Use of chaotic excitation and attractor property analysis in structural health monitoring

Abstract

This work explores the utility of attractor-based approaches in the field of vibration-based structural health monitoring. The technique utilizes the unique properties of chaotic signals by driving the structure directly with the output of a chaotic oscillator. Using the Kaplan-Yorke conjecture, the Lyapunov exponents of the driving signal may be tuned to the dominant eigenvalues of the structure, thus controlling the dimension of the structural response. Data are collected at various stages of structural degradation and a simple nonlinear model, constructed from the undamaged data, is used to make predictions for the damaged response data. Prediction error is then introduced as a "feature" for classifying the magnitude of the damage. Results are presented for an experimental cantilevered beam instrumented with fiber-optic strain sensors.

Nonlinear System Identification for Damage Detection

“…Nichols, Todd, and colleagues have constructed attractor-based auto-and cross-prediction error metrics for a number of bolted joint applications [85,86,87,88,89].The concept here is that a reconstructed attractor may be used to auto-predict itself (or cross-predict another simultaneously sampled attractor) in a baseline condition, and subsequently this prediction will fail as the system changes due to damage.…”

“…This error metric may then be averaged over the whole data set to generate an average prediction error that relates how one attractor "predicts" another [85,86,87,88,89], or local statistics may be computed [92] Regardless of how the specific error metric is formed, the feature can be normalized by either a representation of the geometrical size of the attractor or by an undamaged reference error value in attempt to establish a quantitative sense of the prediction error values Moniz et al [93] used this general concept of correlation and predictability to build a continuity statistic to detect changes in an electrical circuit that was used to simulate a lumped mass structural system…”

Assessment and Localization of Active Discontinuities Using Energy Distribution Between Intrinsic Modes

“…Non-unique solutions of inverse problems, complexity, and variety of systems in the real world are the most important reasons that slow down the progress of SHM from research level to application. For instance, several methods have been proposed to detect breathing cracks such as mode shape curvature [1], model updating [2], energy method [3], and nonlinearities [4][5][6][7]. All of the aforementioned methods were shown to be effective in a specific problem; however, this does not guarantee their generality.…”

“…For example, fundamental frequencies of a beam are not changed more than 2% in presence of a breathing crack with the depth of around 20% of the beam's cross section [9], so it turns out to be quite difficult to detect small breathing cracks using a DI based on fundamental frequencies. The problem can be ameliorated by capturing nonlinear effects of damage since nonlinear features of structural response are generally more sensitive to damage [4][5][6][7]. On the other hand, a DI should not demonstrate a very high sensitivity to changes in a signal since the results of the algorithm are highly affected by noise and hence, not reliable.…”

“…On the other hand, a DI should not demonstrate a very high sensitivity to changes in a signal since the results of the algorithm are highly affected by noise and hence, not reliable. Several methods have been proposed based on different types of nonlinearities such as [4][5][6][7]. Most of the mentioned DIs suffer from one of these two shortcomings: 1) there is no solid physical interpretation behind the damage index such as those which aim to capture changes in the geometry of signal, 2) subjectiveness which makes it very difficult to use the DIs in complex structures and large sensor networks.…”