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Showing 1 to 20 of 27 for “"chaos expansion"”.
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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
… 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 demonstrated in …
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Parametric Yield and Tolerance Optimisation of Electromagnetic Devices using Feature-based Non-Linear Partial Least Squares Polynomial Chaos Expansion Surrogates
… 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 entire …
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Stochastic analyses of mechanical and biomedical structures with uncertainties
… 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 reduction, …
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Computational Methods for Estimating Global Sensitivity Indices and Shapley Values
… based on the truncated sparse polynomial chaos expansion of the function in hand. The control variate estimators are used to estimate the lower and upper Sobol' indices in some applications, and are numerically compared with some of the best Monte Carlo estimators in the literature. The …
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Estimation of Uncertain Vehicle Center of Gravity using Polynomial Chaos Expansions
… 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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Robust optimization techniques and design of Li-ion batteries
… optimization formulation based on polynomial chaos expansion that is applied in the design of the Li-ion battery and a batch crystallization process. The proposed approach yields an analytic expression for the computation of the variance in the optimization objective that is cheap to evaluate …
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A Wiener Chaos Based Approach to Stability Analysis of Stochastic Shear Flows
… and adopt a framework based upon the Wiener Chaos expansion for efficient numerical computations. We explore the stability of stochastic Poiseuille, Couette and Blasius boundary layer type base flows, presenting stochastic results for both the modal and non modal problem, contrasting with the …
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Malliavin Calculus in the Canonical Levy Process: White Noise Theory and Financial Applications.
… is based on the alternative construction of the chaos expansion of square integrable random variable. Then, we showed a Clark-Ocone theorem in L^2(P) and under the change of measure. The result from the Clark-Ocone theorem was used for the mean-variance hedging problem and applied it to …
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On non-stationary Wishart matrices and functional Gaussian approximations in Hilbert spaces
… bounds for approximating sequences with finite chaos expansion. We apply our results to the Brownian approximation of Poisson processes in Besov-Liouville spaces and also derive a functional limit theorem for an edge-counting statistic of a random geometric graph.
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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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Multi-physics and Multilevel Fidelity Modeling and Analysis of Olympic Rowing Boat Dynamics
… sensitivity analysis is based on the polynomial chaos expansion. The coefficients of each random basis in the polynomial chaos expansion are computed using a non-intrusive strategy. Sampling, quadrature, and linear regression methods have been used to obtain the these coefficients from the …
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Uncertainty quantification in the dynamic analysis of offshore structures
… associated with low probability. Polynomial chaos expansion (PCE) is one approach used in developing such surrogate models. However, conventional PCE relies on parametric families to define the polynomials for expansion. Also, for high-dimensional problems, PCE can be inefficient if …
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Agent-based models to couple natural and human systems for watershed management analysis
… Cloud Computing techniques with Polynomial Chaos Expansion (PCE) based variance decomposition approach is developed to conduct global sensitivity analysis with the coupled models, and influential behavioral parameters which are used to simulate agents’ behavior are identified. Being …
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Large Scale Simulation of Spinodal Decomposition
… domain decomposition method, based on the Wiener chaos expansion (WCE) and the Karhunen-Loeve expansion (KLE), is presented. Applying the two expansions to time-space white noise, we transform the CHC equation into a deterministic form. The main advantage of the Wiener chaos approach is that it …
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Enhancements in Markovian Dynamics
… last few decades. Factor analysis, polynomial chaos expansion, principal component analysis, gaussian mixture clustering, vector quantization, and Kalman filter models can all be unified as some variations of unsupervised learning under a single basic linear generative model. Hidden Markov …
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Numerical simulations of die casting with uncertainty quantification and optimization using neural networks
… by coupling surrogate models such as polynomial chaos expansion (PCE) and neural network with OpenCast for uncertainty quantification and optimization. The effects of stochasticity in the alloy composition, boundary and initial conditions on the product quality of die casting are analyzed using …
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Quantification and propagation of nuclear data uncertainties
… PFNS uncertainties. Then, using the polynomial chaos expansion (PCE) on the uncertain output quantities, the stochastic collocation method (SCM) is used to compute the PCE coefficients. Compared to the "brute force" Monte Carlo forward propagation method, the PCE-SCM approach is shown to be …
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Seismic experimental analyses and surrogate models of multi-component systems in special-risk industrial facilities
… burden was alleviated by adopting polynomial chaos expansion (PCE) surrogate models. More precisely, the dimensionality of a seismic input random vector has been reduced by performing the principal component analysis (PCA) on the experimental realizations. Successively, by bootstrapping on the …
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Stochastic modeling in computational electromagnetics
… makes use of the theory of polynomial chaos expansion and the concept of a global impedance/admittance matrix relationship defined over a circular surface enclosing the cross-sectional geometry of the domain of interest to construct a stochastic global impedance/admittance matrix …
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