Balanced Truncation Model Reduction of a Nonlinear Cable-Mass PDE System with Interior Damping
We consider model order reduction of a nonlinear cable-mass system modeled by a 1D wave equation with interior damping and dynamic boundary conditions. The system is driven by a time dependent forcing input to a linear mass-spring system at one boundary. The goal of the model reduction is to produce a low order model that produces an accurate approximation to the displacement and velocity of the mass in the nonlinear mass-spring system at the opposite boundary. We first prove that the linearized and nonlinear unforced systems are well-posed and exponentially stable under certain conditions on the damping parameters, and then consider a balanced truncation method to generate the reduced order model (ROM) of the nonlinear input-output system. Little is known about model reduction of nonlinear input-output systems, and so we present detailed numerical experiments concerning the performance of the nonlinear ROM. We find that the ROM is accurate for many different combinations of model parameters.
B. A. Batten et al., "Balanced Truncation Model Reduction of a Nonlinear Cable-Mass PDE System with Interior Damping," Discrete and Continuous Dynamical Systems - Series B, vol. 24, no. 1, pp. 83-107, American Institute of Mathematical Sciences, Jan 2019.
The definitive version is available at https://doi.org/10.3934/dcdsb.2018162
Mathematics and Statistics
Center for High Performance Computing Research
Keywords and Phrases
Balanced Truncation; Exponential Stability; Interior Damping; Model Reduction; Wave Equation
International Standard Serial Number (ISSN)
Article - Journal
© 2019 American Institute of Mathematical Sciences, All rights reserved.
01 Jan 2019