شناسایی پارامتر سیستم های چندعضوی بر اساس تجزیه و تحلیل حساسیت درجه دوم

An identification procedure for multibody systems is presented to determine optimal values for unknown or estimated model parameters from experimental test data. Based on a non-linear least-square optimization procedure, the Levenberg–Marquardt trust region method is developed to estimate the unknown parameters, in which the second order sensitivity analysis with the hybrid method is applied to improve the convergence and stability. Finally, numerical examples of slider-crank mechanism validate the accuracy and efficiency of the method presented.

Parameter identification of multibody systems is to determine the geometric parameters and inertia parameters according to observed responses of the system, which can be applied in diagnostic or testing procedures to a given system or building the motion equations of systems via inverse modeling methods. The objective functions are often established through the least-square method and a typical optimization problem including variables depending on parameters must be solved. Many optimization methods for estimating unknown parameters in non-linear dynamical systems have been developed. Schiehlen and Hu [1] use correlation techniques to overcome the disadvantage of the least-square method, which yields often biased estimates. Sujan and Dubowsky [2] present a mutual-information-based observability metric for the online dynamic parameter identification of a multibody system. Grotjahn et al. [3] present an approach for the identification of the dynamics of complex parallel mechanisms, which separates friction and rigid-body dynamics using simple PTP motions. Hardeman et al. [4] describe a finite element based approach for the automatic generation of models suitable for dynamic parameter identification. Bauchau and Wang [5] implement a system identification algorithm, which uniquely combines the methods of minimum realization and subspace identification. Kim et al. [6] identify the parameters of several typical damping models for multibody dynamic simulation. Serban and Freeman [7] use Levenberg–Marquardt methods to solve the non-linear least-squares problem, which need partial derivative computed through sensitivity analysis. But only the first order derivative information is considered in their studies while second order sensitivity analysis of the constrained multibody system model is developed recently [8] and [9]. In this paper, an approach of parameter identification for multibody systems based on second order sensitivity analysis is presented. A Levenberg–Marquardt trust region method is used to estimate the unknown parameters, in which the second order sensitivity analysis is applied to improve the convergence and stability.

Based on second sensitivity analysis, a Levenberg–Marquardt trust region method has been developed for parameter identification of multibody systems. With advantage of no using linear search and faster convergence rate, this method can be used for optimization problems of large scale systems. Numerical results validate the accuracy and efficiency of the method. Nevertheless, as the process of second order sensitivity will take quite some time, the efficiency of optimal methods based on second sensitivity analysis for large scale multibody systems still need further study. The identification procedure after removing noise would be further developed since the effects of observation noise on identification precision.