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Showing 1 to 20 of 22 for “"polynomial 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
… 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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Computational Methods for Estimating Global Sensitivity Indices and Shapley Values
… Carlo estimators 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 …
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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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Robust optimization techniques and design of Li-ion batteries
… a robust 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 …
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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
… motion. The 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 …
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Uncertainty quantification in the dynamic analysis of offshore structures
… response levels 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 …
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Agent-based models to couple natural and human systems for watershed management analysis
… Hadoop-based 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. …
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Enhancements in Markovian Dynamics
… during the 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 …
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Numerical simulations of die casting with uncertainty quantification and optimization using neural networks
… presented 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 …
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Quantification and propagation of nuclear data uncertainties
… retain the 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 …
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Seismic experimental analyses and surrogate models of multi-component systems in special-risk industrial facilities
… computational 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 …
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Stochastic modeling in computational electromagnetics
… The methodology 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 …
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Scenario-based uncertainty quantification for deep space optical communications
… 100x data rate improvement at the lowest cost. A Polynomial Chaos Expansion (PCE) is used to calculate the mean and variance of the data rate over a target planet’s orbit in approximately 1/2 the time of a Monte Carlo simulation. Results show that optimal designs vary across planet scenarios, with …
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Analysis, Simulation and Control of Peak Pressure Loads on Low-Rise Structures
… of inflow parameters. A non-intrusive polynomial chaos expansion is then applied to determine the sensitivities. The results show that the gust enhances the destabilization of the separation shear layer, forces it to break down and moves it closer to the roof of the prism. As for the …
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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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Metamodel-based inverse uncertainty quantification of nuclear reactor simulators under the Bayesian framework
… 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 can avoid …
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