We examined strain time series from fiber Bragg gratings sensors located in various positions on a composite material
beam attached to a steel plate by a lap joint. The beam was vibrated using both broad-band chaotic signals (Lorenz
system), and a narrow band signal conforming to the Pierson-Moskowitz frequency distribution for wave height
(ambient excitation). The system was damaged by decreasing the torque on instrumented bolts in the lap joint from very
tight all the way through to a joint with a gap and slippage. We analyzed the strain data by reconstructing the attractor of
the system in the case of chaotic forcing and a pseudo-attractor in the case of sea-wave forcing. Using the highest torque
case as an "undamaged" baseline, we calculated the continuity statistic between the baseline attractor and the attractors
of the various damage levels for both forcing cases. We show where one can and cannot say that the functional
relationship between the attractors changes and how those changes are related to damage levels.
We investigate the use of a vibrational approach for the detection of barely visible impact damage in a composite UAV wing. The wing is excited by a shaker according to a predetermined signal, and the response is observed by a system of fiber Bragg grating strain sensors. We use two different driving sequences: a stochastic signal consisting of white noise, and the output from a chaotic Lorenz oscillator. On these data we apply a variety of time series analysis techniques to detect, quantify, and localize the damage incurred from a pendulum impactor, including classical linear analysis (e.g. modal analyses), as well as recently developed nonlinear analysis methods. We compare the performance of these methods, investigate the reproducibility of the results, and find that two nonlinear statistics are able to detect barely visible damage.
This paper describes two systems that can monitor up to 64 fiber Bragg grating (FBG) strain gauges simultaneously and their use in structural health monitoring applications. One system directly tracks wavelength shifts and provides ~0.3 me sensitivity with data rates to 360 Hz. The second system uses an unbalanced Mach-Zehnder interferometer to convert wavelength to phase. It has a noise floor of ~5 ne/Hz1/2 and data rates to 10 kHz. The wavelength-based system was used in field tests on an all composite hull surface effects ship in the North Sea and on an Interstate highway bridge in New Mexico. The interferometric system has been used to demonstrate enhanced damage detection sensitivity in a series of laboratory experiments that rely on a novel data analysis approach based in nonlinear dynamics and state space analysis. The sensitivity of three of these novel damage detection methods is described.
Recently proposed methodologies in the field of vibration- based structural health monitoring have focused on the incorporation of statistical-based analysis. The structure in question is dynamically excited, some feature is identified for extraction from a measured data set, and that feature is classified as coming from a damaged or undamaged structure by means of some statistical approach. Perhaps the most important aspect of this new paradigm is the selection of a `feature' which accurately details the appearance, and possibly the location and scope, of the damage. In this paper we propose a feature derived from the field of nonlinear time-series analysis. Specifically, system response is classified according to the geometry of its dynamical attractor.
We investigate a number of phenomena which occur in synchronization in coupled or driven chaotic systems and which can cause difficulties in attaining synchronized states. We present direct experimental and numerical evidence for riddled basins of attraction, bursting phenomena, short wavelength bifurcations and size desynchronization effects. We show that typical Lyapunov stability exponents are not the optimal guide in designing such systems.
Now that the theory of nonlinear and chaotic systems is maturing, many people are beginning to consider applications of these phenomena. One application field which has become prominent is communications. This article is an overview of some of the recent advances in linking chaotic behavior to communications systems and signal processing.
We have shown that one may use chaotic signals to drive dynamical systems. When the driven system is stable to the driving signal and the driven system matches the system that produced the chaotic driving signal, the driven system will produce chaotic signals that are synchronized to the driving system. This may be seen in both autonomous and nonautonomous chaotic systems. This synchronized chaos may be useful in spread spectrum communications applications.
KEYWORDS: Complex systems, Chaos, Signal processing, Dynamical systems, Receivers, Digital image processing, Nonlinear dynamics, Data hiding, Telecommunications, Analytical research
Recent work using chaotic signals to drive nonlinear systems shows that chaotic dynamics is rich in new application possibilities. Among these are stable system design and synchronization.
New Driving Signals
Driven systems are easily visualized as dynamical systems which have as one of their input parameters a dynamical variable from another, often autonomous, dynamical system. We often refer to the source of the driving signal as the drive system and to the driven system as the response system. This can be viewed as the drive sending a signal to the response which then alters its behavior according to the signal. Typically, when driven systems are studied or engineered the driving signals come from constant forces or sine wave forcing. The use of signals from a chaotic system to drive a nonlinear system offers a new type of driving signal.
In our approach [1,2,3,4] two major themes stand out. One is the idea of stability as generalized to chaotic systems. Another is the use of a constructive approach to building useful, chaotically driven systems. We cut apart, duplicate, and paste together nonlinear dynamical systems. Many things can be done with some guidance from what is now known in nonlinear dynamics.
We first examine stability.
Stability of Chaotically Driven Systems
Consider a general «-dimensional, nonlinear response system, w = h(w,v), where the w=dw/dt, the driving signal v is supplied by a chaotic system and w and h are «-dimensional vector functions. The question of stability arises when we ask: given a trajectory w(t) generated by this system for a particular drive v, when is w(t) immune to small differences in initial conditions, i.e. when is the final trajectory unique, in some sense? Fig. 1 shows this schematically.
Recent work using chaotic signals to drive nonlinear systems shows that chaotic dynamics is rich in new application possibilities. The approach of using nonlinear dynamics concepts to guide synthesis of new nonlinear systems leads to the concepts of synchronization of chaotic systems and pseudoperiodic driving. These are only the beginnings of new and unique uses of chaotic dynamics.
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