Co-Located Tiangulation fo Position Identification fom a Single SHM Node Seth S. Kessle and Ajay Raghavan Abstact A fundamental limitation fo cuent Stuctual Health Monitoing (SHM) systems is the need fo distibuted synchonous sensos to detemine pecise damage location using taditional tiangulation methods. Accuacy is dictated by senso density (quantity and poximity), which dives complexity, weight and cost to esolve eliable position. This pape intoduces a patent-pending eal-time method to pedict accuate damage location fom a single SHM node. This co-located tiangulation method consists of novel sensos, algoithms and hadwae to achieve a significantly moe efficient means of localizing damage. Results ae pesented fo poof-of-concept expeiments on an aluminum plate using guided waves, as well as theoetical accuacy and limitations fo the method. Finally, a desciption of a pototype unde development is pesented. SHM technology will be citical to educing the oveall cost of owneship fo ai and spacecaft, and the pesent eseach could play an impotant ole in implementing such a system feasibly, pactically and efficiently. Index Tems damage detection, Lamb Waves, piezoelectic senso, Stuctual Health Monitoing, tiangulation S I. INTRODUCTION tuctual Health Monitoing (SHM) implies the incopoation of a non-destuctive evaluation system into a stuctue to povide continuous emote monitoing fo damage. SHM has the oveall goal of impoving vehicle safety and eliability while educing maintenance and inspectionbased life-cycle costs [1-4]. Duing the couse of ecent eseach, Lamb wave methods have been poven a eliable technique to collect valuable infomation about the state of damage within a stuctue. Seveal investigatos have successfully used Lamb waves to detemine the pesence and location of damage within both metallic and composite specimens [5-18]. Typically, Lamb wave methods ae implemented using a distibution of piezoelectic elements popagating ultasonic elastic waves in a pitch-catch mode. This esults in measues of delayed and attenuated signals along each possible actuato and senso path, as well as occasional scatteed eflections fom damage sites. This data can then be used to econstuct damage location by using taditional tiangulation calculations. While this methodology Manuscipt eceived May 19, 008. Seth S. Kessle is with the Metis Design Copoation, Cambidge, MA 0141 USA (phone: 617-661-5616; fax: 617-507-666; e-mail: skessle@metisdesign.com). Ajay Raghavan is with the Metis Design Copoation, Cambidge, MA 0141 USA (e-mail: ajay@metisdesign.com). has shown pomise, accuacy is dependent on the senso netwok density. To esolve small damage pecisely, a lage aay of sensos in close poximity must be employed, which inceases the system complexity, weight and cost with additional wies, acquisition channels and volume of data. This tadeoff has pesented a majo obstacle to deploying a pactical lage-scale SHM system [19]. To emedy this dilemma, the pesent investigatos have developed a patent-pending method to pedict accuate damage location fom a single SHM node. This co-located tiangulation method uses a novel senso design along with an innovative algoithm to geatly educe the senso density equied to localize damage. By inceasing efficiency without sacificing accuacy, this methodology povides a feasible path to deploy a Lamb wave-based SHM system in commecial applications. II. THEORY The co-located tiangulation methodology daws much of its benefit fom the fact that it is pulse-echo based athe than pitch-catch. In pulse-echo mode, an excitation adiates fom a souce (omni-diectional Lamb waves in the pesent case) and subsequent eflections ae measued fom the same location. In the liteatue, pulse-echo testing has been achieved using self-sensing cicuits, which allow a single element to excite and sense simultaneously o in quick succession, as well as side-by-side senso and actuato elements [0-4]. While both of these methods have meit, they pesent logistical and analytical challenges that limit thei applicability to most implementations. Theefoe, the pesent investigatos have invented the patented concept of co-located senso and actuato elements fo pulse-echo applications, whee co-plana elements ae positioned in close poximity to substantially suound each othe (i.e. an actuato cicumscibing a collection of sensos o the convese). These elements can be physically unique, o ceated vitually though selective plating o poling. The pesent eseach embodies this concept with an SHM node compising of 4-senso and 1-actuato elements fabicated in a delibeate patten fom a single piezoelectic wafe. Using this node, co-located tiangulation pedictions can be ealized by using complementay algoithms.
A. Algoithm The damage site is assumed to be a Lamb wave scatte point descibed by its adial and angula position ( and φ) in a pola coodinate system, with the oigin at the cente of the SHM node. The time at which the peak of the wave packet oiginates fom the damage site is t s and t i (i = 1 to 4) is the time the peak of the wave packet aives at each of senso element positions at adius a. The oientation of the sensos fo this deivation is shown in Figue 1. Distance to damage fom each senso can then be descibed by elating the goup speed c g and the espective times of flight: ( a cosφ ) + sin φ = c ( t ) (1) g 1 t s g t s cos φ + ( a sinφ) = c ( t ) () g 3 t s ( a + cosφ ) + sin φ = c ( t ) (3) g 4 t s cos φ + ( a + sinφ) = c ( t ) (4) Simplifying and consolidating equations 1-4 yields: ( t4 t )(. t4 + t ts ) ( t t )(. t + t t ) 3 1 3 1 s tanφ = (5) Since the senso pais 1/3 and /4 ae diagonally opposite and equidistant fom the cente, it is easonable to assume that t + t ) ( t + ). Theefoe equation 5 can be simplified to: ( 4 3 t1 t4 t tanφ = (6) t3 Solving fo φ yields the following pai of equations: φ = atan( t4 t, t3 ) if t4 t t3 (7) = atan( t3, t t4 ) π othewise whee atan is the fou-quadant invese tangent function. In the expeiments, senso 1 was at 45 o elative to the x-axis so esults wee offset by 45 o. Finally, the adial distance was calculated based on the aveage time of flight fom the fou sensos: t1 + t + t3 + t4 = 0.5c g ta (8) 4 whee t a is the peak of the excitation pulse. Theefoe, to solve fo and φ, each of these t values must be mined fom the expeimental data. Senso esponse signals ae detended and filteed with zeo-phase highe-ode Buttewoth filtes to emove noise in the fequency bandwidth outside the excited ange. The diffeence signal between the test and baseline signals ae then poduced, and convolved with the excitation signal to obtain the signal component at the cental fequency. A Hilbet tansfom applied to this signal component poduces a signal envelope, and a peak extaction algoithm applied to this envelope yields the times coesponding to the peaks of the eflections. 3 φ Actuato 4 1 a Figue 1: SHM node oientation and coodinate system B. Method Limitations The accuacies of all wave-based methods ely on seveal paametes [7]. They paametes can be gouped into 3 inteelated categoies: algoithm-dependant, specimendependant and hadwae-dependant eos. While these souces of eo can affect taditional wave-based methods, many of them have a moe diect and significant impact on the pesented method, howeve, due to the sensitivities of govening equations descibed above. The most independent of these potential souces of eo ae the algoithm-dependant paametes. The algoithm must be obust towads poo signal-to-noise atios as typically seen in wave popagation [7]. Next, the pecision with which the eflection peaks can be identified by the algoithm is citical in detemining coesponding time-of-flight. Without eliable peak detection, the algoithm pecision apidly deteioates. Fo specimen-dependant eo, the fist consideation is the atio between size of the damage (d) and the wave mode wavelength (λ). If this atio is too small, the damage causes weak eflection signals, leading to highe algoithm-based eo. As this atio appoaches and exceeds unity, while the eflections ae stonge, the point souce assumption weakens. Consequently, sensos may detect eflections oiginating fom diffeent points of the damage site. Next, wave goup speed c g plays a staightfowad ole in location accuacy. It has a linealy popotional contibution with adial position calculation, as seen in equation (8), and the elative spacing between the peaks of the wave eflection fom the damage site also deceases with inceasing c g, theeby inceasing the potential fo angula position calculated eo. The final consideation is hadwae-dependant eo. Fist, this is the main location fo noise intoduction, both fom poo shielding and intenal cosstalk. Cae must be taken to guaantee good signal fidelity fo the algoithm to be successful. The most fundamental limit, howeve, is placed on this method by the data sampling ate, which detemines how pecisely the individual peaks of eflections can be esolved. Fo example, in the pesent tests with a sampling ate of 10 MHz and a c g of ~.5 km/s, the angula eo caused by an inaccuacy in peak detemination by a single sample point is 1-. The coesponding eo in adial location is negligible (~0.1 mm fo damage at a adius of 5 cm). These eos ae appoximately invesely popotional to data sampling ate, and ae linealy popotional to c g.
III. VALIDATION To validate this co-located tiangulation methodology, pototype nodes and hadwae wee fabicated, and the algoithm was coded within Matlab. The following sections descibe the expeimental pocedue that was followed to localize epesentative damage in a lage aluminum plate. While it was not possible to demonstate evey aspect of this methodology in this initial test, the esults povide sufficient evidence to pove the concept valid. A. Hadwae Design To implement this method, 5 synchonously sampling channels of data acquisition wee equied (4 fo the sensos and 1 fo the actuato fo pecise timing) along with an abitay function geneato and appopiate signal conditioning cicuity. A custom miniatue 100 MHz hadwae system was designed by the pesent investigatos using thei patented Point-of-Measuement technology, and a 5 x 10 x 0 cm pototype system was fabicated. While this pototype was able to successfully conduct testing and collect the equied data, a design flaw led to a pesistent oveheating poblem, equiing the system to e-boot fequently. Theefoe in the inteest of time, and since this hadwae was not a citical element of the poof-of-concept, a 10 MHz Tektonix 3014B and Agilent 330 units wee used to collect the test data. B. SHM Node Design A 4-senso and 1-actuato element SHM node was fabicated to pefom the pescibed tests. The node was shaped by lase fom a single PZT-5A piezoelectic wafe, and selectively electode and poled so that the 5 elements could be accessed independently with a common gound. A flexible cicuit was designed to make electical connections to appopiate electodes and suppess EMI and coss-talk, while not impeding wave popagation. Subsequently, the wafe and flex-cicuit wee assembled using electically conductive filmadhesive in an elevated tempeatue cue unde vacuum, and a miniatue multi-pin connecto was installed to beak out the signals to hadwae, seen in Figue. Figue : Photogaph of pototype SHM node used fo testing C. Expeimental Setup The test specimen was a 0.9 mete squae 3. mm thick 6061 aluminum plate. A cicle of 0.5 metes in diamete was dawn centeed on the plate, and ay lines wee daw evey 10 adiating fom the oigin. Thity-six visual indicatos wee dawn at the intesections of the cicle and the ays to mak the field of damage locations. A common invese damage technique was used, whee stiffness and mass is added to the specimen athe than emoved so that epesentative damage could be intoduced in a evesible, epositionable and epoducible fashion [5]. In this case, 3 sizes of small magnets (3., 6.4 and 1.7 mm diamete) wee placed at the maked positions on the plate using shea couplant gel. Data was collected fo each size magnet at each maked position. D. Test Paametes The guided-wave (GW) mode wavelength and excitability cuves wee computed fo the descibed configuation using peviously developed models [6-7]. The fundamental antisymmetic (A 0 ) Lamb wave mode was stongest at 90 khz, which was also well below the cutoff fequency fo highe ode modes. This mode was selected ove the fundamental symmetic (S 0 ) mode since at this fequency it poduces a seven times lage esponse, and the S 0 mode wavelength (5.94 cm) is much lage than the A 0 mode wavelength (1.67 cm) and the epesentative damage diametes. The actuation signal was a 3.5-cycle tonebust modulated by a Hanning window and theefoe it can be consideed to be naowband excitation. All GW packets ae assumed to tavel at the A 0 mode goup speed at 90 khz (c g = 548 m/s). The baseline (undamaged) and test (damaged) signals wee obtained by aveaging 56 senso esponse signals coesponding to peiodic busts to maximize the signal-to-noise atio. Thee was a 300-ms delay between successive busts to ensue that bounday eflections caused by one excitation bust did not intefee with the esponses to the subsequent bust. IV. RESULTS The expeimental setup descibed in the pevious section was executed using the specified test paametes. A total of 36 data points wee collected fo each size of damage along the 0.5 mete ac, fo a total of 108 tials. Data collection was PC automated using custom Labview softwae. The esulting voltage vesus time files wee steamed into Matlab whee the coded algoithm pocessed the data. Figue 3 pesents the final algoithm esults fo pedicted vesus actual damage fo each magnet size, each plotted as a function of angula position in 10 incements. The fist 3 plots show the angula pediction accuacy, while the final plot shows the accuacy of the adial pedictions. The subsequent section will discuss the implications of these esults in futhe detail.
V. DISCUSSION While not quite achieving the theoetical accuacies fo angle and adius position pediction, both the aveage and maximum eo values fo the pototype system wee quite easonable. Potential souces of eo wee descibed in a pevious section, howeve since cae was taken to minimize hadwae-dependant eo, and the c g fo aluminum is simple to calculate, most of the eo can be attibuted to algoithmdependant souces. A. Angula Position Pediction The esults fo angula position wee pesented in Figue 3. Hee the data points epesent the algoithm pedictions fo each of the 36 test points, the solid line epesents the ideal case (pediction = actual) and the dashed lines epesent ±5% eo bounds (elative to 360 ). A summay of the absolute value and pecentage of maximum and aveage eo can be seen in Table 1. Oveall, the aveage eo fo all cases was 8.6 (.4%), with the highest eo falling at odd multiples of 45 and the lowest at multiples of 90, as anticipated by inspecting equation (7). A slight dependency on damage size was obseved, wheeas the maximum eo seems to incease slowly as the atio of diamete to wavelength appoaches unity (d/λ = 0.19, 0.38 and 0.76 espectively). Table 1: Maximum and aveage angula position pediction eo (degees) (degees) 3.18 1.1 5.9% 8.6.4% 6.35.9 6.4% 8..3% 1.7 4.3 6.8% 9.1.5% Figue 3: Expeimental esults fo pedicted angles and adii B. Radial Position Pediction The esults fo adial position wee also pesented in Figue 3. Hee the data points epesent the algoithm pedictions fo each of the 36 test points fo all 3 damage sizes. The y-axis limits epesent ±4% eo bounds (elative to 5 cm). A summay of the absolute value and pecentage of maximum and aveage eo can be seen in Table. Oveall, the aveage eo fo all cases was.4 mm (0.9%), with no appaent angula dependency, as anticipated by inspecting equation (8). No damage size dependency on eo was appaent in the absolute sense, howeve an inteesting tend obseved was that as damage size inceased, the algoithm tended to moe fequently unde-pedict the distance to damage. This could be due to the fact that while the cente of damage is identical fo each size, the damage peimete bounday physically moves close to the SHM node as the damage diamete gows. Table : Maximum and aveage adial position pediction eo 3.18 6..5% 3. 1.3% 6.35 4.3 1.7% 1.1 0.4% 1.7 6.5.6%.8 1.1%
C. Oveall Position Pediction Though a full ange of angles aound the 0.5 mete diamete cicle, the aveage angula pediction eo was <.5% and the aveage adial pediction eo was <1.0% fo all 3 sizes of epesentative damage tested (3.18, 6.35 and 1.7 mm diamete). Reconciling these angula and adial pediction aveages into a damage pediction aea foms a secto of an annulus. Theefoe, using this methodology, a single 5 mm diamete SHM node could locate damage as small as 8 mm anywhee within a 0.5 m diamete cicle (1963.5 cm ) to within an aea of uncetainty of <1.0 cm. VI. CONCLUSIONS This pape pesents poof-of-concept esults fo a patentpending co-located tiangulation methodology. A novel SHM node design and an innovative damage location algoithm wee developed. A pototype system was applied to a lage aluminum plate to demonstate the technology. While not achieving theoetical accuacy levels, the oveall esults fom poof-of-concept expeiments wee vey impessive. 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