Communications in Nonlinear Science and Numerical Simulation, Volume 18, Issue 4, April 2013, Pages 1016-1026.
Shahab Torkamani, Eric A. Butcher, Firas A. Khasawneh.
Department of Mechanical and Aerospace Engineering, New Mexico State University, Las Cruces, NM 88003-8001, USA and
Department of Civil and Environmental Science, Duke University, Durham, NC 27708, USA.
In this study, a parameter identification approach for identifying the parameters of a periodic delayed system with distributed delay is introduced based on time series analysis and spectral element analysis. Using this approach the parameters of the distributed delayed system can be identified from the time series of the response of the system. The experimental or numerical data of the response is examined with Floquet theory and time series analysis techniques to estimate a reduced order dynamics, or truncated state space to identify the Floquet multipliers. Parameter identification is then completed using a dynamic map developed for the assumed model of the system which can relate the Floquet multipliers to the unknown parameters in the model. The parameter identification technique is validated numerically for first and second order delay differential equations with distributed delay.
The approach introduced in this paper, is further extended and improved to address engineering applications in the following paper of the same authors:
S. Torkamani and Eric Butcher, “Stochastic parameter estimation in nonlinear time-delayed vibratory systems with distributed delay”, Journal of Sound and Vibration, Volume 332, Issue 14, 8 July 2013, Pages 3404–3418.