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Modeling and Simulation of Stochastic Lorenz Systems by Polynomial Chaos Approach

[+] Author Affiliations
Lin Li, Corina Sandu

Virginia Polytechnic Institute and State University, Blacksburg, VA

Paper No. DETC2007-34604, pp. 917-924; 8 pages
doi:10.1115/DETC2007-34604
From:
  • ASME 2007 International Design Engineering Technical Conferences and Computers and Information in Engineering Conference
  • Volume 5: 6th International Conference on Multibody Systems, Nonlinear Dynamics, and Control, Parts A, B, and C
  • Las Vegas, Nevada, USA, September 4–7, 2007
  • Conference Sponsors: Design Engineering Division and Computers and Information in Engineering Division
  • ISBN: 0-7918-4806-X | eISBN: 0-7918-3806-4
  • Copyright © 2007 by ASME

abstract

The Lorenz problem is one of the paradigms of the chaotic systems, which are sensitive to initial conditions and for which the performance is hard to predict. However, in many cases and dynamic systems, the initial conditions of a dynamic system and the system parameters can’t be measured accurately, and the response of the system must indeed be explored in advance. In this study, the polynomial chaos approach is used to handle uncertain initial conditions and system parameters of the Lorenz system. The method has been successfully applied by the authors and co-workers in multi-body dynamics and terrain profile and soil modeling. Other published studies illustrate the benefits of using the polynomial chaos, especially for problems involving large uncertainties and highly nonlinear problems in fluid mechanics, structural vibrations, and air quality studies. This study is an attempt to use the polynomial chaos approach to treat the Lorenz problem, and the results are compared with a classical Monte Carlo approach. Error bars are used to illustrate the standard deviation of the system response. Different meshing schemes are simulated, and the convergence of the method is analyzed.

Copyright © 2007 by ASME

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