Identification of non-linear effects in rotor systems using recursive QR factorization method

There are several non-linear and time variant effects in a rotor-bearing dynamic system. The non-linear characteristics of the rolling element bearing, internal damping, unsymmetrical stiffness of the shaft, cracks on the shaft, and the radial clearance are the typical root causes of these effects [1]. As rotating speeds increase and rotor weights decrease, these non-linear and time variant effects could significantly affect the dynamic characteristics of the rotor system [2–8]. If these non-linear and time variant effects are ignored, the vibration response could lead to incorrect interpretation of the rotor system. This will significantly affect the performance of the rotor vibration control schemes, the accuracy of the diagnosis results, and the performance of any schemes where an accurate rotor model is needed. Therefore, the accurate identification of both the model structure and parameters of a rotor-bearing system, including the non-linear effects, is an important engineering problem. A large body of literature concentrates on this area. Tiwari and Vyas [9] developed a technique for estimating the non-linear stiffness of rolling element bearings. Imam et al. [10] completed an on-line rotor crack detection and monitoring system. Krodkiewski and Ding [11] found a method for on-site estimation of the alignment of multi-bearing rotor systems. Tasker and Chopra [12] used the rotor stability data to estimate the non-linear damping of the system. Compared to the parameter estimation, the non-linear model structure identification is quite difficult. An optimal search scheme is usually needed to find an adequate model among all the possible ones. Desrochers and Mohseni [13] used a model set that has a multi-layered combinatorial tree structure. They showed that searching the tree for the optimal n-term model could be done in n stages. Kanjilal et al. [14] developed a method for fast selection of significant variables in linear-in-the-parameter models by using modified orthogonal-triangular factorization (also called QR factorization). The distinctive characteristic of their method is that estimations of ARTICLE IN PRESS