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Use of fiber Bragg grating array and random decrement for damage detection in steel beam
Engineering Structures 106 (2016) 348–354
Contents lists available at ScienceDirect
Engineering Structures journal homepage: www.elsevier.com/locate/engstruct
Use of fiber Bragg grating array and random decrement for damage detection in steel beam A. Elshafey a, H. Marzouk b,⇑, X. Gu c, M. Haddara d, R. Morsy b a
Department of Civil Engineering, Minoufiya University, Egypt Department of Civil Engineering, Ryerson University, Toronto, Ontario, Canada c Department of Electrical and Computer Engineering, Ryerson University, Toronto, Ontario, Canada d Memorial University of Newfoundland, St. John’s, NL, Canada b
a r t i c l e
i n f o
Article history: Received 4 November 2014 Revised 24 October 2015 Accepted 26 October 2015 Available online 11 November 2015 Keywords: Fiber optical Bragg grating array Strains Damage Random decrement Multichannel random decrement
a b s t r a c t A growing trend in the use of fiber Bragg grating array to detect structural damage has been observed in recent years. This paper describes the use of fiber Bragg grating optical sensors in an array to identify the location and assess the extent of damage on steel structures. A fiber optical sensing array with eight sensing elements has been designed, fabricated, and applied to measure the time history of strain at different points on a simply supported beam subjected to random loading. The wavelength shifts of the sensors are used to calculate the strain distribution along the beam. The random decrement at each point, for different modes, is extracted from the time history of the responses. The random decrements are compared at different damage ratios to an intact case to identify the existence of damage. Multichannel random decrement is applied to extract excited mode shapes. The mode shapes are then used to determine the location of the damage. The results show that the fiber optical sensor array is a reliable, fast, and accurate tool for the identification and localization of damage by using strain measurements. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction Applications of fiber optical sensors in structural health monitoring have been increasing for many years [1]. The approach allows structures to be continuously monitored without interrupting operations or affecting stiffness. Fiber optical sensors that have small diameters are used for the structural health monitoring of aerospace composite structures [2]. Linearly birefringent singlemode optical fibers embedded into woven glass epoxy composites have been used to measure strains in a 1-point loading specimen [3]. Embedded optical fibers with a simple signal attenuation measuring system are used as an inexpensive method to detect significant fatigue damage in composite material [4]. The potential of using plastic optical fibers in conjunction with high-resolution photon counting to detect and estimate the location of cracks in a single fiber glued to a tubular member is studied [5]. The effect of the presence of optical fibers on the structural fatigue behaviors of a host of carbon epoxy laminates has been quantitatively studied, in which optical fiber cables were placed in mid-plane and near the surface of the laminate subjected to loading [6]. A system ⇑ Corresponding author. E-mail addresses: [email protected] (H. Marzouk), [email protected] (X. Gu), [email protected] (M. Haddara). http://dx.doi.org/10.1016/j.engstruct.2015.10.046 0141-0296/Ó 2015 Elsevier Ltd. All rights reserved.
of thin optical fibers integrated into a composite structure during its manufacturing process is suggested as a reliable automatic and remote long-term monitoring means for structural damage [7]. The influence of optical fiber orientation and depth on the sensitivity of a fiber optical system to detect impact damage in composite materials is reported and the optimal configuration has been determined for both orientation and depth [8]. Fiber optic sensor is classified as local, quasi-distributed and distributed sensors, related to the range that will be sensed. Local fiber optic sensors are based on detecting the optical phase change induced in light along the optical fiber. Fiber Bragg grating (FBG) sensors is a kind of quasi-distributed sensors, it has a unique property is encoding the wavelength which has been successfully employed in several civil engineering applications. These FBG sensors could be theoretically wavelength multiplexed up to 64 FBGs gratings in single fiber [9]. FBG sensors are used to evaluate damage in unidirectional carbon fiber/composites that results from both low and high velocity/energy impacts [10]. A distributed fiber optical monitoring methodology based on optical time-domain reflectometry has been developed for the seismic damage identification of steel structures [11]. The use of long FBGs to provide strain measurements is investigated with the purpose of achieving better structural health monitoring as opposed to the use of classical accelerometers because they provide low noisy data [12]. A
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A. Elshafey et al. / Engineering Structures 106 (2016) 348–354
gradient-based optimization algorithm is utilized to update the finite element model of a composite simple structure by using the output from fiber optical sensors and strain modal analysis [13]. A technique for damage detection has been introduced based on continuous strain data obtained from distributed fiber optical sensor arrays and neural networks [14]. An overview of the major types of fiber sensor arrays and their applications in civil structures has been reviewed by Fidanboylu and Efendiog˘lu [15]. Distributed fiber optical sensing has been used in an effort to detect structural damage in steel connections from direct strain measurements. It is found that the technique can be successfully applied in static analysis, but has a limited application in dynamic analysis, as data collection is too slow [16]. Lopez-Higuera et al. used Fabry–Perot interferometric sensors and neural networks to predict the size and location of delamination in laminated glass/epoxy composite beams [17]. Reviewed research and development activities on the use of fiber optical sensors in the health monitoring of various structures, including buildings, piles, bridges, pipelines and tunnels, in which existing problems and promising research efforts are also discussed [18]. An application of using FBG sensors which is the smart FBG weighbridge; traffic are weighted from the deflection of reinforced concrete beam with FBG strain sensors embedded [19]. FBG sensors used to monitor early age deformations and temperature for various materials as high performance concrete [20]. In this paper, an FBG sensor array is used to measure the time history of strains on the surface of a beam subjected to random loading. An FBG sensor array with eight FBG sensors on a single fiber is surface mounted onto a steel beam. The testing is not affected by electromagnetic noise or other sources of noise in the laboratory with different kinds of machineries. Analysis of the modal damping ratio and mode shape can clearly locate and identify structure damage. Random decrement (RD) signatures can be used to describe the free decay response of the system. The advantage of this approach is that one can obtain a free response from the stationary random response of the system. To obtain the RD from a stationary random response, the response is divided into a number of segments, N, each with a length of s and determining the average of this segments to eliminate the random component and resulting the deterministic component introducing the random decrement signature [21]. 2. Random decrement and mode shape extraction techniques 2.1. Random decrement The response of a single degree of freedom linear system is governed by the equation of motion:
€ _ ½MfXðtÞg þ ½CfXðtÞg þ ½KfXðtÞg ¼ fFðtÞg
ð1Þ
where M is the mass, C is the damping, K is the stiffness and F(t) is the excitation force. And after normalizing the equation relative to the mass:
€ þ 2xe XðtÞ _ XðtÞ þ x2 XðtÞ ¼ FðtÞ
ð2Þ
x is the natural frequency, e is the damping ratio and X(t) is the response of the system. Random decrement response extracted from Eq. (2) represents the free decay of the system, assuming that the analyzed response is realization of a zero mean stationary Gaussian stochastic process. By changing the variables indications used in the previous equation to be y1 ¼ x and y2 ¼ x_ y_ 1 ¼ y2
ð3Þ
y_ 2 ¼ 2xo ny2 xo y1 þ f ðtÞ
ð4Þ
By substituting in the probability density function and multiply the two sides with y1 and y2 then integrating the equation with respect to y1 and y2 , where l1 and l2 are the mean values of displacement and velocity,
l€ 1 ¼ l_ 2 ¼ 2xo ny2 þ x2o y1
ð5Þ
The free decay for the structure is derived from the stationary random response,
l€ þ 2nxo l_ þ x20 l ¼ 0
ð6Þ
The technique is based on the classical RD technique, which averages the time history segments of random vibration responses in a time domain. The triggering condition is used to determine the starting point of each time segment. It is assumed that if the structure is subjected to a wideband load, the response will be composed of two components: a random and a deterministic component (free decay). By averaging the response, the random component is cancelled out and the deterministic component is obtained.
xðsÞ ¼
N X xi ðt i þ sÞ
ð7Þ
i¼1
The triggering values are
xi ðt i Þ ¼ xs for i ¼ 1; 2; 3; . . . ; N x_i ðt i Þ P 0 for i ¼ 1; 3; 5; . . . ; N 1 x_i ðt i Þ 6 0 for i ¼ 2; 4; 6; . . . ; N In the current study, multichannel RD [21] is used to extract the excited mode shapes of the tested beam. Multichannel RD extends the approach by applying it at multiple points on the structure at the same time [20].
RDL ¼
N 1X ffX L ðtisL þ sÞjX L ¼ X S g N i¼1
RDNL ¼
N 1X ffX NL ðt iNL þ sÞjt iNL ¼ t isL g N i¼1
ð8Þ
ð9Þ
where RDL is the random decrement at leading channel, X L is the triggering conditions of the leading channel, t isL is the time corresponding to the triggering conditions, and RDNL is the random decrement for the non-leading channels. To keep the phase angle between different points, one channel is used as a leading channel and the triggering condition is applied only to this channel. The times that correspond to the triggering condition in the response are used to extract RDs in other channels. A FORTRAN code was written to extract both single and multi-channel RDs. The code allows the use of constant level crossing as a triggering condition as well as the use of a time interval that is different from that used to record the original data. This capability is needed in some cases for extracting higher mode shapes. Fig. 1 shows the multichannel signals, triggering condition, and times that correspond to the triggering levels. For more details about the approach, the reader may refer to [22,23]. Fig. 2 shows the RD results for each channel. The triggering condition at Channel 1 (Y1) is used as the base triggering value for all of the other channels. The values shown in Fig. 2 are used to extract the mode shape. A fast Fourier transform (FFT) analysis helps to determine the number of modes excited. The mode shape of the structure is composed of a set of numbers at the same time lag as shown in Fig. 2; in this work, the first set of values (RD1, RD2, . . . , RDn) are used. However, the other points still have the same information on the mode shape.
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And then get the modal vectors of the damages structure as shown Eq. (8) and normalized it with respect to the maximum amplitude
T ki ¼ A1 ; A2 ; . . . ; Am
ð12Þ
Then we determine the modal vector difference Dki , where superscript n indicates the normalized values
n n n n T Dki ¼ An1 An 1 ; A2 A2 ; . . . ; Am Am
ð13Þ
By considering the normalized difference as virtual displacements for each node, add (or subtract) the virtual displacements to the coordinates of the un-deformed structure, to get a new coordinates of the virtually deformed structure, The virtually deformed shape will contain clear and enough information about the location of damage (see Fig. 3). 3. Experimental investigation
Fig. 1. Multichannel random decrement procedure.
2.2. Mode shape extraction The normalized random decrements are representing the free response of the structure [21]. The mathematical equation of the free vibration equation is
xi ðtÞ ¼ Ai e2ext cosðxi t ui Þ;
i ¼ 1; 2; 3; . . . ; N
ð10Þ
where xi ðtÞ is the random decrement for certain channel, N is the number of channels, Ai is the amplitude at t ¼ 0, e is the damping coefficient, xi is the natural frequency, and ui is the phase angle. The approach for damage detection using the mode shape is based on normalizing the differences between the intact and damaged mode shape [23]. Assume that modal vectors for the intact structure in Eq. (11) the normalize it with respect to the maximum amplitude
ki ¼ fA1 ; A2 ; . . . ; Am gT
ð11Þ
The FBG sensors were fabricated into the core of a hydrogenloaded single mode fiber (Corning Corp., SMF-28) in the fiber optic lab at Ryerson University. A collimated KrF excimer laser (Lumonics, model PM 844) beam at 248 nm was focused onto a horizontally positioned fiber through a phase mask. The FBGs, apodised with a sin function, had an effective length of 3 mm, and were inscribed at different wavelengths. The eight FBGs were spaced as shown in Fig. 5 by using a single FBG array. After fabrication, all FBGs were annealed at 150 °C for 15 h after FBG inscription to ensure their long-term stability. A steel beam with a length of 3500 mm as shown in Fig. 4 was tested to validate the applicability of the fiber optical sensors in identifying damage extent and location by using a dynamic response. The beam is a hollow structural tube with a wall thickness of 3 mm and has a hollow square cross section that is 25.4 25.4 mm. The beam supports were arranged to allow rotations at the beam-ends. Beam translation perpendicular to the beam was not allowed. The beam supports were attached to rigid steel bases fixed onto a concrete floor as shown in Fig. 5. The beam was subjected to random loading with a wide band spectrum. A computer was used for data logging as well as controlling random loading.
where ki is the mode shape.
Fig. 2. Random decrement signature of different channels.
Fig. 3. Methodology for multichannel random decrement.
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Fig. 4. Beam dimensions, cross section, sensors, and load location.
Fig. 5. Beam support fixture. Fig. 7. FFT for Sensors 2, 4 and 6 on the beam.
The experimental setup was attached to very rigid bases with each base secured onto a solid structural concrete slab on the floor (1000 mm thick) by using 4 steel bolts that were 50 mm in diameter. The experiment setup is shown in Fig. 6, in which an electromagnetic shaker was used for random loading. A computer was used to generate the random load signal which was fed to a power amplifier through a National Instrument data card. The FBG sensors are also shown in Fig. 6 which is surface mounted to a beam and the beam is protected as it is susceptible to shearing. The pinned support allowed only rotation of the end. Damage was intentionally induced at Sensor 6. Three cases were considered. The ratios of damage depth to beam height in the three cases were 25%, 50%, and 75%, which were labeled as d25, d50, and d75 respectively. An optical circulator, which is a three-port device that allows light to only propagate from Port 1 to 2 and from 2 to 3, was used
in the experiment. A broadband light source was connected to Port 1 and the FBG sensing array was connected to Port 2, and the reflected wavelengths from the 8 FBG sensors could be measured from Port 3. Thus, with the use of the circulator, the FBG sensor array became a one-ended device. Due to the high amount of isolation between the input and reflected optical power and its low insertion loss, optical circulators are widely used in advanced communication systems and fiber-optical sensor array applications. Port 3 of the circulator was connected to the input of a sensor interrogation system (Ibsen, model: I-MON E-USB2.0 DAQ system). The DAQ system was connected to a computer through a USB connection. Special software based on the Lab VIEW platform was used to record the FBG wavelength shifts as a function of time. 4. Results and discussion To extract the RD signatures for different modes, a filtering process for the data is required. An FFT analysis was used to determine the frequency range around each natural frequency excited as shown in Fig. 7. The first two modes are used in this study. Table 1 shows the filtering range used to separate the signals corresponding to the used modes. The random decrements corresponding to mode 1 and mode 2 were extracted from the filtered time history data. Fig. 8 shows the RD signatures at different damage ratios for Mode 1 and 2, the figures indicate the damage extent in the steel beam by means of change in the RD signature according to different damage ratios. These RDs are normalized values used to extract the natural frequencies and damping ratios. The logarithmic decrement is used to extract the damping ratio. The values of the natural Table 1 Filtering range used to separate excited modes.
Fig. 6. Experimental setup which shows the steel beam with a fiber optical array installed on its side and an electromagnetic shake.
Mode number
Frequency range (Hz)
Mode 1 Mode 2
6–10 21–25
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Fig. 8. Random decrement signatures of the experimental investigation for different damage ratios at Point 6 for Modes 1 (a) and 2 (b).
Table 2 Mode 1, natural frequency and damping ratio for different damage ratios. Damage ratio
Natural frequency (Hz)
Damping ratio (%)
Intact D25 D50 D75
8.299 8.222 7.996 7.846
3.74 3.86 3.31 4.27
Table 3 Mode 2, natural frequency and damping ratio for different damage ratios. Damage ratio
Natural frequency (Hz)
Damping ratio (%)
Intact D25 D50 D75
23.753 23.664 23.256 22.144
0.776 0.939 0.683 0.939
frequencies and damping ratios are shown in Tables 2 and 3. The RD signature is determined by using the finite element results simulating the beam with the same factors used for damaged ratios to ensure consistency in the results, the finite element results is consistent with the experimental investigation results. In the Finite Element (FE) model, the material of the beam is modeled as steel with modulus of elasticity 20.7 104 MPa. For the first and second mode shapes, the RD signature is calculated using FE for beam state with three different damage ratios are shown in Fig. 9, where it can be noticed that there is changes in the RD signature relative with the damage extent. The RD signature is calculated using triggering level equals to 1.4 times the standard deviation of the response (1.4r, where r is the standard deviation) and the integration was calculated using a time increment of 0.001 s. For conducting the RD, the number of segments is 400 time segment as for better results are the number of segments are more than 100.
Fig. 10. Shape of Mode 1 as extracted by multichannel random decrement.
Fig. 11. Mode shape difference (Mode 1).
In extracting the mode shapes for locating the damage, Fig. 10 shows the first mode shape and it can be noticed that there is some discrepancy in the damage location (at Point 6). Fig. 11 shows the mode shape difference for Mode 1. It can be noticed that the
Fig. 9. Random decrement signatures using FE model for different damage ratios at Point 6 for Modes 1 (a) and 2 (b).
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filter centered on the first natural frequency calculated, the response is given as shown in the below figure;
Acceleration (g)
50 25 0 -25 -50 0
25
50
Fig. 12. Shape of Mode 2 as extracted by multichannel random decrement.
75
100
125
150
175
200
Time (sec) Using the MATLAB coding for the response applying the below equation, it is a time domain averaging of the structure response segments due to random input loads starting from certain level called triggering level. The advantage of the averaging is the noise reduction and discrimination of the random part of the response. In this example, the used triggering level equals to the standard deviation of the response (r = 6.30) as the optimum range for the trig pffiffiffi gering level is 1 2 rx , where the standard deviation of the time response is represented as rx , the integration time increment is equal 0.001 s, the vertical acceleration is measured with sampling rate of 1000 Hz. The segment number equals 400 segments; it provides better results at number of segments more than 100, the variance of RD signature decreases with the number of averages of time segments.
Fig. 13. Mode shape difference (Mode 2).
X Ri ðsÞ ¼
5. Conclusion In this investigation, an FBG sensor array is used to identify and locate structural damage. Experiments have been carried out on a steel beam, on which an array with 8 FBG sensors is surface mounted along the steel beam axis. An FFT analysis has been used to determine the frequency range that can be used to separate each mode shape. The natural frequencies, modal damping ratios, and mode shapes are extracted from a filtered time history response. RD is used to determine the natural frequencies and damping ratios, while multichannel RD is used to determine the mode shapes. The existence of damage is successfully identified by comparing the RD signatures and natural frequencies. The location of the damage is determined by mode shape differences. Our results demonstrate that the FBG sensor array is a reliable and fast tool for measuring strains at high frequency rates. The system as a whole is simple, easy to use, and offers a fast solution for damage identification and location. Appendix A The input of the following example, for applying RD technique, is a response captured using an accelerometer with 1000 Hz sampling rate from the tested steel beam, passing through a band bass
Using the FORTRAN coding, The RD signature is calculated and presented in the figure below;
1.2 0.8
Normalized RD
function is broken at the damage location. More details about the technique for mode shape differences can be found [23]. Fig. 12 shows Mode 2 as extracted by multichannel RD and the mode shape difference between intact and damaged cases for Mode 2 is shown in Fig. 13. The damage can be also identified in Fig. 13 as the mode shape difference function seems to be broken at the damage location.
N 1X xiðti þ sÞ N i¼1
0.4 0 -0.4 -0.8 -1.2 0
0.04
0.08
0.12
0.16
0.2
Using RD signature, the period is calculated using the previous showed equations of the logarithmic decrement and from graph using the average of first three cycles and it found to be equals 0.12 s, the natural frequency equals 8.299 Hz, logarithmic decrement is equal 0.054 and damping ratio equals to 3.74%.
References [1] Culshaw B. Optic fiber sensor technologies: opportunities and – Perhaps-pitfalls. IEEE J Lightwave Technol 2004;22(1):39–50 [196–208; January 2004]. [2] Takeda N, Okabe Y, Mizutani. Damage detection in composites using optical fiber sensors. IMechE, Part G: J Aerosp Eng 2007;221(4):497–508. [3] Waite SR, Tatam RP, Jackson A. Use of optical fiber for damage and strain detection in composite materials. Composites 1998;19(6):435–42. [4] Waite SR. Use of embedded optical fiber for significant fatigue damage detection in composite materials. Composites 1990;21(3):225–31. [5] Kuang KSC, Koh CG. Plastic optical fiber sensor for damage detection in offshore structures. In: Fourth international conference on experimental mechanics, Proc of SPIE, vol. 7522 75223A-1; 2010.
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[6] Silva JMA, Ferreira AM, Devezas TC. Fatigue damage of carbon–epoxy laminates with embedded optical fibres. Mater Sci Technol 2003;19: 809–14. [7] Hofer B. Fiberoptic damage detection in composite structures. Composites 1987;18(4):309–16. [8] Glossop NDW, Dubois S, Tsaw W, Leblanc M, Lymer J, Measures RM, et al. Optical fiber damage detection for an aircraft composite leading edge. Composites 1990;21(1):71–80. [9] Hong-Nan Li, Li Dong-Sheng, Song Gang-Bing. Recent applications of fiber optic sensors to health monitoring in civil engineering. Eng Struct 2004;26 (11):1647–57. [10] Chambers AR, Mowlem MC, Dokos L. Evaluating impact damage in CFRP using fiber optic sensors. Compos Sci Technol 2007;67(6):1235–42. [11] Hou S, Cai CS, Ou J. Seismic damage identification for steel structures using distributed fiber optics. Appl Opt 2009;48(22):4483–9. [12] Schulz WL, Conte JP, Udd E, Kunzler M. Structural damage assessment via modal property identification using macro-strain measurements with fiber Bragg gratings as an alternative to accelerometers. In: Optical fiber sensors conference technical digest, OFS, 1; 2002. p. 67–70. [13] Nosenzo G, Whelan MP, Dalton T. Damage detection in composite structures based on optical fiber strain sensing and finite element model updating. Key Eng Mater 2003;245–246:509–18. [14] Lee J-W, Choi K-H, Huh Y-C. Damage detection method for large structures using static and dynamic strain data from distributed fiber optic sensor. Int J Steel Struct 2010;10(1):91–7.
[15] Fidanboylu K, Efendiog˘lu HS. Fiberoptic sensors and their applications. In: 5th International advanced technologies symposium (IATS’09), May 13–15, Karabuk, Turkey; 2009. [16] Güemes A, Fernandez-Lopez A. Damage detection in bolted joints by fiber optics distributed sensing. In: 2nd International symposium on NDT in aerospace, Radison Blu Hotel, Hamburg Airport, Germany, November 22nd to 24th, paper # MO-2.A.2; 2010. p. 6. [17] Lopez-Higuera JM, Rodriguez Cobo L, Quintela Incera A, Cobo A. Fiber optic sensors in SHM. J Lightwave Technol 2011;29(4):587–608. [18] Dai J, Zhang W, Sun B, Du Y. Applications of fiber optic sensors in concrete structural health monitoring. In: Advanced sensor systems and applications III, proceedings of SPIE, vol. 6830; 2007. p. 68301Q-1–6. [19] Zhou Z, Ou J. Development of FBG sensors for structural health monitoring in civil infrastructures. In: Sensing issues in civil structural health monitoring. Netherlands: Springer; 2005. p. 197–207. [20] Yun YW, Jang IY. Research on early age deformation of high performance concrete by fiber Bragg grating sensor. KSCE J Civ Eng 2008;12(5):323–8. [21] Elshafey A, Haddara M, Marzouk H. On the use of mode shapes in the identification of structural damage. In: Proceedings of ASME 2010 29th international conference on ocean, offshore and arctic engineering OMAE2010, Shanghai, China, paper # 20069, June 6–11; 2010. [22] Elshafey A, Haddara M, Marzouk H. Identification of excitation and reaction forces spectra for offshore platforms. J Can Civ Eng 2010;37:66–75. [23] Elshafey A, Haddara M, Marzouk H. Experimental damage identification using modified mode shape difference. J Mar Sci Appl 2011;10(2):150–5.
Contents lists available at ScienceDirect
Engineering Structures journal homepage: www.elsevier.com/locate/engstruct
Use of fiber Bragg grating array and random decrement for damage detection in steel beam A. Elshafey a, H. Marzouk b,⇑, X. Gu c, M. Haddara d, R. Morsy b a
Department of Civil Engineering, Minoufiya University, Egypt Department of Civil Engineering, Ryerson University, Toronto, Ontario, Canada c Department of Electrical and Computer Engineering, Ryerson University, Toronto, Ontario, Canada d Memorial University of Newfoundland, St. John’s, NL, Canada b
a r t i c l e
i n f o
Article history: Received 4 November 2014 Revised 24 October 2015 Accepted 26 October 2015 Available online 11 November 2015 Keywords: Fiber optical Bragg grating array Strains Damage Random decrement Multichannel random decrement
a b s t r a c t A growing trend in the use of fiber Bragg grating array to detect structural damage has been observed in recent years. This paper describes the use of fiber Bragg grating optical sensors in an array to identify the location and assess the extent of damage on steel structures. A fiber optical sensing array with eight sensing elements has been designed, fabricated, and applied to measure the time history of strain at different points on a simply supported beam subjected to random loading. The wavelength shifts of the sensors are used to calculate the strain distribution along the beam. The random decrement at each point, for different modes, is extracted from the time history of the responses. The random decrements are compared at different damage ratios to an intact case to identify the existence of damage. Multichannel random decrement is applied to extract excited mode shapes. The mode shapes are then used to determine the location of the damage. The results show that the fiber optical sensor array is a reliable, fast, and accurate tool for the identification and localization of damage by using strain measurements. Ó 2015 Elsevier Ltd. All rights reserved.
1. Introduction Applications of fiber optical sensors in structural health monitoring have been increasing for many years [1]. The approach allows structures to be continuously monitored without interrupting operations or affecting stiffness. Fiber optical sensors that have small diameters are used for the structural health monitoring of aerospace composite structures [2]. Linearly birefringent singlemode optical fibers embedded into woven glass epoxy composites have been used to measure strains in a 1-point loading specimen [3]. Embedded optical fibers with a simple signal attenuation measuring system are used as an inexpensive method to detect significant fatigue damage in composite material [4]. The potential of using plastic optical fibers in conjunction with high-resolution photon counting to detect and estimate the location of cracks in a single fiber glued to a tubular member is studied [5]. The effect of the presence of optical fibers on the structural fatigue behaviors of a host of carbon epoxy laminates has been quantitatively studied, in which optical fiber cables were placed in mid-plane and near the surface of the laminate subjected to loading [6]. A system ⇑ Corresponding author. E-mail addresses: [email protected] (H. Marzouk), [email protected] (X. Gu), [email protected] (M. Haddara). http://dx.doi.org/10.1016/j.engstruct.2015.10.046 0141-0296/Ó 2015 Elsevier Ltd. All rights reserved.
of thin optical fibers integrated into a composite structure during its manufacturing process is suggested as a reliable automatic and remote long-term monitoring means for structural damage [7]. The influence of optical fiber orientation and depth on the sensitivity of a fiber optical system to detect impact damage in composite materials is reported and the optimal configuration has been determined for both orientation and depth [8]. Fiber optic sensor is classified as local, quasi-distributed and distributed sensors, related to the range that will be sensed. Local fiber optic sensors are based on detecting the optical phase change induced in light along the optical fiber. Fiber Bragg grating (FBG) sensors is a kind of quasi-distributed sensors, it has a unique property is encoding the wavelength which has been successfully employed in several civil engineering applications. These FBG sensors could be theoretically wavelength multiplexed up to 64 FBGs gratings in single fiber [9]. FBG sensors are used to evaluate damage in unidirectional carbon fiber/composites that results from both low and high velocity/energy impacts [10]. A distributed fiber optical monitoring methodology based on optical time-domain reflectometry has been developed for the seismic damage identification of steel structures [11]. The use of long FBGs to provide strain measurements is investigated with the purpose of achieving better structural health monitoring as opposed to the use of classical accelerometers because they provide low noisy data [12]. A
349
A. Elshafey et al. / Engineering Structures 106 (2016) 348–354
gradient-based optimization algorithm is utilized to update the finite element model of a composite simple structure by using the output from fiber optical sensors and strain modal analysis [13]. A technique for damage detection has been introduced based on continuous strain data obtained from distributed fiber optical sensor arrays and neural networks [14]. An overview of the major types of fiber sensor arrays and their applications in civil structures has been reviewed by Fidanboylu and Efendiog˘lu [15]. Distributed fiber optical sensing has been used in an effort to detect structural damage in steel connections from direct strain measurements. It is found that the technique can be successfully applied in static analysis, but has a limited application in dynamic analysis, as data collection is too slow [16]. Lopez-Higuera et al. used Fabry–Perot interferometric sensors and neural networks to predict the size and location of delamination in laminated glass/epoxy composite beams [17]. Reviewed research and development activities on the use of fiber optical sensors in the health monitoring of various structures, including buildings, piles, bridges, pipelines and tunnels, in which existing problems and promising research efforts are also discussed [18]. An application of using FBG sensors which is the smart FBG weighbridge; traffic are weighted from the deflection of reinforced concrete beam with FBG strain sensors embedded [19]. FBG sensors used to monitor early age deformations and temperature for various materials as high performance concrete [20]. In this paper, an FBG sensor array is used to measure the time history of strains on the surface of a beam subjected to random loading. An FBG sensor array with eight FBG sensors on a single fiber is surface mounted onto a steel beam. The testing is not affected by electromagnetic noise or other sources of noise in the laboratory with different kinds of machineries. Analysis of the modal damping ratio and mode shape can clearly locate and identify structure damage. Random decrement (RD) signatures can be used to describe the free decay response of the system. The advantage of this approach is that one can obtain a free response from the stationary random response of the system. To obtain the RD from a stationary random response, the response is divided into a number of segments, N, each with a length of s and determining the average of this segments to eliminate the random component and resulting the deterministic component introducing the random decrement signature [21]. 2. Random decrement and mode shape extraction techniques 2.1. Random decrement The response of a single degree of freedom linear system is governed by the equation of motion:
€ _ ½MfXðtÞg þ ½CfXðtÞg þ ½KfXðtÞg ¼ fFðtÞg
ð1Þ
where M is the mass, C is the damping, K is the stiffness and F(t) is the excitation force. And after normalizing the equation relative to the mass:
€ þ 2xe XðtÞ _ XðtÞ þ x2 XðtÞ ¼ FðtÞ
ð2Þ
x is the natural frequency, e is the damping ratio and X(t) is the response of the system. Random decrement response extracted from Eq. (2) represents the free decay of the system, assuming that the analyzed response is realization of a zero mean stationary Gaussian stochastic process. By changing the variables indications used in the previous equation to be y1 ¼ x and y2 ¼ x_ y_ 1 ¼ y2
ð3Þ
y_ 2 ¼ 2xo ny2 xo y1 þ f ðtÞ
ð4Þ
By substituting in the probability density function and multiply the two sides with y1 and y2 then integrating the equation with respect to y1 and y2 , where l1 and l2 are the mean values of displacement and velocity,
l€ 1 ¼ l_ 2 ¼ 2xo ny2 þ x2o y1
ð5Þ
The free decay for the structure is derived from the stationary random response,
l€ þ 2nxo l_ þ x20 l ¼ 0
ð6Þ
The technique is based on the classical RD technique, which averages the time history segments of random vibration responses in a time domain. The triggering condition is used to determine the starting point of each time segment. It is assumed that if the structure is subjected to a wideband load, the response will be composed of two components: a random and a deterministic component (free decay). By averaging the response, the random component is cancelled out and the deterministic component is obtained.
xðsÞ ¼
N X xi ðt i þ sÞ
ð7Þ
i¼1
The triggering values are
xi ðt i Þ ¼ xs for i ¼ 1; 2; 3; . . . ; N x_i ðt i Þ P 0 for i ¼ 1; 3; 5; . . . ; N 1 x_i ðt i Þ 6 0 for i ¼ 2; 4; 6; . . . ; N In the current study, multichannel RD [21] is used to extract the excited mode shapes of the tested beam. Multichannel RD extends the approach by applying it at multiple points on the structure at the same time [20].
RDL ¼
N 1X ffX L ðtisL þ sÞjX L ¼ X S g N i¼1
RDNL ¼
N 1X ffX NL ðt iNL þ sÞjt iNL ¼ t isL g N i¼1
ð8Þ
ð9Þ
where RDL is the random decrement at leading channel, X L is the triggering conditions of the leading channel, t isL is the time corresponding to the triggering conditions, and RDNL is the random decrement for the non-leading channels. To keep the phase angle between different points, one channel is used as a leading channel and the triggering condition is applied only to this channel. The times that correspond to the triggering condition in the response are used to extract RDs in other channels. A FORTRAN code was written to extract both single and multi-channel RDs. The code allows the use of constant level crossing as a triggering condition as well as the use of a time interval that is different from that used to record the original data. This capability is needed in some cases for extracting higher mode shapes. Fig. 1 shows the multichannel signals, triggering condition, and times that correspond to the triggering levels. For more details about the approach, the reader may refer to [22,23]. Fig. 2 shows the RD results for each channel. The triggering condition at Channel 1 (Y1) is used as the base triggering value for all of the other channels. The values shown in Fig. 2 are used to extract the mode shape. A fast Fourier transform (FFT) analysis helps to determine the number of modes excited. The mode shape of the structure is composed of a set of numbers at the same time lag as shown in Fig. 2; in this work, the first set of values (RD1, RD2, . . . , RDn) are used. However, the other points still have the same information on the mode shape.
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And then get the modal vectors of the damages structure as shown Eq. (8) and normalized it with respect to the maximum amplitude
T ki ¼ A1 ; A2 ; . . . ; Am
ð12Þ
Then we determine the modal vector difference Dki , where superscript n indicates the normalized values
n n n n T Dki ¼ An1 An 1 ; A2 A2 ; . . . ; Am Am
ð13Þ
By considering the normalized difference as virtual displacements for each node, add (or subtract) the virtual displacements to the coordinates of the un-deformed structure, to get a new coordinates of the virtually deformed structure, The virtually deformed shape will contain clear and enough information about the location of damage (see Fig. 3). 3. Experimental investigation
Fig. 1. Multichannel random decrement procedure.
2.2. Mode shape extraction The normalized random decrements are representing the free response of the structure [21]. The mathematical equation of the free vibration equation is
xi ðtÞ ¼ Ai e2ext cosðxi t ui Þ;
i ¼ 1; 2; 3; . . . ; N
ð10Þ
where xi ðtÞ is the random decrement for certain channel, N is the number of channels, Ai is the amplitude at t ¼ 0, e is the damping coefficient, xi is the natural frequency, and ui is the phase angle. The approach for damage detection using the mode shape is based on normalizing the differences between the intact and damaged mode shape [23]. Assume that modal vectors for the intact structure in Eq. (11) the normalize it with respect to the maximum amplitude
ki ¼ fA1 ; A2 ; . . . ; Am gT
ð11Þ
The FBG sensors were fabricated into the core of a hydrogenloaded single mode fiber (Corning Corp., SMF-28) in the fiber optic lab at Ryerson University. A collimated KrF excimer laser (Lumonics, model PM 844) beam at 248 nm was focused onto a horizontally positioned fiber through a phase mask. The FBGs, apodised with a sin function, had an effective length of 3 mm, and were inscribed at different wavelengths. The eight FBGs were spaced as shown in Fig. 5 by using a single FBG array. After fabrication, all FBGs were annealed at 150 °C for 15 h after FBG inscription to ensure their long-term stability. A steel beam with a length of 3500 mm as shown in Fig. 4 was tested to validate the applicability of the fiber optical sensors in identifying damage extent and location by using a dynamic response. The beam is a hollow structural tube with a wall thickness of 3 mm and has a hollow square cross section that is 25.4 25.4 mm. The beam supports were arranged to allow rotations at the beam-ends. Beam translation perpendicular to the beam was not allowed. The beam supports were attached to rigid steel bases fixed onto a concrete floor as shown in Fig. 5. The beam was subjected to random loading with a wide band spectrum. A computer was used for data logging as well as controlling random loading.
where ki is the mode shape.
Fig. 2. Random decrement signature of different channels.
Fig. 3. Methodology for multichannel random decrement.
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Fig. 4. Beam dimensions, cross section, sensors, and load location.
Fig. 5. Beam support fixture. Fig. 7. FFT for Sensors 2, 4 and 6 on the beam.
The experimental setup was attached to very rigid bases with each base secured onto a solid structural concrete slab on the floor (1000 mm thick) by using 4 steel bolts that were 50 mm in diameter. The experiment setup is shown in Fig. 6, in which an electromagnetic shaker was used for random loading. A computer was used to generate the random load signal which was fed to a power amplifier through a National Instrument data card. The FBG sensors are also shown in Fig. 6 which is surface mounted to a beam and the beam is protected as it is susceptible to shearing. The pinned support allowed only rotation of the end. Damage was intentionally induced at Sensor 6. Three cases were considered. The ratios of damage depth to beam height in the three cases were 25%, 50%, and 75%, which were labeled as d25, d50, and d75 respectively. An optical circulator, which is a three-port device that allows light to only propagate from Port 1 to 2 and from 2 to 3, was used
in the experiment. A broadband light source was connected to Port 1 and the FBG sensing array was connected to Port 2, and the reflected wavelengths from the 8 FBG sensors could be measured from Port 3. Thus, with the use of the circulator, the FBG sensor array became a one-ended device. Due to the high amount of isolation between the input and reflected optical power and its low insertion loss, optical circulators are widely used in advanced communication systems and fiber-optical sensor array applications. Port 3 of the circulator was connected to the input of a sensor interrogation system (Ibsen, model: I-MON E-USB2.0 DAQ system). The DAQ system was connected to a computer through a USB connection. Special software based on the Lab VIEW platform was used to record the FBG wavelength shifts as a function of time. 4. Results and discussion To extract the RD signatures for different modes, a filtering process for the data is required. An FFT analysis was used to determine the frequency range around each natural frequency excited as shown in Fig. 7. The first two modes are used in this study. Table 1 shows the filtering range used to separate the signals corresponding to the used modes. The random decrements corresponding to mode 1 and mode 2 were extracted from the filtered time history data. Fig. 8 shows the RD signatures at different damage ratios for Mode 1 and 2, the figures indicate the damage extent in the steel beam by means of change in the RD signature according to different damage ratios. These RDs are normalized values used to extract the natural frequencies and damping ratios. The logarithmic decrement is used to extract the damping ratio. The values of the natural Table 1 Filtering range used to separate excited modes.
Fig. 6. Experimental setup which shows the steel beam with a fiber optical array installed on its side and an electromagnetic shake.
Mode number
Frequency range (Hz)
Mode 1 Mode 2
6–10 21–25
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Fig. 8. Random decrement signatures of the experimental investigation for different damage ratios at Point 6 for Modes 1 (a) and 2 (b).
Table 2 Mode 1, natural frequency and damping ratio for different damage ratios. Damage ratio
Natural frequency (Hz)
Damping ratio (%)
Intact D25 D50 D75
8.299 8.222 7.996 7.846
3.74 3.86 3.31 4.27
Table 3 Mode 2, natural frequency and damping ratio for different damage ratios. Damage ratio
Natural frequency (Hz)
Damping ratio (%)
Intact D25 D50 D75
23.753 23.664 23.256 22.144
0.776 0.939 0.683 0.939
frequencies and damping ratios are shown in Tables 2 and 3. The RD signature is determined by using the finite element results simulating the beam with the same factors used for damaged ratios to ensure consistency in the results, the finite element results is consistent with the experimental investigation results. In the Finite Element (FE) model, the material of the beam is modeled as steel with modulus of elasticity 20.7 104 MPa. For the first and second mode shapes, the RD signature is calculated using FE for beam state with three different damage ratios are shown in Fig. 9, where it can be noticed that there is changes in the RD signature relative with the damage extent. The RD signature is calculated using triggering level equals to 1.4 times the standard deviation of the response (1.4r, where r is the standard deviation) and the integration was calculated using a time increment of 0.001 s. For conducting the RD, the number of segments is 400 time segment as for better results are the number of segments are more than 100.
Fig. 10. Shape of Mode 1 as extracted by multichannel random decrement.
Fig. 11. Mode shape difference (Mode 1).
In extracting the mode shapes for locating the damage, Fig. 10 shows the first mode shape and it can be noticed that there is some discrepancy in the damage location (at Point 6). Fig. 11 shows the mode shape difference for Mode 1. It can be noticed that the
Fig. 9. Random decrement signatures using FE model for different damage ratios at Point 6 for Modes 1 (a) and 2 (b).
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filter centered on the first natural frequency calculated, the response is given as shown in the below figure;
Acceleration (g)
50 25 0 -25 -50 0
25
50
Fig. 12. Shape of Mode 2 as extracted by multichannel random decrement.
75
100
125
150
175
200
Time (sec) Using the MATLAB coding for the response applying the below equation, it is a time domain averaging of the structure response segments due to random input loads starting from certain level called triggering level. The advantage of the averaging is the noise reduction and discrimination of the random part of the response. In this example, the used triggering level equals to the standard deviation of the response (r = 6.30) as the optimum range for the trig pffiffiffi gering level is 1 2 rx , where the standard deviation of the time response is represented as rx , the integration time increment is equal 0.001 s, the vertical acceleration is measured with sampling rate of 1000 Hz. The segment number equals 400 segments; it provides better results at number of segments more than 100, the variance of RD signature decreases with the number of averages of time segments.
Fig. 13. Mode shape difference (Mode 2).
X Ri ðsÞ ¼
5. Conclusion In this investigation, an FBG sensor array is used to identify and locate structural damage. Experiments have been carried out on a steel beam, on which an array with 8 FBG sensors is surface mounted along the steel beam axis. An FFT analysis has been used to determine the frequency range that can be used to separate each mode shape. The natural frequencies, modal damping ratios, and mode shapes are extracted from a filtered time history response. RD is used to determine the natural frequencies and damping ratios, while multichannel RD is used to determine the mode shapes. The existence of damage is successfully identified by comparing the RD signatures and natural frequencies. The location of the damage is determined by mode shape differences. Our results demonstrate that the FBG sensor array is a reliable and fast tool for measuring strains at high frequency rates. The system as a whole is simple, easy to use, and offers a fast solution for damage identification and location. Appendix A The input of the following example, for applying RD technique, is a response captured using an accelerometer with 1000 Hz sampling rate from the tested steel beam, passing through a band bass
Using the FORTRAN coding, The RD signature is calculated and presented in the figure below;
1.2 0.8
Normalized RD
function is broken at the damage location. More details about the technique for mode shape differences can be found [23]. Fig. 12 shows Mode 2 as extracted by multichannel RD and the mode shape difference between intact and damaged cases for Mode 2 is shown in Fig. 13. The damage can be also identified in Fig. 13 as the mode shape difference function seems to be broken at the damage location.
N 1X xiðti þ sÞ N i¼1
0.4 0 -0.4 -0.8 -1.2 0
0.04
0.08
0.12
0.16
0.2
Using RD signature, the period is calculated using the previous showed equations of the logarithmic decrement and from graph using the average of first three cycles and it found to be equals 0.12 s, the natural frequency equals 8.299 Hz, logarithmic decrement is equal 0.054 and damping ratio equals to 3.74%.
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