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.


Mathematics and Statistics

Research Center/Lab(s)

Center for High Performance Computing Research

Keywords and Phrases

Balanced Truncation; Exponential Stability; Interior Damping; Model Reduction; Wave Equation

International Standard Serial Number (ISSN)

1531-3492; 1553-524X

Document Type

Article - Journal

Document Version


File Type





© 2019 American Institute of Mathematical Sciences (AIMS), All rights reserved.

Publication Date

01 Jan 2019