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Abstract
A high-resolution and wide-range pressure sensor based on π phase-shifted fiber Bragg grating (π-FBG) encapsulated with metal thin-walled cylinder is reported. The sensor has been tested with a wavelength-sweeping distributed feedback laser, photodetector and a H13C14N gas cell. To perceive temperature and pressure synchronously, a pair of π-FBGs are glued on the outer wall of the thin-walled cylinder along the circumferential direction with different angles. The interference of temperature is effectively corrected by a high-precision calibration algorithm. The reported sensor has a sensitivity of 4.42 pm/MPa, a resolution of 0.036% full scale (F.S.), and a repeatability error of 0.045% F.S. in the range of 0-110 MPa that corresponds to an ocean depth resolution of 5 m and a measurement range of eleven thousand meters to cover the deepest trench of the Ocean. The sensor features simplicity, good repeatability, and practicability.
© 2023 Optica Publishing Group under the terms of the Optica Open Access Publishing Agreement
1. Introduction
Oceans are rich in mineral, chemical, and biological resources. Ocean depth (pressure) is one of the most important oceanographic parameters in the deep-sea exploration. It is also an essential calibration for other marine dynamic parameters, such as marine density, salinity, and sound velocity [1–3]. According to the empirical formula of conversion, pressure of the ocean can be converted into vertical spatial coordinates for marine depth [4]. Electric sensors, such as quartz resonance, capacitance, piezoresistive or strain gauge, have certain drawbacks when used as in-situ sensors in an underwater environment, such as easy corrosion and single-point measurement. Optical sensors have advantages due to multiplexing capability, intrinsic safety, anti-electromagnetic interference, and strong environmental adaptability [5–10]. A variety of optical pressure sensors have been reported such as fiber Bragg gratings (FBG) [9–12], Fabry-Perot interferometers (FPI) [13–16], Mach–Zehnder interferometers (MZI) [17–19], etc. Among these configurations, the FBGs-based pressure sensors have merits of robust structure and flexible design. Various sensitized structures such as diaphragm [20], thin-walled cylinders [9,10], and metal bellows [21] have been proposed. Thin-walled cylinder package structures have a good linearity and large range. Ya-Fei Gu et al. proposed a hydraulic pressure sensor based on a thin-walled cylinder with two FBGs. One of them was stuck to the outer wall of the cylinder along the circumferential direction to perceive strain and the second one was attached to the groove on the top of the cylinder as a temperature measurement probe [9]. A resolution of 0.29 MPa with a measurement range of 0-16 MPa was achieved. Zheng et al. reported an optical fiber pressure sensor by fixing two FBGs on the front and side of the thin-walled cylinder. The pressure sensitivity was 1.198 nm/MPa in the range of 0-1 MPa, and the repeatability was less than 1% full scale (F.S.) [10]. However, most above adopt complex and expensive optical spectrum instruments as interrogator with a low precision and small range, that limit the practical application in deep sea. Besides, the decoupling between temperature and pressure need to be improved.
Herein, a high-resolution and large-dynamic range optical pressure sensor is theoretically analyzed and experimentally demonstrated. A thin-walled cylinder encircled by a pair of π-FBGs is utilized as the pressure-sensing probe. A wavelength-sweeping DFB laser by current modulation is used as the light source and one absorption line of H13C14N (HCN) gas functions as a wavelength standard to calibrate the laser wavelength in real-time. The two π-FBGs were configured close to perceive synchronous temperature and pressure. A high-accuracy calibration algorithm is developed. Our experimental results show that the cross-sensitivity of pressure and temperature is well self-compensated. The pressure sensor has a sensitivity of 4.42 pm/MPa, a resolution of 0.036% F.S., and a repeatability error less than 0.045% F.S from 0 to 110 MPa.
2. Sensor structure and principle
The pressure-sensing probe contains a thin-walled cylinder and two π-FBGs as shown in Fig. 1. Two V-grooves with a depth of 500 µm were machined on the sidewall of the thin-walled cylinder to locate the fiber gratings. The cylinder is equivalent to an internal pressure container. When the applied pressure on the inner wall is higher than that of the outer wall, the sidewall will expand along the radial direction and elongate along the axial direction [9,10]. Then, the strain will be delivered to the gratings attached to the cylinder, resulting in resonance shift. Because TC4 alloy has a good memory, corrosion resistance, high yield strength, and good stability, it is chosen as a cylinder material. In order to reduce local stress concentration under high pressure, the outer sidewall and the bottom of the cylinder are connected with an arc-shaped transition area, the top of the cylinder is chamfered, and the upper end of the inter-cylinder is rounded. The structure is circular symmetry.
Fig. 1. (a) Schematic diagram, (b) side view and top view, and (c) image of the thin-walled cylinder.
Due to elastic-optic effect, thermal-optic effect and thermal expansion, the resonance shift ΔλB of the fiber grating, caused by strain and temperature variation ΔT, can be expressed as
To verify the feasibility of the configuration and prevent the sensor from being destroyed, a 3D simulation model was developed using the Finite Element Method. Stress distribution for the cylinder at a load of 110 MPa to the inner surface is shown in Fig. 2. Obviously, the stress mainly lies on the sidewall of the cylinder. The yield stress of TC4 alloy at room temperature is about 880 MPa, and the allowable stress of TC4 alloy is about 293 MPa, with a safety factor selected as 3. The maximum stress of the cylinder under 110 MPa is 258 MPa, which is less than the allowable stress of 293 MPa, indicating feasibility and reasonability of the designed structure.
3. Experiments and analysis
3.1 Test system
The experimental setup is shown in Fig. 3. The light source was a current modulated wavelength-sweeping DFB laser (Power 10 mW, linewidth 2 MHz), divided into three beams. One beam passed through the HCN gas cell, and the other two reached two π-FBG sensing probes. The π-FBGs with a length of 10 mm were uniformly and tightly stuck in the V-grooves on the outer wall of the cylinder along the spiral direction with glue. The data acquisition board collects the signals into a computer to calculate the resonance difference between the gratings and the reference in the time domain.
First, the received spectrum signals of the gratings and the HCN gas cell are normalized as shown in Fig. 4(a). The wavelength scanning range in one cycle is about 1.70 nm. The full width at half maximum of π-FBG1 and π-FBG2 are about 16 and 24 pm, respectively. In Fig. 4(a), two dips of the black line correspond to the absorption peak P9 (1548.95555 nm) and P10 (1549.73051 nm) of HCN molecular gas, respectively.
Fig. 4. (a) The normalized reflection of the gratings and absorption of the HCN, and (b) derivatives of their spectra filtered by a low-pass Butterworth filter.
As the resonance position of the spectrum could be determined more accurately by the crossing-zero point in its first-order derivative of the signal spectrum, the first-order derivative of the signal was used to identify the resonance peak in the scanning spectrum [22,23]. Firstly, the spectral derivatives are computed, as shown in Fig. 4(b). The resonance difference Δt (time delay) in the time domain relating to their wavelength difference were obtained by cross-correlation of their derivatives [24], as shown in Fig. 5. The black line is the cross-correlation production of π-FBG1 and the gas cell, while the red line denotes π-FBG2 and the gas cell. As the absorption spectrum of HCN gas has two absorption peaks, the cross-correlation production has two peaks as P9 and P10, respectively. Here, we chose P10 as the reference wavelength. The time delay to reference P10 for π-FBG1 and π-FBG2 is calculated to be −0.03604 and −0.24020s, respectively.
3.2 Temperature calibration
First, the temperature characteristics of the two π-FBGs were measured at 1-atm (0.1 MPa). The probe was put in a plastic bottle and immersed in a thermostatic bath. Figure 6 shows the outputs of π-FBGs at different temperatures which linearly varies along with the temperature. Although the two π-FBGs were fabricated by UV writing technology under the same mask, their bending angles were different due to different thread spacings when winding the circumference of the cylinder. The decrease of thread spacing leads to an increase of curvature and a decrease of radius of curvature for the space cylindrical spiral. The sensitivity of π-FBG wound on a space cylindrical spiral to external temperature could be estimated as [25,26]
3.3 Pressure calibration
A protective shell and a test pedestal that mechanically matched the thin-walled cylinder were fabricated. The cylinder was fastened between the test pedestal and the protective shell by a pair of matched threads on the protective shell bottom and test pedestal top. The inner part of the cylinder was connected to the piston gauge with a metal tube, as shown in Fig. 3. The piston gauge was calibrated, with a pressure range of 160 MPa and an accuracy of 0.005% F.S.. A standard pressure was obtained by adding the standard weights on the weight disk, and one test point was taken point every 10 MPa from 10 MPa to 120 MPa. When the output pressure was stabilized at the setting pressure, the data was recorded for at least 3 minutes.
The pressure gradually increases from 10 to 110 MPa, and then descends to 10 MPa. Figure 7(a) shows the variation of the original output of two π-FBGs with time. The details of their trends were consistent due to their simultaneously sensing of temperature and pressure. In pressure ascending process, when the piston gauge suddenly pressurized, the liquid oil is compressed, and the mechanical energy is converted into internal energy, resulting in temperature increment. Then, the temperature drops gradually until it is in thermal equilibrium with environment. Therefore, at the pressure point, the signal of each π-FBG shows a downward trend. In process of pressure descending, the liquid volume expands once the pressure suddenly drops and it absorbs the heat. Oppositely, at the pressure point, the signal of each fiber grating has a rise. It is evident the temperature has a great influence on the sensor. The output signal of individual π-FBG cannot accurately measure the pressure. Firstly, we roughly calibrated the sensor according to the signal of the individual π-FBG, as shown in Fig. 7(b). Considering the wavelength-swept rate of 1.70 nm/s, the measured pressure sensitivity of the two π-FBGs are 4.42 and 3.40 pm/MPa, respectively. A fitting degree of 0.999 is obtained by cubic fitting of data.
Next, the sensor is to be calibrated accurately according to the signals of the two π-FBGs. As mentioned above, the effect of temperature is considered to be linear and the pressure response to be cubic polynomial. The output signal of the gratings can be expressed as
where, t1 and t2 are output signals of π-FBG1 and π-FBG2, respectively. The ai, bi, and ci (i = 1,2) are the fitted pressure coefficients. The di is the temperature coefficient, and ei is a constant.Assuming α=d2/d1 is the ratio of the temperature coefficients of the π-FBG2 to the π-FBG1. Combined Eq. (2) and Eq. (3) and eliminating the temperature T, then the change of the sensor output signal Δt, caused by only pressure change can be obtained as
The relationship between Δt and applied pressure can be expressed as
where a, b, and c are the fitting coefficients, and d is a constant.The pressure dependency of the temperature coefficient was studied detailly. According to the experimental data, the coefficient ratios α under different pressures are calculated and a linear fitting is performed as shown in Fig. 8(a). The linear fitting formula between α and pressure is given by
where, m = −7.60909 × 10−4 is the fitting coefficient of the first term, and n = 0.76111 is the constant term. The α is determined with the above-mentioned method, which is from 10 to 110 MPa, followed by a cubic polynomial calibration with the polynomial fit method. Figure 8(b) shows the fitting curve of signal change ΔT and pressure P. The sensor has a root mean square error of the fitting formula of 0.036% F. S. in the range of 10 MPa-110 MPa, and the largest error is 0.046% F. S., indicating an excellent cubic polynomial relationship between the sensor output and pressure.Fig. 8. (a) Ratios of the temperature coefficients versus the pressure, and (b) fitting curve of signal change ΔT and pressure P.
The fit parameters, a to d, are shown in Table 1.
Table 1. Fit parameters, a to d
Therefore, by combining Eq. (4), (5), and (6), one can obtain
based on the above, the coefficients a, b, c, d, m, and n are determined, and the pressure P could be calculated by finding the real root of Eq. (7) from the sensing original signals t1 and t2.The mean of indicating value stabilized at the calibrated pressure point for one minute is taken as the measurement value. Figure 9(a) and Fig. 9(b) shows the measured pressure with time and the pressure deviation at different pressures, respectively. Clearly, the pressure sensor has a maximum deviation of 0.045 MPa in the range of 10-110 MPa, corresponding to a small repeatability error of ±0.04% F.S..
Fig. 9. (a) Change of measured pressure with time, and (b) measured pressure deviation at different pressures.
To measure the stability of the sensor, the sensor tested at the atmosphere for one consecutive hour, as shown in Fig. 10(a). The mean square deviation of the pressure is 0.04 MPa, considered as the smallest detectable pressure variation, corresponding to an achievable pressure resolution of 0.036% F.S. By applying an instantaneous pressure load to the pressure generator, the response time of the probe was tested to be 20 ms, as shown in Fig. 10(b). In ocean depth survey, this pressure sensor has a resolution of 5 m with a measuring range of eleven thousand meters. The sensor has low cost, high precision, simple design, and small hysteresis.
Comparative data of representative FBG-based-pressure sensors are listed in Table 2. Most of them adopt complex and expensive optical spectrum instruments as the demodulation devices. The pressure resolution is limited by the wavelength resolution of the spectrometer. In this work, to improve the stability of the measurement system, an absorption line of HCN gas cell was used to calibrate the laser wavelength in real-time. The temperature and pressure are simultaneously sensed with two decoupled fiber bragg gratings to compensate temperature effect, which significantly reduced pressure measurement error. This pressure sensor has achieved not only a large dynamic range with high accuracy, but also has advantages of low cost, in-situ calibration and low hysteresis.
Table 2. Comparison of typical FBG based pressure sensors
4. Conclusion
A high-resolution and large-dynamic range pressure sensing system has been proposed, designed and experimentally demonstrated in this paper with advantages of low-cost, high-resolution, and in-situ calibration of the drift of the wavelength with a HCN gas absorption line. The temperature and pressure are simultaneously sensed with two decoupled fiber gratings. An effective calibration algorithm has been developed for temperature compensation. This sensor has demonstrated a sensitivity of 4.42 pm/MPa, a pressure resolution of 0.036% F.S., a good repeatability of 0.04% F.S. in the range of 0-110 MPa. The combined theoretical and experimental results proved that the thin-walled cylinder pressure sensor could meet the requirements of the depth measurement for full-sea depth.
Funding
Southern Marine Science and Engineering Guangdong Laboratory (Guangzhou) (GML2021GD0808); National Natural Science Foundation of China (42106183); Key Research and Development Project of the State Department of Science and Technology of China (2019YFC1408600); Key Research and Development Project of Shandong province (2019J22Y0207); Shandong Provincial Standardization and Strategic Key Project (2021-GJ-11); Natural Science Foundation of Shandong Province (ZR2020QF087).
Disclosures
The authors declare no conflicts of interest.
Data availability
Data underlying the results presented in this paper are not publicly available at this time but may be obtained from the authors upon reasonable request.
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