A nonlinear observer for damage evolution tracking

A dynamical systems approach to machinery condition monitoring and failure prediction is presented. The method is based on a state-space based formulation of the damage evolution tracking problem. The damage evolution process is a fast, directly observable subsystem coupled to a slow “hidden” subsystem representing the damage evolution.; A nonlinear observer for tracking drift in hidden variables is described. The drift observer uses two-time-scale modeling strategy based on phase space reconstruction from a measured fast-time scalar time series. The tracking results for three different experimental systems are presented to demonstrate the general applicability of the observer.; In the first system, a restoring force is provided by a battery-powered electromagnet. The state of the battery is taken to be the ‘hidden’ damage state, and strain gauge measurements are used to develop the drift observer. The setup is used to experimentally demonstrate the mapping of the observer output into the change of the local time average of the battery terminal voltage.; The vibrating beam with growing crack system is used to develop a simple empirical model of damage accumulation, which used to construct time-to-failure graphs for two different experiments.; In the third experiment, results of tracking damage evolution in an industrial gearbox system leading to gear-tooth failure are presented. The method shows a potential to not only provide an advance warning of failure, but also to allow acquisition of real-time damage transitional data that is essential for prognosis.; Finally, the nonlinear observer is studied theoretically using a simple mathematical model of the electro-mechanical experimental system. Numerical experiments conducted using the model are in good qualitative agreement with the experimental study, and explicitly show how the tracking metric, or drift observer, is related to drift in system parameters caused by the slow evolution of a hidden variable. Using the idea of averaging, the slow flow equation governing hidden variable evolution is obtained. It is shown that solutions to the slow flow equation correspond to the drift trajectory obtained with the experimental tracking method.