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Showing 1 to 20 of 68 for “"polynomial chaos"”.
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A Polynomial Chaos Approach to Control Design
… H2 control concepts and the numerical method of Polynomial Chaos was developed in order to create a novel robust probabilistically optimal control approach. This method was created for the practical reason that uncertainty in parameters tends to be inherent in system models. As such, the …
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Data-Driven Polynomial Chaos Expansions for Uncertainty Quantification
… indices of the output with respect to inputs, polynomial chaos expansions (PCEs) are widely used. However, a majority of existing PCEs impose parametric distributional assumptions on inputs. Furthermore, existing sensitivity indices for dependent inputs impose strong assumptions on the …
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Uncertainty Analysis of Computational Fluid Dynamics Via Polynomial Chaos
… of Intrusive and Non-Intrusive methods using polynomial chaos for uncertainty representation and propagation. In addition, a methodology was developed to address and quantify turbulence model uncertainty. In this methodology, a complex perturbation is applied to the incoming turbulence and …
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Uncertainty Quantification in Earth System Models Using Polynomial Chaos Expansions
… system models to different random sources, using polynomial chaos (PC) approaches. The following earth systems are considered, namely the HYbrid Coordinate Ocean Model (HYCOM, an ocean general circulation model (OGCM)) for the study of ocean circulation in the Gulf of Mexico (GoM); the Unified …
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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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Vehicle Sprung Mass Parameter Estimation Using an Adaptive Polynomial-Chaos Method
The polynomial-chaos expansion (PCE) approach to modeling provides an estimate of the probabilistic response of a dynamic system with uncertainty in the system parameters. A novel adaptive parameter estimation method exploiting the polynomial-chaos representation of a general quarter-car model is …
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Estimation of Uncertain Vehicle Center of Gravity using Polynomial Chaos Expansions
The main goal of this study is the use of polynomial chaos expansion (PCE) to analyze the uncertainty in calculating the lateral and longitudinal center of gravity for a vehicle from static load cell measurements. A secondary goal is to use experimental testing as a source of uncertainty and as a …
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A Polynomial Chaos Approach for Stochastic Modeling of Dynamic Wheel-Rail Friction
… parameters, a stochastic analysis using the polynomial chaos (poly-chaos) theory is performed using the CoF and wheel-rail dynamics models. The wheel-rail system at a right traction wheel is modeled as a mass-spring-damper system to simulate the basic wheel-rail dynamics and the CoF …
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Efficient multidimensional uncertainty quantification of high speed circuits using advanced polynomial chaos approaches
… 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 efficient and/or …
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Treatment of Uncertainties in Vehicle and Terramechanics Systems Using a Polynomial Chaos Approach
… vehicle and terramechanics systems using a polynomial chaos approach. Algorithms which can predict the geometry of the contact patch and the interfacial forces and torques on the vehicle-soil interfaces are developed. All stochastic models and algorithms are simulated for various scenarios …
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Uncertainty analysis in a shipboard integrated power system using multi-element polynomial chaos
… can be efficiently solved by the generalized Polynomial Chaos (gPC) and Probabilistic Collocation Method (PCM).
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Development and Use of a Spatially Accurate Polynomial Chaos Method for Aerospace Applications
… as few solutions as possible. The Non-Intrusive Polynomial Chaos (NIPC) method has grown in popularity in recent decades due to its ability to propagate both aleatory and epistemic parametric sources of uncertainty in a computationally efficient manner. While traditional Monte Carlo methods might …
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Augmented Neural Network Surrogate Models for Polynomial Chaos Expansions and Reduced Order Modeling
… interpretability. The first focuses on mimicking polynomial chaos (PC) modeling techniques, modifying the structure of a NN to produce polynomial approximations of the underlying dynamics. This methodology allows for an extractable meaning from the network and results in improvement in accuracy …
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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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Polynomial Chaos Approaches to Parameter Estimation and Control Design for Mechanical Systems with Uncertain Parameters
… and external excitation uncertainties. The polynomial chaos approach has been shown to be more efficient than Monte Carlo approaches for quantifying the effects of such uncertainties on the system response. This work uses the polynomial chaos framework to develop new methodologies for the …
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Application of the polynomial chaos expansion to multiphase CFD : a study of rising bubbles and slug flow
… 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 are …
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Parametric Yield and Tolerance Optimisation of Electromagnetic Devices using Feature-based Non-Linear Partial Least Squares Polynomial Chaos Expansion Surrogates
… feature based non-linear partial least squares polynomial chaos expansion (NLPLS-PCE). In the proposed method, yield is approximated at the level of the feature points since the functional relationship between the feature points and geometrical parameters is much less nonlinear compared to the …
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Stochastic analyses of mechanical and biomedical structures with uncertainties
… decomposition, random matrix theory and the polynomial chaos expansion method. Hybrid techniques combining finite element analysis and Galerkin projection polynomial chaos expansion with either deterministic or stochastic model order reduction are then developed. For deterministic model order …
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Robust design optimization with dynamic constraints using numerical continuation
… parameter continuation method combined with polynomial chaos expansions is used to locate stationary points. The use of such an expansion provides the benefit of being able to directly drive the mean and variance of a given response function (or an objective function that uses them) during …
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