32 Fiber Bragg gratings (FBGs) were embedded in a full size, composite twisted rudder to monitor internal
strains during underwater blast loading. During final fabrication, the fibers leading to sensors were broken
rendering the embedded sensors useless. Time domain reflectometry located the breaks and suggested a
likely approach to avoiding such problems in the future. An additional 8 FBGs were surface mounted on the
rudder and used to collect data during the blast loading events. Data were successfully collected at rates up to
9700 Hz during 3 blasts, with strains approaching 4000 με and strain rates of up to 13 ε/s.
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.
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.
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.
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.
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.
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.
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.
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.
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.
This work considers the dominant current methods for fiber Bragg grating wavelength interrogation. In addition, a new interrogation method, based on hybridizing a scanning Fabry-Perot filter for selecting individual reflection wavelengths, and an unbalanced Mach-Zehnder interferometer for high-resolution conversion of wavelength shifts to phase changes, is presented. The method utilizes a 3x3 fiber optic coupler in such a way that a completely passive demodulation algorithm is implemented. The current version interrogates multiple FBGs at frequencies from DC to near 10 kHz with nanostrain resolution across the full band. Low-frequency resolution is maintained with an interferometer drift compensation technique. We describe the system design and operation in detail and present key performance metrics with comparison to other primary FBG interrogation architectures.
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.
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