the algorithms on realistic reactor analysis problems. We demonstrate a new approach for reducing the memory and I/O demands on the host machine, which can be overwhelming for typical adjoint algorithms. Our conclusion is that adjoint depletion calculations using full transport solutions are not only computationally tractable, they are the most attractive option for performing uncertainty quantification on high-fidelity reactor analysis problems.Item Quantification of Uncertainties Due to Opacities in a Laser-Driven Radiative-Shock Problem(2013-03-28) Hetzler, Adam CThis research presents new physics-based methods to estimate predictive uncertainty stemming from uncertainty in the material opacities in radiative transfer computations of key quantities of interest (QOIs). New methods are needed because it is infeasible to apply standard uncertainty-propagation techniques to the O(105) uncertain opacities in a realistic simulation. The new approach toward uncertainty quantification applies the uncertainty analysis to the physical parameters in the underlying model used to calculate the opacities. This set of uncertain parameters is much smaller (O(102)) than the number of opacities. To further reduce the dimension of the set of parameters to be rigorously explored, we use additional screening applied at two different levels of the calculational hierarchy: first, physics-based screening eliminates the physical parameters that are unimportant from underlying physics models a priori; then, sensitivity analysis in simplified versions of the complex problem of interest screens out parameters that are not important to the QOIs. We employ a Bayesian Multivariate Adaptive Regression Spline (BMARS) emulator for this sensitivity analysis. The high dimension of the input space and large number of samples test the efficacy of these methods on larger problems. Ultimately, we want to perform uncertainty quantification on the large, complex problem with the reduced set of parameters. Results of this research demonstrate that the QOIs for target problems agree at for different parameter screening criteria and varying sample sizes. Since the QOIs agree, we have gained confidence in our results using the multiple screening criteria and sample sizes.Item Quantitative Modeling and Estimation in Systems Biology using Fluorescent Reporter Systems(2013-12-10) Bansal, LoveleenaBuilding quantitative models of biological systems is a challenging task as these models can consist of a very large number of components with complex interactions between them and the experimental data available for model validation is often sparse and noisy. The focus in this work is on modeling and parameter estimation of biological systems that are monitored using fluorescent reporter systems. Fluorescent reporter systems are widely used for various applications such as monitoring gene expression, protein localization and protein-protein interactions. This dissertation presents various techniques to facilitate modeling of biological systems containing fluorescent reporters with special attention given to challenges arising due to limited experimental data, simultaneous monitoring of multiple events and variability in the observed response due to phenotypic differences. First, an inverse problem is formulated to estimate the dynamics of transcription factors, a crucial molecule that initiates the transcription process, using data of fluorescence intensity profiles obtained from a fluorescent reporter system. The resulting inverse problem is ill-conditioned and it is solved with the aid of regularization techniques. The main contribution is that, with the presented technique, any complex dynamics of transcription factors can be estimated using limited data of fluorescence measurements. The technique has been evaluated using simulated data as well as experimental data of a GFP reporter system of STAT3. Second, an experimental design formulation is developed to facilitate the use of multiple fluorescent reporters, with overlapping emission spectra, in the same experiment. This work develops a criterion to select the fluorescent proteins for simultaneous use such that the accuracy in the estimated contributions of individual proteins to the overall observed intensity is maximized. This technique has been validated using mixtures of different E. coli strains which express different fluorescent proteins. Finally, a population balance model of a cell population containing a fluorescence reporter system is developed to describe the variability in the observed fluorescence in cells. Factors such as rate of fluorescent protein formation as well as partitioning of the fluorescent protein on cell division have been taken into account to describe the dynamics of fluorescence intensity distributions in the cell populations. The model has been used to obtain preliminary hypotheses to explain the difference in response of HeLa cells containing the Tet-on expression system on stimulation by different levels doxycycline. Thus, this work describes techniques for building robust predictive models of biological systems such as regularization for solving ill-posed estimation problems, experimental design techniques as well as using population balance modeling to model complex multi-scale dynamics. Moreover, while the examples discussed here are motivated for fluorescent reporter systems, the developed techniques can be used for different kinds of linear or non-linear dynamic biological systems.