Some fundamental issues in damage tracking, with application to a low-dimensional model of a gear-pair transmission

摘要

A damage tracking algorithm that uses finite-time model prediction error as a damage state observer has been developed in previous work by the authors. In this paper, some fundamental issues which effect the observability of the damage state are studied theoretically in a state-space context, and applied to a low-dimensional physics-based model for a gear-pair transmission system, The development of the lumped aprameter mathermatical model that describes the fast dynamics of the gear-pair is presented. and we show that, in general, the resulting equations are nonlinear and parameterically driven. The relationship of the effectove forcing to the kinematic and elastic propertie sof the gear-pair is discussed. We show how in an appropriate limit. the model becomes linear and externally driven. The observability theory presented in the paper is illustrated using the reduced, linear model as an example.