Force-monitoring ring based on white-light interferometry for bridge cable force monitoring and its temperature compensation

Abstract

This article proposes a novel white-light interference (WLI) force-monitoring ring for bridge cable force monitoring and temperature compensation. The WLI force-monitoring ring employs a sensing optical fiber wrapped around the outer surface of an elastomer to measure the expansion caused by applied load and temperature. By installing WLI force-monitoring ring between the anchor plate and the spherical plate of the cable, cable force can be captured by the sensing optical fiber and thus measured after temperature compensation. Based on white-light interferometry, two force-monitoring rings with resolution of 0.25 µ are designed. To find a route to temperature compensation, laboratory experiments are carried to study the effects of temperature on WLI force-monitoring ring both in free and forced states. Theoretical analysis and calibration experiments are implemented to verify the effectiveness of the proposed WLI force-testing ring, and the experiment results expose that the temperature-induced strain can be compensated using a WLI force-monitoring ring in free state. As a comparison, similar work is made for four fiber Bragg grating sensors attached to the elastomer evenly near the sensing optical fiber. The comparison results verify that the WLI method achieves better linear relation and repeatability than fiber Bragg grating. The WLI force-monitoring ring provides a high-precision and low-cost method for bridge cable force monitoring.

Keywords

bridge cable force force-monitoring ring temperature compensation white-light interferometry

Introduction

The cables are most important components of bridges such as cable-stayed bridges, suspension bridges, and arch bridges. However, during the construction and operation conditions of the cable-stayed bridge, the cable forces are frequently affected by deck vehicles, wind load, cable corrosion, and so on. Considering the fact that bridge is a statically indeterminate structure, once the cable force deviates from the designed value, the bridge internal force distribution will be changed, and a deterioration in safety may be resulted as a consequence (Sakamoto and Kobori, 1995). Therefore, it is of great benefit to monitor the cable force for the purpose of online evaluation of the structural safety condition.

Long-term monitoring of cable force has been deeply studied. Magneto-elastic method measures the cable force through the calibrated relationship between the permeability and the load after compensating the temperature effect (Wang et al., 2001). Although the cable is magnetized, the advantages of magneto-elastic method are that the physical and mechanical properties of the cable are not affected (Wang et al., 1999), and it is not necessary to install the sensor during the construction period (Sumitro et al., 2002). However, it is difficult to accurately calibrate the relationship between the permeability and the load. The frequency method identifies the natural frequencies from the recorded cable responses by installing the accelerometer on the cable (Hearn and Testa, 1991; Hsieh et al., 2006). Utilizing the relation between natural frequencies and the cable force, the force can be extracted thereafter once the density and length of the cable are known (Cunha et al., 2001). Besides, the development of wireless sensor networks makes frequency method more convenient to monitor the cable force (Cho et al., 2008). The smartphones are also applied in the cable force monitoring (Zhao et al., 2015, 2016). Surely, it will not be a perfect method, because that in addition to the cable force, the natural frequency of bridge cable is also affected by flexural rigidity, boundary conditions, sag, and so on (Li et al., 2011).

Optical sensing technique is relatively practical for long-term monitoring. Existing measurement systems are mainly based on the fiber Bragg grating (FBG). One of them measures the cable force by the intelligent fiber cable, which monitors the internal force of cable wires through the FBG inside the bridge cable (He et al., 2013; Ni et al., 2002). However, the FBG sensors inside the bridge cable are vulnerable, and thus restrict the applicability of fiber cable. The FBG force-testing ring is also introduced for cable force measurement (Li et al., 2015; Nan et al., 2006). The drawback of this system is that every FBG sensor can only monitor the strain of its attached location. The measurement results of all FBG will show a wide variation since the strain on the surface of the force-monitoring ring is not uniform in practice. Generally, if the force-monitoring ring is loaded along the axis with different rotation angle, a large deviation may exist in the determination of the loading forces.

The first optical fiber displacement sensing system based on white-light interferometry was reported in 1984 (Bosselmann and Ulrich, 1984). After that, the WLI sensing technique has been widely applied to monitor displacement (Brundavanam et al., 2008), temperature (Chen and Taylor, 2002), and strain (Yuan and Ansari, 1997). Here, authors proposed a WLI force-monitoring ring to reduce the cable force measurement errors in the scenario of the uneven force distribution on the surface of the force-monitoring ring. This research’s content is described as follows. Section “Principle of white-light interferometry” presents the principle of the WLI. Section “Design of WLI force-monitoring ring” demonstrates the design of WLI force-monitoring ring. In section “Temperature compensation of WLI force-monitoring ring,” the experiments to explore the route for temperature compensation are carried out, and its results show that the temperature effect can be effectively compensated using a WLI force-monitoring ring in a free state. Theoretical analysis and comparative calibration experiments on WLI force-monitoring ring are implemented in section “Comparison of calibration experiments on WLI and FBG.” Section “Conclusion” concludes this article.

Principle of white-light interferometry

The configuration of optical fiber white-light interferometer based on Michelson interferometer is shown in Figure 1 (Zhao and Ansari, 2001). A beam of light emitted from the superluminescent light-emitting diode (SLED) passes through the circulator, along $L_{1}$ reaches a semi-transparent mirror, which separates the light into the transmitted one and reflected one. On one hand, the transmitted light first reaches a mirror along $L_{S}$ , and reflected to reach the circulator again along $L_{S}$ and $L_{1}$ . On the other hand, the reflected light is reflected back to circulator directly along $L_{1}$ . The transmitted and reflected lights are recoupled in the circulator to enter a 50/50 coupler through a single-mode fiber. The function of 50/50 coupler is to separate one beam light into two beams. As a result, the transmitted and reflected lights are separated into two beams, respectively. That is to say, four beams in total are generated subsequently. Two of them are projected onto a moving mirror by a self-focus lens, and then they are reflected onto a photoelectric detector along $L_{2}$ . If the public optical paths with the two beams of light are removed, the optical paths of the two beams of light are $2 \times (L_{1} + L_{2})$ and $2 \times (L_{1} + L_{S} + L_{2})$ , respectively. The another two beams of light are reflected onto a photoelectric detector by a mirror along $L_{3}$ , therefore their optical paths are $2 \times (L_{1} + L_{3})$ and $2 \times (L_{1} + L_{S} + L_{3})$ , respectively. In the white-light interferometer, the $L_{3}$ is greater than $L_{2}$ , so only two beams of light can produce interference when their optical paths are $2 \times (L_{1} + L_{S} + L_{2})$ and $2 \times (L_{1} + L_{3})$ , respectively. In order to make $2 \times (L_{1} + L_{S} + L_{2})$ and $2 \times (L_{1} + L_{3})$ equal, the white-light interferometer changes $L_{2}$ by changing the location of moving mirror using a stepping motor. In other words, the interference signal will be produced when $L_{S}$ is equal to $L_{3} - L_{2}$ . An analog-to-digital (AD) converter converts the interference signals captured by photoelectric detector to electric signals, and finally the electric signals are recorded by a personal computer. Surely, to measure much sensors at the same time, it is necessary to add an optical switch to $L_{1}$ .

Figure 1.

Configuration of white-light interferometer.

In the optical circuit of the white-light interferometer, the location of WLI fringe records the location of moving mirror, and the location of the moving mirror corresponds to the length of the sensing optical fiber. Consequently, the length of the sensing optical fiber can be measured by recording the location of WLI fringe. Before and after the change in length of the sensing optical fiber, two WLI fringes are obtained, and the change in length of the sensing optical fiber can be calculated according to the spacing between the two WLI fringes. Therefore, the following equations can be established

Δ L = (X_{0} - X_{1}) \cdot L_{N} / n = Δ X \cdot L_{N} / n

(1)

ε = Δ L / L_{0}

(2)

where $Δ L$ is the absolute total deformation of the sensing optical fiber; $X_{0}$ and $X_{1}$ are the locations of WLI fringe corresponding to the initial and displaced locations, respectively; $L_{N} = 1.25 μ m$ is the step size of stepping motor; n is the refractive index of optical fiber; $L_{0}$ is the initial length of the sensing optical fiber; and $ε$ is the corresponding strain.

As can be seen from the above equations, when measuring the strain of the sensing optical fiber, the resolution of the white-light interferometer depends on the $L_{0}$ and the accuracy that the stepping motor scans the location of moving mirror. The latter can reach 5 µm resulting in a sensitivity of $5 / L_{0} (μ ε)$ .

Design of WLI force-monitoring ring

The WLI force-testing ring is composed of the elastomer and a WLI sensing optical fiber wrapped around the elastomer. The elastomer is the main component of the WLI force-monitoring ring, which is a hollow cylinder with flanges on upper and lower edges made by the 45# steel, as shown in Figure 2. Note that the flanges on the upper and lower edges are designed to be convex to avoid stress concentration. The outer and inner diameters of the elastomer are 174 and 145 mm, respectively. In real application, the WLI force-testing ring is installed between the anchor plate and the spherical plate as shown in Figure 3. Figure 4 shows the basic calculation model of WLI force-testing ring in a forced state. As the cable anchorage goes through the internal hole of the WLI force-testing ring, the internal WLI sensing optical fiber will sense the compression when the cable force puts the pressure on the elastomer through the anchor. In such a way, the cable force can be finally determined through monitoring the transferred deformation (ΔS) from the cable to the elastomer. Under the action of vertical load, the expansion of the elastomer occurs at the outer surface. By the wrapped sensing optical fiber around the outer surface to measure the expansion, the cable force can be obtained as a result.

Figure 2.

WLI force-monitoring ring: (a) real product and (b) sketch.

Figure 3.

Model of bridge cable.

Figure 4.

Basic calculation model of WLI force-testing ring in a forced state.

The length of the sensing optical fiber wrapped around the outer surface of the elastomer is 20 m, so the resolution of the designed WLI force-monitoring ring can reach to $5 / 20 = 0.25 (μ ε)$ according to equation (2). The two ends of the sensing optical fiber are fixed on the elastomer with glue and connected with optical fiber patch cords to connect with the white-light interferometer. Besides, to compare the performance of the WLI with FBG, four FBG sensors in series are attached to the elastomer evenly near the sensing optical fiber of WLI, as shown in Figure 2. When installing the four FBG sensors, the FBG sensors are individually fixed using glue rather than installed by a chain with equally spaced FBG sensors. The reason why we do in this way is that the three joints of the four FBG sensors will be fragile if the four FBG sensors are installed in the way of a chain and only the termination of the chain is glued to the elastomer. There are two identical sets of WLI force-monitoring ring, one of which is used to measure the force, and another compensates the effect of temperature.

Temperature compensation of WLI force-monitoring ring

The sensing element of WLI force-monitoring ring is the optical fiber, which is sensitive to both the strain and the temperature. In bridge cable force monitoring, there is generally a large variation of temperature. For the purpose of accurately measuring the cable force, it is indispensable to compensate the effect of temperature.

The current design of WLI force-monitoring ring includes the elastomer and the sensing optical fiber which is wrapped around the elastomer. Consequently, the effect of temperature on the WLI force-monitoring ring can be categorized into two parts. One part comes from the expansion and shrinkage of the elastomer produced by the variation of experimental temperature, and another part comes from the deformation of the sensing optical fiber caused by the change of temperature. Surely, the effect of temperature on both of the elastomer and the sensing optical fiber should be removed.

In this article, a WLI force-monitoring ring in a free state is employed to compensate the temperature effect of the one in a forced state. The temperature compensation is used to compensate the temperature effects both on the elastomer and on the mechanical effects on the reading of the sensing optical fiber. The premise of such strategy is that the effect of temperature is the same on WLI force-monitoring ring either in a free and forced state. To verify the premise, this section demonstrates the effect of temperature on WLI force-monitoring ring in free and forced states through theoretical and experimental investigations.

Effect of temperature on WLI force-monitoring ring in free state

The sensing optical fiber of WLI force-monitoring ring is affected by both the axial force generated by the expansion of the elastomer and the change of temperature. Because both the sensing optical fiber and the elastomer operate within the extent of elasticity, the strain of the sensing optical fiber is linearly proportional to the axial force of the sensing optical fiber and the temperature difference as well. It can be expressed as follows

ε = K_{f} \cdot f + K_{T} \cdot Δ T

(3)

where $ε$ is the strain of the sensing optical fiber in $μ ε$ , f is the axial force of the sensing optical fiber in kN, $Δ T$ is the temperature difference in °C, and $K_{f}$ and $K_{T}$ are both linear coefficients.

In free state, the axial force f generated by the expansion of the elastomer caused by the change of temperature can be expressed by

f = k_{e} \cdot α \cdot L_{0} \cdot Δ T

(4)

where $k_{e}$ is the spring constant of the sensing optical fiber and $α$ is the temperature linear expansion coefficient of the elastomer.

Combining equations (3) and (4), the strain $ε_{T 1}$ of the sensing optical fiber generated by the expansion of the elastomer when temperature changes can be determined as

ε_{T 1} = K_{f} \cdot k_{e} \cdot α \cdot L_{0} \cdot Δ T

(5)

The own strain $ε_{T 2}$ of the sensing optical fiber caused by the change of temperature can be expressed by

ε_{T 2} = K_{T} \cdot Δ T

(6)

According to equations (5) and (6), the total strain $ε_{T}$ of the sensing optical fiber caused by the change of temperature gives

ε_{T} = ε_{T 1} + ε_{T 2} = (K_{f} \cdot k_{e} \cdot α \cdot L_{0} + K_{T}) \cdot Δ T

(7)

If the temperature coefficient $ξ$ of the sensing optical fiber is defined as

ξ = K_{f} \cdot k_{e} \cdot α \cdot L_{0} + K_{T}

(8)

Equation (7) can be written as

ε_{T} = ξ \cdot Δ T

(9)

It can be found that, in a free state of WLI force-monitoring ring, the strain of the sensing optical fiber is proportional to the change of temperature. To verify equation (9), a static temperature experiment on the WLI force-monitoring ring in a free state is carried out in the laboratory. The designed WLI force-monitoring ring is put into a water tank to be heated in water bath as shown in Figure 5(a) with the $Δ T$ varying from 0°C to 60°C. Because the experiment is finished in short time, the influence of humidity (e.g. corrosion of elastomer and looseness in two ends of the sensing optical fiber) can be ignored. The initial location of WLI fringe $X_{0}$ is recorded at the room temperature. A group of data including three readings is collected per variation of 15°C. At each temperature level, the temperature is held for 10 min and the location of WLI fringe is measured accordingly. The experiment is repeated for three cycles. Figure 5(b) to (d) illustrates the relationship between the temperature difference and the strain of the sensing optical fiber of a free-state WLI force-monitoring ring. Apparently, the linear relation indeed exists. Figure 5(e) indicates that the results of the three cycles are pretty close, so that the temperature effect on the strain of the sensing optical fiber has a favorable repeatability.

Figure 5.

Temperature tests on WLI force-monitoring ring in a free state: (a) temperature test setup, (b) first cycle, (c) second cycle, (d) third cycle, and (e) repeatability.

Effect of temperature on WLI force-monitoring ring in forced state

The last experiment shows the effect of temperature on WLI force-monitoring ring in a free state. To illustrate that the effect of temperature on WLI force-monitoring ring does not depend on the force state, an experiment is carried out in the laboratory as shown in Figure 6(a).

Figure 6.

Temperature compensation of WLI force-monitoring ring: (a) temperature test setup and (b) experimental result.

During the experiment, a WLI force-monitoring ring is placed on a press machine and subjected to a continuous loading up to 400 kN. At the same time, another WLI force-monitoring ring in a free state is placed on the side to monitor the change of temperature. The initial locations of WLI fringe $X_{0}$ of two WLI force-monitoring rings are recorded before the experiment begins. The experiment lasts for 5 h, and the WLI strain data are recorded every 10 min. According to the premise, there should be a constant difference between the strain of WLI force-monitoring ring in the forced state and in the free state and that difference represents the strain under the load of 400 kN after the effect of temperature has been canceled out. The experimental result is shown in Figure 6(b), where the differences are approximately constant, which validates the premise that the effects of temperature on the WLI force-monitoring ring in free and forced states are same. As a result, the temperature compensation of the WLI force-monitoring ring can be realized by a WLI force-monitoring ring in a free state.

Comparison of calibration experiments on WLI and FBG

The strain of the sensing optical fiber in the WLI force-monitoring ring includes the effects from the load and the change of temperature. Section “Temperature compensation of WLI force-monitoring ring” has verified that there is no coupling of the load and the temperature. Therefore, if the effect of the temperature is removed, the axial force of the sensing optical fiber becomes linearly related to the load on the WLI force-monitoring ring, which can be described as

f = β \cdot F

(10)

where F is the load on WLI force-monitoring ring in kN and $β$ is the linear coefficient between f and F.

If the load coefficient $η$ of WLI force-monitoring ring is defined as

η = K_{f} \cdot β

(11)

The strain $ε_{F}$ of the sensing optical fiber after temperature compensation can be determined from equations (3), (10), and (11) as follows

ε_{F} = η \cdot F

(12)

According to equations (9) and (12), the total strain $ε_{W}$ of the sensing optical fiber in WLI force-monitoring ring under load and the change of temperature can be expressed by

ε_{W} = η \cdot F + ξ \cdot Δ T

(13)

Equation (13) shows that the strain of the sensing optical fiber is proportional to the cable force after removing the temperature effect using a WLI force-monitoring ring in free state. To verify equation (13), a calibration experiment of the WLI force-monitoring ring is carried out using the same arrangement as Figure 6(a) with the load F varying from 100 to 600 kN. The initial locations of WLI fringe $X_{0}$ of two WLI force-monitoring rings are recorded before the experiment begins. A group of data including three readings is collected per increment of 100 kN. At each load level, the load is held for 5 min and the location of WLI interference fringe is measured accordingly. The experiment is repeated in three cycles for repeatability check. As a comparison, the wavelengths of FBG in force-monitoring ring are simultaneously recorded by the FBG demodulator.

The strains of the four FBGs after temperature compensation are shown in Figure 7, where the FBG1, FBG2, FBG3, and FBG4 are the FBG sensors attached to the elastomer of the WLI force-monitoring ring, and the strain used to compensate temperature is the average of four FBG sensors in the WLI force-monitoring ring in free state. It is shown that the strain of every FBG sensor is approximately linear to the load on force monitoring, and the results of the three cycles are nearly close. However, the strains of the four FBG sensors are different at the same load level and the linear relationship between the load and the strain is poor especially when the load is less than 300 kN, where the slopes of FBG1 and FBG4 increase, but the corresponding slopes of FBG2 and FBG3 decrease compared to those with greater loads. Through the above analysis, one possible reason why the precision of FBG sensors is worse is that the pressed WLI sensor suffers slight eccentricity press when the load is less than 300 kN because of the machining error of the elastomer or uneven surface of the press machine. Another possible reason is that the less precision of the FBG is due to the use of the glue. When the sensor is pressed on press machine, the FBGs were stretched, but the elongation of the FBGs was restricted by the glue.

Figure 7.

Strain of FBG1 to FBG4 after temperature compensation under loading and unloading: (a) first cycle, (b) second cycle, and (c) third cycle.

The comparison of calibration results between WLI and FBG are shown in Figure 8 where $ε'_{W}$ and $ε'_{F}$ are, respectively, the strains of WLI force monitoring and FBG after temperature compensation. Obviously, the WLI force-monitoring ring achieves a good linear relationship between the measured strain and the applied load. According to the calibrated equations in Figure 8(a) to (c), the sensitivity of the WLI force-monitoring ring is about 0.133 µε/KN, and the strain of WLI force-monitoring ring is about 53 µε under the load of 400 kN, which is very close to the one (about 56 µε) in Figure 6(b). In addition, the precision is not affected even when the load is smaller than 300 kN. By contrast, the coefficients of the WLI force-monitoring ring that determine the fitted lines are always higher than those of FBG, and the repeatability of FBG is also superior.

Figure 8.

Comparison of calibration results between WLI and FBG under loading and unloading: (a) first cycle, (b) second cycle, (c) third cycle, and (d) repeatability.

From the comparison between the WLI and FBG, it can be concluded that the WLI has better performance to monitor the applied load than FBG. Besides, the fabrication process of the WLI sensor is easier because only the two ends of the sensing optical fiber need to be fixed. In addition, the WLI monitoring of the average strain of the sensing optical fiber is a significant advantage to monitor the strain distributed in large area.

Conclusion

For the purpose of accurately measuring the cable force, a novel type of WLI force-monitoring ring is proposed in this article. Based on the principle of white-light interferometry, the WLI force-monitoring ring is designed, in which a bending optical fiber with known length is wrapped around the outer surface of elastomer to measure the load of force-monitoring ring. Since the strain of the sensing optical fiber depends on the applied load and environmental temperature, their effects are theoretically and experimentally studied. It shows that the strain of the sensing optical fiber is linearly related to the load and the temperature, and the temperature effect can be compensated by measuring another WLI force-monitoring ring in a free state. By comparing its performance with the FBG-based method, the high accuracy of the proposed WLI sensor, even in the condition of uneven strain, is demonstrated. The WLI force-monitoring ring has numerous advantages such as high measuring accuracy and, especially, lower cost, allowing effective cable force monitoring of bridges.

The proposed WLI force-monitoring ring presents excellent performance to monitor the applied load under laboratory conditions. However, the ends of the WLI sensing optical fiber are fixed on the elastomer using glue, which will be a threat to the durability of the sensor used in real cable force monitoring. In future studies, a metal clamp will be presented to replace the glue and increase the durability of the WLI force-monitoring ring.

Footnotes

Declaration of Conflicting Interests

The author(s) declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article.

Funding

The author(s) disclosed receipt of the following financial support for the research, authorship, and/or publication of this article: This work was supported by the National Natural Science Foundation (Grant No. 51278085) and the Fundamental Research Funds for the Central Universities of China (Grant No. DUT16ZD219).

References

Bosselmann

Ulrich

(1984) High-accuracy position-sensing with fiber-coupled white-light interferometers. In: Second international conference on optical fiber sensors, Stuttgart, 15 November, vol. 514, pp. 361–364. Bellingham, WA: SPIE.

Brundavanam

Viswanathan

Rao

(2008) Nanodisplacement measurement using spectral shifts in a white-light interferometer. Applied Optics 47(34): 6334–6339.

Chen

Taylor

(2002) Multiplexed fiber Fabry–Perot temperature sensor system using white-light interferometry. Optics Letters 27(11): 903–905.

Cho

Yun

Lynch

et al . (2008) Smart wireless sensor technology for structural health monitoring of civil structures. International Journal of Steel Structures 8(4): 267–275.

Cunha

Caetano

Delgado

(2001) Dynamic tests on large cable-stayed bridge. Journal of Bridge Engineering 6(1): 54–62.

Zhou

(2013) Optic fiber sensor-based smart bridge cable with functionality of self-sensing. Mechanical Systems and Signal Processing 35(1–2): 84–94.

Hearn

Testa

(1991) Modal analysis for damage detection in structures. Journal of Structural Engineering 117(10): 3042–3063.

Hsieh

Halling

Barr

(2006) Overview of vibrational structural health monitoring with representative case studies. Journal of Bridge Engineering 11(6): 707–715.

Zhou

(2011) Development and sensing properties study of FRP–FBG smart stay cable for bridge health monitoring applications. Measurement 44(4): 722–729.

10.

Ren

(2015) FBG force-testing ring for bridge cable force monitoring and temperature compensation. Sensors and Actuators A: Physical 223: 105–113.

11.

Nan

Jiang

Liang

(2006) Study and application of FBG force-testing ring. Journal of Huazhong University of Science and Technology 34(9): 63–65 (in Chinese).

12.

Zheng

(2002) Dynamic analysis of large-diameter sagged cables taking into account flexural rigidity. Journal of Sound and Vibration 257(2): 301–319.

13.

Sakamoto

Kobori

(1995) Research, development and practical applications on structural response control of buildings. Smart Materials and Structures 4(1A): A58–A74.

14.

Sumitro

Jarosevic

Wang

(2002) Elasto-magnetic sensor utilization on steel cable stress measurement. In: First FIB congress on concrete structures in the 21st century, Osaka, Japan, 13–19 October, pp. 79–86. Japan Prestressed Concrete Engineering Association and Japan Concrete Institute.

15.

Wang

Lloyd

Hovorka

(2001) Development of a remote coil magnetoelastic stress sensor for steel cables. In: 6th annual international symposium on NDE for health monitoring and diagnostics, Newport Beach, CA, 4–8 March, vol. 4337, pp. 122–128. Bellingham, WA: SPIE.

16.

Wang

Satpathi

Koontz

et al . (1999) Monitoring of cable forces using magneto-elastic sensors. Computational Mechanics in Structural Engineering 337: 347.

17.

Yuan

Ansari

(1997) White-light interferometric fiber-optic distributed strain-sensing system. Sensors and Actuators A: Physical 63(3): 177–181.

18.

Zhao

Han

Ding

et al . (2015) Portable and convenient cable force measurement using smartphone. Journal of Civil Structural Health Monitoring 5(4): 481–491.

19.

Zhao

Han

et al . (2016) Smartphone-based mobile testing technique for quick bridge cable–force measurement. Journal of Bridge Engineering 22(4): 06016012.

20.

Zhao

Ansari

(2001) Quasi-distributed fiber-optic strain sensor: principle and experiment. Applied Optics 40(19): 3176–3181.