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Showing 1 to 14 of 14 for “"Polynomial chaos expansions"”.
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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 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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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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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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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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Accelerated Bayesian experimental design for chemical kinetic models
… is computationally intensive. Instead, polynomial chaos expansions are introduced to capture the dependence of observables on model parameters and on design conditions. Under suitable regularity conditions, these expansions converge exponentially fast. Since both the parameter space and …
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Multiple objective resource allocation in product and process development
… methods. The enabling technology is the use of polynomial chaos expansions to represent process and decisions models. A compact representation of uncertainty permits a rapid evaluation of expected values and variances in the decision models. In typical applications the computational burden was …
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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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Parametric uncertainty analysis for complex engineering systems
… equivalent modeling method (DEMM), which applies polynomial chaos expansions and the probabilistic collocation approach to transform the stochastic model into a deterministic equivalent model. By transforming the model the task of determining the probability density function of the model response …
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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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Bayesian design of experiments for complex chemical systems
… including Markov Chain Monte Carlo, Polynomial Chaos Expansions, and a prior sampling formulation for computing utility functions, such simplifications are no longer necessary. In this work, these methods have been integrated into the decision theory framework to allow the application …
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Automatic reaction mechanism generation :
… to efficiently compute and construct polynomial chaos expansions (PCE) to approximate the dependence of outputs on a subset of uncertain inputs. Both local and global methods provide similar qualitative insights towards identifying the most influential input parameters in a model. The …
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A multiscale approach to state estimation with applications in process operability analysis and model predictive control
… the moments of the measurement and model errors, polynomial chaos expansions, and an approximation using Gaussian quadrature and Monte Carlo simulation. A sample of smaller case studies shows the range of uses of the algorithm. Three larger case studies demonstrate the multiscale state estimator …
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Stochastic numerical approximation approaches for estimation of traffic volume under travel demand uncertainties
The traditional deterministic process of trip assignment does not account for uncertainties in traffic demands. These point-estimate based solutions often results in large differences between forecasted and actual traffic volumes thereby imposing huge financial burdens upon development agencies. In …