We introduce a detection and tracking algorithm for panoramic imaging systems intended
for operations in high-clutter environments. The algorithm combines correlation- and model-based
tracking in a manner that is robust to occluding objects but without the need for a separate
collision prediction module. Large data rates associated with the panoramic imager necessitate
the use of parallel computation on graphics processing units. We discuss the queuing and
tracking algorithms as well as practical considerations required for real-time implementation.
The theory behind compressive sampling pre-supposes that a given sequence of observations may be exactly represented by a linear combination of a small number of vectors. In practice, however, even small deviations from an exact signal model can result in dramatic increases in estimation error; this is the so-called basis mismatch" problem. This work provides one possible solution to this problem in the form of an iterative, biconvex search algorithm. The approach uses standard ℓ1-minimization to find the signal model coefficients followed by a maximum likelihood estimate of the signal model. The process is repeated until a convergence criteria is met. The algorithm is illustrated on harmonic signals of varying sparsity and outperforms the current state-of-the-art.
Range performance is often the key requirement around which electro-optical and infrared camera systems are designed. This work presents an objective framework for evaluating competing range performance models. Model selection based on the Akaike’s Information Criterion (AIC) is presented for the type of data collected during a typical human observer and target identification experiment. These methods are then demonstrated on observer responses to both visible and infrared imagery in which one of three maritime targets was placed at various ranges. We compare the performance of a number of different models, including those appearing previously in the literature. We conclude that our model-based approach offers substantial improvements over the traditional approach to inference, including increased precision and the ability to make predictions for some distances other than the specific set for which experimental trials were conducted.
An automated approach for detecting the presence of watercraft in a maritime environment characterized by regions of land, sea, and sky, as well as multiple targets and both water- and land-based clutter, is described. The detector correlates a wavelet model of previously acquired images with those obtained from newly acquired scenes. The resulting detection statistic outperforms two other detectors in terms of probability of detection for a given (low) false alarm rate. It is also shown how the detection statistics associated with different wavelet models can be combined in a way that offers still further improvements in performance. The approach is demonstrated to be effective in finding watercraft in previously collected short-wave infrared imagery.
KEYWORDS: Associative arrays, Data modeling, Image quality, Image compression, Super resolution, Denoising, Chemical species, Wavelets, Video, Short wave infrared radiation
We present several improvements to published algorithms for sparse image modeling with the goal of
improving processing of imagery of small watercraft in littoral environments. The first improvement
is to the K-SVD algorithm for training over-complete dictionaries, which are used in sparse
representations. It is shown that the training converges significantly faster by incorporating multiple
dictionary (i.e., codebook) update stages in each training iteration. The paper also provides several
useful and practical lessons learned from our experience with sparse representations. Results of three
applications of sparse representation are presented and compared to the state-of-the-art methods; image
compression, image denoising, and super-resolution.
We present an approach for discriminating among dierent classes of imagery in a scene. Our intended application
is the detection of small watercraft in a littoral environment where both targets and land- and sea-based clutter
are present. The approach works by training dierent overcomplete dictionaries to model the dierent image
classes. The likelihood ratio obtained by applying each model to the unknown image is then used as the
discriminating test statistic. We rst demonstrate the approach on an illustrative test problem and then apply
the algorithm to short-wave infrared imagery with known targets.
We present a technique for small watercraft detection in a littoral environment characterized by multiple targets
and both land- and sea-based clutter. The detector correlates a tailored wavelet model trained from previous
imagery with newly acquired scenes. An optimization routine is used to learn a wavelet signal model that
improves the average probability of detection for a xed false alarm rate on an ensemble of training images.
The resulting wavelet is shown to improve detection on a previously unseen set of test images. Performance is
quantied with ROC curves.
This work offers a comparison of broadband shortwave infrared, defined as the spectral band from 0.9 to 1.7 μm, and hyperspectral shortwave infrared imagers in a marine environment under various daylight conditions. Both imagers are built around a Raytheon Vision Systems large format (1024×1280) indium-gallium-arsenide focal plane array with high dynamic range and low noise electronics. Sample imagery from a variety of objects and scenes indicates roughly the same visual performance between the two systems. However, we show that the more detailed spectral information provided by the hyperspectral system allows for object detection and discrimination. A vessel was equipped with panels coated with a variety of paints that possessed spectral differences in the 0.9 to 1.7 μm waveband. The vessel was imaged at various ranges, states of background clutter, and times of the day. Using a standard correlation receiver, it is demonstrated that image pixels containing the paint can be easily identified. During the exercise, it was also observed that both bow waves and near-field wakes from a wide variety of vessel traffic provide a spectral signature in the shortwave infrared waveband that could potentially be used for object tracking.
The emerging field of compressed sensing has potentially powerful implications for the design of optical imaging devices. In particular, compressed sensing theory suggests that one can recover a scene at a higher resolution than is dictated by the pitch of the focal plane array. This rather remarkable result comes with some important caveats however, especially when practical issues associated with physical implementation are taken into account. This tutorial discusses compressed sensing in the context of optical imaging devices, emphasizing the practical hurdles related to building such devices, and offering suggestions for overcoming these hurdles. Examples and analysis specifically related to infrared imaging highlight the challenges associated with large format focal plane arrays and how these challenges can be mitigated using compressed sensing ideas.
This work explores the influence of head window thickness on the performance of a mid-wave infrared, panoramic
periscope imager. Our focus is on transparent spinel ceramic as the head window material. Spinel is an attractive
material for IR applications due to its good strength and transmission properties (visible through mid-wave).
However, there is some degradation in spinel transmission near the high end of the mid-wave band ( 5μm) as
the head window thickness increases. In this work we predict the relationship between head window thickness
and imager performance, as quantified by the Noise Equivalent Temperature Difference, and compare these
predictions to values estimated from experimental data. We then discuss the implications for imager design and
demonstrate a possible approach to correcting for the headwindow-induced losses. The imager used in this study
is a compact, catadioptric, camera that provides a 360o horizontal azimuth by -10o to +30o elevation field of
view and uses a 2048 x 2048, 15μm pitch InSb detector.
KEYWORDS: Diffusion, Sensors, Image fusion, Data acquisition, Physics, Data fusion, Principal component analysis, Image registration, Signal processing, Analytical research
This work considers the problem of combining high dimensional data acquired from multiple sensors for the
purpose of detection and classification. The sampled data are viewed as a geometric object living in a highdimensional
space. Through an appropriate, distance preserving projection, those data are reduced to a lowdimensional
space. In this reduced space it is shown that different physics of the sampled phenomena reside on
different portions of the resulting "manifold" allowing for classification. Moreover, we show that data acquired
from multiple sources collected from the same underlying physical phenomenon can be readily combined in the
low-dimensional space i.e. fused. The process is demonstrated on maritime imagery collected from a visible-band
camera.
A high-resolution midwave infrared panoramic periscope sensor system has been developed. The sensor includes an f/2.5 catadioptric optical system that provides a field of view with 360-deg horizontal azimuth and -10- to +30-deg elevation without requiring moving components (e.g., rotating mirrors). The focal plane is a 2048×2048, 15-µm-pitch InSb detector operating at 80 K. An onboard thermoelectric reference source allows for real-time nonuniformity correction using the two-point correction method. The entire system (detector-Dewar assembly, cooler, electronics, and optics) is packaged to fit in an 8-in.-high, 6.5-in.-diameter volume. This work describes both the system optics and the electronics and presents sample imagery. We model both the sensor's radiometric performance, quantified by the noise-equivalent temperature difference, and its resolution performance. Model predictions are then compared with estimates obtained from experimental data. The ability of the system to resolve targets as a function of imaged spatial frequency is also presented.
We use a nonlinear dimensionality reduction technique to improve anomaly detection in a hyperspectral imaging
application. A nonlinear transformation, diffusion map, is used to map pixels from the high-dimensional spectral
space to a (possibly) lower-dimensional manifold. The transformation is designed to retain a measure of distance
between the selected pixels. This lower-dimensional manifold represents the background of the scene with high
probability and selecting a subset of points reduces the computational overhead associated with diffusion map.
The remaining pixels are mapped to the manifold by means of a Nystr¨om extension. A distance measure is
computed for each new pixel and those that do not reside near the background manifold, as determined by
a threshold, are identified as anomalous. We compare our results with the RX and subspace RX methods of
anomaly detection.
We present image data and discuss naval sensing applications of SWIR and Hyperspectral SWIR imaging in littoral and
marine environments under various light conditions. These environments prove to be challenging for persistent
surveillance applications as light levels may vary over several orders of magnitude within and from scene to scene.
Additional difficulties include imaging over long water paths where marine haze and turbulence tend to degrade
radiation transmission, and discrimination of low contrast objects under low-light and night imaging. Image data
obtained from two separate passive sensor systems, both of which are built around an RVS large format (1280 x 1024)
InGaAs FPA with high dynamic range and low noise electronics, are presented. The SWIR camera imager is equipped
with a custom 300 mm focal length f/2 narrow field-of-view (6° diagonal) refractive telescope. The Hyperspectral
imager has a custom selectable 900/1800 mm focal length telescope with corresponding 1.55°/0.79° field-of-view and fnumbers
of 3/6 respectively. The sensor uses 1280 pixels in the spatial direction and a window of 192 are used for the
spectral and operates at a nominal frame rate of 120 Hz. To assess field performance of the SWIR/Hyperspectral
imagers, comparison is made to output from a scientific grade VNIR camera and two state-of-the-art low-light sensors.
A high-resolution mid-wave infrared panoramic periscope sensor system has been developed. The sensor includes a catadioptric optical system that provides a 360° horizontal azimuth by -10° to +30° elevation field of view without requiring moving components (e.g. rotating mirrors). The focal plane is a 2048 x 2048, 15μm pitch InSb detector operating at 80K. An on-board thermo-electric reference source allows for real-time nonuniformity
correction using the two-point correction method. The entire system (detector-dewar assembly, cooler, electronics and optics) is packaged to fit in an 8" high, 6.5" diameter volume. This work describes both the system optics and electronics and presents sample imagery. We also discuss the sensor's radiometric performance, quantified by the NEDT, as a function of key system parameters. The ability of the system to resolve targets as a function of imaged spatial frequency is also presented.
KEYWORDS: Nonlinear filtering, Signal detection, Signal processing, Receivers, Statistical analysis, Electronic filtering, Linear filtering, Sensors, Complex systems, Analytical research
Higher-order spectral analysis is one approach to detecting deviations from normality in a received signal. In
particular the auto-bispectral density function or "bispectrum" has been used in a number of detection applications.
Both Type-I and Type-II errors associated with bispectral detection schemes are well understood if the
processing is performed on the received signal directly or if the signal is pre-processed by a linear, time invariant
filter. However, there does not currently exist an analytical expression for the bispectrum of a non-Gaussian
signal pre-processed by a nonlinear filter. In this work we derive such an expression and compare the performance
of bispectral-based detection schemes using both linear and nonlinear receivers. Comparisons are presented in
terms of both Type-I and Type-II detection errors using Receiver Operating Characteristic curves. It is shown
that using a nonlinear receiver can offer some advantages over a linear receiver. Additionally, the nonlinear
receiver is optimized using genetic programming (differential evolution) to choose the filter coefficients.
Numerical simulations are used to improve in-band disruption of a phase-locked loop (PLL). Disruptive inputs
are generated by integrating a system of nonlinear ordinary differential equations (ODEs) for a given set of
parameters. Each integration yields a set of time series, of which one is used to modulate a carrier input to the
PLL. The modulation is disruptive if the PLL is unable to accurately reproduce the modulation waveform. We
view the problem as one of optimization and employ an evolutionary algorithm to search the parameter space of
the excitation ODE for those inputs that increase the phase error of the PLL subject to restrictions on excitation
amplitude or power. Restricting amplitude (frequency deviation) yields a modulation that approximates a
square wave. Constraining modulation power leads to a chaotic excitation that requires less power to disrupt
loop operation than either the sinusoid or square wave modulations.
Higher-order spectra (HOS) appear often in the analysis and identification of nonlinear systems. The auto-bispectrum
is one example of a HOS and is frequently used in the analysis of stationary structural response data
to detect the presence of structural nonlinearities. In this work we derive an expression for the auto-bispectrum
of a multi-degree-of-freedom structure with quadratic nonlinearities. A nonlinearity detection strategy, based on
estimates of the bispectrum, is then described. The performance of several such detectors is quantified using
Receiver Operator Characteristic (ROC) curves illustrating the trade-off between Type-I error and power of
detection (1-Type-II error).
Higher-order spectra have become a useful tool in spectral analysis, particularly for identifying the presence and
sometimes type of nonlinearity in a system. Two such spectra that have figured prominently in signal processing
are the bispectrum and trispectrum. The bispectrum is well-suited to capturing the presence of quadratic
nonlinearities in system response data while the trispectrum has proved useful in detecting cubic nonlinearities.
In a previous work, the authors developed an analytical solution for the auto-bispectrum for multi-degree-of-freedom
systems. Here this analysis is extended to the trispectrum. Specifically, an expression is developed for
the trispectral density of a multi-degree-of-freedom system subject to Gaussian excitation applied at an arbitrary
location. The analytical expression is compared to those obtained via estimation using the direct method.
In this work we detect damage in a composite to metal bolted joint subject to ambient vibrations and strong
temperature fluctuations. Damage to the joint is considered to be a degradation of the connection strength
implemented by loosening the bolts. The system is excited with a signal that conforms to the Pierson-Moskowitz
distribution for wave height and represents a possible loading this component would be subject to in situ. We
show that as the bolts are loosened, increasing amounts of nonlinearity are introduced in the form of impact
discontinuities and stick-slip behavior. The presence of the nonlinearity, hence the damage, is detected by drawing
comparisons between the response data and surrogate data conforming to the null hypothesis of an undamaged,
linear system. Two metrics are used for comparison purposes: nonlinear prediction error and the bicoherence.
Results are displayed using Receiver Operating Characteristic (ROC) curves. The ROC curve quantifies the
trade-off between false positives (type I errors) and false negatives (type II errors). Type I errors can be
expressed as the probability of false alarm and 1 - type II error is the probability of detection. We demonstrate
that ROC curves provide a unified quantifiable approach for directly comparing the merits of different detection
schemes.
Higher order spectral analysis techniques are often used to identify nonlinear interactions in modes of dynamical systems. More specifically, the auto and cross- bispectra have proven to be useful tools in testing for the presence of quadratic nonlinearities based on a system's stationary response. In this paper a class of mechanical system represented by a second-order nonlinear equation of motion subject to random forcing is considered. Analytical expressions for the second-order auto- and cross-spectra are determined using a Volterra functional approach and the presence and extent of nonlinear interactions between frequency components are identified. Numerical simulations accompany the analytical solutions to show how modes may interact nonlinearly producing intermodulation components at the sum and/or difference frequency of the fundamental modes of oscillation. A closed-form solution of the Bispectrum can be used to help identify the source of non-linearity due to interactions at specific frequencies. Possible applications include structural health monitoring where damage is often modeled as a nonlinearity. Advantages of using higher-order spectra techniques will be revealed and pertinent conclusions will be outlined.
Higher-order spectra (HOS) appear often in the analysis and identification of nonlinear systems. The auto-bispectrum
is one example of a HOS and is frequently used in the analysis of stationary structural response data
to detect the presence of certain types structural nonlinearities. In this work we use a closed-form expression
for the auto-bispectrum, derived previously by the authors, to find the bispectral frequency most sensitive to
the nonlinearity. We then explore the properties of nonlinearity detectors based on estimates of the magnitude
of the auto-bispectrum at this frequency. We specifically consider the case where the bispectrum is estimated
using the direct method based on the Fourier Transform. The performance of the detector is quantified using
a Receiver Operator Characteristic (ROC) curve illustrating the trade-off between Type-I error and power of
detection (1-Type-II error). Theoretically derived ROC curves are compared to those obtained via numerical
simulation. Results are presented for different levels of nonlinearity. Possible consequences are discussed with
regard to the detection of damage-induced nonlinearities in structures.
A system for interrogating fiber optic Bragg grating arrays at kiloHertz sampling rates with sub-microstrain resolution was presented recently. The system makes use of a tunable fiber Fabry-Perot filter for demultiplexing and a path-imbalanced Mach-Zehnder interferometer for wavelength conversion. The operationally-passive demodulation technique for the interferometer makes use of probing the 3x3 coupler at the interferometer output for its coupling parameters to execute the technique. In this work, we discuss the effects of how errors in determining these parameters translate into
measurement error and harmonic distortion. We compare measured effects in the laboratory with predictive models to give error
sensitivity metrics. We also consider two modes of sampling errors for such frequency-modulated systems and propose a generalized sampling criterion for minimizing harmonic distortion and measurement error.
Many architectures of fiber Bragg grating (FBG) interrogation systems used for mechanical motion (strain, acceleration, etc.) detection utilize interferometry for some part of the demodulation process. Using a hybrid Mach-Zehnder/tunable filter/3-by-3 coupler system architecture as a testbed, this paper examines error sources in the demodulation process giving rise to both/either accuracy and/or resolution degradation in the demodulated output. In particular, realizations of degradation metrics such
as noise rise and harmonic distortion are reported due to inaccuracy in demodulation parameters, such as coupler parameters or photodetector voltages. Error models are developed where appropriate for comparison between prediction and measurement.
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.
Vibration-based structural health monitoring has largely considered applied excitations as the primary means
of inducing structural vibration. Here we consider how ambient vibrations might be used to assess the level of
damage in a composite UAV wing. The wing consists of a foam core and a carbon fiber skin. We subject the
wing to various amounts of impact damage in order to cause internal delaminations. The wing is then excited
using a gust loading waveform in an effort to simulate the forcing the wing is expected to see in flight. We then
use a probabilistic description of the structure's dynamics to assess the level of damage-induced nonlinearity in
the wing. The approach is capable of making the diagnosis in the absence of a representative baseline data set
from the "healthy" wing.
KEYWORDS: Sensors, Composites, Structural health monitoring, Information technology, Algorithms, Data modeling, Fiber optics sensors, Feature extraction, Signal processing, Complex systems
An information-theoretic approach is described for detecting damage-induced nonlinearities in structures. Both the time-delayed mutual information and time-delayed transfer entropy are presented as methods for computing the amount of information transported between points on a structure. By comparing these measures to "linearized" surrogate data sets, the presence and degree of nonlinearity in a system may be deduced. For a linear, five-degree-of-freedom system both mutual information and transfer entropy are derived. An algorithm is then described for computing both quantities from time-series data and is shown to be in agreement with theory. The approach successfully deduces the amount of damage to the structure even in the presence of simulated temperature fluctuations. We then demonstrate the approach to be effective in detecting varying levels of impact damage in a thick composite plate structure.
Structural system identification, historically, has largely consisted of seeking linear relationships among vibration time series data, e.g., auto/cross-correlations, modal analysis, ARMA models, etc. This work considers how dynamical relationships may be viewed in terms of 'information flow' between different points on a structure. Information or interdependence metrics (e.g., time-delayed mutual information) are able to capture both linear and nonlinear aspects of the dynamics, including higher-order correlations. This work computes information-based metrics on a frame experiment where nonlinearity is introduced by the loosening of a bolt. Both linear and nonlinear measures of dynamical interdependence are then used to assess the degree of degradation to the joint. Results indicate clear differences in the way linear and nonlinear measures quantify the bolt loosening.
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.
A new algorithm is presented for detecting damage in structures subject to ambient or applied excitation. The approach is derived from an attractor-based technique for detecting nonstationarity in time series data and is referred to as recurrence quantification analysis (RQA). Time series data collected from the structure are used to reconstruct the system's dynamical attractor in phase space. The practitioner then quantifies the probabilities that a given trajectory will visit local regions in this phase space. This is accomplished by forming a binary matrix consisting of all points that fall within some predefined radius of each point on the attractor. The resulting recurrence plot reflects correlations in the time series across all available time scales in a probabilistic fashion. Based on the structure found in recurrence plots a variety of metrics are extracted including: percentage of recurrence points, a measure reflecting determinism, and entropy. These "features" are then used to detect and track damage-induced changes to the structure's vibrational response. The approach is demonstrated experimentally in diagnosing the length of a crack in a thin steel plate. Structural response data are recorded from multiple locations on the plate using a novel fiber-based sensing system.
KEYWORDS: Aluminum, Structural health monitoring, Sensors, Feature extraction, Control systems, Data modeling, Linear filtering, Data acquisition, Nondestructive evaluation, Stochastic processes
Structural health monitoring is an important field concerned with assessing the current state (or "health") of a structural system or component with regard to its ability to perform its intended function appropriately. One approach to this problem is identifying appropriate features obtained from time series vibration responses of the structure that change as structural degradation occurs. In this work, we present a novel technique adapted from the nonlinear time series prediction community whereby the structure is excited by
an applied chaotic waveform, and predictive maps built between structural response attractors are used as the feature space. The structural response is measured at several points on the structure, and pairs of attractors are used to predict each other. This approach is applied to detecting the preload loss in a bolted joint in an aluminum frame structure.
In past work we have demonstrated a vibration based health monitoring
methodology which was experimentally validated on several plate and beam systems. The method is based on processing time series data by
transforming the data into a state space object, an attractor, and then identifying geometric features of the attractor. The system's structural health or level of damage is monitored by tracking the evolution of the geometric feature as the system evolves. Our previous research indicated that low dimensional inputs work best for characterizing the features. Also discovered was the fact that the features could be characterized with minimal performance loss by using a band limited noise input. The current work assess whether an ambient excitation can serve as the input to the structure and still successfully identify and track geometric features of the system in much the same way that the band limited noise was able to characterize the system. The system in question is a 2D typical section airfoil model with a control surface. A reduced order aerodynamic approach developed by Peters is used to model the fluid loading on the structure. Damage is induced on the structure by introducing increasing amounts of freeplay in the restoring torque of the control surface. The novel and most important component of the
model from the stand point of implementing an on-line structural health monitoring system is the use of an ambient source of excitation namely atmospheric gust loading.
In past work, we have presented a methodology for vibration
based damage detection derived from the characterization of
changes in the geometric properties of the time domain response
of a structure. In brief, input forcing signals and output
response signals can be transformed into state space geometrical
representations. When allowed to evolve to a steady state, the
geometric object is called an attractor. Certain properties of
the attractor, such as the local variance of neighborhoods of
points or prediction errors between attractors, have been shown
to correlate directly with damage.
While most inputs will generate some type of attracting geometric
object, prescribing a low dimensional input forcing signal helps to maintain a low dimensional output signal which in turn simplifies the
calculation of attractor properties. Work to date has incorporated
the use of a chaotic input forcing signal based on its low dimensionality yet useful frequency content. In this work we
evaluate various forms of shaped noise as alternative effectively low
dimensional inputs. We assess whether the intrinsic properties of the chaotic input leads to better damage detection capabilities than various shaped noise inputs. The experimental structure considered is a
thin plate with weld line damage.
Recently, a new approach in vibration-based structural health monitoring has been developed utilizing features extracted from concepts in nonlinear dynamics systems theory. The structure is excited with a low-dimensional chaotic input, and the steady-state structural response attractor is reconstructed using a false nearest neighbors algorithm. Certain features have been computed from the attractor such as average local "neighborhood" variance, and these features have been shown in previous works to exceed the damage resolving capability of traditional modal-based features in several computational and experimental studies. In this work, we adopt a similar attractor approach, but we present a feature based on nonlinear predictive models of evolving attractor geometry. This feature has an advantage over previous attractor-based features in that the input excitation need not be monitored. We apply this overall approach to a steel frame model of a multi-story building, where damage is incurred by the loosening of bolted connections between model members.
KEYWORDS: Sensors, Fiber Bragg gratings, Oscillators, Control systems, Error analysis, Statistical analysis, Data acquisition, Structural health monitoring, Photography, Data modeling
This paper describes results from an investigation into weld line unzipping. The experiments use a series of steel plates (762 x 408 x 3.17 mm) instrumented with five fiber Bragg grating strain gauges. We rely on tuned chaotic excitation using a Lorenz oscillator to maintain a low dimension system suitable for chaotic attractor property analysis. Weld unzipping is simulated by leaving gaps in a weld line which start at one edge of the plate and extend for 34 or 74 mm (8 or 18% of the plate width). Two speeds of the Lorenz
oscillator are used for excitation. These correspond to positive Lyapunov exponents of 5 and 10 and provide insight into our ability to control the dimensionality of the system. Strain data from the sensors are cast into attractors and analyzed for changes using a feature called nonlinear prediction error. The nonlinear prediction error results demonstrate that the LE=5 excitation barely excites any structure dynamics while the LE=10 excitation clearly excites the first LE of the structure. At the 95% confidence limit with LE=10 excitation three of the five sensors can distinguish all three damage cases with the other two sensors able to separate damaged from undamaged. At the 95% confidence limit with LE= 5, only one sensor was able to distinguish damaged from undamaged and no sensors could distinguish the two damage cases.
KEYWORDS: Damage detection, Time-frequency analysis, Time metrology, Phase measurement, Algorithm development, Signal processing, Feature extraction, Structural health monitoring, Detection and tracking algorithms, Data modeling
This paper discusses the development of a general time-frequency data analysis method, the Empirical Mode Decomposition (EMD) and Hilbert Spectrum, and its application to structural health monitoring. The focus of this work is on feature extraction from structural response time series data. This is done by tracking unique characteristics of the adaptive decomposition components and developing a damage index based on previously introduced fundamental relationships connecting the instantaneous phase of a measured time series to the structural mass and stiffness parameters. Damage detection applications are investigated for a laboratory experiment of a simple frame (a model of a multi-story building) where damage is incurred by removing bolts at various locations. The frame is excited by a low dimensional deterministic chaos input as well as by broadband random signal. The time series output of the frame response is then analyzed with the EMD method. The time-frequency features and instantaneous phase relationships are extracted and examined for changes which may occur due to damage. These results are compared to results from other newly developed detection algorithms based on geometric properties of a chaotic attractor. Our results illustrate that the EMD and instantaneous phase detection approach, based on time-frequency analysis along with simple physics-based models, can be used to determine the presence and location of structural damage and permits the development of a reliable damage detection methodology.
KEYWORDS: Sensors, Damage detection, Finite element methods, Systems modeling, Oscillators, System identification, Data modeling, Matrices, Linear filtering, Complex systems
We present a new methodology for vibration based damage detection derived from the characterization of changes in the geometric properties of the time domain response of a structure. Many new features present themselves when the geometry of attracting objects in phase space are considered. The most promising avenue of study are metrics that describe changes to the attractor shape or dimension. In particular, the utility of a feature consisting of the ratio of average local variance (or spatial dispersion) of the input to the average local variance of the response is assessed. Presenting the results of the geometric time domain method in a statistical framework highlights the method's increased sensitivity to subtle damage-inflicted changes to the structure when compared to more traditional modal based methods. In addition the geometric method demonstrates a more robust handling of changes due to ambient environmental fluctuation. Results are presented from a finite element model of a thin plate with weld line damage implemented through a relaxation of a boundary condition.
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.
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