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

R. Manikantan, Sayan Chakraborty, Thomas K. Uchida and C. P. Vyasarayani
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R. Manikantan: National Aerospace Laboratories, Bangalore 560017, India
Sayan Chakraborty: Department of Electrical Engineering, Indian Institute of Technology Hyderabad, Kandi, Sangareddy 502285, Telangana, India
Thomas K. Uchida: Department of Mechanical Engineering, University of Ottawa, 161 Louis-Pasteur, Ottawa, ON K1N 6N5, Canada
C. P. Vyasarayani: Department of Mechanical and Aerospace Engineering, Indian Institute of Technology Hyderabad, Kandi, Sangareddy 502285, Telangana, India

Mathematics, 2020, vol. 8, issue 7, 1-16

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.

Keywords: engine mount; genetic algorithm; homotopy optimization; magnetorheological damper; modelling; parameter estimation; particle swarm optimization; van der Pol–Duffing oscillator (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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