Uncertainty propagation in puff-based dispersion models using polynomial chaos

A simple three-dimensional Gaussian puff-based dispersion model is designed to study the effect of uncertainties in the model parameters on the solution. A polynomial chaos approach to solve stochastic systems with parametric and initial uncertainties is described. The solution of the dispersion model is investigated numerically using this approach. The polynomial chaos solution is found to be an accurate approximation to ground truth, established by Monte Carlo simulation, while offering an efficient computational approach for large nonlinear systems with a relatively small number of uncertainties.

[1]  W. T. Martin,et al.  The Orthogonal Development of Non-Linear Functionals in Series of Fourier-Hermite Functionals , 1947 .

[2]  Adrian Sandu,et al.  Uncertainty quantification and apportionment in air quality models using the polynomial chaos method , 2009, Environ. Model. Softw..

[3]  B. Goldstein,et al.  Methods for assessing exposure of human and non-human biota , 1991 .

[4]  R. Ghanem,et al.  Stochastic Finite Elements: A Spectral Approach , 1990 .

[5]  F. Owen Hoffman,et al.  An overview of the IAEA Safety Series on procedures for evaluating the reliability of predictions made by environmental transfer models , 1988 .

[6]  K. S. Rao.  Uncertainty Analysis in Atmospheric Dispersion Modeling , 2005 .

[7]  S. Isukapalli.  UNCERTAINTY ANALYSIS OF TRANSPORT-TRANSFORMATION MODELS , 1999 .

[8]  A. Rood,et al.  Stochastic Estimates of Exposure and Cancer Risk from Carbon Tetrachloride Released to the Air from the Rocky Flats Plant , 2001, Risk analysis : an official publication of the Society for Risk Analysis.

[9]  N. Cutland,et al.  On homogeneous chaos , 1991, Mathematical Proceedings of the Cambridge Philosophical Society.

[10]  Adrian Sandu,et al.  Modeling Multibody Systems with Uncertainties. Part I: Theoretical and Computational Aspects , 2006 .

[11]  T. Mikkelsen,et al.  Description of the Atmospheric Dispersion Module RIMPUFF , 1999 .

[12]  L. Morawska,et al.  A review of dispersion modelling and its application to the dispersion of particles : An overview of different dispersion models available , 2006 .

[13]  R. Errico.  What is an adjoint model , 1997 .

[14]  T. Singh,et al.  Uncertainty Propagation for Nonlinear Dynamic Systems Using Gaussian Mixture Models , 2008 .

[15]  Paolo Zannetti,et al.  Air pollution modeling , 1990 .

[16]  H. Najm,et al.  Uncertainty quantification in reacting-flow simulations through non-intrusive spectral projection , 2003 .

[17]  John Red-Horse,et al.  Propagation of probabilistic uncertainty in complex physical systems using a stochastic finite element approach , 1999 .

[18]  Adrian Sandu,et al.  Modeling Multibody Dynamic Systems With Uncertainties . Part I : Theoretical and Computational Aspects , 2004 .

[19]  O. L. Maître,et al.  Uncertainty propagation in CFD using polynomial chaos decomposition , 2006 .

[20]  Dongbin Xiu,et al.  The Wiener-Askey Polynomial Chaos for Stochastic Differential Equations , 2002, SIAM J. Sci. Comput..

[21]  Jon C. Helton,et al.  Survey of sampling-based methods for uncertainty and sensitivity analysis , 2006, Reliab. Eng. Syst. Saf..

[22]  S. Isukapalli,et al.  Stochastic Response Surface Methods (SRSMs) for Uncertainty Propagation: Application to Environmental and Biological Systems , 1998, Risk analysis : an official publication of the Society for Risk Analysis.

[23]  Habib N. Najm,et al.  Uncertainty Quantification and Polynomial Chaos Techniques in Computational Fluid Dynamics , 2009 .