A nonlinear dynamical systems framework for structural diagnosis and prognosis

Abstract

This work aims to establish a nonlinear dynamics framework for diagnosis and prognosis in structural dynamic systems. The objective is to develop an analytically sound means for extracting features, which can be used to characterize damage, from modal-based input–output data in complex hybrid structures with heterogeneous materials and many components. Although systems like this are complex in nature, the premise of the work here is that damage initiates and evolves in the same phenomenological way regardless of the physical system according to nonlinear dynamic processes. That is, bifurcations occur in healthy systems as a result of damage. By projecting a priori the equations of motion of high-dimensional structural dynamic systems onto lower dimensional center, or so-called ‘damage’, manifolds, it is demonstrated that model reduction near bifurcations might be a useful way to identify certain features in the input–output data that are helpful in identifying damage. Normal forms describing local co-dimension one and two bifurcations (e.g. transcritical, subcritical pitchfork, and asymmetric pitchfork bifurcations) are assumed to govern the initiation and evolution of damage in a low-order model. Real-world complications in damage prognosis involving spatial bifurcations, global bifurcation phenomena, and the sensitivity of damage to small changes in initial conditions are also briefly discussed.