A novel distributed fiber-optic strain sensor

IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 51, NO. 4, AUGUST 2002

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A Novel Distributed Fiber-Optic Strain Sensor Miguel J. García, Juan A. Ortega, Juan A. Chávez, Jordi Salazar, and Antoni Turó

Abstract—The theory of operation of a fiber-optic-based strain sensor system, suitable for long structures, is described. The proposed sensor design is composed of several hundreds of sections separated by reflectors in order to monitor structures of more than 1 km of length. A quasi-distributed sensor structure accomplishes the best condition monitoring, where each section of the sensor integrates the measured magnitude, obtaining a value associated to the average shortening or elongation in this section. Tools for the design of the optical reflectors of the sensor are also provided, including a study of the optical noise due to multireflection within the system. Index Terms—Fiber-optic sensors, long length gage, strain sensors.

I. INTRODUCTION

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HE condition of large structures such as bridges, beams, clamping ropes, foundation structures, and dams, from hundreds of meters to more than one kilometer of length, needs to be monitored for such reasons, as safety of operation, cost, or a basic wholeness diagnosis. In this sense, the kind of sensor proposed in this work is intended to measure the mechanical parameters associated to the deformation and deterioration of structures, overcoming inspection difficulties using the present facilities. Our study is motivated by the specific need of monitoring the condition of marine platform clamping ropes. Other measurement applications can be found in suspension bridge ropes and large concrete structures, such as dams. The inspection of these ropes involves several difficulties. For example, the ropes are coated with organic covers, and usually it is necessary to extract the rope in order to monitor its condition, which makes the work difficult and may cause rope breaks. In an attempt to overcome this problem, sometimes the rope is oversized in order to decrease the risk of breaking, but this is an expensive alternative. There are several antecedents of measurements using optic or metallic gauges, and several works devoted to nonmechanical parameter measurements, such as moisture and corrosion. The optoelectronic instrumentation can offer an interesting alternative for rope monitoring using a distributed fiber-optic strain sensor along the whole length [1], [2]. This paper performs a theoretical study as a preliminary step to validate the model by means of a prototype system, which could be expensive to build. Section II presents the sensor theory of operation. Then, Section III studies the behavior of an equalManuscript received May 29, 2001; revised April 17, 2002. This work was supported by the Comissió Interdepartamental de Recerca i Innovació Tecnològica, CIRIT, and by the Department of Electronic & Electrical Engineering, University of Strathclyde, Glasgow, U.K. The authors are with the Universitat Politecnica de Catalunya, Barcelona, Spain. Digital Object Identifier 10.1109/TIM.2002.803090

ized and nonequalized system. Finally, Section IV presents a study of the optical-induced noise. Conclusions of the work and a list of references are also included. II. THEORY OF OPERATION We propose to measure tensile and/or compressive strain using a fiber-optic-based sensor, which is embedded directly in the element to be measured. The fiber-optic sensor is embedded following the measurement direction and along the whole length to be measured. A quasi-distributed sensor structure accomplishes the best condition monitoring, where each section of the sensor integrates the measured magnitude, obtaining a value associated to the average shortening or elongation in this section. When deterioration begins in a section, it can be identified because it presents greater elongation than the adjacent ones. The elongation of ropes, whose length may be about 1 km, can reach up to 10%. The supervision should be carried out in sections no longer than 4 m, since this length is suitable for correct monitoring of the whole rope. Thus, the measurement system will have to manage with several hundreds of different measurement sections for each rope. As the maximum elongation in the fiber optic should be below 1% compared with the 10% allowed in ropes, a mechanical demultiplication structure is used (see Fig. 1). This structure makes the fiber work near its maximum strain, minimizing the temperature effect on the strain measurement. The primary sensor is composed of a monomode fiber optic up to a 1000 m long containing several hundreds of contiguous identical size sections [3]. Let us propose a working reference: a 1-km length sensor system containing 250 four-meter length sections. These figures were chosen as a compromise between the number of sections, the section length, and the total length of the sensor system. According to this structure, the system might be qualified as a quasi-distributed optical strain sensor (QDOSS). In a system with sections, two consecutive reflectors limit each section and accordingly, each reflector separates two conreflecsecutive sections (see Fig. 2). This means that are required. We have placed the tors numerated from 0 to “number 0 reflector” as the furthest reflector, at the opposite end of the multisensor interrogation instrumentation. The “ ” ” reflectors and section is situated between the “ ” and “ the “ ” section is the closest one to the instrumentation. These reflectors are built in the core of the fiber optic, and the reflection coefficient cannot be too high (normally under 1%) in order to allow the light to travel forward and backward for the whole inspected length of the fiber. In addition, they must not necessarily be spectrally selective.

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IEEE TRANSACTIONS ON INSTRUMENTATION AND MEASUREMENT, VOL. 51, NO. 4, AUGUST 2002

tectable change in the output of the measurement system. Resolution in our system can be mainly associated to the errors due to several causes such as electrical or optical noise, instability of the measured magnitude, nonlinearity, quantification procedures, etc. In Section IV, a model able to predict the optical noise is presented. The phase and the time sensitivities with respect to the strain are immediately derived from (4) and (2) Fig. 1. Mechanical elongation demultiplication structure.

(6)

The proposed system belongs to the optical time domain reflectometry (OTDR) kind of measurement systems [4]. The sensor interrogation is done as following. A light burst is transmitted into one end of the fiber, and light signals reflected from the partial reflectors along the fiber length are recovered from the same fiber end. The burst is essentially a light signal nearly 100% modulated by a microwave subcarrier, in the GHz band, and windowed by a rectangular pulse envelope. The light burst, traveling along the fiber, is reflected sequentially at each couple of contiguous reflectors. The temporal between two consecutive reflections can be asseparation sociated with the distance between reflectors (1) is the time difference where is the length of the section, between two consecutive arriving pulses from the reflectors associated to this section, is the refraction index of the fiber, and is the light speed in vacuum. in the section length produces a change A change time, given by in the (2) is the change in the arrival time and is the where is the effective index of refraction of the fiber under strain. unitary strain, which is described in [5] as (3) , the photo-elastic conwhere for the Poisson’s ratio and , the refractive index stants , and nm, the effective index is . The arrival time difference can also be expressed as a phase between the microwave subcarrier phase of the difference two reflections of the burst (4) where is the microwave subcarrier pulsation. The measurement of the strain, , can be made by means of or the equivalent . The strain the evaluation of either the associated to the phase error can be easily derived error from (4)

and (7) A low-cost commercial semiconductor laser, typically used in fiber-optic data communications, is proposed as the light source. The lack of high coherence usually associated to this kind of source (with a typical coherence length of several millimeters) should not affect the sensor system performance in practice. The reasons are that the phase difference between two reflections is detected from the microwave subcarrier; the low reflection coefficient reflectors feature enough bandwidth, either if they are built introducing sharp longitudinal changes in the fiber reflection index or if they are composed of a Bragg diffractor with few elements; and, finally, the effects due to the fiber disperse behavior can be neglected for distances below a couple of kilometers. III. STUDY OF THE INPUT TO RECOVERED SIGNAL POWER RATIO COEFFICIENT (D) A. The “

” Coefficient in Equalized Systems

In the proposed optical system, the attenuation due to the propagation path, can be considered negligible. The light traveling forward to a reflector and returning back is affected by the , associated to each reinput to recovered power coefficient flector of the system. Let us define this coefficient as the power , with the optical transmitted power, and ratio the recovered power from a certain “ ” reflector, at the reference plane in the nearest end of the fiber. This power is usually associated to specific information. Taking into account that reflector “ ” is the closest one to the instrumentation, the input to recovered power coefficient, , associated to reflector can be described as (8) , with and the transmission and where reflection coefficients associated to reflector , respectively. It is of interest for the signal conditioning and signal processing subunits that all the recovered signals have the same or similar amplitude. The latter can be achieved when all the coefficients are of the same value; this is the equalized system , the amplimain property. Equating coefficients tude equalization condition can be obtained

(5) or The system resolution is defined as the minimum change in the quantity of the measuring magnitude able to produce a de-

(9)

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Fig. 2. Example of a basic structure and composition of a QDOSS.

D

Fig. 3. Input to recovered power coefficient of the section 0, , versus the reflection coefficient for several values of the total number of sections N .

From here, if , and discarding second and higher order infinitesimal terms, it is possible to obtain the ratio between two reflectors separated by sections, as (10) In order to avoid energy losses at the distant end, let us make This condition means that no light passes through the last reflector. Discarding second and higher order infinitesimal , for a certain terms, the maximum number of sections, coefficient (associated to the nearest mirror), is obtained as (11)

Fig. 4. Nonequalized coefficient,  versus the reflection coefficient, R, for several values of the total number of sections N .

where is the number of sections of the sensor. The recovered power coming from the furthest reflector is the one affected by the smallest coefficient, i.e., (13) Coefficient

takes its maximum value (14)

for a certain value of

, which is a function of (15)

Considering the ratio between the flectors separated by sections

coefficients of two re(16)

B. The “D” Coefficient in Nonequalized Systems For an industrial system, it is of great interest that all the reflectors can be built in identical manner. Consequently, they will have the same reflection coefficient, , resulting in a nonequalized optical system. This section studies the effects in the optical performance assuming that all the reflectors are identical. coefficient for the “ ” generic In this particular case, the reflector is (12)

and specifying the worst case, the “0” and the “ ” reflectors, we define the nonequalization coefficient, , as (17) value for values There is a smooth decrease of the (associated to the “maximum” value); greater than see Fig. 3. There is a faster rate of decrease of for values ; see Fig. 4. A reflection coefficient between 0.9 below value is recommended. and 1.2 of the

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Fig. 5. Model of reflected and transmitted light at the I reflector.

IV. OPTICAL-INDUCED NOISE ASSOCIATED MULTIREFLECTED LIGHT

TO

In an optical system such as the one we are studying, some part of the light travels along the main path going to a certain “ ” reflector and then returning as a result of the reflection. This light carries the time and phase information for this reflector. On the other hand, the light passing through all previous mirrors is affected by multiple reflections, changing its traveling direction several times. Part of this “noisy” light, after multiple reflections, arrives at the detector mixed with the light coming from the “ ” reflector, which is affected by only one reflection. As an alternative to a quite detailed mathematical description, which will be complex in the case of an optical subsystem containing more than one hundred reflectors, it is possible to generalize the optical signal-to-noise ratio model by using a time and space discrete numerical model. This model is described in the following paragraphs. The optical system previously described contains reflectors. These reflectors are arranged from to 0 and are separated by an identical optical path of length . The , is . The origin of observation time interval, time is taken at the instant when a short duration and unitary energy burst crosses the reference plane. Let us situate the reference plane at the reflector . Then, the reflected light energy fraction, (back-propagating path), and the transmitted (forward-propagating path), at the light energy fraction reflector and at the time as indicated in Fig. 5, are defined by the following expressions: (18) (19) are the transmission and reflection coefficients, Here, and and are transmitted respectively, for the reflector. ” reflector and reflected from the “ ” reflector by the “ ” time. These energy fractions, respectively, both at the “ energy fractions are the only two light sources arriving at the “ ” detector at the “ ” time.

Fig. 6. Signal-to-noise ratio versus the number of the section for equalized and nonequalized systems of 250 sections (# = 0 is the distal section).

The light in the system is calculated each second, but the energy returning to the reference plane can be obtained only s. This is due to the fact that the light travels half the each 2 time toward the reflector along an integer number of sections, and the other half of the time it travels from the reflector toward the reference plane. Coherence in light is not considered in this model since energy contributions arriving at the reference plane at a certain time are added, considering only their amplitude but not their phases. Thus, the total recovered “inseparable” amplitude value “noise” module added for the Section I is composed of the . Nevertheless, the value to the signal module, , which is equivalent to the coefficient, can be calculated from (6) or (10). Then, the optical multi-reflected signal-tonoise ratio can be determined as (20) Fig. 6 shows the predicted signal-to-noise ratio (SNR) of each section of a system, for equalized and nonequalized systems,

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both with 250 reflectors. The simulations have been carried out using MATLAB, and in both systems, the reflection coefficient . As can be of the last reflector has been considered is improved by seen, when the system is equalized, the 3 dB. The maximum error associated to the amplitude is obtained in a noise in phase with the signal (worst case), with the amplitude relative error, (21)

Miguel J. García received the M.S. Telecommunication Engineer and the Ph.D. degrees in telecommunications from the Universitat Politecnica de Catalunya (UPC), Barcelona, Spain, in 1979 and 1988, respectively. He is a Professor with the UPC. Since 1992, he has been managing the UPC Sensor Systems Group, and since 1989, he has been teaching courses in electronic technology, circuits, and electronics instrumentation areas. From 1979 to 1986, he was with Bioingeniería S.A., Spain, as Project Manager of the Ultrasound Medical Imaging Department. His current R&D areas of interest include direct and indirect measurement techniques, ultrasound diathermy, pollution optical sensor systems, piezoelectric transducer design, processing of acoustic signals, and pulsed acoustical holography.

The worst case error associated to the phase demodulation signal corresponds to the noise in quadrature with the signal. The phase error, , associated to each one of the received signals is given by (22) This is an approximation for small angles. For small error and are coincident in value. values,

V. CONCLUSION A novel approach to a distributed fiber-optic strain sensor has been presented. The sensor could be able to monitor large structures such as marine platform clamping ropes. A discrete time and space model allows us to predict the SNR of the system. An equalized system shows only a 3-dB improvement in the SNR compared with a nonequalized system. Sometimes this improvement is not worth it due to the major technological complexity of the equalized system.

ACKNOWLEDGMENT The authors would like to thank Dr. Brian Culshaw and Dr. Deepak Uttamchandany for their valuable technical discussions, comments, and suggestions.

Juan A. Ortega received the M.S. Telecommunication Engineer and the Ph.D. degrees in electronics from the Universitat Politecnica de Catalunya (UPC), Barcelona, Spain, in 1994 and 1997, respectively. In 1994, he joined the UPC Sensor Systems Group in the Department of Electronic Engineering as a full time Associate Lecturer teaching courses of microprocessors and signal processing. In 1998, he obtained a tenured position as an Associate Professor in the same UPC department. His current R&D areas of interest include ultrasonic instrumentation for industrial and medical applications, ultrasound applied to nondestructive evaluation, and modeling of ultrasonic systems and transducers, infrared absorption pollution-gas detectors, smart sensors, and microprocessor systems.

Juan A. Chávez was born in Andújar, Spain, in 1967. He received the M.S. Telecommunication Engineer and the Ph.D. degrees in electronics from the Universitat Politecnica de Catalunya (UPC), Barcelona, Spain, in 1991 and 1997, respectively. In 1992, he joined the UPC Sensor Systems Group as a full time Associate Lecturer. In November 1998, he obtained a tenured position as an Associate Professor in electronics in the Department of Electrical Engineering, UPC. His current R&D areas of interest include ultrasonic instrumentation for industrial and medical applications, ultrasound applied to nondestructive evaluation, and modeling of ultrasonic systems and transducers, infrared absorption pollution-gas detectors, smart sensors, and thermoelectric coolers.

REFERENCES [1] B. Culshaw, “Monitoring systems and civil engineering: Some possibilities for fiber-optic sensors,” in Proc. Int. Workshop Fiber-Optic Sens. Construction Mater. Bridges, May 3–6, 1998, pp. 29–43. [2] D. Uttamchandani, B. Culshaw, M. S. Overington, M. Parsey, and M. Facchini, “Distributed sensing of strain in synthetic fiber rope and cable constructions using optical fiber sensors,” in Proc. SPIE, Sept. 20–22, 1999, pp. 273–275. [3] The Distributed Fiber Optic Sensing Handbook, Springer-Verlag, New York, 1990, pp. 73–76. [4] B. D. Zimmerman and R. O. Claus, “Spatially multiplexed optical fiber time domain sensors for civil engineering applications,” in Applicat. Fiber Opt. Sens. Eng. Mech., New York, 1993, pp. 280–287. [5] Y. J. Rao, “Fiber bragg grating sensors: Principles and applications,” in Optical Fiber Sensors Technology, K. T. V. Grattan, Ed, London, U.K.: Chapman & Hall, 1998, vol. 2, pp. 355–378.

Jordi Salazar was born in Barcelona, Spain, in 1967. He received the M.S. Telecommunication Engineer and the Ph.D. degrees in electronics from the Universitat Politecnica de Catalunya (UPC), Barcelona, in 1991 and 1997, respectively. In 1993, he joined the Department of Electronic Engineering, UPC, in the UPC Sensor Systems Group, first as a full time Associate Lecturer and then, since 1998, in a tenured position as an Associate Professor. His current activity is centred on ultrasonic short pulse generation, inverse problems, and nondestructive testing.

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Antoni Turó received the M.S. Telecommunication Engineer and the Ph.D. degrees in electronics from the Universitat Politecnica de Catalunya (UPC), Barcelona, Spain, in 1989 and 1998, respectively. In 1993, he joined the UPC Sensor Systems Group. In December 1998, he obtained a tenured position as an Associate Professor of electronics with the Department of Electrical Engineering, UPC. From December 1990 to December 1992, he was working as an R&D Engineer in the area of TV set design at the R&D Labs of Sanyo Company. In 2000, he spent seven months working with the Khuri-Yakub Ultrasonics Group at Stanford University, Stanford, CA. His current R&D activity includes ultrasonic instrumentation for industrial and medical applications, modeling of ultrasonic systems and transducers, nondestructive evaluation, and smart sensors.