Cable Force Health Monitoring of Tongwamen Bridge Based on Fiber Bragg Grating

Dongtao Hu 1, Yongxing Guo 2,3,*, Xianfeng Chen 1 and Congrui Zhang 1 1 School of Resources and Environmental Engineering, Wuhan University of Technology, Wuhan 430070, China; eastao@whut.edu.cn (D.H.); cxf618@whut.edu.cn (X.C.); zcrwhut@163.com (C.Z.) 2 Key Laboratory of Metallurgical Equipment and Control Technology, Ministry of Education, Wuhan University of Science and Technology, Wuhan 430081, China 3 Hubei Key Laboratory of Mechanical Transmission and Manufacturing Engineering, Wuhan University of Science and Technology, Wuhan 430081, China * Correspondence: yongxing_guo@wust.edu.cn; Tel.: +86-134-1952-9869


Introduction
Large suspension bridges are common in river-crossing and gulf-crossing transportation projects. Magnitude and distribution of cable tension force can reflect the stress state of a bridge, and a reasonable cable force state is extremely important for the safe operation of a bridge. With the rapid development of China's transportation system, heavy load and overloaded vehicles are common in transportation. As a result, operation loads of the bridge often exceed the design load, resulting in damage and failure to the bridge structure. Therefore, the long-term real-time cable force state and parameter measurements are critical to bridge engineering safety monitoring during the operation of suspension bridges [1,2].
Fiber Bragg grating (FBG) sensors have received considerable attention in research publications and a wide range of applications have been implemented due to their advantages, such as immunity to electromagnetic noise, small size, light weight, ease of incorporation into a sensor network, and long signal transmission distance [3][4][5][6]. Although use of fiber grating sensing technology in civil engineering applications such as bridges and tunnels has spanned over several decades, fiber Bragg grating based structural health monitoring technology has undergone rapid growth in recent years, and research and applications in various engineering fields have been reported consistently by numerous

Measurement Method
According to the theory of string vibration, the relation between tension T acting on a two-end fixed tightened string and the characteristic frequency of the string vibration can be written as: where l, m and f n are length, linear density and n-th order characteristic frequency of the string, respectively. Since the physical size of the suspension cable is known, cable force can be obtained as long as the vibration frequency of the suspension cable can be measured in real time. The actual cross section of the suspender is comprised of 19 thin wires connected in parallel, which form one suspension cable with a diameter of 70 mm. A PVC protection tube tightly wraps all suspension cables. Compared to the cable, rigidity of PVC tube is small, so its linear density can be ignored during the calculation of Appl. Sci. 2017, 7, 384 3 of 11 cable force using Equation (1). For this purpose, according to their vibration frequency characteristics, FBG vibration sensors for Tongwamen bridge were developed, as described in detail in the next section.
On each side (north and south) of Tongwamen bridge, there are 19 suspension cables, among which 8 were selected for monitoring. Accordingly, a total of 16 FBG vibration sensors were mounted on Tongwamen bridge. As Figure 1a shows, on both north and south sides of the bridge, sensors are located on the 3rd, 5th, 7th, 9th, 11th 13th, 15th and 17th suspension cables, in the direction from Shipu to Dongmen island. As shown in Figure 1b, sensors on the south and north sides are numbered as S 1 -S 8 and N 1 -N 8 , respectively. Sensors on either side were concatenated through a single-mode optical fiber, which were then connected to the control room. A homemade FBG demodulator (channels: 8, acquisition frequency: 0-5000 Hz, accuracy: 3 pm, resolution: 0.1 pm) is used to record the wavelength of the sensor at a sampling frequency of 200 Hz. The bandwidth of light source in the interrogator is 80 nm (1525-1605 nm), where each channel can accommodate at least 20 FBG vibration sensors with a different central wavelength. Appl. Sci. 2017, 7, x FOR PEER REVIEW  3 of 11 cables. Compared to the cable, rigidity of PVC tube is small, so its linear density can be ignored during the calculation of cable force using Equation (1). For this purpose, according to their vibration frequency characteristics, FBG vibration sensors for Tongwamen bridge were developed, as described in detail in the next section. On each side (north and south) of Tongwamen bridge, there are 19 suspension cables, among which 8 were selected for monitoring. Accordingly, a total of 16 FBG vibration sensors were mounted on Tongwamen bridge. As Figure 1a shows, on both north and south sides of the bridge, sensors are located on the 3rd, 5th, 7th, 9th, 11th 13th, 15th and 17th suspension cables, in the direction from Shipu to Dongmen island. As shown in Figure 1b, sensors on the south and north sides are numbered as S1-S8 and N1-N8, respectively. Sensors on either side were concatenated through a single-mode optical fiber, which were then connected to the control room. A homemade FBG demodulator (channels: 8, acquisition frequency: 0-5000 Hz, accuracy: 3 pm, resolution: 0.1 pm) is used to record the wavelength of the sensor at a sampling frequency of 200 Hz. The bandwidth of light source in the interrogator is 80 nm (1525-1605 nm), where each channel can accommodate at least 20 FBG vibration sensors with a different central wavelength.

Design of FBG Vibration Sensor
Through an earlier field test on the bridge suspension cables, it was found that the cable's vibration frequencies are generally within 6 Hz. Thus, the resonant frequency of the FBG vibration sensor should be far higher than 6 Hz so as to avoid interference caused by superimposition of the resonant frequency of the sensor with measured frequencies. Principles of fiber grating vibration sensors vary widely, and have been a hot research topic in the field of optical fiber sensing [14][15][16][17][18][19][20][21][22] [14 -16]. As a classic elastic element, cantilever beam shows broad applications in the design of FBG vibration sensors. Sensors based on this principle are simple and reliable with strong engineering applicability. Due these favorable reasons, FBG vibration sensor based on an equal-strength cantilever beam was designed. Compared with other cantilever-based vibration sensors, this FBG vibration sensor possesses a simpler structure of just an original equal-strength cantilever beam, which avoids complex assembly and has higher reliability. In our previous work [20], a high

Design of FBG Vibration Sensor
Through an earlier field test on the bridge suspension cables, it was found that the cable's vibration frequencies are generally within 6 Hz. Thus, the resonant frequency of the FBG vibration sensor should be far higher than 6 Hz so as to avoid interference caused by superimposition of the resonant frequency of the sensor with measured frequencies. Principles of fiber grating vibration sensors vary widely, and have been a hot research topic in the field of optical fiber sensing [14][15][16][17][18][19][20][21][22]. As a classic elastic element, cantilever beam shows broad applications in the design of FBG vibration sensors. Sensors based on this principle are simple and reliable with strong engineering applicability. Due these favorable reasons, FBG vibration sensor based on an equal-strength cantilever beam was designed. Compared with other cantilever-based vibration sensors, this FBG vibration sensor possesses a simpler structure of just an original equal-strength cantilever beam, which avoids complex assembly and has higher reliability. In our previous work [20], a high frequency FBG vibration sensor was made through metallization packaging. The sensor possesses a high resonance frequency of 3.6 kHz but a low sensitivity of 0.17 pm/(m/s 2 ), which is not suitable for measuring cable vibration with low frequency and high measurement sensitivity. As shown in Figure 2, a FBG was attached on the beam surface, and a block mass was fixed on the free end of the beam. Under the influence of external vibration acceleration, the beam vibrated with inertial force on the mass, generating alternating bending strain on the surface. This bending strain was detected and converted into wavelength shift by the FBG sensor (Fenglan Tech, Co, Ltd, Anshan, China). Thus, external vibration acceleration was retrieved using wavelength shift information detected by the demodulator.
Appl. Sci. 2017, 7, x FOR PEER REVIEW 4 of 11 frequency FBG vibration sensor was made through metallization packaging. The sensor possesses a high resonance frequency of 3.6 kHz but a low sensitivity of 0.17 pm/(m/s 2 ), which is not suitable for measuring cable vibration with low frequency and high measurement sensitivity. As shown in Figure 2, a FBG was attached on the beam surface, and a block mass was fixed on the free end of the beam. Under the influence of external vibration acceleration, the beam vibrated with inertial force on the mass, generating alternating bending strain on the surface. This bending strain was detected and converted into wavelength shift by the FBG sensor (Fenglan Tech, Co, Ltd, Anshan, Liaoning., China). Thus, external vibration acceleration was retrieved using wavelength shift information detected by the demodulator. Based on the principle from mechanics of materials, for a cantilever beam of equal strength, relationship between its deflection w and force acting on its end can be written as: where L is length of the beam, b is width of the beam's fixed end, h is thickness, and E is Young's modulus of the beam. The force on the free-end of the beam is inertia force F generated by the block mass under external acceleration a can be calculated by: where m is mass of mass block.
For an equal-strength beam, the relationship between strain ε of its surface, which can be sensed and measured by the FBG, and its deflection w, can be described as: For a FBG with initial central wavelength λ, its wavelength shift Δλ has the following relationship with its longitudinal strain change Δε and its environmental temperature change ΔT: where αf, ξ, and Pe are optical fiber's thermal expansion coefficient, thermo-optic coefficient and elasto-optic coefficient, respectively. Pe is approximately 0.22 at normal temperature. For the vibration acceleration sensor, which only measures frequency, wavelength shift caused by temperature change has no impact on the frequency. Therefore, only effect of the strain change Δε remained on grating wavelength, and Equation (5)   Based on the principle from mechanics of materials, for a cantilever beam of equal strength, relationship between its deflection w and force acting on its end can be written as: where L is length of the beam, b is width of the beam's fixed end, h is thickness, and E is Young's modulus of the beam. The force on the free-end of the beam is inertia force F generated by the block mass under external acceleration a can be calculated by: where m is mass of mass block.
For an equal-strength beam, the relationship between strain ε of its surface, which can be sensed and measured by the FBG, and its deflection w, can be described as: For a FBG with initial central wavelength λ, its wavelength shift ∆λ has the following relationship with its longitudinal strain change ∆ε and its environmental temperature change ∆T: where α f , ξ, and P e are optical fiber's thermal expansion coefficient, thermo-optic coefficient and elasto-optic coefficient, respectively. P e is approximately 0.22 at normal temperature. For the vibration acceleration sensor, which only measures frequency, wavelength shift caused by temperature change has no impact on the frequency. Therefore, only effect of the strain change ∆ε remained on grating wavelength, and Equation (5) can be rewritten as: Appl. Sci. 2017, 7, 384 5 of 11 By combining Equations (2)-(4) and (6), relationship between wavelength shift ∆λ of the designed FBG sensor and external vibration acceleration can be expressed as: Equation (7) is the basic measuring principle of the developed FBG vibration sensor. A 'B & K 4808' vibration test system (Brüel & Kjaer, Naerum, Denmark) and a standard 'B & K 4371' piezoelectric accelerometer (Brüel & Kjaer, Naerum, Denmark) were used to measure amplitude-frequency and linearity response of the vibration sensor. Figure 3 shows the typical performance test results for the developed 16 FBG sensors. Figure 3a is the amplitude-frequency curve, which was obtained by exerting different frequencies from 0.5 to 21.5 Hz at an acceleration of 0.2 m/s 2 . It can be observed that the resonance frequency is approximately 15 Hz, which exceeds the required 6 Hz and meets monitoring requirements. As shown in Figure 3b acceleration performance test was repeated three times. Average data was fit to obtain sensitivity as 109.667 pm/(m/s 2 ), and the measurement showed favorable repeatability of 3.12%. (1 ) By combining Equations (2)- (4) and (6), relationship between wavelength shift Δλ of the designed FBG sensor and external vibration acceleration can be expressed as: Equation (7) is the basic measuring principle of the developed FBG vibration sensor. A 'B & K 4808' vibration test system (Brüel & Kjaer, Naerum, Denmark) and a standard 'B & K 4371' piezoelectric accelerometer (Brüel & Kjaer, Naerum, Denmark) were used to measure amplitude-frequency and linearity response of the vibration sensor. Figure 3 shows the typical performance test results for the developed 16 FBG sensors. Figure 3a is the amplitude-frequency curve, which was obtained by exerting different frequencies from 0.5 to 21.5 Hz at an acceleration of 0.2 m/s 2 . It can be observed that the resonance frequency is approximately 15 Hz, which exceeds the required 6 Hz and meets monitoring requirements. As shown in Figure 3b acceleration performance test was repeated three times. Average data was fit to obtain sensitivity as 109.667 pm/(m/s 2 ), and the measurement showed favorable repeatability of 3.12%. To verify the applicability of the proposed FBG vibration sensor, a contrast experiment has been carried out. A FBG vibration sensor and a 'B & K 4371' piezoelectric accelerometer have been fixed together on the exciter and applied by a sine excitation signal with different frequencies of 2, 5, and 8 Hz, respectively. Figure 4 shows the contrast of the two sensors in responses of time-domain waveforms and frequency spectrums under different excitation signal. From the comparison charts, it can be seen that the FBG vibration sensor is consistent with the piezoelectric accelerometer, which demonstrates the applicability of the proposed sensor.  To verify the applicability of the proposed FBG vibration sensor, a contrast experiment has been carried out. A FBG vibration sensor and a 'B & K 4371' piezoelectric accelerometer have been fixed together on the exciter and applied by a sine excitation signal with different frequencies of 2, 5, and 8 Hz, respectively. Figure 4 shows the contrast of the two sensors in responses of time-domain waveforms and frequency spectrums under different excitation signal. From the comparison charts, it can be seen that the FBG vibration sensor is consistent with the piezoelectric accelerometer, which demonstrates the applicability of the proposed sensor.        Figure 5a is the photo of the manufactured FBG vibration sensor, which was fixed on the suspension cable through buckles. Figure 5b is the photo of the sensor installed on the suspension cable.

Monitoring Results
Sensor arrays on each side were composed of eight vibration sensors with a wavelength interval of three nanometers. Then, sensors on north and south sides were connected into the FBG

Monitoring Results
Sensor arrays on each side were composed of eight vibration sensors with a wavelength interval of three nanometers. Then, sensors on north and south sides were connected into the FBG demodulator through a single-mode optical fiber. The wavelength sampling precision of the demodulator was three picometers and sampling frequency was set as 200 Hz. Given the larger number of sensors and large volume of real-time collected data, here, monitoring data collected for 160 s from the first vibration sensor (Sensor N 1 ) on the north side of the bridge is used as an example. Figure 6 shows the time-domain waveform of sensor N 1 for 160 s. To facilitate measurement of fundamental cable frequency, every 20 s in a time span of 160 s was taken as a measurement time unit. Then, frequency spectrum within this time period was acquired using fast Fourier transform (FFT). Figures 7 and 8 show time-domain waveform and frequency-domain spectrum for each 20 s. Taking the 0-20 s data in Figure 7 as an example, the fundamental frequency of the cable is obtained as 5.71 Hz and multiplier frequencies are 11.57 Hz and 17.53 Hz, and the resonant frequency of the sensor is 15.5 Hz. Results from the other time periods are the same. Therefore, it can be concluded the that vibration frequency of the cable can be successfully measured by the sensor.
For the 3rd cable, where sensor N 1 was located, effective length and weight are 19.502 m and 218 kg, so linear density is 218/19.502 = 11.178 kg/m. Then, the corresponding terms in Equation (1) are: m = 11.178 kg/m, l = 19.502 m, fundamental frequency f n within 0-20 s is 5.71 Hz, for n = 1, and cable force can be obtained as T = 554.44 kN. Forces in remaining time units for sensor N 1 can be calculated similarly. By this method, cable forces measured by all 16 sensors can be obtained. In addition, measurement results can be influenced by wind or gusts because wind load will cause whole-body vibration of the bridge. This whole-body vibration has an influence on the sensor measurements. However, compared with cables, the whole-body vibration frequency is usually much lower than the fundamental frequency of cables, so fundamental frequency measurement will not be affected. When environmental temperature changes, the amplitude of the vibration waveform changes correspondingly, whereas the frequency of the vibration waveform after FFT still remains unchanged. So, vibration sensors for frequency measurement do not need temperature compensation. Figure 9a,b shows the dynamic force distribution over time for all 16 cables on south and north sides, respectively. As can be seen, for most cables, forces were around 550 kN. However, measured forces on the 15th and 17th cables on north side with sensors N 7 and N 8 were found to be abnormal. The average force of the 15th cable was 780 kN, which exceeds the normal value of 550 kN, whereas the force of the 17th cable was only 250 kN. From these two cables, it can be concluded that they are in a critical state and in urgent need for maintenance and repairs. Monitoring results have been reported to the bridge management department, and were taken seriously. Current monitoring results can provide accurate data for making scientific decisions on further safe operation and maintenance of the bridge. In addition, if an independent measure like magnetic flux method or piezoelectric acceleration sensor measurement is carried out to measure the cable force, a comparison of the two measuring results would be significant. However, we did not perform this during the project implementation about half a year ago, which is an oversight of our work. demodulator through a single-mode optical fiber. The wavelength sampling precision of the demodulator was three picometers and sampling frequency was set as 200 Hz. Given the larger number of sensors and large volume of real-time collected data, here, monitoring data collected for 160 s from the first vibration sensor (Sensor N1) on the north side of the bridge is used as an example. Figure 6 shows the time-domain waveform of sensor N1 for 160 s. To facilitate measurement of fundamental cable frequency, every 20 s in a time span of 160 s was taken as a measurement time unit. Then, frequency spectrum within this time period was acquired using fast Fourier transform (FFT). Figures 7 and 8 show time-domain waveform and frequency-domain spectrum for each 20 s. Taking the 0-20 s data in Figure 7 as an example, the fundamental frequency of the cable is obtained as 5.71 Hz and multiplier frequencies are 11.57 Hz and 17.53 Hz, and the resonant frequency of the sensor is 15.5 Hz. Results from the other time periods are the same. Therefore, it can be concluded the that vibration frequency of the cable can be successfully measured by the sensor.
For the 3rd cable, where sensor N1 was located, effective length and weight are 19.502 m and 218 kg, so linear density is 218/19.502 = 11.178 kg/m. Then, the corresponding terms in Equation (1) are: m = 11.178 kg/m, l = 19.502 m, fundamental frequency fn within 0-20 s is 5.71 Hz, for n = 1, and cable force can be obtained as T = 554.44 kN. Forces in remaining time units for sensor N1 can be calculated similarly. By this method, cable forces measured by all 16 sensors can be obtained. In addition, measurement results can be influenced by wind or gusts because wind load will cause whole-body vibration of the bridge. This whole-body vibration has an influence on the sensor measurements. However, compared with cables, the whole-body vibration frequency is usually much lower than the fundamental frequency of cables, so fundamental frequency measurement will not be affected. When environmental temperature changes, the amplitude of the vibration waveform changes correspondingly, whereas the frequency of the vibration waveform after FFT still remains unchanged. So, vibration sensors for frequency measurement do not need temperature compensation. Figure 9a,b shows the dynamic force distribution over time for all 16 cables on south and north sides, respectively. As can be seen, for most cables, forces were around 550 kN. However, measured forces on the 15th and 17th cables on north side with sensors N7 and N8 were found to be abnormal. The average force of the 15th cable was 780 kN, which exceeds the normal value of 550 kN, whereas the force of the 17th cable was only 250 kN. From these two cables, it can be concluded that they are in a critical state and in urgent need for maintenance and repairs. Monitoring results have been reported to the bridge management department, and were taken seriously. Current monitoring results can provide accurate data for making scientific decisions on further safe operation and maintenance of the bridge. In addition, if an independent measure like magnetic flux method or piezoelectric acceleration sensor measurement is carried out to measure the cable force, a comparison of the two measuring results would be significant. However, we did not perform this during the project implementation about half a year ago, which is an oversight of our work.      1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18

Conclusions
According to characteristics of Tongwamen bridge suspension cables, a cable force health monitoring scheme was proposed based on the theory of string vibration and FBG sensing. FBG sensors with high sensitivity and good repeatability suitable for detection of suspension cable frequency were developed. A total of 16 sensors were installed on 16 suspension cables. Vibration frequencies of the cables were measured and cable forces were calculated. From the monitoring results, two cables with abnormal tension forces were found using the proposed method. This monitoring method has strong practical applications in structural health monitoring of significant engineering and equipment, owing to its broad application prospects.

Conclusions
According to characteristics of Tongwamen bridge suspension cables, a cable force health monitoring scheme was proposed based on the theory of string vibration and FBG sensing. FBG sensors with high sensitivity and good repeatability suitable for detection of suspension cable frequency were developed. A total of 16 sensors were installed on 16 suspension cables. Vibration frequencies of the cables were measured and cable forces were calculated. From the monitoring results, two cables with abnormal tension forces were found using the proposed method. This monitoring method has strong practical applications in structural health monitoring of significant engineering and equipment, owing to its broad application prospects.