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research-article

Dual Faceted Linearization of Nonlinear Dynamical Systems Based on Physical Modeling Theory

[+] Author and Article Information
Haruhiko Harry Asada

Fellow, 77 Massachusetts Avenue, MIT Room 3-346, Cambridge MA 02139
asada@mit.edu

Filippos Sotiropoulos

Department of Mechanical Engineering, Massachusetts Institute of Technology
fes@mit.edu

1Corresponding author.

ASME doi:10.1115/1.4041448 History: Received December 24, 2017; Revised August 28, 2018

Abstract

A new approach to modeling and linearization of nonlinear lumped-parameter systems based on physical modeling theory and a data-driven statistical method is presented. A nonlinear dynamical system is represented with two sets of differential equations in an augmented space consisting of independent state variables and auxiliary variables that are nonlinearly related to the state variables. It is shown that the state equation of a nonlinear dynamical system having a Bond Graph model of integral causality is linear, if the space is augmented by using the output variables of all the nonlinear elements as auxiliary variables. The dynamic transition of the auxiliary variables is investigated as the second set of differential equations, which are linearized by using statistical linearization. It is shown that the linear differential equations of the auxiliary variables inform behaviors of the original nonlinear system that the first set of state equations alone cannot represent. The linearization based on the two sets of linear state equations, termed Dual Faceted Linearization (DFL), can capture diverse facets of the nonlinear dynamics and, thereby, provide a richer representation of the nonlinear system. The two state equations are also integrated into a single latent model consisting of all significant modes with no collinearity. Finally, numerical examples verify and demonstrate the effectiveness of the new methodology.

Copyright (c) 2018 by ASME
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