Vibration-based damage assessment utilizing state space geometry changes: local attractor variance ratio

Abstract

A novel feature extracted from a nonlinear time series is presented within the context of vibration-based damage detection in a system. An eight-degree-of-freedom spring-mass-damper 'structure' is considered with damage incurred by a stiffness degradation in one spring. The system is excited with a chaotic input, and by tuning the Lyapunov exponents of the chaotic excitation to the dominant eigenvalue of the structure the dimensionality of the entire system is effectively controlled. Both the input and output are viewed in state space as geometric objects, and the effect of the damage is shown to alter the geometric properties of the corresponding attractors at a local level, which may be captured in construction of the feature. The utility of the feature is compared with that of a number of modal-based features and shown to be superior in resolving capability and in robustness.

Damage Detections in Nonlinear Vibrating Thermally Loaded Plates

“…It can be concluded that: 1) The influence of the temperature changes is essential and can change substantially the nonlinear dynamic response of the plate and this is why temperature changes should be taken into account when developing a damage assessment procedure; 2) Temperature loadings which lead to either buckling or chaotic behaviour of the plate, might render the damage criterion suggested by Eqs. (18), (19) and (20) inappropriate. This is because even small damage, resulting in stiffness reduction of the plate, could lead to dramatic changes in the Poincaré maps of the response and consequently to unreliable results.…”

“…The pseudo-load mode superposition method (PLMS) [2,11,[18][19][20][21] is applied to solve the problem for nonlinear vibration of plates. It will be only briefly presented here.…”

“…Then an iterative procedure with respect to time is applied for the solution of the obtained system of ordinary differential equations. It is out of the scope of this paper to concentrate on the details of the solution method and the reader is referred to the above mentioned papers [2,[18][19][20][21] where the method is applied for undamaged plates and in [11] -for damaged ones. Thus the solution procedure will be presented only in brief:…”

“…where E 1n ,E 2n ,F 1n ,F 2n ,F 3n denote complicated mathematical expressions containing ω n , ξ n and τ (see [19]) and…”

Nonlinear System Identification for Damage Detection

“…Any changes to the system resulting from damage alter the way in which the signal is filtered. The benefits of using a chaotic excitation of the system relate to the way attractor stability (in the Lyapunov sense) and geometry (dimension) interact, and this is discussed in detail in [84].…”