Parameter Identification in Nonlinear Mechanical Systems with Noisy Partial State Measurement Using PID-Controller Penalty Functions

Manikantan, R. and Chakraborty, Sayan and Uchida, Thomas K. and Vyasarayani, C. P. (2020) Parameter Identification in Nonlinear Mechanical Systems with Noisy Partial State Measurement Using PID-Controller Penalty Functions. Mathematics, 8 (7). p. 1084. ISSN 2227-7390

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Abstract

Dynamic models of physical systems often contain parameters that must be estimated from experimental data. In this work, we consider the identification of parameters in nonlinear mechanical systems given noisy measurements of only some states. The resulting nonlinear optimization problem can be solved efficiently with a gradient-based optimizer, but convergence to a local optimum rather than the global optimum is common. We augment the dynamic equations with a morphing parameter and a proportional-integral-derivative (PID) controller to transform the objective function into a convex function; the global optimum can then be found using a gradient-based optimizer. The morphing parameter is used to gradually remove the PID controller in a sequence of steps, ultimately returning the model to its original form. An optimization problem is solved at each step, using the solution from the previous step as the initial guess. This strategy enables use of a gradient-based optimizer while avoiding convergence to a local optimum. The efficacy of the proposed approach is demonstrated by identifying parameters in the van der Pol-Duffing oscillator, a hydraulic engine mount system, and a magnetorheological damper system. Our method outperforms genetic algorithm and particle swarm optimization strategies, and demonstrates robustness to measurement noise.

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IITH Creators:

IITH Creators	ORCiD
Vyasarayani, Chandrika Prakash	http://orcid.org/0000-0002-3396-0484

Item Type:

Article

Uncontrolled Keywords:

Engine mount; Genetic algorithm; Homotopy optimization; Magnetorheological damper; Modelling; Parameter estimation; Particle swarm optimization; Van der pol-duffing oscillator

Subjects:

Physics > Mechanical and aerospace
Physics

Divisions:

Department of Mechanical & Aerospace Engineering

Depositing User:

. LibTrainee 2021

Date Deposited:

28 Jun 2021 07:20

Last Modified:

04 Mar 2022 05:08

URI:

http://raiithold.iith.ac.in/id/eprint/8024