An active temperature compensated fiber Bragg grating vibration sensor for high-temperature application

CHEN Bao-jie，JIA Ping-gang，QIAN Jiang，FENG Fei，HONG Ying-ping，LIU Wen-yi，XIONG Ji-jun

(1. Key Laboratory of Instrumentation Science and Dynamic Measurement (North University of China)，Ministry of Education，Taiyuan 030051，China；2. Science and Technology on Electronic Test & Measurement Laboratory, North University of China，Taiyuan 030051，China)

Abstract： An active temperature compensated fiber Bragg grating (FBG) vibration sensor with a constant section cantilever beam is proposed for the simultaneous measurement of temperature and vibration, and the sensor is verified by a temperature compensation feedback system. The high-temperature vibration sensor is composed of a quartz cantilever beam and a femtosecond Bragg grating. The feedback control demodulation system of active temperature compensation can adjust the laser wavelength to stabilize the grating offset point and realize simultaneous measurement of temperature and vibration. On this basis, the performance of the sensor is tested and analyzed within the range of 20-400 ℃ by setting up a high-temperature vibration test system. The experimental results show that the sensitivity of the sensor is about 132.33 mV/g, and the nonlinearity is about 3.33%. The sensitivity between the laser wavelength and temperature is about 0.013 07 nm/℃. In addition, the active temperature compensated fiber Bragg grating vibration sensor has the advantages of a simple structure, stable performance, easy demodulation and high sensitivity. Moreover, the sensor can achieve high temperature vibration signal monitoring and has good practical application value．

Key words： fiber Bragg grating (FBG); vibration sensor; active temperature compensation; cantilever beam; feedback control

0 Introduction

Measurement of vibrations in harsh environments is of great significance for the monitoring of parameters such as bridge construction, oil well extraction, biomedicine, power industry, aircraft engines and so on[1-4]. At present, high-temperature vibration sensors commonly used in engineering applications mainly include magnetoelectric vibration sensors, piezoresistive vibration sensors, capacitive vibration sensors, piezoelectric vibration sensors and optical vibration sensors[5-9]. Compared with the traditional electrical vibration sensor, the optical sensors have the characteristics of small volume, light weight and good anti electromagnetic interference ability, which is especially suitable for the measurement of physical quantities in a strong magnetic field or during exposure to radiation, corrosion, high temperatures and other environments[10-12]. Because fiber has many advantages in sensing, the sensing technology of the fiber Bragg grating (FBG) has also been researched and developed.

FBG vibration sensors mainly include the simple beam FBG vibration sensor, the non-contact FBG vibration sensor and the equal strength beam FBG high/low frequency vibration sensor[13-15]. Because it has advantages of small size, embeddability, multi-point distributed measurement, reusability and so on, it has attracted significant attention in many industries.

In recent years, there has been some research and exploration on fiber grating vibration sensors. Casas-Ramos et al developed a cantilever beam FBG vibration sensor based on the axial property of the FBG with a sensitivity of 339 pm/g[16]. Satoshi et al designed a fiber-optic mechanical vibration sensor that uses a land piezoelectric geophone (LPG) as a sensing element, which has a dynamic response range of 90 dB[17]. Zhang et al designed a new type of special structure vibration sensor based on the FBG with a measurement range of 0 Hz-100 Hz[18]. Khan et al studied a FBG accelerometer based on L-shaped cantilever, with a sensitivity of 306 pm/g under 150 Hz frequency[19]. However, the FBG vibration sensors studied currently cannot meet the test requirements in a high-temperature environment, and FBG sensors will have a temperature coupling phenomenon in high-temperature environments, which reduces their measurement accuracy[20-21].

Based on these factors, a high-temperature resistant vibration sensor which uses quartz as a cantilever beam and the femtosecond Bragg grating as a sensing element is proposed in this paper. We adopt a demodulation method for the active feedback control system which can adjust the laser wavelength to stabilize the grating offset point to test the performance of the high-temperature fiber grating vibration sensor. Moreover, a proportional-integral-derivative (PID) feedback control system is used to control the laser wavelength in real time, which can not only demodulate the vibration signal, but also eliminate the influence of temperature on the grating drift[22-23]. The performance of the sensor is tested and analyzed within the range of 20 ℃-400 ℃ by setting up a high-temperature vibration test system.

1 Sensing principle

The structure of the active temperature compensated FBG vibration sensor is shown in Fig.1.

Fig.1 Schematic diagram of vibration sensor

The femtosecond FBG is bonded to a full quartz constant section cantilever beam (length: 20 mm, width: 5 mm, thickness: 0.2 mm) with a quartz mass (length: 5 mm, width: 5 mm, thickness: 1 mm) on the surface of the free end. At the other end of the constant section, the quartz cantilever beam integrated with the mass at the free end is fixed to the Hastelloy base to form a mass-spring-damper system. The length of the femtosecond FBG is 3 mm. When the FBG is excited by the acceleration in the vertical direction of the cantilever beam, the mass generates relative movement under the action of the inertial force, so that the reflection spectrum signal of the femtosecond FBG changes accordingly. The constant section cantilever beam structure is analyzed and the periodic variation in the intensity of the grating’s spectral signal is obtained, allowing the measurement of the vibration signal.

In a constant section cantilever structure, when the cantilever with fiber grating is excited by the acceleration along the vertical direction of the cantilever, the structure of the sensor can be simplified as a single degree of freedom forced vibration system. If the influence of the volume of the mass on the deflection of the cantilever beam is ignored, the strain on the surface of the constant section cantilever beam with mass at the free end can be expressed as

(1)

whereEis the elastic modulus;Fis the force on the inertial mass;xis the distance from any point on the cantilever to the fixed end;L,bandhare the length, width, and thickness of the constant section cantilever beam, respectively.

When the external physical quantity acts on the fiber grating, the center wavelength of the grating drifts, which can be expressed as

(2)

whereneffis the effective refractive index of the fiber core,Λis the period of the fiber grating,Peis the effective elastic coefficient of the fiber grating,εxis the strain at any point on the cantilever, andλBis the center wavelength of the fiber grating.

Therefore, the change in the center wavelength of the Bragg grating at any point on the cantilever can be expressed as

(3)

According to Newton's second law, Eq.(3) can be expressed as

(4)

wheremis the equivalent mass of the mass-spring-damper system. From Eq.(4), it can be seen that acceleration is linear related to the wavelength change of the fiber grating.

When the fiber grating is subjected to temperature change, the drift of the central wavelength of the FBG can be expressed as[24]

(5)

where ΔλBis the change in the center wavelength of the fiber grating, Δneffis the change in the refractive index of the core, ΔΛis the change in the period of the fiber grating grid, and ΔTis the change in temperature. Therefore, the fiber grating can be calibrated before the experimental test, and then the sensitivity of the central wavelength with temperature can be obtained based on Eq.(4), so that the influence of temperature on the fiber grating can be detected. The active feedback system and PID control can be used to stabilize the offset point of the FBG to compensate for the temperature.

The principle diagram of grating intensity demodulation is shown in Fig.2.

Fig.2 Demodulation schematic

Due to the small change in the grating caused by acceleration, it can be regarded as a linear change of light intensity in a small wavelength range; that is, FBG is subject to uniform strain. Then, the wavelength bar of the tunable laser is adjusted to the offset point of the FBG, that is, the position of the wavelength (λ0) corresponding to point Q in the linear part of the reflection spectrum. When the vibration signal causes the reflection spectrum to shift, the reflected light intensity changes accordingly, and vibration information is obtained by detecting the change in light intensity. Considering that the intensity between the reflection spectra A and B is linear, and the slope at the wavelength (λ0) position at point Q isk, then the spectral shift is Δλunder the acceleration. At the same time, the change in reflected light intensity is

ΔI=kΔλ.

(6)

The corresponding light intensity signal is converted into a voltage output signal through a photodetector (Model 2053, New Focus, San Jose, CA, America), that is, the output voltage change is

ΔV=DηΔI,

(7)

whereDis the product of the photodetector wavelength influence factor and the magnification factorηis the attenuation coefficient of light in the system.

From Eqs.(3), (6), (7) and Newton’s second law, the output voltage change is given as

(8)

2 System construction and experimental test

A schematic diagram of the active temperature compensated FBG vibration sensor test system based on the constant section cantilever beam is shown in Fig.3. A high-temperature experimental device was set up to calibrate and test the FBG vibration sensor in real time. This experimental setup consisted of a ThermConcept (GSL-1100X-S, HF kejing, Hefei, China), a sensing and demodulation system, and a vibration calibration system. In the vibration calibration system, the signal generator and power amplifier controlled the vibration exciter (TV 50101, Tira, Thuringen, Germany) to apply the required vibration signal to the sensor. The high-temperature ThermConcept was fixed vertically above the vibration exciter, providing a high-temperature working environment for the sensor. In the sensing and demodulation system, when the tunable laser (GM82009, Guilin GM Technology Industry Ltd, Guilin, China) light source emitted a beam, it passed through the coupler (1310/1550-SSC) to the sensor and demodulation system. The FBG vibration sensor with Hastelloy base was fixed to the top of the quartz rod, and together put into the ThermConcept. The quartz rod was connected to the vibration exciter. Another path of light was reflected back through the photodetector and the feedback system to demodulate the vibration signal. Afterwards, the data passed through the data acquisition technology (USB2833, Beijing ART Technology, Beijing, China) and the PID feedback control module was established based on Labview software on the host computer to control the laser wavelength automatically. Continuous tracking deviation of the center wavelength stabilized the grating offset point and the use of a photodetector obtained the change in light intensity in the liner region. Thus real-time monitoring of temperature and vibration signals was finally achieved.

Fig.3 High-temperature FBG vibration sensor test system

2.1 Temperature experiment and test results

In order to analyze the influence of temperature on the FBG, the temperature drift of the FBG was tested under static conditions. At the beginning of the experiment, the obtained initial central wavelength of the FBG sensor was 1 549.905 nm by an optical analyzer (Micron Optics Inc., SM125, America) at 20 ℃, and then the temperature was increased from 20 ℃ to 400 ℃ with an increment of 100 ℃ by using a ThermConcept. Each temperature was maintained for 10 min, and we tested the corresponding spectrum signals after the temperature stabilized. Then, the central wavelength of the fiber grating was analyzed and demodulated by Micron Optics Inc. (MOI) under static conditions, and the change value of the central wavelength was recorded at 20 ℃, 100 ℃, 200 ℃, 300 ℃ and 400 ℃, respectively. Fig.4(a) shows the optical spectrogram of the sensing fiber grating at different temperatures measured by the optical analyzer. It can be seen that the spectral signal of FBG demonstrates a shift phenomenon with a rise in temperature, that is, it moves in the long wavelength direction. Fig.4(b) shows the change in the central wavelength of the fiber grating with temperature. Through fitting, we found that the temperature drift coefficient is 0.013 05 nm/℃, and the correlation coefficientR2is 0.993 46.

(a) Spectral diagram of FBG changes with temperature

(b) Relationship of FBG central wavelength changes with temperature

In order to eliminate the influence of temperature drift, as the temperature of the sensor increased in the high-temperature vibration experiment, the laser wavelength was controlled by PID feedback to stabilize the offset point of the grating, thereby achieving the effect of temperature compensation for the sensor. When the laser was working normally, we obtained the relationship between the working wavelength of the laser and the temperature at 20 ℃, 100 ℃, 200 ℃, 300 ℃ and 400 ℃, respectively. As shown in Fig.5, after feedback control, the laser wavelength and temperature demonstrate a linear relationship. The linear relationship has anR2value of 0.999 14, and the temperature sensitivity of the sensor is 0.013 07 nm/℃.

Fig.5 Relationship between sensor temperature and laser wavelength controlled by PID feedback

2.2 Vibration experiment and results

In the vibration experiment test, the sensor was heated from 20 ℃ to 400 ℃ with an increment of 100 ℃ by a high-temperature ThermConcept, and the vibration signals were tested at different vibration accelerations from 0 g to 8 g. We tested vibration signal of the sensor at a frequency of 100 Hz and a acceleration of 5 g. The output signal and frequency response of the sensor are shown in Fig.6.

(a) Waveform graph of output voltage over time

(b) Fast Fourier transform spectrum of waveform

It can be seen from Fig.6(a) that the sensor can output a stable sinusoidal vibration signal at 100 Hz. According to the peak-peak voltage value of the waveform, the voltage sensitivity of the system is about 132.33 mV/g. It can be seen from Fig.6(b) that the sensor has a good frequency response under 100 Hz frequency, which is in good agreement with the frequency of the vibration exciter.

At a room temperature of 20 ℃, we performed three repeatability tests to verify the stability of the sensor. The test results are shown in Fig.7. It can be seen that the amplitude voltage of the sensor output gradually increases with the acceleration value. After calculation and fitting, the three curves basically coincide, and the repeatability error and nonlinear error of the vibration sensitivity of the sensor are about 2.8% and less than 1.55%, respectively.

Fig.7 Vibration repeatability diagram at room temperature

In the high-temperature vibration experiment, the temperature of ThermConcept was increased from 20 ℃ to 400 ℃ with an increment of 100 ℃. When the temperature is stable for a period of time, the vibration signal was measured at a frequency of 100 Hz, and the acceleration value was from 0 g to 8 g. The output signal of the vibration sensor changed during the with acceleration. The linearity curve of the amplitude voltage and acceleration is shown in Fig.8 where the center wavelength of FBG drifted with the change in temperature. The central wavelength was measured after red shift as the new central wavelength, and the offset point of FBG was searched again by the automatic feedback control system to demodulate the vibration signal, so as to reduce the influence of temperature on the central wavelength of the fiber grating. From Fig.8, we can see that the minimum nonlinearity of the vibration signal is 3.33% under high-temperatures.

Fig.8 Relationship between acceleration and amplitude voltage at different temperatures

In the high-temperature vibration sensing test, the vibration signal and temperature were measured by the change in the bias point of the grating at the same time. However, the offset point can be affected by the temperature, therefore the temperature feedback control system was used to correct the offset point. For FBG, the increase in temperature will change the period of the grating, so that the spectrum of the fiber grating appears to have a red shift with the change of temperature; that is to say, it moves in the long wavelength direction. When testing vibration signals at high-temperatures, the temperature will affect the sensitivity of the sensor. The sensitivity versus temperature curve of the vibration signals measured at different temperatures is shown in Fig.9. It can be seen that the sensitivity of the sensor decreases as the temperature increases, and the linear relationship has anR2value of 0.989 83.

It can be seen from Fig.4(b) that the central wavelength of the fiber grating increases as the temperature increases, and its correlation coefficient (R2) is 0.993 46. According to the measured temperature and the relationship with sensitivity shown in Fig.9, the offset point and sensitivity of the sensor were corrected to achieve temperature decoupling. The measured acceleration value and standard acceleration value at 20 ℃, 100 ℃, 200 ℃, 300 ℃ and 400 ℃ with decoupling are shown in Fig.10. The maximal error of the acceleration after temperature decoupling is less than 3.33% within the acceleration range of 0 g-8 g. After temperature decoupling of the sensor, the measured acceleration of the sensor is basically the same as the standard acceleration, and the experiment proves that the sensor is practical and reliable.

Fig.9 Sensitivity drift diagram with temperature

Fig.10 Acceleration measurement results after temperature decoupling

3 Conclusion

In this paper, an active temperature compensated FBG vibration sensor with a quartz constant section cantilever beam was introduced, and the temperature and vibration signals were studied experimentally by the active temperature compensation method using the PID automatic control laser wavelength. The performance of the sensor was tested and analyzed within the temperature range of 20 ℃-400 ℃ by setting up a high-temperature vibration test system. The experimental results show that the acceleration sensitivity of the vibration sensor is about 132.33 mV/g, and the nonlinearity is about 3.33%. The laser wavelength was controlled by PID feedback to stabilize the offset point of the grating for temperature compensation. The sensitivity of the laser wavelength and temperature is about 0.013 07 nm/℃, and the correlation coefficient (R2) is about 0.999 14. In conclusion, the active temperature compensated FBG vibration sensor has a stable sensing performance, easy demodulation, simple structure and a higher sensitivity. Moreover, the sensor is suitable for online monitoring of vibration signals at high-temperatures and has good practical application value.