J. M. Nichols

Detecting impact damage in experimental composite structures: an information-theoretic approach

This work describes a procedure for detecting the presence of damage-induced nonlinearities in composite structures using only the structures vibrational response. Damage is assumed to change the coupling between different locations on the structure from linear to nonlinear. Utilizing concepts from the field of information theory, we are able to deduce the form of the underlying structural model (linear/nonlinear), and hence detect the presence of the damage. Because information theoretics are model independent they may be used to capture both linear and nonlinear dynamical relationships. We describe two such metrics, the time delayed mutual information and time delayed transfer entropy, and show how they may be computed from time series data. We make use of surrogate data techniques in order to place the question of damage in a hypothesis testing framework. Specifically, we construct surrogate data sets from the original that preserve only the linear relationships among the data. We then compute the mutual information and the transfer entropy on both the original and surrogate data and quantify the discrepancy in the results as a measure of nonlinearity in the structure. Thus, we do not require the explicit measurement of a baseline data set. The approach is demonstrated to be effective in diagnosing the presence of impact damage in a thick composite sandwich plate. We also show how the approach can be used to detect impact damage in a composite UAV wing subject to ambient gust loading.

Modeling and Detection of Joint Loosening using Output-Only Broad-Band Vibration Data

Damage detection and structural health monitoring techniques based on vibration data have seen increased attention in recent years. Among the different vibration-based methods, the ones based on random vibrations are of particularly interest, especially when they do not require measurement of the input(s). In this work, several frequency and time domain signal processing techniques are explored in their respective abilities to detect damage in a bolted composite structure. First, a joint loosening model is developed and used to simulate the dynamic response to a stationary Gaussian excitation. Informed by the model, two signal processing techniques are used to assess the connection strength. The first method relies on basic statistical properties of the measured strains and their time derivatives, while the second is based on the signal power in different frequency bands. Both approaches are then used to assess progressive bolt loosening on an experimental composite-to-metal joint. All strain response data were obtained using a fiber optic strain sensing system. Results are presented in the form of Receiver Operating Characteristic (ROC) curves, showing both Type-I and Type-II errors associated with the proposed detection schemes.

Chaotic signal detection and estimation based on attractor sets: Applications to secure communications.

We consider the problem of detection and estimation of chaotic signals in the presence of white Gaussian noise. Traditionally this has been a difficult problem since generalized likelihood ratio tests are difficult to implement due to the chaotic nature of the signals of interest. Based on Poincares recurrence theorem we derive an algorithm for approximating a chaotic time series with unknown initial conditions. The algorithm approximates signals using elements carefully chosen from a dictionary constructed based on the chaotic signals attractor. We derive a detection approach based on the signal estimation algorithm and show, with simulated data, that the new approach can outperform other methods for chaotic signal detection. Finally, we describe how the attractor based detection scheme can be used in a secure binary digital communications protocol.

A Wavelet-based, Distortion Energy Approach to Structural Health Monitoring

A method for quantifying damage-induced distortions to the vibrational response of an experimental plate is presented. By examining a wavelet representation of the difference in strain response between the damaged and the undamaged structures, the distortion energy may be computed on multiple timescales. This feature is tested in its ability to detect both the presence and the location of degradation of the plate. In addition, the effects of competing excitation mechanisms, including the outputs of Lorenz and Rossler systems, as well as a 0-225 Hz Gaussian noise are studied. The results indicate that the distortion energies, statistically speaking, are significantly higher under damaged conditions compared to those extracted under undamaged conditions, implying that the new distortion energy approach will yield adequate features for detecting the presence as well as possibly the location of damage in a structure.

Use of Fiber-optic Strain Sensors and Holder Exponents for Detecting and Localizing Damage in an Experimental Plate Structure

The vibration-based structural health monitoring paradigm is predicated on the practitioners ability to acquire accurate structural response data and then to use that information to infer something about the structures health. Here the authors combine advances in both sensing and signal analysis and demonstrate the ability to detect damage in a simple experimental structure. A distributed network of nine fiber-optic strain sensors is used to acquire time series data from a rectangular steel plate where damage is considered as a cut of varying lengths. Both the sensors and the associated optical hardware are described. A new feature, Holder continuity, is then introduced as a means of identifying the presence and location of the cut length. This particular metric is derived from the field of nonlinear dynamics and is based on a phase space description of a structures dynamic response. Specifically, the authors compute the Holder exponent which quantifies the differentiability of the functional relationship between an ‘undamaged’ and a ‘damaged’ structural response. As damage is incurred, this relationship is expected to degrade. Both univariate and multivariate applications of the method are presented. The metric shows sensitivity to damage comparable to that exhibited by the plates modal frequencies, a traditionally used feature in health monitoring applications.

Characterization of a compressively sampled photonic link

A compressively sampled, photonic link has been described. By appropriately modulating the incoming signal prior to digitization, slow sampling rates can be used to accurately recover data as if it had been sampled at much higher rates. By performing the modulation in the optical domain there exists a potential path toward the recovery of signals in the 100GS/s regime.

Using chaotic forcing to detect damage in a structure

In this work we develop a numerical test for Holder continuity and apply it and another test for continuity to the difficult problem of detecting damage in structures. We subject a thin metal plate with incremental damage to the plate changes, its filtering properties, and therefore the phase space trajectories of the response chaotic excitation of various bandwidths. Damage to the plate changes its filtering properties and therefore the phase space of the response. Because the data are multivariate (the plate is instrumented with multiple sensors) we use a singular value decomposition of the set of the output time series to reduce the embedding dimension of the response time series. We use two geometric tests to compare an attractor reconstructed from data from an undamaged structure to that reconstructed from data from a damaged structure. These two tests translate to testing for both generalized and differentiable synchronization between responses. We show loss of synchronization of responses with damage to the structure.

Mapping the Information Landscape: Discerning Peaks and Valleys for Ecological Monitoring

We investigate previously unreported phenomena that have a potentially significant impact on the design of surveillance monitoring programs for ecological systems. Ecological monitoring practitioners have long recognized that different species are differentially informative of a system’s dynamics, as codified in the well-known concepts of indicator or keystone species. Using a novel combination of analysis techniques from nonlinear dynamics, we describe marked variation among spatial sites in information content with respect to system dynamics in the entire region. We first observed these phenomena in a spatially extended predator–prey model, but we observed strikingly similar features in verified water-level data from a NOAA/NOS Great Lakes monitoring program. We suggest that these features may be widespread and the design of surveillance monitoring programs should reflect knowledge of their existence.

A NOTE ON THE RESPONSE SPECTRUM MAP

A plot of frequency, or spectral, content versus a system parameter was introduced in a recent paper by Billings and Boaghe [2001] as a useful alternative to bifurcation diagrams in nonlinear dynamics. The current contribution illustrates the same approach based on data taken from two experimental mechanical systems in which hysteresis is featured.

Short communication: Automated, rapid classification of signals using locally linear embedding

This paper demonstrates the utility of the locally linear embedding (LLE) dimensionality reduction technique for automated, rapid classification of signals. Specifically, we focus on classifying RF signals as belonging to one of four different emitters. The classifier is trained on samples from each type, first using LLE to build a low-dimensional data manifold and using a support vector machine (SVM) to divide the manifold into sections corresponding to each signal type. New signals are then rapidly projected directly onto the data manifold where an SVM performs the classification.