Online State and Parameter Estimation of a Nonlinear Gear Transmission System

This study aims at modeling the nonlinear dynamic response of a gear transmission system, based on substructuring techniques. More specifically, a finite element (FE) model is introduced for the housing of the gearbox, while the essential effects of the gear-pair, the bearings and the shafts are described by a lumped parameter model. The latter is characterized by strongly nonlinear characteristics that account for gear backlash, meshing stiffness, transmission error properties and bearing stiffness nonlinearities. Accordingly, a joint state and parameter estimation (JS&PE) problem is formulated on the basis of the lumped model. The proposed framework uses vibration acceleration measurements from sensors attached on the housing and, through their propagation to the lumped nonlinear model via the FE substructure, an Unscented Kalman Filter (UKF) is activated for the solution of the JS&PE problem. In contrast to other alternatives (e.g., the Extended Kalman Filter), the UKF features a number of advantages in treating nonlinear systems, including a derivative free calculation and a capacity for higher order nonlinearities. The method’s performance is examined using both numerical simulations and experimental tests.

[1]  Alberto Corigliano,et al.  Impact induced composite delamination: state and parameter identification via joint and dual extended Kalman filters , 2005 .

[2]  S. Theodossiades,et al.  NON-LINEAR DYNAMICS OF GEAR-PAIR SYSTEMS WITH PERIODIC STIFFNESS AND BACKLASH , 2000 .

[3]  Branko Ristic,et al.  Beyond the Kalman Filter: Particle Filters for Tracking Applications , 2004 .

[4]  A. Corigliano,et al.  Parameter identification in explicit structural dynamics: performance of the extended Kalman filter , 2004 .

[5]  Jiuchao Feng,et al.  Real-time nonlinear structural system identification via iterated unscented Kalman filter , 2012 .

[6]  Eleni Chatzi,et al.  Semi-active control for vibration mitigation of structural systems incorporating uncertainties , 2015 .

[7]  S. Natsiavas,et al.  Effect of non-linearities in the identification and fault detection of gear-pair systems , 2006 .

[8]  Chandramouli Padmanabhan,et al.  Analysis of periodically forced nonlinear Hill’s oscillator with application to a geared system , 1996 .

[9]  Stefano Mariani,et al.  Unscented Kalman filtering for nonlinear structural dynamics , 2007 .

[10]  Jeffrey K. Uhlmann,et al.  New extension of the Kalman filter to nonlinear systems , 1997, Defense, Security, and Sensing.

[11]  R. E. Kalman,et al.  A New Approach to Linear Filtering and Prediction Problems , 2002 .

[12]  Andrew W. Smyth,et al.  Application of the unscented Kalman filter for real‐time nonlinear structural system identification , 2007 .

[13]  Rajendra Singh,et al.  Interactions between time-varying mesh stiffness and clearance non-linearities in a geared system , 1991 .

[14]  Eleni Chatzi,et al.  The unscented Kalman filter and particle filter methods for nonlinear structural system identification with non‐collocated heterogeneous sensing , 2009 .

[15]  Rudolph van der Merwe,et al.  The Unscented Kalman Filter , 2002 .

[16]  Eleni Chatzi,et al.  Experimental application of on-line parametric identification for nonlinear hysteretic systems with model uncertainty , 2010 .

[17]  A. Nayfeh,et al.  Applied nonlinear dynamics : analytical, computational, and experimental methods , 1995 .