Session: MSNDC-04-01

Paper Number: 138811

138811 - A Pdd-Narx Approximation for Uncertainty Quantification in Complex Dynamical Systems 

This paper presents a new mathematical construct, accompanied by robust numerical algorithms, for time-dependent uncertainty quantification (UQ) analysis of high-dimensional, complex dynamical systems subject to random input following an arbitrary probability measure. The proposed effort will involve: (1) a new stochastic adaptation of the Nonlinear Auto Regressive with eXogenous input (NARX) model to accurately capture the underlying dynamical system behavior [1]; (2) novel theoretical developments of the time-dependent polynomial dimensional decomposition (PDD) for UQ analysis [2], establishing the integrated PDD-NARX method; and (3) new formulae or scalable algorithms for estimating the statistical moments and probability density function of a general stochastic dynamic response, followed by error analysis of the PDD-NARX approximation. The PDD-NARX proposed is distinguished from conventional deterministic system identification tools by accounting for uncertainties arising both from the dynamic system properties (e.g., mass, stiffness, damping) and from the external forces (e.g., amplitude and frequency content of excitation time series). The underlying UQ analysis by PDD will challenge or disrupt existing computational thinking, notably, polynomial chaos expansion, stochastic collocation, and sparse-grid quadrature, by addressing highly nonlinear input-output transformations, potentially hundreds of random variables, and arbitrarily large uncertainty of input. Therefore, a long-standing UQ problem associated with the curse of dimensionality will be alleviated to an appreciable magnitude. Numerical results indicate that a low-order PDD-NARX approximation provides computationally efficient and accurate estimates of the probabilistic characteristics of linear and nonlinear dynamical systems subject to uncertainty.

Acknowledgment:
The authors acknowledge financial support by the U.S. Department of Education (Grant No. P116S210005).

References:
[1]   Billings, S. A., Nonlinear System Identification: NARMAX methods in the Time, Frequency, and Spatio-Temporal Domains, John Wiley & Sons, 2013.
[2]   Rahman, S., “A Polynomial Dimensional Decomposition for Stochastic Computing,” International Journal for Numerical Methods in Engineering, Vol. 76, pp. 2091-2116, 2008.

 

 

 

 

 

Presenting Author: Amin Ebadollahi The University of Iowa

Presenting Author Biography: Graduate Research Assistant

Authors:

Amin Ebadollahi The University of Iowa
Sharif Rahman The University of Iowa