16 H INERNAIONAL CONFERENCE ON COMPOSIE MAERIALS SHAPE IDENIFICAION USING DISRIBUED SRAIN DAA FROM EMBEDDED OPICAL FIBER SENSORS Mayuko Nishio*, adahito Mizutani*, Nobuo akeda* *he University of okyo Keywords: shape identification, optical fiber sensors, distributed strain data, inverse analysis, easureent error distributions, robust estiation ethod Abstract he accurate shape sensing ethod is expected to be useful for large scaled structural health onitoring of aircraft structures. his research is trying to construct a high-accuracy structural shape identification ethod using distributed strain data fro an optical fiber strain sensing syste; pulseprepup Brillouin optical tie doain analysis (PPP-BODA) syste. In addition, the optical fiber can be ebedded in coposite aterial, which has recently been applied for the structural aterial of aircrafts or soe other large-scaled structures. In this paper, we firstly considered the characteristics of distributed data fro PPP-BODA syste by the bea bending test using coposite specien with an ebedded optical fiber. In addition, the verification of easureent error distributions was carried out. And then, we proposed an appropriate shape identification algorith for bea banding deflection. he robust estiation ethod was adopted to correspond to outliers, and showed the effectiveness of the ethod. 1 Introduction his paper reports considerations for the construction of a shape identification syste using ebedded optical fiber sensors in CFRP coposite structures. We use distributed strain data obtained by one of the optical fiber strain sensing systes; pulseprepup Brillouin optical tie doain analysis (PPP-BODA). CFRP coposite aterial is increasingly used as the structural aterial of aircraft structures. hey require high safety and reliability in operation, even though they are used under severe environental conditions. his is the reason why the structural health onitoring (SHM) technology is regarded as iportant in the aerospace field. hus, the strain or teperature easureent technologies using optical fiber sensors have been paid attention for SHM syste. Moreover, the optical fiber is possible to be ebedded in coposite aterial. his akes it possible to realize a sart structure that is an integral structure of sensors. he accurate shape identification ethod is expected to be useful for large scaled structural onitoring of future aerospace structures. So far, several researches, which try to detect fatal daage of coposite aterial, have been conducted. However, as CFRP coposite is increasingly used, large scaled coposite structures, such as wing structures of aircrafts, are positively considered. herefore, the full-scaled shape identification syste will also be of advantage for SHM of large scaled coposite structures. It can ake it possible to detect undesirable deforations of wings or body of aircrafts in real-tie. Moreover, this syste is useful for detection of the theral displaceent in anufacturing process of large coposite structures. One of the points of our research is using distributed strain data. We use distributed strain easureent syste; PPP-BODA syste. Using this syste, strain distribution along an optical fiber can be obtained. here are few challenges for using distributed strain data to ake shape identification algorith. Soe prior researches tried the shape identification proble using discrete strain data obtained by FBG sensors or strain gages [1] [2]. However, in the use of these sensors, the nuber and the placeent of sensors greatly affect the accuracy of the estiated value. Moreover, it is difficult to put sensors on pre-deterined positions with accuracy. On the other hand, we can use optical fibers without any spatial processing like FBG sensors in the PPP-BODA syste. he sensor part is the whole length of the fiber. his akes it possible to lay optical fiber sensors networks on the whole of structures easily. herefore, such 1
MAYUKO NISHIO, adahito Mizutani, Nobuo akeda distributed strain sensor is suitable for full-field structural shape onitoring. he other point of this research is that we did verification using an ebedded optical fiber in the coposite specien. his akes it possible to show the possibility of sart structures, in which sensors for SHM are already internally installed. Reconstruction of displaceent fro strain data is to say an inverse proble. In general, such an inverse proble has ill-posedness, which eans that the proble does not necessarily satisfy the condition of existence, uniqueness, and stability of its solution. his point eans that the estiated values greatly depend on the easureent data characteristics. In this paper, firstly we explain the PPP- BODA syste; the easureent echanis and the spatial resolution of distributed data. hen, we report the result of bea bending test using a coposite specien with an ebedded optical fiber. Fro this experient, it was also udged whether the appropriate strain distribution can be obtained by the PPP-BODA syste. In addition, we verified easureent error distributions of PPP-BODA syste by iterative easureents of an unloaded optical fiber. Fro results of these experients, we considered the characteristics of distributed strain data obtained by PPP-BODA syste and the appropriate shape identification ethod. After that, we proposed a deforation identification ethod, and the estiation was carried out using the distributed strain data fro PPP-BODA syste. And then, the values of estiated deflection were exained, and effectiveness of the identification ethod was verified. 2 Principle of PPP-BODA Syste he pulse-prepup Brillouin optical tie doain analysis (PPP-BODA) sensing syste ipleents the stiulated Brillouin scattering technique [3]. Figure 1 shows the principle of this syste. wo laser beas, a pup pulse and a probe light (continuous wave), are inected into an optical fiber fro both its ends. he interaction of these two laser beas excites Brillouin scattering. he Brillouin scattering is excited in each frequency of the probe light. he value of the strain can be estiated by easuring the peak frequency of Brillouin gain spectru, while its position along the fiber is calculated fro the light round-trip tie. Figure 2 is a picture of the equipent of PPP- BODA sensing syste; NBX-6000. his easuring syste can set the spatial resolution, the sapling interval along the fiber. In its axiu perforance, the syste ensures up to 100 spatial resolution, 50 sapling interval, and ±0.0025% strain easureent accuracy [4]. Fig. 1. Principle of PPP-BODA syste Fig. 2. Equipent of PPP-BODA syste 3 Distributed Strain Measureent using PPP- BODA Syste 3.1 Bea Bending est using Ebedded Optical Fiber 3.1.1 Fabrication of the Specien In order to ake a sufficient nuber of sapling points of PPP-BODA syste, the length of the specien had to be long enough against its spatial resolution or sapling interval. o fabricate a coposite bea of alost 1 in length, Vacuu assisted Resin ransfer Molding (VaRM) ethod was adopted as the fabrication ethod. his ethod is attracting uch interest as a fabrication ethod of large-scaled coposite structures in recent years. Figure 3 is a diagra of VaRM ethod. he process of VaRM is firstly lainating of carbon fiber sheets on the foring old. Secondly, the lainated carbon fiber sheets are packed by plastic fil and the inside of baggage is vacuued up. And then, liquid epoxy resin is transferred into the 2
SHAPE IDENIFICAION USING DISRIBUED SRAIN FROM EMBEDDED OPICAL FIBER SENSORS baggage, and the epoxy is interpenetrated and cured. Figure 4 is the picture of lainated carbon fiber sheets. Soe optical fibers were placed between the sheets. We fabricated a flat plate with 1000 in length and 250 in width, and cut out several bea speciens. he actual size of the specien was 1000 in length, 70 in width, and 7 in thickness. he lainate configuration was [0] 32, and fiber direction was parallel to the length direction. he carbon fiber was oray / Soficar, 800S (tensile odulus: 294 GPa), and the epoxy resin was DENAOOL XNR6809 (tensile odulus: 2.3 GPa). he tensile odulus of fabricated coposite was 144 GPa in the fiber direction. his value was derived by tensile test using test pieces, which were cut out fro the fabricated coposite plate. Ebedded positions of the optical fiber are shown in Fig.5. here were two optical fiber lines, one was placed between 1st layer and 2nd layer, and the other was placed between 31st layer and 32nd layer. he noinal thickness of one layer was about 0.2, and, therefore, the optical fiber was ebedded 0.2 inner fro the surface. Figure 6 is a picture of the cross section of the ebedded area. We used the polyiide-coated single-ode optical fiber, and its diaeter was approxiately 150. Fig. 5. Ebedded positions of the optical fiber Fig. 6. Ebedded optical fiber 3.1.2 Configuration of the Experient Figure 7 shows the configuration of cantilever bea bending test. he strain sensors were not only the optical fiber sensor, but also eight strain gages, which were attached in 100 interval. he deflection was also easured using a dial gage and two scales. One end portion was claped to provide the fixed-end boundary condition. herefore, the actual length of the bea was 850. he load direction is y direction in Fig.8, and the applied load was 49 N and 100 N. Figure 8 is a picture of the experiental setup. Fig. 3. VaRM ethod Fig. 7. Configuration of bea bending test Fig. 4. Pictures of specien fabrication 3
MAYUKO NISHIO, adahito Mizutani, Nobuo akeda distance of 0 becoes alost 200. Such differences are considered to be significant outliers in the inverse analysis. Fig. 8. Setup of easuring syste 3.1.3 Results he output of the PPP-BODA syste is the peak frequency of the Brillouin scattering spectru along the optical fiber. he peak frequency shift is shown in Fig.9 (load: 100 N). he spatial resolution was 100, sapling interval was 50. It can be shown that the peak frequency shifts within the region of the ebedded optical fiber in the specien. he spectru change of the stiulated Brillouin scattering (SBS) at the easuring point A in Fig.9 is shown in Fig.10. he value of peak frequency gets lower in loaded condition. he left side in Fig.9 is copression area and the right side is tension area. Fro the aount of this peak frequency shift, the strain distribution can be calculated. Figure 11 is distribution plots of strain data fro PPP-BODA syste, strain gages, and theoretical distribution calculated by Euler bea theory. Fro this figure, the distribution profile of PPP-BODA syste is alost linear, which is typical strain distribution of a cantilever bea bending with a concentrated load. he value of strain also corresponds to values fro strain gages and theoretical distribution. Fro this result, it can be said that we can obtain appropriate strain distributions by the PPP-BODA syste. On the other hand, the distribution profile is different fro theoretical distribution at both ends of the bea. At the distance of 0, the absolute value of PPP-BODA syste is lower than the theoretical value, and the distribution profile is nonlinear at the both ends. his is because the distributed strain data is the ean strain of its spatial resolution. At the sapling points near the ends of bea, where the strain distribution is discontinuous along the fiber, the strain value includes inforation of unloaded area, as shown in the diagra in Fig.12. Such changes of the distribution profile at discontinuous points are the feature of distributed strain data. he difference with theoretical value at Fig. 9. Peak frequency shift Fig. 10. Brillouin scattering spectru at point A Fig. 11. Strain distributions 4
SHAPE IDENIFICAION USING DISRIBUED SRAIN FROM EMBEDDED OPICAL FIBER SENSORS Fig. 12. Mean strain at discontinuous points 3.2 Measureent Error Distribution In the inverse analysis, the easureent error distribution and the stability of data are great significant. his is because the least-square ethod, which is often used in inverse analysis, can be used strictly only when the error distribution of data shows noral distribution. o obtain the easureent error distribution of the PPP-BODA syste, iterative easureents of an unloaded optical fiber (strain free) was carried out. One set of easureents was held in alost sae conditions (fiber, teperature, huidity). And then, a histogra was ade by deviations fro the ean value of data. Fro the histogra, we derived the ean value, the standard deviation, the skewness, and the kurtosis to verify the degree of noral distribution. Figure 13 shows error distributions of two sets of easureents, and their statistic values are shown in able 1. he paraeter of two data is the nuber of averaging in PPP-BODA syste. he accuracy of data becoes higher when the nuber of averaging is increased. It can be shown by the value of standard deviations in able 1. he degree of noral distribution can be verified by the values of skew ness and kurtosis. When these values shows zero, the distribution is the noral distribution. However, the values of kurtosis are higher than zero in both distributions, and the values of skewness have also differences. herefore, it can be said that the degree of noral distribution of these error distribution is low. Moreover, the profiles of error distributions in Fig.13 show any outliers, and the ranges of deviations becoe wide. he histogras are ore siilar to Cauchy distribution than noral distribution. In addition, we observed that soe data showed unpredictable shifts of distributions; the distribution shifted even in sae easureent condition. Figure 14 shows one of such data. he profile of peak frequency distribution shifts in the direction of the optical fiber. Such distribution shifts are considered to be derived fro the instability of light scattering and slight changes of easureent conditions. For these verifications, the PPP-BODA data showed outliers in soe easureents points and soe unusual distributions. It is considered that the strain easureent of PPP-BODA syste is very sensitive against changes of slight easureent conditions. And then, the degree of the noral distribution is low, so it can be said that it is difficult to use the least-square ethod strictly in the shape identification algorith. We have to consider a robust ethod against such outliers. a) Averaging: 2^15 b) Averaging: 2^16 Fig. 13. Measureent error distribution of PPP-BODA syste 5
MAYUKO NISHIO, adahito Mizutani, Nobuo akeda able 1. Level of noral distribution Standard Skew Mean Kurtosis deviation -ness 2^15 1E-10 10.9-0.1 1.4 2^16 3E-16 9.7-0.7 6.1 he estiation of the value a 1 and a 2 is the polynoial fitting proble using easured strain data. o ake the estiation ethod robust against outliers, we used M-estiation ethod [5]. his ethod is basically the iterative weighted leastsquare ethod. he robustness is derived fro adustent of weight using Biweight ethod, which akes it possible to add light weight to outliers. First, the data fro PPP-BODA syste was configured to D atrix. x D 1 1 L L x n n he calculation flow of the robust estiation ethod is as follows. he estiate values are a 1 and a 2 in equation (1). Fig. 14. Unpredictable shift of the peak frequency distribution 4 Displaceent Derivation using Distributed Strain Data Using the distributed strain data obtained fro PPP-BODA syste, we carried out the inverse analysis to estiate the deflection of cantilever bea bending. Consideration of results in section 3, we propose a robust estiation ethod against outliers of data, and verify the advantage of the ethod. 4.1 Robust Estiation Method he estiated strain distribution e (x) of a cantilever bea bending with concentrated load is represented as a linear expression (1). his function can be easily integrated, and the deflection w e (x) is derived as (2). he value x is the coordinate of bea length direction (0 x L, L=850 ), and the subscript e eans estiated values. he value z =6.6 is the length in thickness direction between top and botto ebedded optical fibers. Using equation (1) and (2), when the value a 1 and a 2 are estiated, the deflection w e (x) can be derived easily in this proble. w e x e (x)=a e1 +a e2 x (1) 2 z L 0 e x dxdx (2) 1) Estiate the initial value using the usual leastsquare ethod. he value is the iteration nuber. =0 (x)=a 1(=0) +a 2(=0) x (3) 2) Calculate the residual value between strain data and estiated strain at easureent points x i (i=1~n). v i0 i ( x i ) (4) 3) Decide weights of each easureent points using the Biweight ethod. ad i 1 vi cs 0 2 v i cs otherwise (5) he value s is the edian of v i. he value c is the constant nuber, which decides threshold aount to ake weight zero. Fro the value i ad, the weight i eff can be derived as follows. eff i n n i1 ad i ad i (6) 4) Estiate the value a 1 and a 2 by the weighted least-square ethod using the weight value i eff. In the least-square ethod, an error function to be iniized can be defined as follows. 6
SHAPE IDENIFICAION USING DISRIBUED SRAIN FROM EMBEDDED OPICAL FIBER SENSORS i e i i eff x x E (7) e n i0 Equation (7) is the su of differences between estiated strain values and easured strain values. his error function has a iniu if E a k 0 for k 1, 2. In addition, the prior inforation can be used to iprove the accuracy of estiated values. In this cantilever bea bending proble, the strain value at free end (distance x=850 ) becoes zero ((850) =0). Using this inforation as a constraint condition, the least-square proble with Lagrange ultiplier can be solved. o siplify calculations, the error function equation can be expressed as G W Ga G W d (8) he vector d, a, and atrix G, W are deterined fro D atrix as follow. d, a a 1 L n a1 2 4.2 Results of Estiation 4.2.1 Estiated strain distribution and deflection When the robust estiation ethod was carried out using distributed strain data fro PPP- BODA syste, the strain distribution and the deflection were able to be estiated. he results are shown in Fig.15 and Fig.16. he data, which was used for the estiation, was sae as the data shown in Fig.12. Figure 15 shows the estiated strain distribution e (x) =a e1 +a e2 x. Fro this estiated strain, the deflection can be estiated using the equation (2) in section 4.1, as shown in Fig.16. Fro the deflection, the estiation error, which is the difference between the estiated value and the easured value, is only +0.87 % at the distance x=800. he positive value of the estiation error eans that the absolute value of the estiated deflection is larger than that of easured value. herefore, it can be said that very reasonable the estiated deflection can be obtained by the proposed robust estiation ethod. 1 L 1 eff G x x, W diag i 1 L n he prior inforation (850)=a 1 +a 2 850 = 0 can be express as follows. Fa 0 (9) F 1 850 Using the Lagrange ultiplier the equations (8) and (9) can be express as follows. G W G F F a G 0 λ W d 0 (10) Fig. 15. Estiated strain distribution Ap=B, p=a -1 B Fro the calculated p, the values a 1 and a 2 can be estiated. 5) Using the estiated strain distribution (x) =a 1 +a 2 x, calculate the residual value using equation (4). If the suation of v i does not becoe sall enough, return to process 3), and repeat the weighted least-square ethod. Fig. 16. Estiated displaceent 7
MAYUKO NISHIO, adahito Mizutani, Nobuo akeda 4.2.2 Effects of robust estiation ethod o verify the effectiveness of the robust estiation ethod, we copared estiated values between using the robust estiation ethod and using the least-square ethod. he least-square ethod was only the process 4) in section 4.1, and the weight values are 1 (no weight). Firstly, we copared dispersions of estiation errors of deflection. In such inverse analysis, estiated values greatly depend on the strain data. Figure 17 is the plot of estiation errors of deflection, which are calculated by each estiation ethods using ten different distributed strain data. Fro this result, estiation errors, which are calculated by the robust ethod, get generally lower than those by the least-square ethod. In addition, it can be said that the ean of estiation errors get near to zero by using the robust estiation ethod. his is because the data of the easureent point near the end of the bea specien (easuring point No.1 in Fig.15), which has difference against theoretical strain distribution because of the influence of spatial resolution of 10 c, has low weight in the robust estiation. Fro these results, it can be said that adusted weights in the robust ethod work effectively in the estiation. Secondly, the verification of the effectiveness against outliers was carried out. We ade an outlier in the distributed strain data, which was used in the estiation in the section 4.2.1. he artificial outlier, -50 or -100 was added to one of the data points of distributed strain data (easuring point No.2 in Fig.15). And then, the robust estiation ethod was carried out using each distributed strain data. Figure 18 shows estiated strain distributions. Fro this figure, the plots of two estiated strain distributions were alost overlapped. able 2 is the coparison of estiation errors of displaceent between the value derived fro the robust estiation ethod and that derived fro the leastsquare ethod. Coparing the changes of estiation errors, there are little differences in the values derived fro the robust estiation ethod. On the other hand, the values derived fro the leastsquare ethod show larger fluctuations. herefore, it can be said that the proposed ethod is robust against outliers of data. Fro these verifications, it is shown that the robust estiation ethod is very suitable for the shape identification using distributed strain data fro PPP-BODA syste. Fig. 17. Plot of the displaceent estiation errors Fig. 18. Estiated strain with an artificial outlier able 2. Estiation error with outliers Artificial Outlier Robust estiation least-square ±0 (raw data) 0.87 % -1.48 % -50-100 5 Conclusions 0.93 % (+0.06) 0.90 % (+0.03) -0.68 % (+0.80) 0.13 % (+1.61) In this paper, we considered the shape identification ethod, which is suitable for the characteristic of the distributed strain data fro PPP- BODA optical fiber sensing syste. In the experient, the distributed strain data were obtained by bea bending test using a coposite bea specien with an ebedded optical fiber. It was shown that the strain distribution fro PPP-BODA syste was appropriate to the deflection of the 8
SHAPE IDENIFICAION USING DISRIBUED SRAIN FROM EMBEDDED OPICAL FIBER SENSORS specien. However, at the discontinuous point of the strain distribution along the fiber, the accurate value can not be obtained because of the influence of the spatial resolution of distributed data. Moreover, by verification of the easureent error distribution, it was shown that it was not strictly noral distribution and recognized soe outliers and unpredictable shifts of distributions. Fro these results, we proposed the robust estiation ethod for shape identification algorith, and verified the effectiveness of this ethod. By using this ethod, the estiation error of deflection was decreased, and the robustness against outliers of data was shown. As one of the future works, we will construct the robust shape identification ethod for ore intricately deforation of coposite structures. Acknowledgeent One of the authors (M. Nishio) was supported through the 21 st Century COE Progra, Mechanical Systes Innovation, by the Ministry of Education, Culture, Sports, Science and echnology. In the fabrication of the specien with VaRM ethod, we received technical assistance fro KADO Corporation. In addition, we received technical advices of the strain easureent using PPP-BODA syste fro Neubrex Co., Ltd, respectively. References [1] A. essler, J.L. Spangler, A Least-squares variational ethod for full-field reconstruction of elastic deforations in shear-deforable plates and shells, Coputer ethod of applied echanics and engineering, 194, 327-339 (2005). [2] Philip B. Bogert, Eric Haugse, Ralph E. Gehrki, Structural shape identification fro experiental strains using a odal transforation technique, AIAA Paper. 2003-1626. [3] Bao X., Brown A., Deerchent M., Sith J., Characterization of the Brillouin-loss spectru of single-ode fibers by use of very short (<10 μs) pulses, Optical Letters, 24(8), 501-510 (1999). [4] K. Kishida, C.-H. Li, K. Nishiguchi, Pulse pre-pup ethod for c-order spatial resolution of BODA, Proceeding of the SPIE, Volue 5855, 559-562 (2005). [5] A.E. Beaton, J.W. ukey, he fitting of power series, eaning polynoials, illustrated on bandspectroscopic data, echnoetrics, Vol.16, 147-192 (1974). 9