Fifth International Conference on Motion and Vibration Control (MOVIC 000), 4-8 Dec. 000, Sydney, Australia FIBER BRAGG GRATING ACCELEROMETER FOR STRUCTURAL HEALT H MONITORING Akira Mita* and Isamu Yokoi** *Graduate School of Science and Technology, Keio University, Yokohama, JAPAN **Tokyo Sokushin, Co., Ltd., Tokyo, JAPAN ABSTRACT A design strategy for a new optical accelerometer that uses a fiber Bragg grating element is presented. The mechanism employed here ensures uniform strain distribution in the Bragg grating element so that the Bragg reflection peak will not be deteriorated. To compare with a reference servo-type accelerometer, a shake table test was conducted to show good performance of a prototype accelerometer. The lifetime of the accelerometer was also probabilistically evaluated.. INTRODUCTION A health monitoring system started getting strong attentions in Japan after the 995 Hyogo-Ken Nanbu (Kobe) Earthquake in which more than 6,000 people were killed and 40,000 buildings were destroyed. As was the case after the 994 Northridge Earthquake, many steel buildings suffered sever damages mainly at their beam-column joints. It was a surprising fact that the damages were not found until removing fire-protection coatings on beam-column joints. In most cases, it was not possible to find the correct degree of the damages by a simple eye-inspection of the structure surface because there were no major visible damages on the surface of fire-protection material. This fact prompted strong demands in real-time nondestructive assessment systems for buildings. One possible system currently under study is the one utilizing the dynamic response of a building. The method is excellent to identify the global health of a building, though it is not suited for detecting small damages. Accelerometers play a key role in such nondestructive assessment systems. However, the current electric accelerometers have certain limitations to apply for such a purpose. Among others, heavy cabling labor and sensitivity to electromagnetic fields is often an obstacle when installing them into a building. An optical fiber Bragg grating (FBG) accelerometer has many advantages over conventional electrical sensors such as their immunity to electromagnetic interference and their capability to transmit signals over long distance without any additional amplifiers. In addition, since a Bragg grating element uses only a narrow band of inserted lights, it has a multiplexing capability that reduces a cabling labor drastically. In the early stage in development, the optical accelerometers have been typically configured within an interferometric architecture (e.g. []). Recently, several accelerometers based on FBG have been proposed for structural monitoring. Berkoff et al. ([]) proposed an FBG accelerometer. They embedded a Bragg grating element into a commercially available elastomer that is attached to a mass. The natural frequency of the sensor was set at about KHz or higher to detect high frequency components. This sensor, however, suffers from cross-axis sensitivity and birefringence-splitting of the Bragg reflection peak. Todd et al. ([3]) improved the performance of an FBG accelerometer by using beam-plates. They were able to minimize the cross-axis sensitivity to less than % of the primary axis sensitivity. Though their system has many desirable features, the resolution of.5 µ strain/g is not enough for civil and building application. Moreover the distribution of strain along the beam-plate to which a Bragg grating element is glued is not uniform so that the Bragg reflection peak may be broadened to result in reduced resolution. In this paper, a design strategy for a new FBG-based accelerometer is presented. The system consists of a cantilevered beam and a mass. In the system, a Bragg grating element is not directly glued to a cantilever to avoid possible non-uniform strain in the element. Instead, the Bragg grating element is tensioned after being placed onto the system to achieve a uniform strain distribution. The FBG-based accelerometer presented here requires a bias strain. The level of this bias strain is much higher than the value normally allowed for fiber cables used for communication. A strategy to overcome this shortcoming is also presented.
Fifth International Conference on Motion and Vibration Control (MOVIC 000), 4-8 Dec. 000, Sydney, Australia. MECHANISM Mechanism of a fiber Bragg grating (FBG) accelerometer is depicted in Fig.. The accelerometer consists of an L-shaped rigid cantilever beam, a concentrated mass, a spring and an Bragg grating element. To detect strains due to applied acceleration, a Bragg grating element is placed at the center of points A and B. The element is bonded to the accelerometer at points A and B as indicated in Fig.. The Bragg grating element is post-tensioned so that the element is always under certain level of tension stress. By employing this configuration, the Bragg grating element is always subject to uniform strain distribution along its measuring length resulting in a sharp reflection characteristics with no broadening in its reflection spectrum. This feature is attractive to keep a good resolution of the sensor in a wide amplitude range. The interior view of the prototype FBG accele rometer is shown in Fig.. A leaf spring is used in the sensor to minimize cross-axis sensitivity. In the following analysis, the accelerometer is modeled by a single-degree-of-freedom system with no damping. The stiffness of the Bragg grating element is represented by K as indicated in Fig., while the leaf spring by K. The equation of motion for the system shown in Fig. subject to the ground acceleration a g is written as where M& y + ( K + ( a / b) K ) y = Ma g () a = && () g y g The dots represent temporal differentiation. Dividing both sides by the mass M results in where & y ω y = (3) + 0 a g ω = K ( a / b) K ) / M (4) 0 ( + represents the natural frequency of the accelerometer. Considering a harmonic ground acceleration of circular frequency ω a iωt g = Ag e (5) y L allows us to express motion of the mass in the form A Bragg grating K B y iωt = Ye (6) yg a b mass M spring K Acceleration The amplitude of motion of the mass is obtained by substituting Eqs. (5) and (6) into Eq. () as = (7) Y A ( ) g ω ω ω 0 0 Fig. Mechanism of FBG accelerometer It is understood that the ground acceleration is proportional to the displacement motion of the mass in a low frequency range and that the amplitude is in inverse proportion to squared natural frequency. From Eq. (7), the strain value ε induced in the Bragg grating element can be approximated in sufficiently low frequency region as ε κa g (8) in which the sensitivity κ is defined by the following expression. a / b κ = (9) L ω 0 Fig. Interior view of FBG accelerometer
Fifth International Conference on Motion and Vibration Control (MOVIC 000), 4-8 Dec. 000, Sydney, Australia 3. OPTIMIZATION 3. Formulation From Eq. (9), it is clearly understood that sensitivity of an FBG accelerometer decreases monotonically as the natural frequency increases. However, the natural frequency is a function of five parameters a, b, K, K and M as shown in Eq. (4) so that the sensitivity may become the maximum for a set of optimum parameters. In a practical situation, it is often desirable to obtain the optimum parameters to maximize the sensitivity when the natural frequency of the accelerometer is prescribed. In the configuration depicted in Fig., the mass M and spring K may be determined by the physical constraints before starting optimization process. Considering the constraints, the optimum procedure for determining the remaining parameters a, b and K are described below. Substituting Eq. (4) into Eq. (9) yields the following relation. M a / b κ = (0) LK + ( K / K )( a / b) Introducing non-dimensional parameters as K a α =, β = K b Eq. (0) can be rewritten in the form M β κ = LK + αβ () () Differentiating the inside of the parenthesis with respect to β and equating to zero gives αβ ( + αβ ) = 0 (3) The denominator of Eq. (3) is always positive. Therefore, the sensitivity becomes the maximum when the following condition is satisfied. β = (4) α The maximum sensitivity satisfying Eq. (4) can be obtained in the form Substituting the relation expressed in Eq. (4), the optimum condition given in Eq. (4) can be modified into M β opt = ω0 (6) K From Eqs. (4) and (6), the optimu m spring K opt is obtained in the form K opt βopt K = (7) When b is prescribed, a opt can be calculated as a opt M = bω0 (8) K 3. Prototype Design The design constraints for a prototype accelerometer were determined considering the spatial constraints for monitoring of building structures. The values employed here for designing a prototype FBG accelerometer are listed in Table. The Young s modulus E G of the Bragg grating element was assumed to be the same with glass. The natural frequency of prototype FBG accelerometer f 0 was decided to have a good resolution for major frequency components observed during earthquake response of a building structure. The size of the prototype accelerometer under consideration is shown in Fig. 3. Table Design constraints for prototype accelerometer Parameters Value Unit M 0.05 kg L 0.030 m b 0.00 m f 0 50.0 Hz E G 80.0 GPa 40mm Bragg grating 5mm mm Mβ κ max = (5) LK Fiber cable Leaf spring Mass Case Fig. 3 Schematic of prototype FBG accelerometer
Fifth International Conference on Motion and Vibration Control (MOVIC 000), 4-8 Dec. 000, Sydney, Australia The natural frequency of the prototype accelerometer f 0 is related to the circular frequency ω 0 as ω 0 = πf 0 (9) Neglecting the coating material and assuming the diameter of Bragg grating element to be 5µm, the spring constant of the Bragg grating element is obtained from the Young s modulus E G and the length of Bragg grating element L as frequency. Due to this amplification, the high frequency components in the data taken by the FBG accelerometer are larger than those taken by the servo-type accelerometer. This fact results in larger peak values for the time history of the FBG accelerometer. However, traceability of the FBG accelerometer was excellent. 4 K = 3.7 0 (N/m) (0) When the above value is given, the optimum spring constant K opt can be calculated by substituting the K into Eq. (7) as K opt = 7.40 0 (N/m) () Accordingly the optimum length a opt is given by a = 0.003 (m) () opt Under these optimum values, the optimum sensitivity becomes κ 498 (µ strain/g) (3) max = When a,550nm-wavelength Bragg grating element is used, the strain-to-wavelength sensitivity is about. pm/ µ strain (see[6]). Therefore, the sensitivity of the FBG accelerometer in terms of wavelength shift is obtained as ' κ 597 (pm/g) (4) max = The design strategy developed here is applicable for a wide class of accelerometers as well. 3.3 Shake Table Test A prototype FBG accelerometer was fabricated based on the design strategy explained in 3.. The dynamic characteristics of the FBG accelerometer was examined through a series of shake table tests. In Fig. 4, the setup of a shake table test is shown. An example test result for a random excitation is presented in Fig. 5. The time history of the FBG accelerometer was compared with the reference accelerometer. The reference accelerometer was chosen to be a servo-type accelerometer. The natural frequency of the FBG accelerometer was 49 Hz. The damping ratio was 0.05. Therefore, a large amount of amplification is observed in the vicinity of the natural Fig. 4 Shake table test Fig. 5 Comparison of time histories 4. LIFETIME A Bragg grating element in the prototype accelerometer is always subject to a bias strain due to post-tensioning. When a measurement range of plus and minus,000 Gal is necessary, at least,000 µ strain (=0.% strain) should be applied to the element as the bias strain. However, most production process for Bragg grating elements involves removal of coating material to write clear gratings to ensue sufficient reflectivity. Though recoating is made after writing the gratings, the tension strength of the fiber is drastically reduced due to scratches made on the surface during the removal process. In some cases, Bragg grating elements do not
Fifth International Conference on Motion and Vibration Control (MOVIC 000), 4-8 Dec. 000, Sydney, Australia tolerate a strain level as low as 5,000 µ strain. The use of such an element to this type of accelerometer is not feasible. Recently, however, a direct writing method over coating material has been established (see [4]). By this production method, the strength of a Bragg grating element is kept almost the same with its original strength. Komachiya et al. ([5]) have demonstrated that the long lifetime can be achieved by increasing the screening strain for a proof-test. For telecommunication fibers screening strain of 0.5% is normally adopted in a proof-test. Although increasing the screening strain results in several failures in a long fiber, the sound fiber length is still long enough to manufacture sensors. In the following, lifetime estimation is made for Bragg grating elements produced by the direct writing method proposed by Imamura et al. ([4]). The failure of glass fibers is caused by growth of a surface flaw or a microcrack in the glass fibers. When a screening strain ε p was applied to a sensor fiber for t p seconds as a proof-test, the probabilistic lifetime is expressed in the form (see [4]) ln( F ) ( n+ ) / m s n T = ( εp / εs ) LN p t p (5) where L is the length of a sensor fiber, F s is the failure probability in time T, and ε s is the constant strain in its service situation. The fatigue constant n and a characteristic parameter m describing a distribution of the crack size are determined from tests and are given as 3.9 and 4, respectively, for a single -mode glass fiber (see [5]). The number of failures per kilometer N p is experimentally determined. To estimate the lifetime of an FBG sensor system, a sensor system with ten FBG accelerometers multiplexed on one fiber cable is considered. Each FBG accelerometer utilizes an FBG element of its length 30mm. Therefore, the total length L of the sensor fiber under large strains that should be considered in the lifetime estimation is 300mm or 3 0-4 km. The failure probability F s for this system is set as small as 0-7. To see the effects of screening strain levels, two levels of screening strain,.5% and 3.5% were considered. The parameters used for lifetime estimation for the Bragg grating sensor system consisting of 0 FBG accelerometers are summarized in Table. The number of failures per kilometers is assumed to be the same with the number used by Komachiya et al. ([5]). In Fig. 6, the lifetime estimation under the condition listed in Table is shown. From Fig. 6, it may be found that a long lifetime of more than 50 years can be achieved even for an FBG accelerometer with the service strain level of 5,000 µ strain by producing the element by the direct writing and using large screening strain of more than.5 % strain. Table Parameters for lifetime estimation Parameters Unit Case Case Screening strain Loading time Failure probability Fiber length N p m n % sec km.5.0.0x0-7 3.0x0-4 4 3.9 3.5.0.0x0-7 3.0x0-4 6 4 3.9 Fig. 6 Lifetime estimation for two screening levels The number of failures per kilometer N p may depend on production quality. Therefore, it is desirable to know the effects of N p on the maximum allowable strain level for a sensor. The maximum allowable strain level for a given lifetime is obtained by solving Eq. (3) for ε s as in the form n m n t n ( + ) / p ln( Fs ) ε s = ε p T (6) LN p Assuming a lifetime of 50 years, the maximum allowable strain levels for a sensor system consisting of FBG accelerometers were obtained. The parameters used here are the same with those listed in Table except the number of failures per kilometer N p. The number of failures was varied from to 0,000. The results are shown in Fig. 7. From Fig. 7, it is clearly understood that even with a relatively large number of failures the maximum allowable strain level can be kept reasonably
Fifth International Conference on Motion and Vibration Control (MOVIC 000), 4-8 Dec. 000, Sydney, Australia large. For the prototype FBG accelerometer, the maximum allowable strain level of 5,000 µ strain corresponds to approximately plus and minus.5g. sensor system consisting of ten FBG accelerometers is extended well beyond 50 years. Fig. 7 Maximum allowable strain for 50 years lifetime 5. CONCLUDING REMARKS Optical accelerometers have many advantages over conventional electrical accelerometers such as their immunity to electromagnetic interference and their capability to transmit signals over long distance without any additional amplifiers. Among others, a fiber Bragg grating (FBG) accelerometer is considered to be the most promising for structural health monitoring. The mechanism employed here ensures uniform strain distribution in the Bragg grating element so that the Bragg reflection peak will not be deteriorated. In addition, the cross-axis sensitivity has been minimized by a leaf spring. A design strategy for an FBG accelerometer was derived to ensure the maximum sensitivity under given design constraints. A prototype FBG accelerometer was designed based on the strategy for optimization. The shake table test showed a good performance of the prototype FBG accelerometer when compared with a servo-type accelerometer. Though large amplification was observed in the vicinity of the natural frequency of the FBG accelerometer because no damping mechanism was introduced, traceability was excellent. The Bragg grating element needed to apply post-tension to induce an appropriate bias strain. The shortcomings resulting from this bias strain can be overcome by the direct writing procedure and the use of high screening strain in a proof-test. By doing so, the lifetime of a ACKNOWLEDGEMENT The authors are grateful to fruitful discussions with Mr. Iwaki at Shimizu Corporation. REFERENCES [] A. D. Kersey, D. A. Jackson and M. Corke, High Sensitivity Fiber-Optic Accelerometer, Electronics Letters, 8, 559-56 (98) [] T. A. Berkoff and A. D. Kersey, Experimental Demonstration of a Fiber Bragg Grating Accelerometer, IEEE Photonics Technology Letters, 8, 677-679 (996) [3] M. D. Todd, G. A. Johnson, B. A. Althouse and S. T. Vohra, Flexural Beam-Based Fiber Bradd Grating Accelerometers, IEEE Photonics Technology Letters, 0, 605-607 (998) [4] K. Imamura, T. Nakai, K. Moriura, Y. Sudo and Y. Imada, Mechanical Strength Charanteristics of Tin-Codoped Germanosilicate Fibre Bragg Gratings by Writing Through UV-Transparent Coating, Elecronics Letters, 34, 06-07 (998) [5] M. Komachiya, R. Minamitani, T. Fumino, T. Sakaguchi and S. Watanabe, Proof-testing and probabilistic lifetime estimation of glass fibers for sensor applications, Applied Optics, 38, 767-774 (999) [6] Y. -J. Rao, In-Fibre Brag Grating Sensors, Meas. Sci. Technol., 8, 355-375 (997)