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Information Theoretic Tools for Parameter Estimation and Model Order Reduction for Mechanical Systems

[+] Author Affiliations
Jared D. Elinger, Jonathan D. Rogers

Georgia Institute of Technology, Atlanta, GA

Paper No. IMECE2017-70744, pp. V04AT05A031; 9 pages
doi:10.1115/IMECE2017-70744
From:
  • ASME 2017 International Mechanical Engineering Congress and Exposition
  • Volume 4A: Dynamics, Vibration, and Control
  • Tampa, Florida, USA, November 3–9, 2017
  • Conference Sponsors: ASME
  • ISBN: 978-0-7918-5837-0
  • Copyright © 2017 by ASME

abstract

Parameter estimation and model order reduction (MOR) are important techniques used in the development of mechanical system models. A variety of classical parameter estimation and MOR methods are available for nonlinear systems but performance generally suffers when little is known about the system model a priori. Recent advancements in information theory have yielded a quantity called causation entropy, which is a measure of the influence between multivariate time series. In parameter estimation problems involving dynamic systems, causation entropy can be used to identify which functions in a discrete-time model are important in driving the subsequent state values. This paper extends on previous works’ use of a Causation Entropy Matrix to nonlinear systems modeled from the real world. This work explores the conversion of continuous systems to a discrete model and applies the causation entropy matrix to the system. Results show that model structure can be estimated by the causation entropy matrix. This work extends the previous work by showing that the method can be applied to general nonlinear systems. Previously shown examples were toy, additively separable nonlinear problems. This work shows that the methodology can be extended to any nonlinear system, including time varying systems, which provides a framework to examine parameter estimation for general nonlinear systems.

Copyright © 2017 by ASME

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