CN110470426A - A kind of fiber-optic grating sensor and measurement method that can measure temperature and pressure simultaneously - Google Patents

Abstract

The invention discloses an optical fiber grating sensor capable of simultaneously measuring temperature and pressure and a measuring method thereof. The sensor comprises a thin-walled tube with an open bottom, and a protective shell packaged outside the thin-walled tube. The gap between the thin-walled tube and the protective shell is There is a gap; the outer surface of the thin-walled tube is fixed with a first fiber grating and a second fiber grating, and the fiber pigtails of the first and second fiber gratings pass through the top of the protective shell, and the cross-section of the thin-walled tube It is a quasi-elliptical shape surrounded by two straight sides and two semicircular arcs respectively connecting the two ends of the two straight sides, and the first fiber grating is fixed on the surface of the thin-walled tube along the axis direction of the thin-walled tube. In the center, the second fiber grating is fixed on the center of the semicircular surface of the thin-walled tube along the axial direction of the thin-walled tube, and the centers of the first and second fiber gratings are at the same height as the center of the thin-walled tube. The sensor disclosed by the invention has the advantages of novel structure, high sensitivity, reliable measurement result and wide application.

Description

A fiber grating sensor and measurement method capable of simultaneously measuring temperature and pressure

technical field

The invention relates to an optical fiber grating sensor, in particular to an optical fiber grating sensor capable of simultaneously measuring temperature and pressure and a measuring method.

Background technique

Pressure is an important physical parameter, which has important measurement value in marine, national defense, petrochemical, medical, aviation, electric power and other fields. Through pressure measurement, we can understand the safety status of the equipment, the operating status of the system, the change of the environment and the depth of a certain position under the sea, etc. Most of the existing pressure sensors are electrical sensors, which have some problems in anti-electromagnetic interference, safety in use, and long-distance signal transmission. Therefore, they are limited in applications such as strong electromagnetic interference, flammable and explosive, and long-distance parameter monitoring. . The optical fiber pressure sensor based on the optical signal not only has the intrinsic safety of the sensor, but also can realize the long-distance transmission of the signal without interference.

The commonly used fiber optic pressure sensors mainly include fiber grating pressure sensors and fiber optic Fabry-Perot pressure sensors. The optical fiber Fabry-Perot pressure sensor is small in size and simple in structure. It is often used for single-point pressure measurement, but it is not suitable for distributed measurement of sensors. Fiber Bragg grating is a kind of optical fiber sensing device with mature technology and stable performance, and fiber Bragg grating sensor is convenient for distributed measurement, and has been widely used in actual production and life. Due to the low pressure sensitivity of the fiber Bragg grating itself (only about 0.003nm/MPa), in order to achieve high-resolution pressure measurement, many related design schemes use different sensitization structures to improve the sensitivity of the fiber optic pressure sensor. Existing pressure-sensitizing structures include diaphragm type, thin-walled cylinder type, polymer-coated type, spring tube type and other structures. However, diaphragm pressure sensors often need to be matched with metallized packaging, the manufacturing process is more complicated, and the cost is relatively high; spring tube type grating pressure sensors need reliable cooperation between parts, otherwise it is prone to zero drift problems; polymer pressure sensors have Aging and creep issues during long-term use.

People such as Shen Rensheng of Dalian University of Technology invented a thin-walled strain tube-type optical fiber Bragg grating pressure sensor (reference patent: inner arc-shaped top thin-walled strain tube input type optical fiber Bragg grating pressure sensor, publication number: CN101266179), this The sensor consists of a metal thin-walled inner cylinder, a metal thick-walled outer cylinder, a pressure measurement grating, a temperature compensation grating and a sealing gasket. According to the description in the article, the cross-section of the metal thin-walled inner cylinder of this sensor is circular, and the pressure sensitivity is only 0.033nm/MPa, which cannot meet the demand when applied to some occasions with high sensitivity requirements. In addition, in this scheme, the temperature compensation grating is fixed on the top of the thin-walled cylinder, and the pressure grating is fixed on the outside of the cylinder wall along the axial direction of the thin-walled cylinder. Because the spatial orientation of the two fiber gratings is vertical and the distance is relatively long, the position of the two gratings The temperature gradient is too large, the decoupling response time is too long, and the temperature-compensated grating located outside the top of the thin-walled cylinder is easily disturbed by the external temperature.

Contents of the invention

In order to solve the above-mentioned technical problems, the present invention provides a fiber grating sensor and a measuring method that can simultaneously measure temperature and pressure, with high sensitivity, fast temperature response, good water tightness, simple structure, and can be applied to pipeline pressure, seawater depth (pressure ) and other measurements.

To achieve the above object, the technical scheme of the present invention is as follows:

A fiber grating sensor capable of measuring temperature and pressure at the same time, comprising a thin-walled tube with an open bottom, a protective shell packaged outside the thin-walled tube, and a gap exists between the thin-walled tube and the protective shell; the outer shell of the thin-walled tube The surface is fixed with a first fiber grating and a second fiber grating, and the fiber pigtails of the first fiber grating and the second fiber grating pass through the top of the protective shell, and the cross section of the thin-walled cylinder is composed of two straight sides and A quasi-elliptical shape surrounded by two semicircular arcs respectively connecting the two ends of the two straight sides, the first fiber grating is fixed in the center of the surface of the thin-walled tube along the axial direction of the thin-walled tube, and the second The fiber grating is fixed on the center of the semicircular surface of the thin-walled tube along the axial direction of the thin-walled tube, and the centers of the first fiber grating and the second fiber grating are at the same height as the center of the thin-walled tube.

In the above solution, the outer edge of the bottom of the thin-walled cylinder is integrally connected with an annular fixed plate, the outer edge of the bottom of the protective shell is a groove structure, the annular fixed plate is embedded in the groove, and the bolts are used to connect the two. To connect, the ring-shaped fixing plate and the outer edge of the bottom of the protective shell are provided with a pressure fixing hole at the same position, and the sensor can be fixed on the pressure calibration platform with bolts for sensor testing.

In the above scheme, a threaded hole is provided on the top of the protective shell, and a pigtail outlet hole communicated with the gap is provided at the bottom of the threaded hole. A compression device is connected to the threaded hole through a thread, and the compression device is connected to the threaded hole. A graphite sealing gasket is arranged between the bottom of the hole, the rear end of the pressing device is connected to the caudal vertebral tube through a connecting sleeve, and the optical fiber pigtail passes through the pigtail leading hole, passes through the graphite sealing gasket, compression Tightening device, connecting sleeve and caudal canal. The tail cone is used for the extraction of the optical fiber and can prevent the excessive bending of the optical fiber from increasing the optical transmission loss of the optical fiber.

By using the graphite sealing gasket to cooperate with the pressing device, the effective sealing of the pigtail lead-out hole can be realized. The principle is that when the compression device exerts force on the graphite sealing gasket, the graphite sealing gasket will be deformed, and then the graphite will fill the pigtail outlet hole to realize the sealing of the pigtail outlet hole.

In a further technical solution, the pressing device and the connecting sleeve are connected through threads.

In a further technical solution, the outer wall of the connecting sleeve is provided with an annular slot, and the connecting sleeve is connected to the caudal vertebral canal through the annular slot.

In the above solution, the gap between the protective shell and the thin-walled cylinder is in a vacuum state, so as to avoid the atmospheric pressure error introduced by the sensor due to the difference in altitude or geographical location.

In a further technical solution, the connection between the thin-walled cylinder and the protective shell is filled with silicone rubber.

A measurement method of an optical fiber grating sensor that can measure temperature and pressure at the same time. During measurement, the optical fiber grating sensor is connected to the pipeline to be measured or put into seawater, so that the measured medium enters the cavity of the thin-walled cylinder, and the thin-walled Due to the different pressure on the inner and outer sides of the barrel, deformation will occur, and it will be transmitted to the first fiber grating and the second fiber grating. The first fiber grating is subjected to positive strain, which shows a red shift of the center wavelength, and the second fiber grating shows a blue shift of the center wavelength. . Use the following decoupling equations to calculate the temperature and pressure of the measured medium:

Among them, K _T1 , K _T2 , K _P1 , K _P2 are the temperature coefficient and pressure coefficient of the first fiber grating and the second fiber Bragg grating respectively, which can be measured through experiments;

Δλ ₁ and Δλ ₂ are respectively the central wavelength shifts of the first fiber grating and the second fiber grating;

T and P are the temperature and pressure of the medium to be measured, respectively.

Through the above technical solution, the thin-walled tube of the fiber grating sensor that can simultaneously measure temperature and pressure provided by the present invention is a cylindrical structure with a sub-elliptical cross section. The inner side of this structure is in direct contact with the measured medium. The introduction of pressure; the outer side is in contact with the reference pressure medium (vacuumization treatment), when the pressure on both sides of the cylinder wall is different, strain will be generated on the cylinder wall, and the surface (front) where the straight edge of the cylinder wall section is located will be stretched , the surface (side) where the cross-section arc is located will shrink, causing the strain on the fiber grating on the front to increase with the increase of pressure, while the strain on the fiber grating on the side will decrease. Due to the different deformation characteristics of the fixed positions of the two fiber gratings, the wavelengths move differently, and the pressure characteristics of the two fiber gratings are different. After obtaining the temperature and pressure characteristics of the two fiber gratings, the simultaneous acquisition of temperature and pressure data can be realized through data processing.

The advantage of the optical fiber grating sensor of the present invention is: the present invention improves the pressure sensitivity of the sensor by improving the sensitization structure that the shape of the thin-walled cylinder causes; The temperature consistency and response speed of the two fiber gratings; the sealing problem at the outlet hole of the pigtail is solved by the graphite gasket, and the reference medium (the invention is vacuuming) between the thin-walled cylinder and the protective shell is prevented from being subjected to external pressure The impact of the sensor improves the water tightness of the sensor, thereby improving the environmental adaptability of the sensor.

Through experimental testing, the pressure sensitivity of the sensor of the present invention in the range of 0 to 1Mpa reaches 1.198nm/MPa, which solves the problem of temperature cross sensitivity and realizes the simultaneous measurement of temperature and pressure; and the sensor package of the present invention has good watertightness, not only can It can be applied to the measurement of pipeline pressure, and can also be applied to the measurement of seawater pressure, and then according to the linear correspondence between seawater depth and pressure, the value of seawater depth can be obtained. The sensor has a wide range of applications and a huge market potential.

Description of drawings

In order to more clearly illustrate the embodiments of the present invention or the technical solutions in the prior art, the following briefly introduces the drawings required for the description of the embodiments or the prior art.

Fig. 1 is an axial sectional view of a fiber grating sensor capable of simultaneously measuring temperature and pressure disclosed in an embodiment of the present invention;

Fig. 2 is a schematic diagram of the three-dimensional structure of the thin-walled cylinder disclosed in the embodiment of the present invention;

Fig. 3 is the comparison diagram of the sensitivity test of the sensor;

Figure 4 is a comparison chart of pipeline pressure tests;

Figure 5 is a distribution diagram of pipeline pressure test errors.

In the figure, 1. thin-walled tube; 2. protective shell; 3. first fiber grating; 4. second fiber grating; 5. front grating groove; 6. side grating groove; Hole; 9, threaded hole; 10, pigtail lead-out hole; 11, pressing device; 12, graphite sealing gasket; 13, connecting sleeve; 14, tail vertebral tube; 15, optical fiber pigtail; 16, ring slot ; 17. Bolt connection holes.

Detailed ways

The following will clearly and completely describe the technical solutions in the embodiments of the present invention with reference to the drawings in the embodiments of the present invention.

The present invention provides a fiber grating sensor capable of simultaneously measuring temperature and pressure. The sensor has a novel structure, high sensitivity, fast temperature decoupling response speed, and more accurate measurement results.

As shown in Figure 1, a fiber grating sensor that can measure temperature and pressure at the same time includes a thin-walled tube 1 with an open bottom, a protective shell 2 packaged outside the thin-walled tube 1, and between the thin-walled tube 1 and the protective shell 2 There is a gap; the outer surface of the thin-walled tube 1 is fixed with the first fiber grating 3 and the second fiber grating 4 , and the fiber pigtails 15 of the first fiber grating 3 and the second fiber grating 4 pass through the top of the protective shell 2 . In this embodiment, the thin-walled tube 1 is made of metal copper, and the protective shell 2 is made of stainless steel.

As shown in Figure 2, the cross-section of the thin-walled tube 1 is a quasi-elliptical shape surrounded by two straight lines and two semicircular arcs connecting the two ends of the two straight lines respectively. The front grating groove 5 and the side grating groove 6, the first fiber grating 3 is fixed in the front grating groove 5 in the center of the surface where the straight edge of the thin wall cylinder 1 is along the axis direction of the thin wall cylinder 1, and the second fiber grating 4 is fixed along the thin wall cylinder 1 along the axis direction of the thin wall cylinder 1. The axial direction of the wall cylinder 1 is fixed in the side grating groove 6 in the center of the semi-circular surface of the thin-wall cylinder 1, and the centers of the first fiber grating 3 and the second fiber grating 4 are located at the same center as the center of the thin-wall cylinder 1. height.

The outer edge of the bottom of the thin-walled tube 1 is integrally connected with an annular fixed disk 7, and the outer edge of the bottom of the protective shell 2 is a groove structure, and the annular fixed disk 7 is embedded in the groove, and the bolt connection hole 17 located on it is used between the two. Bolt connection, pressure fixing hole 8 is set on the same position on the ring fixing plate 7 and the outer edge of the bottom of the protective shell 2, the sensor can be fixed on the pressure calibration platform with bolts for testing the temperature coefficient and pressure coefficient of the sensor.

The top of the protective shell 2 is provided with a threaded hole 9, the bottom of the threaded hole 9 is provided with a pigtail outlet hole 10 communicating with the gap, the threaded hole 9 is threadedly connected with a compression device 11, and the compression device 11 and the bottom of the threaded hole 9 are provided with Graphite sealing gasket 12, the rear end of the compression device 11 is connected to the caudal vertebral canal 14 through the connecting sleeve 13, and the optical fiber pigtail 15 passes through the pigtail outlet hole 10, passing through the graphite sealing gasket 12 and the compression device 11 in turn , connecting sleeve pipe 13 and caudal vertebral canal 14. The tail cone 14 is used for leading out the optical fiber pigtail 15 and can prevent the optical fiber pigtail from being excessively bent to increase the optical transmission loss of the optical fiber.

By using the graphite sealing gasket 12 to cooperate with the pressing device 11, the effective sealing of the outlet hole of the pigtail can be realized. The principle is that when the compression device 11 applies force to the graphite sealing gasket 12, the graphite sealing gasket 12 will be deformed, and then the graphite will fill the fiber pigtail outlet hole 10 to seal the fiber pigtail outlet hole 10.

In this embodiment, the pressing device 11 is connected to the connecting sleeve 13 through threads; the outer wall of the connecting sleeve 13 is provided with an annular slot 16 , and the connecting sleeve 13 is connected to the caudal vertebral canal 14 through the annular slot 16 .

In the above scheme, the gap between the protective shell 2 and the thin-walled cylinder 1 is in a vacuum state, so as to avoid the atmospheric pressure error introduced by the sensor due to the difference in altitude or geographical location.

The connection between the thin-walled cylinder 1 and the protective shell 2 is filled with silicon rubber to prevent foreign substances from entering the cavity and affecting the measurement effect.

The fabrication process of the sensor is as follows:

First, use an ultrasonic cleaning machine to clean the surface of the quasi-elliptical thin-walled cylinder 1. After cleaning, the first fiber Bragg grating 3 and the second fiber Bragg grating 4 can be fixed. In order to ensure that the first fiber Bragg grating 3 and the second fiber Bragg grating 4 Always in a straightened state, it is necessary to apply prestress to the first fiber Bragg grating 3 and the second fiber Bragg grating 4 during the fixing process. The specific method is to first use glue to fix one end of the fiber grating, and then pull the free end of the fiber grating with a weight. After the fiber grating is fixed, the sensor needs to be aged for a certain period of time (usually in a thermostat at 80°C for 10 hours) to stabilize the characteristics of the sensor. Then, a layer of silicone rubber is coated on the outer wall of the thin-walled cylinder 1 to prevent the cured glue from being ineffective due to direct contact between water and the cured glue. The pressure and temperature characteristics of the sensor are obtained before packaging, and the pressure and temperature coefficients of the two fiber gratings are determined before the sensor is packaged. When assembling the protective shell 2 , some silicon rubber is applied to the contact position between the protective shell 2 and the thin-walled tube 1 to ensure the sealing of the gap formed by the thin-walled tube 1 and the protective shell 2 .

Put the graphite sealing gasket 12 in the threaded hole 9 at the end of the protective shell 2, fit the compression device 11 through the thread with the protective shell 2, draw the optical fiber pigtail 15 from the pigtail lead-out hole 10, and then place it in the vacuum box To ensure that there is a vacuum between the cavity formed between the thin-walled cylinder 1 and the protective shell 2, tighten the compression device 11 with a wrench in the vacuum box.

Fix the connecting sleeve 13 on the tail of the pressing device 11, and apply some silicone rubber to ensure the sealing during the fixing process. The fiber pigtail 15 is led out from the connecting sleeve 13, and a 900 μm loose tube, a 3.0 mm yellow tube and a tail cone 14 are sequentially placed on the fiber pigtail 15 for protection of the fiber pigtail. In order to absolutely ensure the vacuum, it is recommended that this step be carried out in a vacuum box.

Compared with thin-walled cylinders, the quasi-elliptical thin-walled cylinder 1 used in the present invention has the advantages of high pressure sensitivity, rapid temperature response and good consistency. When the pressure is measured, the pressure difference between the inner and outer sides of the cylinder wall will cause the deformation of the cylinder wall. When a circular thin-walled cylinder is used, the force on the circular section is uniform in all directions (the circular section has a strong constraint on all directions) , so the deformation of the cross-section is the same in all directions; when the quasi-elliptical thin-walled tube 1 is used, the stress in each direction is different due to the unevenness of the cross-sectional shape (the constraints of the quasi-elliptical cross-section on all directions are relatively circular Weaker shape), the deformation degree of the front and side is different, using this feature, not only can obtain multiple responses to the same pressure at different positions of the cylinder wall, but also the maximum deformation amount under the same pressure difference is also different from that of the cylinder structure. Larger lift (that is, under the same pressure, the force of the circular thin-walled cylinder is uniform in all directions, so the deformation is the same; the oval thin-walled cylinder 1 is not uniform in all directions, so the deformation is also different , the deformation is the largest at the center of the straight side of the cross section, and the smallest at the center of the arc edge).

Because temperature and pressure will affect the central reflection wavelength of FBG at the same time, how to solve the cross-coupling effect of temperature and pressure is an important issue that determines the measurement accuracy of FBG sensors. In the present invention, the central height positions of the two optical fiber gratings coincide, so the temperature fields where they are located are basically the same. Since the fixed positions of the two fiber gratings on the cylinder wall are the places with the largest deformation and the minimum deformation respectively, and different positions in the thin-walled cylinder 1 have different pressure deformations, so the strains of the two fiber gratings are also different.

According to the above principles, the measurement method of a fiber grating sensor capable of simultaneously measuring temperature and pressure of the present invention is as follows: when measuring, connect the fiber grating sensor to the pipeline to be measured or put it into seawater, so that the measured medium enters the thin wall In the cavity of tube 1, the thin-walled tube 1 will be deformed due to the pressure difference between the inner and outer sides, and the deformation will be transmitted to the first fiber grating 3 and the second fiber grating 4. Red shift, the second fiber grating 4 shows a blue shift of the central wavelength; use the following decoupling equation to calculate the temperature and pressure of the measured medium:

Wherein, K _T1 , K _T2 , K _P1 , K _P2 are the temperature coefficient and pressure coefficient of the first fiber Bragg grating 3 and the second fiber Bragg grating 4 respectively, which can be measured through experiments;

Δλ ₁ and Δλ ₂ are the central wavelength shifts of the first fiber Bragg grating 3 and the second fiber Bragg grating 4, respectively;

T and P are the temperature and pressure of the medium to be measured, respectively.

Performance test experiment:

The pressure characteristic test of the sensor is carried out with the patent in the background technology (publication number: CN101266179) and the reference (Novel integrated optical fiber sensor for temperature, pressure and flow measurement, DOI: 10.1016/j.sna.2018.07.034) In contrast, the obtained curve between the shift of the central wavelength and the pressure difference on both sides of the thin-walled tube is shown in Figure 3. The pressure sensitivity of the sensor of the present invention in the range of 0-1Mpa reaches 1.198nm/MPa, and the pressure sensitivity of the thin-walled cylinder pressure sensor (references) with the same material, the same wall thickness and similar size is increased by 7.6 times (the pressure of patent CN101266179 The sensitivity is 0.033nm/MPa, and the pressure sensitivity of the reference is 0.158nm/MPa).

Connect the sensor to the pressure pipeline and compare it with a standard pressure gauge. The results of the comparison are shown in Figure 4 and Figure 5. After the test of the pressure rise and fall, the relationship between the standard pressure and the measured pressure and the sensor's Error distribution. It can be seen that within the pressure range of 0-1MPa, the accuracy of the sensor is 1% F.S., and the error is within ±0.01MPa.

The above description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the present invention will not be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims (8)

1. A fiber grating sensor capable of measuring temperature and pressure simultaneously, comprising a thin-walled tube with an open bottom, a protective shell packaged on the outside of the thin-walled tube, and there is a gap between the thin-walled tube and the protective shell; the thin-walled The outer surface of the barrel is fixed with a first fiber grating and a second fiber grating, and the fiber pigtails of the first fiber grating and the second fiber grating pass through the top of the protective shell, and the feature is that the cross section of the thin-walled barrel is A quasi-elliptical shape surrounded by two straight sides and two semicircular arcs respectively connecting the two ends of the two straight sides, the first optical fiber grating is fixed on the surface of the thin-walled tube along the axis direction of the thin-walled tube In the center, the second fiber grating is fixed in the center of the semicircular surface of the thin-walled tube along the axial direction of the thin-walled tube, and the centers of the first fiber grating and the second fiber grating are at the same height as the center of the thin-walled tube superior. 2. A fiber grating sensor capable of simultaneously measuring temperature and pressure according to claim 1, characterized in that, the outer edge of the bottom of the thin-walled cylinder is integrally connected with an annular fixing plate, and the outer edge of the bottom of the protective shell is concave. Groove structure, the annular fixed disk is embedded in the groove, and the two are connected by bolts, and a pressure fixing hole is opened on the same position of the annular fixed disk and the outer edge of the bottom of the protective shell. 3. A fiber grating sensor capable of simultaneously measuring temperature and pressure according to claim 1, wherein a threaded hole is provided at the top of the protective housing, and a pigtail leading out of the gap communicated with the gap is provided at the bottom of the threaded hole hole, the threaded hole is threadedly connected with a compression device, a graphite sealing gasket is arranged between the compression device and the bottom of the threaded hole, and the rear end of the compression device is connected to the caudal vertebral canal through a connecting sleeve. The optical fiber pigtail passes through the pigtail lead-out hole, and passes through the graphite sealing gasket, the pressing device, the connecting sleeve and the tail vertebral tube in sequence. 4 . A fiber grating sensor capable of simultaneously measuring temperature and pressure according to claim 3 , wherein the pressing device and the connecting sleeve are connected by threads. 5. A fiber grating sensor capable of simultaneously measuring temperature and pressure according to claim 3, characterized in that, the outer wall of the connecting sleeve is provided with an annular slot, and the connecting sleeve is connected to the caudal vertebra through the annular slot. tube connection. 6 . A fiber grating sensor capable of simultaneously measuring temperature and pressure according to claim 1 , wherein the gap between the protective shell and the thin-walled tube is in a vacuum state. 7. A fiber grating sensor capable of simultaneously measuring temperature and pressure according to claim 2, characterized in that the connection between the thin-walled cylinder and the protective shell is filled with silicone rubber. 8. a kind of measuring method of the fiber grating sensor that can measure temperature and pressure simultaneously as claimed in claim 1, it is characterized in that, during measurement, this fiber grating sensor is connected on the pipeline to be measured or drops into seawater, so that it is The measured medium enters the cavity of the thin-walled cylinder, and the thin-walled cylinder will be deformed due to the different pressures on the inner and outer sides, and will be transmitted to the first and second fiber gratings. The positive strain on the first fiber grating is expressed as the center wavelength Red shift, the second fiber grating shows a blue shift of the central wavelength; use the following decoupling equation to calculate the temperature and pressure of the measured medium: Among them, K _T1 , K _T2 , K _P1 , K _P2 are the temperature coefficient and pressure coefficient of the first fiber grating and the second fiber Bragg grating respectively, which can be measured through experiments; Δλ ₁ and Δλ ₂ are respectively the central wavelength shifts of the first fiber grating and the second fiber grating; T and P are the temperature and pressure of the medium to be measured, respectively.