<title>Nonlinear damage models for diagnosis and prognosis in structural dynamic systems</title>

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 loworder 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.

A data-model-fusion prognostic framework for dynamic system state forecasting

“…Model-based approaches typically involve building models (or mathematical functions) to describe the physics of the system states and failure modes; they incorporate physical understanding of the system into the estimation of system state and/or remaining useful life (RUL) (Adams, 2002;Luo et al, 2003;Chelidze and Cusumano, 2004). Model-based approaches, however, may not be suitable for many industrial applications where the physical parameters and fault modes may vary under different operation conditions (Pecht and Jaai, 2010).…”

Review of prognostic problem in condition-based maintenance

“…Adams [20] proposed to model damage accumulation in a structural dynamic system as first/second order nonlinear differential equations.…”

Particle Filter-Based Approach to Estimate Remaining Useful Life for Predictive Maintenance

“…Another principal disadvantage of data-driven methods is that the prognostic reasoning process is usually opaque to users [6]; consequently, they sometimes are not suitable for some applications where forecast reasoning transparency is required. Physics-based approaches typically involve building models (or mathematical functions) to describe the physics of the system states and failure modes; they incorporate physical understanding of the system into the estimation of system state and/or RUL [7][8][9]. Physics-based approaches, however, may not be suitable for some applications where the physical parameters and fault modes may vary under different operation conditions [10].…”