Global ETD Search
Search theses and dissertations gathered from participating repositories worldwide. Every result links back to the library that holds it. No account is needed.
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Showing 1 to 15 of 15 for “"generalized polynomial chaos"”.
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Efficient multidimensional uncertainty quantification of high speed circuits using advanced polynomial chaos approaches
… thesis presents novel approaches based on the generalized polynomial chaos (gPC) theory for the efficient multidimensional uncertainty quantification of general distributed and lumped high-speed circuit networks. The key feature of this work is the development of approaches which are more …
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Uncertainty analysis in a shipboard integrated power system using multi-element polynomial chaos
… these systems can be efficiently solved by the generalized Polynomial Chaos (gPC) and Probabilistic Collocation Method (PCM).
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Terrain and Vehicle-Terrain Sensing and Estimation in Real-Time for Use in Autonomous Vehicles
… the estimation model of interest is the generalized polynomial chaos extended Kalman filter (gPC-EKF). This filter is used to estimate the vehicle and tire slip angles, as well as the yaw rate using a regression model. Project Chrono was used to collect data from a FED Alpha for the …
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Parametric Optimal Design Of Uncertain Dynamical Systems
… unavailable. The computational framework uses Generalized Polynomial Chaos methodology to quantify the effects of various sources of uncertainty found in dynamical systems; a Least-Squares Collocation Method is used to solve the corresponding uncertain differential equations. This technique is …
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Real-Time Ground Vehicle Parameter Estimation and System Identification for Improved Stability Controllers
… This research significantly improves the Generalized Polynomial Chaos Extended Kalman Filter (gPC-EKF) for state-space systems. Here it is also expanded to parameter regression, where it shows excellent capabilities for estimating parameters in linear regression problems. The modeling of …
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Uncertainty Quantification, State and Parameter Estimation in Power Systems Using Polynomial Chaos Based Methods
… Dissertation will mainly focus on developing the polynomial chaos based method to replace the traditional ones. Using it, the uncertainties from the model and the measurement are propagated through the polynomial chaos bases at a set of collocation points. The approximated polynomial chaos …
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Prediction of Laser Ablation In Brain: Sensitivity, Calibration, and Validation
… validation.</p> <p>The sensitivity study is via generalized polynomial chaos (gPC) paired with a transient finite element (FEM) model. Uniform probability distribution functions (PDFs) capture the plausible range of values suggested by the literature for five model parameters. The five PDFs are …
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Robust State Estimation, Uncertainty Quantification, and Uncertainty Reduction with Applications to Wind Estimation
… describes the theory and process for using generalized polynomial chaos (gPC) to re-cast the dynamics of a system with non-deterministic parameters as a deterministic system. The concepts are applied to the problem of wind estimation and characterizing the precision of wind estimates over …
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Model-based robust and stochastic control, and statistical inference for uncertain dynamical systems
… schemes based on a spectral methods known as generalized polynomial chaos that can be used to approximate the propagation of uncertainties through dynamical systems. The proposed analysis and design methods are shown to be computationally efficient and accurate alternatives to sampling-based …
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A reduced-basis method for input-output uncertainty propagation in stochastic PDEs
… media. Monte-Carlo based sampling methods, generalized polynomial chaos and stochastic collocation methods are some of the popular approaches that have been used in the analysis of such problems. This work proposes a non-intrusive reduced-basis method for the rapid and reliable evaluation of …
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Stochastic methods for uncertainty quantification in radiation transport
… of stochastic spectral expansions, specifically generalized polynomial chaos (gPC) and Karhunen-Loeve (KL) expansions, is investigated for uncertainty quantification in radiation transport. The gPC represents second-order random processes in terms of an expansion of orthogonal polynomials of …
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Dynamically orthogonal field equations for stochastic fluid flows and particle dynamics
… (POD) equations and the generalized Polynomial-Chaos (PC) equations; thus the new methodology generalizes these two approaches. For the efficient treatment of the strongly transient character on the systems described above we derive adaptive criteria for the variation of …
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Metamodel-based inverse uncertainty quantification of nuclear reactor simulators under the Bayesian framework
… measurement data. Metamodels constructed with generalized Polynomial Chaos Expansion (PCE), Sparse Gird Stochastic Collocation (SGSC) and GP were applied respectively for these three problems to replace the full models during MCMC sampling. We proposed an improved modular Bayesian approach that …
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Local polynomial chaos expansion method for high dimensional stochastic differential equations
<p>Polynomial chaos expansion is a widely adopted method to determine evolution of uncertainty in dynamical system with probabilistic uncertainties in parameters. In particular, we focus on linear stochastic problems with high dimensional random inputs. Most of the existing methods enjoyed the …
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Application of the polynomial chaos expansion to multiphase CFD : a study of rising bubbles and slug flow
… simulation can be run). Chapter 2 introduces the generalized Polynomial Chaos (gPC) expansion, which has shown promise for reducing the computational cost of performing UQ for a large class of problems, including heat transfer and single phase, incompressible flow simulations; example applications …