Application of the transient proper orthogonal decomposition method for order reduction of rotor systems with faults

The physical significance of the transient proper orthogonal decomposition (TPOD) method is proposed based on the energy of the proper orthogonal mode (POM). The POM energy can reveal the amount occupation of the dynamical characteristics of the reduced model relative to the original one. The TPOD method is compared with the traditional POD method; the bifurcation diagrams and the transition curves of POM energy are applied to verify the efficiency and accuracy of the TPOD method. On the basis of the POM energy analysis, the optimal order reduction model can be provided by the TPOD method. Two examples of the rotor-bearing systems are established by the Newton’s second law to study the physical significance of the TPOD method: One is the rotor system with pedestal looseness at one end and the other is looseness at both ends. The effects of the initial conditions (displacement and velocity) to the frequency components of the original systems and the order reduction efficiency are discussed. The variations of the frequency components can provide the guidance to the fault detections of the rotor systems.