Two-dimensional distributed strain sensing with an Archimedean spiral arrangement in optical frequency domain reflectometry

Nanotechnology and Precision Engineering 1 (2018) 187–190

Contents lists available at ScienceDirect

Nanotechnology and Precision Engineering journal homepage: http://www.keaipublishing.com/en/journals/nanotechnologyand-precision-engineering/

Two-dimensional distributed strain sensing with an Archimedean spiral arrangement in optical frequency domain reflectometry Yamei Guo, Zhenyang Ding ⁎, Kun Liu, Junfeng Jiang, Chenhuan Wang, Tiegen Liu School of Precision Instrument and Opto-Electronics Engineering, Tianjin University, Tianjin 300072, China Institute of Optical Fiber Sensing of Tianjin University, Tianjin 300072, China Tianjin Optical Fiber Sensing Engineering Center, Tianjin 300072, China Key Laboratory of Opto-Electronics Information Technology, Ministry of Education, Tianjin 300072, China

a r t i c l e

i n f o

Available online 20 August 2018 Keywords: Optical frequency domain reflectometry (OFDR) Archimedean spiral Distributed optical fiber sensing

a b s t r a c t We demonstrate a distributed two-dimensional (2D) strain-sensing system in optical frequency domain reflectometry (OFDR) with an Archimedean spiral arrangement of the sensing fiber. The Archimedean spiral describes a simple relationship between the radial radius and polar angle, such that each circle (the polar angle from 0 to 2π) can sense the 2D strain in all directions. The strain between two adjacent circles can also be easily obtained because an Archimedean spiral facilitates sensing of every angle covering the full 2D range. Based on the mathematical relation of Archimedean spirals, we deduce the relationship between the one-dimensional position of the sensing fiber and 2D distribution in polar coordinates. The results of the experiment show that an Archimedean spiral arrangement system can achieve 2D strain sensing with different strain load angles. Copyright © 2018 Tianjin University. Publishing Service by Elsevier B.V. on behalf of KeAi Communications Co., Ltd.

1. Introduction Distributed optical fiber strain sensing can provide real-time strain information along a region of interest with low-cost optical fiber, offering advantages such as immunity from electro-magnetic interference, electrical isolation, and multiplexing possibilities.1,2 Froggatt et al.3 presented a method to achieve high-sensitivity highspatial-resolution distributed strain measurements using spectrally shifted Rayleigh backscattering for a single mode fiber (SMF) in OFDR. Distributed optical fiber strain sensing can provide real-time strain information in OFDR that is imperative for some applications, and could be used in fields such as medicine, aerospace, shipping, or the construction industry.4,5 The high sensitivity and high spatial resolution of fiber optic sensors enable a number of attractive features, making these sensors one of the most popular areas of research focus in the fields of geology and geotechnical engineering monitoring.6 An OFDR strain sensor has potential applications in many fields such as structural health monitoring in which modal frequencies may be an indication of health. The real-time monitoring ability of such sensors also makes them ideal to monitor seismic activity and detect intrusion.7 In general, the sensing fiber is deployed in a one-dimensional (1D) linear strain sensing arrangement.8,9 Two-dimensional (2D) strain distribution is less easily ⁎ Corresponding author at: School of Precision Instrument and Opto-Electronics Engineering, Tianjin University, Tianjin 300072, China. E-mail address: [email protected] (Z. Ding).

achieved, and several sensing-based OFDR methods have been suggested to accomplish this. One such method involves arranging the sensing fiber in unidirectional parallel lines, in a snake-like manner.10 However, this method poses some problems, the biggest of which is its insensitivity to orthogonal strain, which cannot be sensed as fiber bonded on the diameter in one direction, and cannot be located between two parallel lines. Another method is to arrange the sensing fiber in several circular loops, which can measure strain at various loads and load angles11; however, the density of this arrangement is not sufficient for 2D strain sensing. In this paper, we demonstrate a distributed 2D strain sensing system in OFDR with an Archimedean spiral arrangement of sensing fiber. The Archimedean spiral describes a simple relationship between the radial radius and the polar angle, such that each circle (the polar angle from 0 to 2π) can sense 2D strain in all directions. Compared with closed graph arrangements (such as rectangles and circles), the arrangement of the Archimedean spiral makes the detection of strain at any angle possible. Any of its segments can be used entirely for sensing and can cover the same area with shorter fibers. The strain between two adjacent circles could also be easily obtained because this arrangement can sense every angle over the full 2D range. Using the mathematical principles of the Archimedean spiral enables us to deduce the relationship between the 1D position of the sensing fiber and 2D distribution in the polar coordinate system. The results of the experiment show that an Archimedean spiral arrangement system can achieve 2D strain sensing at different strain load angles, allowing the location of the strain source to be located easily.

https://doi.org/10.1016/j.npe.2018.07.002 1672-6030/Copyright © 2018 Tianjin University. Publishing Service by Elsevier B.V. on behalf of KeAi Communications Co., Ltd.

188

Y. Guo et al. / Nanotechnology and Precision Engineering 1 (2018) 187–190

Archimedean spiral can be described in the polar coordinate system by the following equation: r ðθÞ ¼ aθ:

ð1Þ

where, (r, θ) are polar coordinates, and a is a constant that is proportional to the distance between two adjacent circles. In Eq. (1), we set the origin point (θ = 0) as the center of the structure being tested, as shown in Fig. 1. We assume that the origin point of the sensing fiber is the same as that of the structure under examination. Thus, the length of the sensing fiber can be obtained as follows:  qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi a aθ ln θ þ a2 þ θ2 þ a2 þ θ2 ; 2 2

LðθÞ ¼

Fig. 1. Illustration of the Archimedean spiral. The blue line shows how the fiber is bonded onto the structure in the test.

ð2Þ

where L(θ) is the length of the sensing fiber. In practice, the polar angle θ cannot be too small. With this condition in place, θ is much larger than a, so we can simplify Eq. (2) as: aθ2 : 2

LðθÞ ¼

ð3Þ

We simulate the relationship between the polar angle and the fiber length using Eqs. (2) and (3), as shown in Fig. 2. In the simulation, we set a = 0.01, and the total simulation length at about 25 m. Two curves overlapping well indicate that the simplification in Eq. (3) is feasible. The polar angle can be described as follows: rffiffiffiffiffi 2L : a

θðLÞ ¼

ð4Þ

Eq. (4) calculates the 1D position of the sensing fiber related to 2D coordinates distribution by the Archimedean spiral. 3. Experimental results and discussion

Fig. 2. Simulation results of the relationship between the polar angle and the length of fiber using Eq. (2) (blue line) and Eq. (3) (red line). Two curves overlapping well indicate that the simplification in Eq. (3) is feasible.

2. Principle In OFDR, we can obtain the fiber strain as a function of fiber length directly, i.e., 1D strain distribution. If we want to obtain 2D strain distribution, we need to deduce the relationship between the 1D position of the sensing fiber and 2D distribution in the polar coordinate system. The

Auxiliary interferometer ν

Circulator γ

Coupler 50/50

In this paper, the OFDR experimental measurement system for distributed strain sensing is shown in Fig. 3. A tunable light source (TLS) (Agilent 81600B) is employed in the OFDR system. The tuning speed, tuning range, and starting wavelength of the TLS are 5 × 103 GHz/s (40 nm/s), 2.5 × 103 GHz (20 nm), and 1520 nm, respectively. The light from the laser is split into two paths by a 1:99 coupler. A small amount of light (1%) is sent to an auxiliary interferometer (a Michelson interferometer) with two Faraday rotating mirrors and a delay fiber of 300 m. The auxiliary interferometer provides an external clock (f-clock) to trigger the data acquisition card, which samples the interference signal Computer

SMF FRM

300m

FRM

BPD

f-clock

t Coupler

TLS

BPD

PC 1/99

Coupler

Coupler

50/50

50/50

Circulator

D A BPD Q

Sensing Fiber

Fig. 3. OFDR system for distributed two-dimensional (2D) strain sensing. TLS is a tunable laser light source. FRM denotes Faraday rotating mirror; PC is a polarization controller; BPD is the balanced light detector. DAQ denotes the data acquisition card. The sensing fiber constitutes the measuring arm of the main interferometer. The sensing fiber is arranged with an Archimedean spiral and adheres to the organic glass plate.

Y. Guo et al. / Nanotechnology and Precision Engineering 1 (2018) 187–190

189

Fig. 6. Illustration of linear strain test. The linear red strip indicates the intensity (high) and position of the strain produced. Green and blue areas indicate places under little to no strain. Fig. 4. Illustration of point strain test. The red point indicates the position of the strain produced. The green area indicates areas under no strain; the coordinates x, y show the position of the fiber; strain is the relative quantity, where 1 represents a 1 kg weight.

at equidistant instantaneous optical frequency points to reduce the nonlinearity of the frequency tuning of the TLS. The remaining amount of light (99%) is sent to the main (Mach–Zehnder) interferometer. The measurement arm of this main interferometer consists of the sensing fiber, which we arrange as an Archimedean spiral (a 25 m sensing fiber attached to the organic glass plate in the practical experiments). In Ref 12, we calibrated the relationship between the spectral shift of Rayleigh backscattering and fiber strain using a standard single mode fiber in the OFDR system. The sensitivity of this method (the ratio of the spectral shift of Rayleigh backscattering and strain) is 0.0338 GHz/με. In the same study, we also analyzed the relationship between the spatial resolution and the minimum measurable strain. In this system, as the spatial resolution is 18 cm, the minimum measurable strain is 15 με.12 The main interferometer detects Rayleigh backscattering from the sensing fiber, caused by random refractive index fluctuations along an optical fiber. Rayleigh backscattering can be modelled as a long, weak

Fiber Bragg grating (FBG) with random periods. The change in strain causes a local Rayleigh backscattering spectra (RBS) shift, which can be calculated using the cross-correlation between the measurement RBS and the reference RBS.3 We measure the RBS shift along the sensing Fiber; thus, we can obtain strain as a function of fiber length, namely, a 1D strain distribution. In the experiment, we first test single-point strain sensing using the proposed system. A weight is placed on the structure as a unidirectional source of strain, and a peak in the 2D strain distribution is found, as depicted in Fig. 4. Opposite strain peaks occur on both sides of the forward peak shown in Fig. 4, which is due to the strain being affected by the weight of the plate at the corner. When the weight presses the plate, the adjacent corner is lifted up. The corner's weight will press back against the plate too, which causes the two sides necessary to produce the opposing strains. Secondly, we test the orthogonal strainsensing using this system. We attach two weights in the orthogonal directions. Fig. 5 shows two peaks occurring at the positions of the two weights. A notable feature of the Archimedean spiral method is that it allows us to sense strain at different angles with a high spatial resolution. Meanwhile, we can see that the value of strain is not zero in the no-strain area, mainly because deformation occurs on the organic glass plate when the weight is pressed onto it. The plate is supported at four places by boxes, and strain also occurs in these support areas. Next, we use a long rectangular object as a source of weight, placing this along the radial direction of the spiral. The resulting strain region is depicted in Fig. 6. The straight strain distribution line that is visible verifies the validity of the algorithm. 4. Conclusions We demonstrate a distributed 2D strain sensing system in OFDR with an Archimedean spiral arrangement of sensing fiber. The results of the experiment show that the system can achieve 2D strain sensing at different strain load angles. Acknowledgements

Fig. 5. Illustration of orthogonal strain test. The red points indicate the position of the strain produced. The green region indicates areas under no strain, and the coordinates x, y show the position of the fiber. Strain is a relative quantity, where 1 represents a 1 kg weight.

This work is supported in part by the National Natural Science Foundation of China (Grant Nos. 61505138, 61635008, 61475114, 61735011); in part by the Tianjin Science and Technology Support Plan Program Funding (Grant No. 16JCQNJC01800); in part by the China Postdoctoral Science Foundation (Grant Nos. 2015M580199, 2016T90205); in part by the National Instrumentation Program (Grant No. 2013YQ030915); and in part by the National Key Research and Development Program (Grant No. 2016YFC0100500).

190

Y. Guo et al. / Nanotechnology and Precision Engineering 1 (2018) 187–190

References 1. Lee B. Review of the present status of optical fiber sensors. Opt Fiber Technol 2003;9(2): 57-79. 2. Kersey AD. A review of recent developments in fiber optic sensor technology. Opt Fiber Technol 1996;2(3):291-317. 3. Froggatt M, Moore J. High-spatial-resolution distributed strain measurement in optical fiber with Rayleigh scatter. Appl Optics 1998;37(10):1735-40. 4. Tosi D, Schena E, Molardi C, et al. Fiber optic sensors for sub-centimeter spatially resolved measurements: review and biomedical applications. Opt Fiber Technol 2018;43:6-19. 5. Saito N, Yari T, Enomoto K. Flight demonstration testing with distributed optical fiber sensor. EWSHM-7th European Workshop on Structural Health Monitoring; 2014. 6. Maurin L, Rougeault S, Dewynter-Marty V, et al. OFDR distributed temperature and strain measurements with optical fibre sensing cables: application to drain pipeline monitoring in a nuclear power plant. EWSHM-7th European Workshop on Structural Health Monitoring; 2014.

7. Kreger ST, Klein JW, Rahim NAA, et al. Distributed Rayleigh scatter dynamic strain sensing above the scan rate with optical frequency domain reflectometry. Fiber Optic Sensors and Applications XII. International Society for Optics and Photonics; 2015. 8. Klute SM, Sang AK, Gifford DK, et al. Defect detection during manufacture of composite wind turbine blade with embedded fiber optic distributed strain sensor. 2011 SAMPE Fall Technical Conference; 2011. 9. Castellucci M, Klute S, Lally EM, et al. Three-axis distributed fiber optic strain measurement in 3D Woven composite structures. Industrial and commercial applications of smart structures technologies. Proceedings of the SPIE-International Society for Optics and Photonics; 2013. 10. Huang J, Lilliu S, Alqahtani A, et al. 2D directional surface strain mapping through distributed optical fiber sensors. Lasers and Electro-Optics Pacific Rim. IEEE; 2013. 11. Gifford DK, Froggatt ME, Sang AK, et al. Multiple fiber loop strain rosettes in a single fiber using high resolution distributed sensing. IEEE Sensors J 2011;12(1): 55-63. 12. Ding Z, Yang D, Du Y, et al. Distributed strain and temperature discrimination using two types of fiber in OFDR. IEEE Photonics J 2016;8(5):1-8.