Nonlinear System Identification of Physical Parameters for Damage Prognosis and Localization in Structures

Abstract

The understanding of how structural components endure loads, in particular variable loads, is that these components gradually, over some period of time depending on the nature of the loading and the material, develop a microcrack. After some additional time and loading, the microcrack grows to a size that might be detected. Beyond that point, the microcrack propagates in a manner that can be reliably predicted by computer analysis codes. Consequently, one can define different stages for the life of a structural component. These are: 1) the period prior to the formation of a microcrack, 2) the period of microcrack growth, and finally 3) the period of crack growth. To date, structural health monitoring approaches that seek to detect cracks offer no insight into the extent of deterioration occurring in the initial stage that is a precursor to the formation of the microcrack or its growth. However, an approach that would facilitate monitoring the extent of the deterioration that takes place during this stage promises to improve life prediction capabilities of structural components.

The challenge, thus, is to develop quantitative assessment of damage accumulation from the earliest stages of the fatigue process and to provide a structure's signature that is dependent of the damage stage. One such signature is the structure's response to forced excitation. The realization of such a goal would help in advancing structural health monitoring procedures using interrogative system identification techniques and determine sensitivities of physical parameters to damage. Additionally, vibration-based spectral quantities are related to physical properties of the structure under test.

In this thesis, nonlinear response to parametric excitation is exploited for nonlinear system identification of metallic and composite beam-mass systems before damage initiation through intermediate states of damage progression to failure. Parametric identification procedure combines linear and higher order spectral analysis of vibration measurements and perturbation techniques for the derivation of the approximate solution of the system nonlinear governing differential equation. The possibility of using optical Fiber Bragg Grating sensors technology for damage localization is also assessed. Spectral moments and quantities obtained from fiber optic strain measurements are evaluated near and away from cracks to assess the relation between these moments and cracks.

Variations in parameters representing natural frequency, damping and effective nonlinearities for different levels of progressive damage in a beam-mass system have been determined. Their percentage variations have been quantified to establish their sensitivities to damage initiation. The results show that damping and effective nonlinearity parameters are more sensitive to damage conditions than the natural frequency of the first mode. Crack localization is assessed by means of optical fiber technology for a composite beam-mass system. The results show that noise levels in fiber optic signals are high in comparison to strain gage signals. Of particular interest, however, is the observation that the nonlinear response is more pronounced near the cracks than away from them.