This work first considers a review of the dominant current methods for fibre Bragg grating wavelength interrogation. These methods include WDM interferometry, tunable filter (both Fabry–Perot and acousto-optic) demultiplexing, CCD/prism technique and a newer hybrid method utilizing Fabry–Perot and interferometric techniques. Two applications using these techniques are described: hull loads monitoring on an all-composite fast patrol boat and bolt pre-load loss monitoring in a composite beam in conjunction with a state-space modelling data analysis technique.
The rapid emergence and growth of the modern telecommunications industry over the last decade has directly stimulated the development and the improvement of fibre optic technology to support it. Light sources and source controllers, couplers, connectors, add/drop multiplexers, optical filters and many other components and sub-systems are being utilized by the industry as critical elements in the growth of communications capabilities. Since optical fibre supports up to several hundred gigahertz of usable information bandwidth—orders of magnitude more than conventional copper wiring—the industry made a clear turn towards optical networks. This trend has made fibre optic equipment significantly more commercially available at competitive costs.
The fibre optic sensor community has benefited from this availability and economic effect, as many new fibre sensor architectures and deployment applications of fibre sensors have been demonstrated in recent years. Recent collections of these applications may be found in Ansari (1998), Claus & Spillman (2000), Mignani & Lefevre (2000), Asundi et al. (2001) and Chang (2001), and in part IV of Lopez-Higuera (2002). Fibre optic sensors, essentially regardless of specific sensor type or architecture, have a number of advantages over other sensors, including immunity to electromagnetic noise, negligible weight penalty, extremely high resolution, large bandwidth and large multiplexing capability, even with heterogeneous sensor types (e.g. strain gauges and accelerometers). Fibre optic sensors also may be utilized over a wide range of physical length-scales, which lends significant flexibility to structural health monitoring applications. Fibre sensors based on fibre Bragg gratings (FBGs), for example, may interrogate length-scales in the millimetre range, while low-coherence Michelson interferometry may interrogate length-scales in the tens of metres range (Elamari et al. 1994). Recently, research at the US Naval Research Laboratory has exploited coherent Rayleigh backscatter in optical fibre to develop a sensor with tunable gauge lengths (Posey et al. 2000). Finally, the small size, small footprint and material properties of optical fibre allow such sensors to be embedded inside materials such as composites during the fabrication process, leading to more fully realized ‘smart structure’ concept.
In many health monitoring applications, because damage in structures often initiates at the material level or relatively local geometric level, small-gauge length sensing is a common requirement. The most exploited fibre optic sensor technology that readily meets this need is FBGs, which are simple intrinsic (in-fibre) periodic structures that are directly photowritten into silica fibre by ultraviolet radiation (Hill et al. 1978; Stone 1987). Germanium-doped optical fibres have electronic absorption regimes in the ultraviolet range, and the formation of Ge sub-oxides readily causes local defects in the fibre core (Friebele et al. 1974). These defects in turn affect the local refractive index via the Kramers–Kronig effect. If the ultraviolet photowriting process illuminates the fibre core in a periodic fashion, then a corresponding periodic modulation of the refractive index is achieved. Typical photowriting processes are interferometric holography inscription (Meltz et al. 1989) or, now more commonly, phase mask inscription (Hill et al. 1993). The former technique involves focusing two beams of coherent ultraviolet light transversely upon a small section of fibre (1 cm), where the two beams are interfered at some prescribed slant angle. The interference pattern established on the core provides the periodicity which results in the grating's structure. The phase mask inscription technique consists of a one-dimensional periodic (square-wave) surface relief structure etched using photolithography. The fibre is placed in very near contact with the structure, and incident ultraviolet light normal to the structure passes through and diffracts due to the square-wave corrugations. The two first-order diffracted beams then interfere to provide the periodicity, similar to interferometric holography. The zero-order diffraction beam is kept suppressed by proper choice of the corrugation depth (Hill & Meltz 1997).
The subsequent periodic modulation of the core refractive index acts like a narrowband notch filter of the light propagating down the core. If light is propagated down the fibre as a guided mode, as the light interacts with each grating structure, some of the light is scattered due to the refractive index change. This scattered light will continue to accrue constructively, establishing a backward-propagating (reflective) mode, provided that an appropriate phase-matching condition is met. The rest of the light will continue to transmit as a forward-propagating mode. The phase-matching condition in the reflected mode implies maximal modal coupling, which occurs at the Bragg resonance wavelength λr given by(1.1)where n is the effective fibre core modal index and T is the grating period. The practical width of the reflection wavelength, depending upon how the grating was manufactured, is typically 0.1–0.3 nm.
Equation (1.1) establishes that a measurement of the reflected wavelength equates with either a measurement of the grating period or the effective refractive index. Thus, any perturbation to the fibre that affects either of these properties (e.g. axial compression or tension, temperature change or hydrostatic pressure change) would result in a wavelength shift. Considering the application of applied displacement (strain) and ignoring temperature or pressure dependence, the resulting wavelength shift is given by(1.2)where equation (1.1) has been differentiated with respect to both T and n; (for 1550 nm light) is the overall photoelastic constant; and ϵ is the average applied strain over the grating's gauge length.
The initial grating period T may be specified during manufacturing for either primary manufacturing method. Thus, a common wavelength-based multiplexing technique is to inscribe an array of gratings at unique reflection wavelengths. Broadband light is launched into the fibre, and each grating will ‘slice’ out a 0.1–0.3 nm portion of the launched wavelength spectrum (figure 1 (right)). As any of the individual fibre locations where the gratings are written are strained, a corresponding proportional shift in λr is observed according to equation (1.2).
Therefore, the principal requirement for developing a grating-based measurement system, regardless of what specific fields the gratings are designed to measure, is to track the various grating wavelength reflection shifts. A number of approaches have been proposed, but most of them may be broadly classed into conventional wavelength-division demultiplexers (WDMs; Kersey et al. 1992), scanning Fabry–Perot (SFP) filter interrogation (Kersey et al. 1993), tunable acousto-optic filter (AOTF) interrogation (Xu et al. 1993) and prism/CCD-array techniques (Askins et al. 1995). More recently, a hybrid technique has been demonstrated that retains certain advantages from some of the earlier methods while improves overall performance (Johnson et al. 2000; Todd et al. 2001a). Firstly, this paper will briefly review these classes of grating interrogation methods; a good discussion of variations of these themes may be found in Kersey et al. (1997). Secondly, the hybrid method will be discussed in a bit more detail, and several key performance test results will be presented. Both performance and implementation comparisons will be drawn among all the other methods in order to assess the current state of Bragg grating-based sensor system development. Finally, two deployments of these systems will be described: hull load monitoring of an all-composite fast patrol boat during sea-keeping trials and bolt pre-load loss monitoring in a metal-to-composite bolted beam.
2. Bragg grating interrogation systems
(a) WDM interferometry method
The oldest grating interrogation method is the use of WDM filters with Mach–Zehnder interferometry. This method is shown in figure 2. Light from a broadband source is used to illuminate an FBG sensing array, and the reflections are coupled back directly into a path-imbalanced Mach–Zehnder interferometer. The interferometer converts the reflected wavelength to a phase difference according to the general relationship(2.1)where ϕ is the phase difference, λ is the peak reflection wavelength of a particular grating, n is the refractive index of the fibre core, d is the path imbalance, and ϕenv is a term included to indicate the presence of slowly varying, environmentally induced random phase shifts due to variations in n and d, which typically arise from temperature fluctuations occurring at slow (near-DC) time-scales. As such, this term does not depend upon λ. Light is then inserted into a wavelength division demultiplexer which guides the light at each grating wavelength on to a separate detector. As with any direct interferometric signal, demodulation must be performed, and a phase-sensitive carrier demodulation technique (using a controlled piezoelectric element in one arm of the interferometer) is typically used (Dandridge et al. 1982). Once the phase shift ϕ is recovered, the resulting strain ϵ on an individual grating may be determined by(2.2)which is obtained by differentiating equation (2.1) with respect to λ and utilizing the photoelastic equation, equation (1.2). By choosing an appropriate interferometer path difference, high strain resolution in the sub-nanostrain range as well as wide frequency response bandwidth into the tens of kilohertz are possible. However, multiplexing is burdensome due to the WDM filters. Recent telecommunications innovations in dense wavelength-division multiplexing (DWDM) have produced smaller, higher channel systems, but typical system racks are similar to the one shown in figure 2b. Some hybrid versions of this method incorporate time-division multiplexing (TDM) where sub-arrays of gratings may reflect at common wavelengths but are discriminated with appropriate time gating. Another drawback for this method is that it requires some sort of drift compensation device for retaining accuracy at low frequencies, due to the influences of the ϕenv term in equation (2.1). Examples of such compensation schemes have included active reference fibre compensation (Jackson et al. 1980), source modulation (Jackson et al. 1982a, b) or the use of phase-generated reference carriers and phase-sensitive detection (Dandridge et al. 1982).
(b) Tunable filter methods
In the non-interferometric arena reside both the SFP and tunable AOTF methods. Both the methods interrogate grating arrays on essentially the same principle, but with different components for doing the individual wavelength discrimination (figure 3a). In the former method, light reflected from the grating array is coupled into a SFP filter. This device only passes a narrowband wavelength, which depends on the spacing of mirrors inside it. This spacing, and thus the passband, is controlled by applying a stepped triangle-wave voltage to a piezoelectric device driving the mirrors. A typical SFP filter has a passband of ca 0.3 nm, and since FBGs have a reflection bandwidth of ca 0.1–0.3 nm, only one grating reflection will pass through the SFP filter at a given time. The SFP filters may be scanned over a free spectral range of ca 50 nm, so the available source spectrum may be covered. After passage through the SFP filter, the reflected light is sent to a single photodetector. The detector voltage trace is differentiated, and the times of the zero-crossings of the derivative (corresponding to the grating peak locations) are noted, as shown in figure 3b(i). The zero-crossing times are compared to the corresponding SFP filter drive voltage, which has been calibrated to wavelength, so that the zero-crossing times are essentially a measure of the wavelength during a given scan cycle. Strain resolution near 1 microstrain has been achieved, and the frequency response function is basically flat down to DC. However, in order to maintain accuracy and resolution, the SFP filter, since it is a mechanical device, cannot be scanned too quickly, or resonance phenomena may corrupt the measurement, as calibration between wavelength and SFP drive voltage is made under static conditions. The SFP filters usually cannot be driven past ca 1 kHz when used in this capacity, and many applications of this technology have reported lower acceptable rates (Todd et al. 1999a). Nevertheless, this method has become popular due to its relative simplicity and ability to resolve static to quasi-static strains without complex components. Microversions of tunable filters have recently emerged that have larger free spectral ranges (up to 100 nm) and faster scanning capability (up to the megahertz range) than conventional tunable filters. A laboratory comparative test comparing these components is shown in figure 4. While still immature, such MEMS filters could expand the performance capabilities of the SFP method.
In the tunable acousto-optic method, the SFP filter is replaced with an AOTF. An AOTF is a solid-state, electronically tunable narrowband optical filter. In an AOTF, the broadband light interacts with a high-frequency ultrasonic sound wave inside an optically polished crystal block. At each acoustic frequency, a relatively narrowband of optical wavelengths satisfy the anisotropic Bragg diffraction condition. By sweeping the acoustic frequency, the selected wavelength band can be varied, similar to how a stepped voltage wave was applied to the SFP filter to cover its spectral range. This is often achieved with a voltage-controlled oscillator (VCO), as shown in figure 3b(ii). A feedback circuit is shown which is first disabled in order to scan the wavelength range, then enabled to track an individual grating. The stepped frequency signal applied to the AOTF causes a square-wave AM signal in the voltage at the detector, where the peak-to-peak modulation depends on the difference between the grating reflection wavelength and the centre wavelength of the AOTF and its sign depends on the sign of that difference. The simple feedback circuit then tracks by using a square-wave modulating signal, and once the wavelength of the grating equals the wavelength of the AOTF, the amplitude modulation at the dither frequency will drop to 0. Since the current frequency is known, and that determines the current AOTF wavelength, the grating wavelength may be monitored. AOTFs may be driven much more rapidly than SFP filters, resulting in wider bandwidth capability. However, the spectral bandwidth of typical AOTFs is in the range 2–30 nm, although a few are specified to as low as 0.4 nm. These higher bandwidths do not match grating bandwidths as well as SFP filters, and grating spacing becomes an important issue. In other words, it is not always possible to multiplex as many gratings with a single AOTF filter as it may be with an SFP filter. However, AOTF free spectral ranges cover hundreds of nanometres in most cases, so the trade-off may be alleviated, assuming source bandwidth is available. Finally, as both filters are mechanical devices, voltage-to-wavelength (or frequency) calibration generally depends upon temperature, and care is usually taken to package such filters, when part of strain measurement systems, in thermally isolated ways.
(c) CCD linear array method
One potential drawback of the tunable filter methods is that they only use a small portion of the optical spectrum at any given time. When a wide spectral range of FBGs are interrogated at a given scanning frequency, the amount of reflected light energy from each FBG per scan is equal to the product of the FBG's reflectivity, the source spectral intensity, the FBG's spectral width and the scan period. Using typical FBG, source and tunable filter characteristics, the detectable optical power is on the order of 1% of the reflected optical power. This means that very high grating reflectivities or very bright sources are needed for acceptable wavelength detection. This penalty is completely voided by the parallel whole-spectrum interrogation possible with a charge-coupled device (CCD) spectrometer. Wavelength discrimination is achieved with a fixed dispersive element such as a prism or a plane grating which converts an incipient wavelength to an image on an array of detector elements by means of a collimator, as in figure 5. With a typical spectrometer and plane grating, an FBG reflection will be dispersed across more than one pixel (line) on the detector array, and a centroid calculation is performed in order to find the maximum (centre) wavelength. Resolution has been demonstrated with a typical CCD spectrometer in the nanostrain range with sampling capability into the kilohertz regime. Possible drawbacks with this method include reliance upon optical wavelengths below ca 900 nm (fewer and more expensive components, including sources) and the need for bulk optics components (collimating lens).
(d) Hybrid tunable filter/Mach–Zehnder approach
A hybrid FBG interrogation method is shown in the schematic of figure 6. In this technique, light reflected from the FBG sensor array is coupled back through a scanning SFP, which, as described earlier, passes only a narrowband wavelength. Use of the SFP filter in this way serves to discriminate the individual grating signals in the array. However, the SFP filter in this method is only being used as a wavelength gatekeeper, and not as a wavelength calculator, as was described in the previous SFP-based method. Since precise comparison between scan voltage and zero-crossings is not being made, the frequency of the signal used to drive the SFP filter in the current method may be much higher, as signal distortion is not of much importance.
As the SFP filter passband passes a given FBG reflection peak, the light is transmitted to an unbalanced Mach–Zehnder interferometer with a small optical path difference (of the order of 3 mm). Light is then passed through a 3×3 coupler, where phase offsets (ideally, 120°) are induced between the three outputs, and finally the light from the three coupler outputs is passed to three photodetectors for voltage conversion. It is in this optical architecture that the term ‘hybrid’ as a descriptor is apparent: both an SFP filter and an interferometer have been used at this point.
Interferometric measurements are well known to be affected at very low frequencies by ‘drift’ in the interferometer, as mentioned, represented by the ϕenv term in equation (2.1). Tracking this drift is crucial for detection of static to quasi-static FBG wavelength (phase) shifts. As shown in figure 6, light emitted from the source is not only sent to a 2×2 coupler, and the outputs of that coupler carry light to both the sensing array, as described, but also to a simple FBG wavelength compensation module. The reference module consists of two gratings in a small sealed package, one bonded to a glass strip (λG) and the other to an aluminium strip (λAl). These gratings are sensitive only to thermally induced wavelength shifts, so the changes in phase of the FBGs in this reference device may be directly computed as(2.3)where λG and λAl are the material thermal expansion coefficients, ΔT is the temperature change and ϕenv corrupts both phase changes equally at the interferometer. Two equations with two unknowns (ΔT and Δϕenv) allow for simultaneous tracking of the interferometer and determination of thermal effects. The solution can be easily written as(2.4)
The solution exists provided the materials do not have the same thermal expansion coefficients. On the phase unit circle, the reference FBG phase changes, as described in equation (2.3), may be interpreted as follows: if the interferometer is drifting (regardless of its source) and the temperature is steady, then ϕenv is changing, and the two FBG phases ΔϕG and ΔϕAl will move together around the circle at a constant relative angle of separation (global phase translation). If, however, the interferometer is stable but the temperature is changing at the compensation gratings, the phases will move in such a way that their relative angle of separation will change, in proportion to the difference of the aluminium and glass thermal expansion coefficients (global phase dilation).
The compensation grating array may be sampled any time as determined by the application and is interrogated serially with the sensor array. Since little phase shift (wavelength shift) is typically associated with the compensation array, the compensation FBGs may be written with closely spaced reflection wavelengths and placed globally at one far extreme in the SFP filter scan wavelength band. In this way, the compensation array costs a negligible penalty in the dynamic range of the sensor array. Further gains in interferometer drift minimization may also be achieved by keeping the optical path difference as small as possible without sacrificing too much sensitivity, and this overall optimization is an attractive feature due to its inherent passivity.
The phase measurement encoding the FBG wavelength (and thus strain) information is performed using all three photodetector outputs. The three voltages Vn (n=1, 2, 3) may be expressed as (Todd et al. 1999b)(2.5)where an is related to the nominal Bragg reflection intensity, bn is related to the modulation depth of the interferometer, ϕ is the phase as before and θ is the coupler angle. In an ideal 3×3 coupler, these angles are 0, 120 and −120°; deviations from these ideal angles are often observed, however, usually due to polarization sensitivity. It may be shown through trigonometric relationships that(2.6)where αn=an/a1; βn=bn/b1; μn=βncos θn/αn; γn=βnsin θn/αn; and the are the three photodetector voltages normalized by the corresponding αn. This is an exact solution for tan ϕ, and since digital processing chips exist which allow taking the continuous (full unit circle) arctangent with absolute phase unwrapping, this solution may also be considered exact for ϕ. The various μn, γn and θn may all be obtained by a calibration signal of known size, as these values are related to the fundamental coupler constants (Weighs et al. 1996). However, these ‘constants’ have certain sensitivities to temperature and state of polarization and will typically vary by a couple percent over time. For long-term monitoring applications where high levels of accuracy in these constants are required, they must be monitored and re-computed at some prescribed interval. Inaccuracy in these values leads to error in the recovery of ϕ in equation (2.6), and in some extreme cases, this error can be a few percent. Evidence of these effects has been recently reported in Wiener & Todd (2002), and a discussion of the resulting distortion from these effects is reported in Todd et al. (2002).
This method of obtaining the phase shift offers the advantage of passivity, with no active components to limit or distort frequency response or dynamic range. Furthermore, the method is immune to source intensity fluctuations, provided enough light impinges the detectors, which is usually in the 10 μW range. The overall light level scales out in equation (2.6), since everything may be expressed as ratios.
Several tests were performed to demonstrate the features of the full system. First, a grating was mounted to a cantilever beam and co-located with a conventional resistive strain gauge (RSG), and the simultaneous responses of the two gauges as the beam was loaded are shown in figure 7a. An artificial 100 μϵ offset was applied to the resistive gauge trace in order to distinguish the responses as the beam was manually bent and sent into free vibration. Clearly, the FBG response, from an accuracy point of view, is indistinguishable from the resistive gauge. The noise floor of the system was measured in situ in the laboratory without any acoustic or thermal isolation of the interferometer, and the amplitude spectral density calculation is shown in figure 7b, in optical units on the left and equivalent mechanical (strain) units on the right. Above ca 100 mHz, a resolution of ca is achieved, which, for the interferometer used (ca 3 mm optical path difference), is ca . Such strain resolution capability exceeds by several orders of magnitude the capabilities of typical commercial, structural-grade RSG systems, exceeds the older SFP filter method and rivals the WDM method capability.
Results to test the performance of the demodulation scheme are shown in figure 7c,d. In figure 7c, a large-amplitude signal of just less than 4π rad (ca 900 μϵ) is applied to a four-grating array, and the figure shows that the arctangent calculation, with phase unwrapping, is performed properly. Figure 7d shows the result when a constant sinusoidal signal is applied to a single grating while the light source is modulated randomly. Arrows drawn on the figure indicate which vertical scale corresponds to each trace. The figure clearly indicates that although the voltage at the detectors (one of the three is shown in the bottom trace) is fluctuating, the resulting demodulated grating signal (the top trace) remains stationary.
A series of tests were also performed to test the effectiveness of the compensation module. A single sensor grating was attached to the system, and both the interferometer and the reference grating system were subject to various conditions. The test conditions, particularly with regard to the induced thermal fluctuations, were chosen to exceed conditions which may be encountered in a challenging field application. The first test consisted of acoustically isolating both the interferometer and the compensation gratings, and then placing the sensor grating in a thermal chamber held at 30°C for 14 h. The room temperature was observed to change approximately ±2°C over the 14 h. A typical FBG has a thermal sensitivity of approximately 10 μϵ °C−1. Given that the thermal fluctuations in the chamber are of the order of a few tenths of 1°C, a compensated drift of the order of 1 μϵ or so is expected. The uncompensated data, conversely, fluctuated 40 μϵ peak-to-peak, and this fluctuation would be falsely interpreted as mechanical strain.
The second test consisted of thermally loading the interferometer between 10 and 40°C while holding the reference system at 0°C. The uncompensated false mechanical strain signal approached 300 μϵ, while the maximum error in the compensated signal reached only 19.3 μϵ, representing less than 0.4% of full scale.
In the final test, both the interferometer and the compensation gratings were subject to rapid thermal loading from 20 to 50°C over less than 1 h. The uncompensated signal deviated almost 400 μϵ, while the maximum error in the compensated signal was ca 33 μϵ, or ca 0.6% of full scale. The largest error in the compensated signal occurred during the most rapid rise of the temperature in the first hour of the test, and the most likely source of error here is the mismatch in thermal inertias of the glass and aluminium substrates to which the reference gratings were bonded. The present reference algorithm does not account for thermal dynamic effects such as thermal inertia, and future materials selection should include the matching of thermal masses (conductivities) in the substrates used. This conclusion is supported by the fact that once the temperature stabilized after the first hour, the maximum compensated error was only 13 μϵ, so it is likely that the temperatures were being miscalculated during the transient portion of the test.
In all the cases, the temperature compensation significantly reduced errors in the signal. The errors manifest themselves as accuracy errors (with regard to measuring purely mechanical strain) but do not affect the resolution capability of the system as such at frequencies away from DC. In other words, temperature-induced fluctuations would still permit high resolution (nano-strain level) of strain in time-evolving strain field, but the absolute accuracy of the measurement (mean value) would be degraded. In this way, this system behaves the same way as a traditional RSG system behaves.
A broad summary table of relevant performance metrics is shown in table 1 for each of the Bragg interrogation methods considered in this paper. Each method clearly has its strengths and weaknesses, and only an end-user can appropriately judge the importance of a given metric for a certain application of a given method. For example, lower frequency applications may benefit from an SFP filter method, but high-resolution applications would benefit from either the AOTF or hybrid method. The CCD method is very conducive to high levels of multiplexing and has the advantage of true simultaneous interrogation of all FBGs in an array, but it relies on sub-900 nm components and bulk optics, and it has not been as fully deployed in field applications to test robustness and packaging. The new hybrid method appears to fill a wide variety of application requirements for structural monitoring, including excellent strain resolution, high multiplexing capability, wide dynamic range and relatively simple architecture.
3. Experimental application: hull monitoring of a composite fast patrol boat
In Spring 1999, a new pre-series fast patrol boat, KNM Skjold, was delivered by Kvaerner Mandal to the Norwegian Navy. The ship was a 45 m long twin-hull surface-effect ship (SES) made of fibre reinforced polymer sandwich composite. A photograph of the boat is shown in figure 8. By using the SES design, the drag on the hull was reduced by lifting the ship on an air cushion confined by the twin hulls and two flexible ‘curtains’ fore and aft. This design combined with the high speed (more than 40 knots), required a carefully weight-optimized design in order to minimize fuel consumption. During sea-keeping tests in the North Sea, the Norwegian Navy Material Command cooperated with the Composite Hull Embedded Sensor System (CHESS) programme, which was a cooperative fibre optic sensor technology research programme run by the US Naval Research Laboratory (NRL) and the Norwegian Defence Research Establishment (FFI). The main objective of the CHESS programme was to develop a hull monitoring system using a network of fibre optic Bragg grating strain sensors. An experimental version of this system, which includes a PC-network for signal processing and data storage, was installed on the KNM Skjold for full-scale evaluation and was also used during the sea tests.
During the sea trials, a number of runs were made under different conditions with respect to sea-state, heading and speed, as shown in the map of figure 8. Since it was built as a pre-series ship, the performance of the ship was systematically tested, with special emphasis on rough seas for design robustness confirmation. The test matrix consisted of 20 min runs at headings of 0, 45, 90, 135 and 180° with respect to the seaway. For each heading, four runs were taken: (i) surface-effect fans off, full speed diesel engines; (ii) fans on, full speed diesel; (iii) fans on, gas-turbine engine at 25 knots; and (iv) fans on, full speed gas-turbine engine (ca 50 knots). The wave profiles, sea-state and movements of the ship were determined by means of an instrumentation package consisting of a movement recording unit (MRU), a GPS system and a wave radar in the front of the ship installed and operated by Marintek, Inc. The CHESS system was used to measure global bending in the hull, local strain in selected areas and strain in the waterjet propulsion system. The placements of the 56 FBG sensors, also shown in figure 8, were based on extensive finite element method (FEM) analysis performed by the ship designers. The FEM analyses were used to determine the global response for the dominant load components and to establish the link between force and strain. Two systems were used for FBG sensor interrogation: hull events were monitored with the tunable SFP system; and higher frequency waterjet monitoring was performed with the WDM/interferometric method. This dual architecture had to be hybridized into a common system, and the complete system is shown in figure 9. Fibre couplers were used to bifurcate the sensor arrays as shown such that a common broadband optical source could be used for cost reduction. Sample rates for the two sub-systems were set at 360 Hz for the hull monitoring and 20 kHz for the waterjet monitoring. The 56 sensors were placed throughout the ship on 11 arrays that all terminated in the ship's control room where the instrumentation was located.
One rough-sea scenario of particular interest to the ship designers is the so-called wet deck-slamming event. In this event, an impacting swell of water is essentially trapped between the two hulls causing a violent jarring of the ship, giving rise to peak strain levels several times the normal strains encountered, even in higher sea states. Wave impacts provide most of the energy for exciting the global and local modes of the ship and the hull sub-structure. Wave slamming refers to the most extreme cases of wave impacts and concerns the designers owing to the peak loads encountered during these events. Wave-slam loads may cause core-crushing or core-shear failures due to overloading, and these core fractures will grow progressively into a delamination when they appear in the sandwich structure. In addition, slamming occurring in the forward part of the hull results in a peak sagging moment including whipping effects. To reduce the risk for overloading the core, the hull has been designed to withstand extreme wave pressures against the wet deck. On this weight-optimized structure, it is therefore of interest to monitor the peak strains, magnitude, direction and associated transient responses of the slamming events to evaluate the need for the current reinforcements.
Figure 10 shows the strain levels encountered in one of the harder wave slams encountered. Three longitudinal sensors are shown from arrays A, C and D. Whereas even in very rough seas (sea-state 6) the typical strain levels of these sensors is between ±200 μϵ, the slamming event seen near 413 s gives rise to strain levels up to 2500 μϵ. These slamming events may be visualized in the plane wherever a strain gauge rosette is present. In a planar strain state, the axial strain at any angle in the plane may be obtained from knowledge of the three rosette components:(3.1)This coordinate transformation may be computed at each time instant. Graphically connecting the polar plot snapshots taken at each instant is convenient for identifying the orientation of the principal strain axes as it evolves under the constantly varying loading conditions of the swell state and wave impacts. Figure 10 follows the strain concentration at the location of the K array during a data run head-on into the wave-front at full speed. In the top left, the raw data are plotted. A subset of the data containing a slamming event is cast into polar form on the lower right, and a zoomed view of the event is shown on the lower left. A colour scale is convenient to distinguish between tensile (red) and compressive (blue) strain. The vertical axis in the picture corresponds to the transverse ship direction, while the horizontal plane represents the longitudinal direction. This event indicates a strong transverse strain due to the slam, but slightly off axis with respect to the ship's coordinates. Such a time-evolved state of plane strain gives important information regarding how a slam event loads the composite material such that the layup of ply directions could be optimized for dominant loading directions.
The propulsion system for the boat consists of two waterjets, the impellers of which are powered by diesel engines at low speeds and a gas turbine engine at high speeds. As mentioned earlier, sensors were also placed on the waterjet tubes to monitor both high-frequency machinery vibrations as well as strain imparted on the tubes by the coupling to the hull. Figure 11 shows an aft view on the boat as it is accelerated from idle to cruise. A real-time spectrogram, showing the frequency content in the grating array in time, is also shown. Clear streaks corresponding to the engine's fundamental rotational speed and its harmonics are observed, gradually increasing the frequency as the throttle is increased.
The real power of the FBG sensors in this application lies in their low-noise characteristics. Figure 12a shows a comparative plot between amplitude spectral densities of the waterjet sensor responses immediately after acceleration to cruising speed and several minutes later. Sub-microstrain resolution capability in such a system allows for possible detection of subtle engine characteristics: there is a very clear transition in this plot from the higher noise floor right at the end of the acceleration phase to the lower noise floor during cruise, and small deviations from this in either time or magnitude may be interpreted as sub-optimal waterjet performance. Another similar example of the high-performance characteristics of this system is shown in figure 12b. Here, both time-series and corresponding amplitude spectral densities taken from the waterjet sensor array are presented under three conditions: engines off, cruise in normal seas and rough seas. Again, the high-resolution capability of the system allows easy discrimination of these operational conditions, and this information is vital in designing algorithms for robustly diagnosing the appearance of damage in the structure.
4. Experimental application: joint degradation assessment
In another application, the hybrid Bragg grating 3×3 interrogation system was used to help assess bolt pre-load loss in a hybrid material joint. The bolt fastens a steel member to a composite material member, and over time (particularly under elevated temperatures or mechanical loads), the composite material creeps, leading to loosening, pre-load decrease and loss of functionality. The goal of this experiment was to determine whether features extracted from vibration measurements made with the fibre optic strain measurement system could be used to track this pre-load loss. The hybrid measurement system is particularly useful in applications such as this owing to the embedding capability of the fibre within the composite material or within the gap between the metal and composite section; other sensor types are much more likely to affect the joint's functionality or to be corrupted by extraneous electromagnetic noise. Given that these hybrid joints are being considered for superstructure connections in the next-generation US Navy destroyer DD-X, this latter advantage is of particular importance with significant onboard electromagnetic activity created by communications and weapons systems.
Over the last 2 years, a new vibration technique for structural damage detection based on chaotic attractor property analysis has been introduced (Todd et al. 2001b; Nichols et al. 2003a, b). The technique involves applying a chaotic dynamic excitation to the structure and extracting properties of the resulting chaotic structural response. The structural response may be represented in its state-space, where each state variable traces out some trajectory in time; ultimately, if given a stationary input, the state approaches an attractor, which may be thought of as a geometric subset of the state-space. The idea in structural health monitoring is that as damage progresses on the structure, the dynamics are affected in such a way as to affect the properties of the attractor. Attractor-based analysis and state-space methods in general have been used in a number of other applications, such as system identification (Nichols et al. 2001; Nichols & Virgin 2002, 2003), data cleansing (Kantz et al. 1993), detecting non-stationarity (Schreiber 1997), and building predictive models (Sauer 1993). Essentially, the current method uses a model-building approach to predict and compare attractors between damaged and undamaged structures; the feature exploited in this comparison was the nonlinear cross-prediction error (NCPE). In this current work, we extend this approach to predict and compare relationships between attractors on the structure and to observe how this relationship changes as damage progresses, rather than just how a specific attractor changes as damage progresses. This newer idea is motivated by the damage scenario which will be studied, that of connectivity loss in a bolted joint. As the physical connectivity is gradually lost between members, it is expected that relative dynamics between locations on either side of the damaged area may be optimally sensitive to such damage. This approach is not unlike the use of transmissibility functions (relative frequency-response functions) in the modal analysis paradigm (Worden et al. 2003).
A thorough review of this newer approach may be found in Todd et al. (2004). Sensor responses to chaotic excitation are measured at various locations, and corresponding state-space models are constructed. The general idea is to quantify a functional relationship between the any two pairs of attractors, Xi and Yi, and observe how that relationship may change over time. The relationship is established by using one attractor to forecast the evolution of the error and build an error metric (‘prediction error’) between them as the forecasting ability breaks down. Prediction errors close to unity indicate a lack of a continuous functional relationship. The working hypothesis is that such a relationship does exist due to strong coupling between the two structural locations chosen for attractor reconstruction, and that damage will cause the relationship to change.
This approach was tested on a composite beam measuring 1.219 m in length ×17.15×10−2 m in width ×19.05×10−3 m in thickness. The beam was bolted at both ends to two steel plates, and the entire assembly was then clamped to a fixed base as shown in figure 13. The composite material utilizes a quasi-isotropic layup consisting of (0/90) and (±45) knit EGlass fabric. The specific layup is [(+−45), (0/90)]6S meaning there are six sets of (+−45), (0/90) plies stacked on top of each other in the first half of the laminate. The ‘S’ is used to denote a symmetric laminate meaning that the other half of the laminate is six sets of (90/0), (−+45) plies stacked on top of each other. The structure is bolted to a steel frame using 19×1.9 cm thick bolts 8.9 cm long. Each of the bolts is ALD-DYNAGAGE instrumented bolts capable of measuring axial force. Excitation was provided by means of a B&K electrodynamic shaker located at the mid-span of the beam and oriented such that the stinger was pressing down on the beam. Between the stinger and the beam is an OMEGA LCFD-25 load cell for recording the input signal. Labview data acquisition software was used to transform the pre-recorded chaotic Lorenz signal into a voltage suitable for the shaker controller. A sample excitation wave-form is shown in figure 14 along with its corresponding phase space representation. Both the plots show the characteristic ‘lobes’ of the Lorenz system used to excite the beam. Essentially the system oscillates between two fixed points at banded, but varying, frequencies. The structure in the phase portrait is a hallmark of chaotic systems and is what guarantees the practitioner the ability to build low-dimensional models of the dynamics. It is worth mentioning that this approach to excitation is no more difficult to implement than white noise, or swept-sine inputs. The only difference is that the values output to the shaker controller are the output of a dynamical system as opposed to a random process, or non-stationary ‘chirp’ equation.
Ten different levels of bolt pre-load (Nd=10) were assigned to the bolts at one end of the beam, starting at approximately 50 kN for the baseline case. The torque on every bolt could not be exactly controlled to 50 kN due to variations in the individual connections and uncontrollable creep in the composite material. Figure 15 shows the progression of axial load for each of the four instrumented bolts. The locations of these bolts are displayed in figure 13. The bolts on the undamaged end of the beam remain relatively unchanged for the duration of the study; however, as mentioned, there is a slight amount of creep that takes place. This effect is deemed negligible as the creep changes the axial load by 3–5% while manually controlled pre-load loss on the damaged end of the beam is near total (99%). Although creep is the normal mechanism by which pre-load is lost, manual control of pre-load over a wide dynamic range allowed a more complete study in a shorter period of time.
Structural response data were collected on either side of the connection using FBG strain sensors interrogated by the hybrid 3×3 system described previously. One sensor was located on the steel plate while the other was located approximately 7.5 cm from the bolts on the composite beam. They are labelled sensor 2 and sensor 1, respectively, as shown in figure 13. All data are subjected to a detrending and normalization procedure prior to implementing the NCPE model. The detrending process removes the best straight-line fit linear trend from the data. Each time history is then normalized by subtracting the mean value of the signal and then dividing by the standard deviation. This was done in order to minimize operational variability-induced changes in signal mean and/or variance from being identified as damage.
At each pre-load level (figure 15), five experiments were conducted. Sample attractor reconstructions for the two systems are shown in figure 16 for the case of no damage (pre-load at 50 kN). Data collected from the steel plate show a slightly more ‘blurred’ attractor. Since the sensor at this location was further from the driving signal, the integrity of the ‘true’ waveform is somewhat diminished. For each attractor pair, a total of 1000 individual cross prediction errors were computed resulting in 25 000 total values for each pre-load level. The resulting sets of prediction error were resampled so that confidences could be generated based on the mean values. Based on the resulting normal distribution, confidence intervals of 95% were constructed and are displayed in figure 17. We will adopt the notation 2→1 to denote the usage of sensor 2 data to forecast data taken from sensor 1 and vice versa.
Figure 17a shows the progression of the confidence intervals with damage, while the lower plot shows the corresponding probability density functions. Confidence limits for the undamaged case are highlighted in grey. Any subsequent interval that lies inside this area is commensurate with the no-damage null hypothesis; hence damage cannot be detected at the 95% confidence level. Conversely, intervals which do not overlap this region are in favour of the alternative hypothesis that dynamical change to the system has occurred. Clearly, pre-load loss is detectable at approximately 17.8 kN of pre-load. At this point, the mean prediction error begins to climb and damage is indicated. At the 22.2 kN level, damage is detected at approximately the 50% confidence level, possibly indicating that the bolt is beginning to become loose. The overall magnitude of the prediction error is low, ca 3.5% of the signal variance. This is a strong indication that a functional relationship exists. As the connection degrades, the functional relationship is diminished thus reducing the ability of one sensor to predict the dynamics of the other. This is evidence of a reduction in the strength of the coupling between the dynamics on either side of the connection with damage. This test may also be used to discern the magnitude of the axial load. The trend is such that many of the intervals are separate from one another indicating that the algorithm identifies the data as coming from several different dynamical processes, each corresponding to a different load.
The test can also be applied in reverse, i.e. using sensor 1 to make predictions for sensor 2 data. Results for this test are shown in figure 17b. While a clear functional relationship still exists (the magnitude of the error is O(10−1)), the ability for this relationship to serve as a damage indicating feature is degraded. In fact, a clear indication of pre-load loss does not occur until the load is approximately 4.4 kN. One possible reason for the discrepancy concerns the relative quality of the data being used to make predictions. Sensor 2 tended to produce a stronger, more deterministic strain response, hence a more well-defined attractor (figure 16). Therefore, using sensor 2 data as the model for making predictions would seem to result in an improved ability to capture the dynamics and consequently dynamical change. Another possible reason concerns the functional relationship, Ψ. There is no way to know a priori what this function looks like or how it is affected by damage to the system. Consequently, there is no way to assess which operator Ψ or Ψ−1 is a better indicator of damage.
As a comparison, a time-domain autoregressive (AR) model was built to make predictions from one response location to the other. AR models regress future dynamics on weighted sums of past and present dynamics in time, rather than in state-space geometry, as with the NCPE approach. Based on the data autocorrelation, a sixth-order AR model was constructed using the data collected from sensor 2. Predictions one step into the future were then made on the sensor 1 response. The test was then reversed, using sensor 1 data to forecast the response of sensor 2. The resulting AR prediction error for both sets of tests is displayed in figure 18.
Using the AR modelling approach, pre-load loss is not detected until the axial bolt load has dropped below 13.3 kN. Furthermore, this approach did not produce a monotonic trend with damage. Such a trend is helpful if the feature progression is to be used to make predictions about remaining useful structure life (in this case axial load on a bolt). It is unclear that why the AR residual error drops for the ca 0.9 kN loading scenario. One possibility is that building a model based on average temporal correlations can obscure certain local dynamic subtleties. The second comparison (1→2) again resulted in a diminished ability to classify bolt load. No changes in the beam dynamics are observed until the axial bolt load approaches 0.9 kN. It is hypothesized that the reason is the same as that for the NCPE, namely quality of data. While not as effective as the NCPE, the AR approach still yielded useful results and should not be discounted for this type of application. Although the approach is less general in terms of modelling, it is easy to implement and takes less time to run. For example, the AR approach can generate a single set of 2000 predictions (enough for one resampled value) in ca 2 s while the NCPE takes approximately 10 s on a 880 MHz digital computer. Neither approach takes a prohibitively long time (a real-time version of NCPE has been implemented successfully by the authors) but there may be certain instances where the increase in processing speed is important.
This paper has presented and performance-compared various common Bragg grating wavelength shift demodulation architectures which have been incorporated into strain measurement systems for structural monitoring. These methods included WDM/interferometry, tunable filter approaches, CCD/prism approaches and hybrid tunable filter/interferometric method. Two applications using these systems were presented. First, both a tunable filter system and a WDM/interferometry system were used to monitor hull loads and waterjet performance on a composite material fast patrol boat during sea-keeping exercises. Second, the hybrid system was used in conjunction with a new technique in attractor-to-attractor mapping to detect bolt pre-load loss in a composite-to-metal bolted joint.
The authors acknowledge Dr Gregg Johnson of Optinel Inc. (formerly of the US Naval Research Laboratory Code 5673) and Charles Askins of the US Naval Research Laboratory (Code 5675) for useful technical discussions and development. The authors acknowledge Dr Frank Bucholtz, of the US Naval Research Laboratory (Code 5650), for his technical study of the MEMS tunable Fabry–Perot filter. The authors also acknowledge Keith Berube of the University of Maine for providing the hybrid joint specimens. This work was supported in various parts by the Federal Highways Administration (Dr Richard Livingston, program manager), the Office of Naval Research (Dr Roshdy Barsoum, program manager) and the National Research Council.
One contribution of 15 to a Theme Issue ‘Structural health monitoring’.
- © 2006 The Royal Society