Two-dimensional fiber grating tilt angle sensor and solving method

Abstract

This invention discloses a two-dimensional fiber Bragg grating tilt sensor and its calculation method, belonging to the field of fiber optic sensing technology. The sensor consists of a ring base, a ring protective shell, a mass sphere, three sensing fiber Bragg gratings, a fiber optic fixing base, and a loose tube. The three gratings are symmetrically distributed at 120° and subjected to equal preload. One end is fixed to the mass sphere, and the other end is led out through the fixing base and the loose tube. Based on the principle of static equilibrium, this invention collects the Bragg wavelength drift of each grating under different tilt and tilt angle directions. Through interactive differential calculation of the three sets of wavelength changes, environmental temperature drift is offset, solving the problem of cross-sensitivity of fiber Bragg grating temperature strain. The tilt angle and tilt direction can be calculated simultaneously. This sensor has a compact structure, is easy to assemble, and has a fast response. It also possesses high precision, high stability, and strong anti-electromagnetic interference capability, strong environmental adaptability, and is suitable for long-term online monitoring. It can be widely used in aerospace, bridge engineering, geological disaster monitoring, and other fields.

Description

Technical Field

[0001] This invention relates to the field of fiber optic grating sensing technology, and in particular to a two-dimensional fiber optic grating tilt sensor and a calculation method thereof. Background Technology

[0002] Tilt measurement has wide applications in civil engineering, aerospace, machinery manufacturing, and geological disaster monitoring. Existing tilt sensors mostly employ MEMS (Micro-Electro-Mechanical Systems), electrolyte, or resistive sensing principles. While these electrical sensors have achieved engineering applications, their anti-interference capabilities, long-term stability, and durability remain insufficient under harsh conditions such as strong electromagnetic interference, explosive environments, humidity, and long-term buried monitoring. Furthermore, existing technologies suffer from limitations such as complex structure, large size, high manufacturing cost, difficulty in balancing measurement range and detection sensitivity, and cross-sensitivity to temperature and tilt angle, affecting the accuracy and long-term reliability of measurement results. Therefore, there is an urgent need to develop a fiber optic tilt sensor with a simple structure, strong environmental adaptability, the ability to simultaneously achieve a large measurement range and high accuracy, and the ability to effectively suppress temperature cross-sensitivity effects. Summary of the Invention

[0003] The purpose of this invention is to solve the technical problems existing in the prior art and to provide a two-dimensional fiber optic tilt sensor and a calculation method thereon.

[0004] To achieve the above objectives, the technical solution provided by the present invention is: a two-dimensional fiber optic tilt sensor, the sensor comprising an annular base, a mass sphere, three sensing fiber optic gratings, an optical fiber fixing base, and an optical fiber loose tube; Optical fiber fixing seats are fixedly installed on the annular base at 120° angular intervals, that is, the optical fiber fixing seats are fixedly distributed at the edges of the annular base in the 0°, 120° and -120° directions; small holes for optical fiber pigtails to pass through are opened on the three optical fiber fixing seats along the radial direction of the annular base. A mass sphere is positioned at the center of the annular base. Three equal-length sensing fiber gratings with the same center wavelength are fixed at both ends on the surface of the mass sphere and the fiber optic mounting base, respectively. The three sensing fiber gratings are symmetrically distributed in a trident shape at equal angles of 120°, and all are pre-tensioned with the same force to bear the gravitational components of the mass sphere in each direction on the plane of the sensing fiber gratings when tilting occurs. The pigtails of the three sensing fiber gratings pass through the annular base through small holes in the fiber optic mounting base. The pigtails of the sensing fiber gratings are protected by fiber optic loose tubes, coated with glue, cured, and then led out.

[0005] Preferably, the sensor further includes an annular protective shell, and the outer ring of the upper end face of the annular base is provided with an arc-shaped stepped assembly and bonding surface, which is located between every two fiber optic fixing seats, and each fiber optic fixing seat is provided with an assembly screw hole. The outer contour of the annular protective shell matches the outer contour of the annular base; the annular protective shell has through holes corresponding to the positions of each mounting screw hole; the annular protective shell covers the upper end face of the annular base; the lower end face of the annular protective shell is pressed against the arc-shaped step mounting surface of the annular base to achieve assembly; after the mounting screw holes are aligned with the through holes on the annular protective shell, locking bolts are inserted to fasten and lock the annular protective shell and the annular base, forming a sealed protective cavity.

[0006] This invention also discloses a method for calculating the tilt angle of a two-dimensional fiber optic grating tilt sensor. Using the aforementioned two-dimensional fiber optic grating tilt sensor, the steps for calculating the tilt angle and tilt direction of the sensor are as follows: S1. Place the sensors horizontally to monitor and record the initial center wavelength of each sensing fiber optic grating. ; S2. Collect the change in the center wavelength of the three sensing fiber optic gratings; When the sensor is tilted, the mass ball is in a state of force equilibrium. The component of the mass ball's gravity on the sensor plane and the resultant force of the axial tension of the three sensing fiber gratings are zero. The change in the axial tension of the sensing fiber grating causes the sensing fiber grating to generate axial strain. The change in the center wavelength of the three sensing fiber gratings under the axial strain is collected in real time. S3. Perform temperature self-compensation processing on the collected changes in the center wavelength of the three sensing fiber optic gratings. The three sensing fiber gratings are in the same temperature field and have the same temperature sensitivity coefficient. The pairwise difference operation is performed on the change in the center wavelength of the three sensing fiber gratings to completely eliminate the wavelength drift introduced by the ambient temperature. S4. Determining the direction of the tilt angle; The three sensing fiber optic gratings are sorted in ascending order of their center wavelength changes, with the one with the smallest wavelength change value defined as the dominant grating. The other two are designated as the first and second auxiliary gratings, respectively, in ascending order of their center wavelength changes. Based on the relationship between the three values, the tilt direction is divided into a horizontal zero tilt direction, six tilt direction zone measurement conditions, and six regional boundary critical conditions. S5. Solve the tilt direction and tilt angle of the sensor using static modeling; Static modeling and solution: Based on the component of gravity of the mass sphere in the sensor plane, a planar static equilibrium equation is constructed. Gravity is bidirectionally decomposed along the directions parallel and perpendicular to the dominant grating. Based on the differential result of the change in the center wavelength of the sensing fiber optic grating, a system of equations is solved to first determine the local tilt direction. The tilt direction is then obtained by superimposing the local tilt direction with the fixed placement angle of the dominant grating. Finally, by simultaneously solving the two sets of force equilibrium equations, the tilt angle of the sensor plane can be obtained.

[0007] Preferably, in step S4, the sensor tilt direction region is determined as follows: The plane containing the three sensing fiber Bragg gratings is denoted as the sensor plane. The three sensing fiber Bragg gratings are labeled FBG1, FBG2, and FBG3 in counterclockwise order, respectively. The angle between the projection of the mass sphere's gravitational force onto the sensor plane and FBG1 is the tilt angle direction. On the sensor plane, when When FBG1 rotates counterclockwise within the range of 0° to 180°, it takes a positive value. The value is negative when FBG1 rotates clockwise from 0° to 180°; the angle between the sensor plane and the horizontal plane is the tilt angle. ; On the sensor plane, the radial direction of FBG1 is selected as the initial zero-position reference for the tilt direction, and the tilt directions of the three sensing fiber optic gratings are determined: the angle between FBG1 and the initial zero-position reference for the tilt direction is 0°, i.e. The angle between FBG2 and the initial zero-position reference in the tilt direction is 120°, that is... The angle between FBG3 and the initial zero-position reference in the tilt direction is -120°, that is... ; The sensor plane is divided into six regions with a span of 60° each. Starting from FBG1, the regions are rotated counterclockwise, and the ranges of each 60° span are region A, region B, region C, region D, region E, and region F, respectively. Under constant ambient temperature, the change in center wavelength of the sensing fiber grating is negative when it is compressed and positive when it is stretched. The center wavelength changes of the three sensing fiber gratings are dynamically sorted from smallest to largest. The sensing fiber grating with the smallest wavelength change is the dominant grating, the sensing fiber grating with the second smallest wavelength change is the first auxiliary grating, and the sensing fiber grating with the largest wavelength change is the second auxiliary grating. Among them, the mass sphere exerts the greatest pressure on the dominant grating, and the projection of the mass sphere's gravity direction onto the sensor plane is closest to the dominant grating; the angle between the projection of the mass sphere's gravity onto the sensor plane and the dominant grating is the local tilt angle direction. ,when The value is positive when the dominant grating rotates counterclockwise from 0° to 60°. Negative values ​​are taken within the clockwise range of 0° to 60° of the dominant grating; based on the local tilt angle direction. In the area where it is located, calculate the dip direction. value.

[0008] Preferably, in step S3, the temperature self-compensation processing includes: since the three sensing fiber gratings are in the same temperature environment and are made of the same material, their temperature sensitivity coefficients... Consistent, the temperature effect is eliminated by subtracting the changes in center wavelength pairwise:

[0009] In formula (0), The initial center wavelength of the sensing fiber optic grating; The strain sensitivity coefficient of the fiber optic grating is used for sensing. The Young's modulus of the sensing fiber optic grating; The radius of the sensing fiber optic grating cross section; This is the difference between the center wavelength change of FBG1 and the center wavelength change of FBG2. This is the difference between the center wavelength change of FBG1 and the center wavelength change of FBG3. This is the difference between the center wavelength change of FBG2 and the center wavelength change of FBG3. This is compared to the change in the center wavelength of FBG1 when the sensor tilt angle is 0°. This is compared to the change in the center wavelength of FBG2 when the sensor tilt angle is 0°. This is the change in the center wavelength of FBG3 compared to when the sensor tilt angle is 0°; The axial tensile force of FBG1, The axial tensile force of FBG2 This refers to the axial tensile force of FBG3.

[0010] Preferably, the horizontal zero-tilt condition includes: the center wavelength changes of FBG1, FBG2, and FBG3 satisfying At this time, the tilt angle of the sensor is 0°, the sensor is placed horizontally, and there is no tilt direction.

[0011] Preferably, the measurement conditions for the six tilt directions include: Condition A: The center wavelength changes of FBG1, FBG2, and FBG3 satisfy... Then, using FBG1 as the dominant grating, FBG2 as the first auxiliary grating, and FBG3 as the second auxiliary grating, the local tilt direction is determined. Located in area A; The static modeling and solution are as follows: The components of the mass sphere's gravity in the sensor plane satisfy the following equation: ; ; In formulas (1) and (2), Let be the component of the mass sphere's gravity on the sensor plane. For the mass of the ball, For local gravitational acceleration, For the mass of the sphere material, Let the mass of the sphere be the volume. Let be the radius of the mass sphere. For the sensor tilt angle, Decomposed into the parallel and perpendicular directions of the dominant grating, we obtain: ; In formula (3), for The component in the direction parallel to the dominant grating for The component in the vertical direction of the dominant grating The direction of the local tilt angle; in the sensor, the sensing fiber grating is always in a straight state, and the displacement of the mass sphere during the tilting process is negligible relative to the size of the entire sensor and the mass sphere. Therefore, the force direction of each sensing fiber grating is along its initial arrangement direction, thus establishing a static equilibrium model: ; ; Substituting formula (3) into formulas (4) and (5) respectively, and dividing formula (5) by formula (4) to obtain the local tilt direction. : ; As can be determined by the tilt direction, the tilt direction is the sum of the local tilt direction and the position of the dominant grating in the corresponding tilt direction: ; Substituting formula (0) into formulas (6) and (7), the local tilt direction is calculated. ; This is the difference between the center wavelength change of FBG3 and the center wavelength change of FBG2. This is the difference between the center wavelength change of FBG2 and the center wavelength change of FBG1. This is the difference between the center wavelength change of FBG3 and the center wavelength change of FBG1. Inclination direction ; From formulas (3), (4), and (5), we get: ; By taking the square root of both sides of the equation, rearranging the terms, and taking the arcsine of both sides, we obtain the angle of inclination: ; Substituting formula (0) into formula (9), the inclination angle is obtained. ; Condition B: The center wavelength changes of FBG1, FBG2, and FBG3 satisfy... Then, using FBG2 as the dominant grating, FBG1 as the first auxiliary grating, and FBG3 as the second auxiliary grating, the local tilt direction is determined. Located in region B; the static modeling and solution steps are the same as for case A; the local tilt direction is obtained from the solution. , Inclination direction ;inclination ; Condition C: The center wavelength changes of FBG1, FBG2, and FBG3 satisfy... Then, using FBG2 as the dominant grating, FBG3 as the first auxiliary grating, and FBG1 as the second auxiliary grating, the local tilt direction is determined. Located in region C; the static modeling and solution steps are the same as for case A; the local tilt direction is obtained from the solution. , Inclination direction ;inclination ; Condition D: The center wavelength changes of FBG1, FBG2, and FBG3 satisfy... Then, using FBG3 as the dominant grating, FBG2 as the first auxiliary grating, and FBG1 as the second auxiliary grating, the local tilt direction is determined. Located in region D; the static modeling and solution steps are the same as for case A; the local tilt direction is obtained from the solution. , Inclination direction ;inclination ; Operating condition E: The center wavelength changes of FBG1, FBG2, and FBG3 satisfy... Then, using FBG3 as the dominant grating, FBG1 as the first auxiliary grating, and FBG2 as the second auxiliary grating, the local tilt direction is determined. Located in region E; the static modeling and solution steps are the same as for case A; the local tilt direction is obtained from the solution. , Inclination direction ;inclination ; Condition F: The center wavelength changes of FBG1, FBG2, and FBG3 satisfy... Then, using FBG1 as the dominant grating, FBG3 as the first auxiliary grating, and FBG2 as the second auxiliary grating, the local tilt direction is determined. Located in region F; the static modeling and solution steps are the same as for case A; the local tilt direction is obtained from the solution. , Inclination direction ;inclination .

[0012] Preferably, the six critical operating conditions at the regional boundaries include: Operating condition a: The center wavelength changes of FBG1, FBG2, and FBG3 satisfy... FBG1 is used as the dominant grating, and FBG2 and FBG3 are used as auxiliary gratings; the local tilt direction is determined. Located on the boundary line between region F and region A, i.e., in the direction of the dip angle. 0°; Static modeling to solve for the tilt angle The procedure is the same as in condition A; tilt angle ; Condition b: The center wavelength changes of FBG1, FBG2, and FBG3 satisfy... FBG1 and FBG2 are used as the dominant gratings, and FBG3 is used as the auxiliary grating; the local tilt direction is determined. Located on the boundary line between region A and region B, i.e., in the direction of the dip angle. The angle is 60°; static modeling is used to solve the tilt angle. The procedure is the same as in condition A; tilt angle ; c. Operating condition: The center wavelength changes of FBG1, FBG2, and FBG3 satisfy... FBG2 is used as the dominant grating, and FBG3 and FBG1 are used as auxiliary gratings; the local tilt direction is determined. Located on the boundary line between region B and region C, i.e., in the direction of the dip angle. The angle is 120°; static modeling is used to solve the tilt angle. The procedure is the same as in condition A; tilt angle ; Operating condition d: The center wavelength changes of FBG1, FBG2, and FBG3 satisfy... FBG2 and FBG3 are used as the dominant gratings, and FBG1 is used as the auxiliary grating; the local tilt direction is determined. Located on the boundary line between region C and region D, i.e., in the direction of the dip angle. 180°; Static modeling to solve for the tilt angle The procedure is the same as in condition A; tilt angle ; e-condition: The center wavelength changes of FBG1, FBG2, and FBG3 satisfy... FBG3 is used as the dominant grating, and FBG1 and FBG2 are used as auxiliary gratings; the local tilt direction is determined. Located on the boundary line between region D and region E; i.e., in the direction of the dip angle. -120°; Static modeling to calculate the tilt angle The procedure is the same as in condition A; tilt angle ; Operating condition f: The center wavelength changes of FBG1, FBG2, and FBG3 satisfy... FBG1 and FBG3 are used as the dominant gratings, and FBG2 is used as the auxiliary grating; the local tilt direction is determined. Located on the boundary line between region E and region F, i.e., in the dip direction. -60°; Static modeling to calculate the tilt angle The procedure is the same as in condition A; tilt angle .

[0013] Beneficial effects of this invention: a. It possesses security features and strong anti-interference capabilities.

[0014] This invention reflects the static equilibrium state of a mass sphere under different tilt angles and tilt directions by monitoring the strain changes of a sensing fiber optic grating. The sensor device is a completely passive structure, possessing excellent resistance to electromagnetic interference and environmental corrosion. It can achieve long-term online monitoring of the tilt state of the measured component throughout its entire life cycle, without any safety hazards such as leakage or short circuits, resulting in higher overall safety for the monitoring operation.

[0015] b. It has a large measurement range and the measurement accuracy can be flexibly adjusted.

[0016] This invention arranges three sensing fiber Bragg gratings in a centrally symmetrical manner with equal angles. The tilt angle measurement range is [0°, 90°], and the tilt direction measurement range covers [-180°, 180°], enabling comprehensive monitoring of various tilt postures of the measured plane. Furthermore, the magnitude of the axial strain of the sensing fiber Bragg grating corresponding to a unit angle can be adjusted by modifying the material and geometry of the mass sphere, thereby achieving on-demand adaptation of measurement accuracy to meet the accuracy requirements under different working conditions.

[0017] c. Fast response speed, no measurement hysteresis.

[0018] This invention utilizes the gravitational component of a mass sphere to generate an axial force on a sensing fiber optic grating. By monitoring the change in the center wavelength of the grating, the axial strain of the grating is obtained, leading to the tilt angle and tilt direction of the measured plane. This invention features a simple structure with no redundant mechanical transmission devices and a concise sensing link, resulting in rapid sensor signal response and no measurement lag during the monitoring process.

[0019] d. It has strong environmental adaptability, flexible installation methods, and a wide range of applications.

[0020] This invention employs a small, sealed cavity structure, isolating the core sensing components from the external environment. It can be directly mounted on the surface of the component being measured or pre-embedded within prefabricated components, significantly improving the reliability and survivability of the sensor in construction scenarios. The product boasts strong environmental adaptability, enabling real-time tilt angle monitoring in various complex working conditions and environments, and has a wide range of applications.

[0021] e. Effectively solves the problem of cross-sensitivity to temperature strain.

[0022] This invention employs three sets of centrally symmetrically arranged sensing fiber Bragg gratings. By performing pairwise difference operations on the wavelength changes of each sensing fiber Bragg grating, the center wavelength drift interference caused by ambient temperature can be offset. This scheme eliminates the need for an additional temperature-compensated reference grating, simplifying the overall structure of the sensing system and effectively reducing equipment operating costs. Attached Figure Description

[0023] The accompanying drawings, which are provided to further illustrate the invention and constitute a part of this invention, are illustrative embodiments of the invention and their descriptions are used to explain the invention and do not constitute an undue limitation of the invention.

[0024] Figure 1 This is a front view of the structure of a two-dimensional fiber optic grating tilt sensor according to the present invention; Figure 2 This is a three-dimensional schematic diagram of the internal structure of a two-dimensional fiber optic tilt sensor according to the present invention; Figure 3 This is a three-dimensional schematic diagram of the overall structure of a two-dimensional fiber optic tilt sensor according to the present invention; Figure 4 This is a schematic diagram of the planar region division and tilt direction, and local tilt direction of a two-dimensional fiber optic tilt sensor according to the present invention; Figure 5 This is a schematic diagram of the tilt angle of a two-dimensional fiber optic grating tilt sensor according to the present invention; Figure 6 This is a schematic diagram of the static equilibrium force of a two-dimensional fiber optic tilt sensor according to the present invention.

[0025] Attached image captions: 1-Fiber optic loose tube, 2-Fiber optic fixing base, 3-Assembly screw hole, 4-Sensing fiber optic grating, 5-Mass sphere, 6-Annular base, 7-Arc-shaped step assembly mating surface, 8-Annular protective shell. Detailed Implementation

[0026] This section will describe in detail specific embodiments of the present invention. Preferred embodiments of the present invention are shown in the accompanying drawings. The purpose of the drawings is to supplement the textual description with graphics, so that people can intuitively and vividly understand each technical feature and overall technical solution of the present invention, but they should not be construed as limiting the scope of protection of the present invention.

[0027] In the description of this invention, it should be understood that the orientation descriptions, such as up, down, front, back, left, right, etc., are based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing this invention and simplifying the description, and do not indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limiting this invention.

[0028] In the description of this invention, "several" means one or more, "more than" means two or more, "greater than," "less than," and "exceeding" are understood to exclude the stated number, while "above," "below," and "within" are understood to include the stated number. The use of "first" and "second" in the description is merely for distinguishing technical features and should not be construed as indicating or implying relative importance, or implicitly indicating the number of indicated technical features, or implicitly indicating the order of the indicated technical features.

[0029] In the description of this invention, unless otherwise explicitly defined, terms such as "set up," "install," and "connect" should be interpreted broadly, and those skilled in the art can reasonably determine the specific meaning of the above terms in this invention in conjunction with the specific content of the technical solution.

[0030] Reference Figure 1 , Figure 2 , Figure 3 As shown, the present invention discloses a two-dimensional fiber optic tilt sensor, which consists of an annular base 6, an arc-shaped stepped assembly and bonding surface 7, an annular protective shell 8, three sensing fiber optic gratings 4, a mass sphere 5, an optical fiber fixing seat 2, and an optical fiber loose tube 1.

[0031] Optical fiber fixing seats 2 are fixedly installed on the annular base 6 at 120° equal angular intervals, that is, the optical fiber fixing seats 2 are fixedly distributed at the edges of the annular base 6 in the 0°, 120° and -120° directions; small holes for optical fiber pigtails to pass through are opened on the three optical fiber fixing seats 2 along the radial direction of the annular base 6. A mass sphere 5 is positioned at the center of an annular base 6. Three equal-length sensing fiber gratings 4 with the same center wavelength are fixed at both ends on the surface of the mass sphere 5 and the fiber optic mounting base 2, respectively. The three sensing fiber gratings 4 are symmetrically distributed in a trident shape at equal angles of 120°, and all are pre-tensioned with the same preload to bear the gravitational components of the mass sphere 5 in each direction on the plane of the sensing fiber gratings 4 when tilting occurs. The pigtails of the three sensing fiber gratings 4 pass through the annular base 6 through the small holes opened in the fiber optic mounting base 2. The pigtails of the sensing fiber gratings 4 are protected by fiber optic loose tubes 1, coated with glue, cured, and led out. The outer ring of the upper end face of the ring base 6 is provided with an arc-shaped step assembly and bonding surface 7. The arc-shaped step assembly and bonding surface 7 is located between every two fiber optic fixing seats 2. At the same time, each fiber optic fixing seat 2 is provided with an assembly screw hole 3. The outer contour of the annular protective shell 8 matches the outer contour of the annular base 6; the annular protective shell 8 has through holes at the positions of each mounting screw hole 3. During assembly, the annular protective shell 8 is covered on the upper end face of the annular base 6, and the lower end face of the annular protective shell 8 is pressed onto the arc-shaped step mounting and fitting surface 7 of the annular base 6 to achieve assembly. After the mounting screw holes 3 are aligned with the through holes on the annular protective shell 8, locking bolts are inserted to fasten and lock the annular protective shell 8 and the annular base 6. Specifically, the annular protective shell 8 and the annular base 6 are assembled to form a cylindrical shell, and the interior of the cylindrical shell is a sealed protective cavity. The mass sphere 5 and three sensing fiber optic gratings 4 form a sensing structure and are set inside the sealed protective cavity. The cylindrical shell can protect the internal sensing structure and isolate it from external environmental interference.

[0032] This invention also provides a method for calculating the tilt angle of a two-dimensional fiber optic grating tilt sensor. Using the aforementioned two-dimensional fiber optic grating tilt sensor, the steps for calculating the tilt angle and tilt direction of the sensor are as follows: S1. Place the sensors horizontally to monitor and record the initial center wavelength of each sensing fiber optic grating 4. ; S2. Collect the change in the center wavelength of the three sensing fiber optic gratings 4; When the sensor is tilted, the mass ball 5 is in a state of force equilibrium. The component of the gravity of the mass ball 5 on the sensor plane and the resultant force of the axial tension of the three sensing fiber optic gratings 4 are zero. The change in the axial tension of the sensing fiber optic gratings 4 causes the sensing fiber optic gratings 4 to generate axial strain. The change in the center wavelength of the three sensing fiber optic gratings 4 under the axial strain is collected in real time. S3. Perform temperature self-compensation processing on the center wavelength changes of the three sensing fiber optic gratings 4. The three sensing fiber gratings 4 are in the same temperature field and have the same temperature sensitivity coefficient. The pairwise difference operation is performed on the change in the center wavelength of the three sensing fiber gratings 4 to completely eliminate the wavelength drift introduced by the ambient temperature. S4. Determining the direction of the tilt angle; The three sensing fiber optic gratings 4 are sorted in ascending order of the center wavelength change from smallest to largest. The sensing fiber optic grating 4 with the smallest wavelength change value is defined as the dominant grating, and the other two are designated as the first auxiliary grating and the second auxiliary grating in ascending order of the center wavelength change value. Based on the relationship between the three values, the tilt direction is divided into the horizontal zero tilt direction working condition, the 6 tilt direction zone measurement working conditions, and the 6 regional boundary critical working conditions. S5. Solve the tilt direction and tilt angle of the sensor using static modeling; Static modeling and solution: Based on the component of gravity of mass sphere 5 in the sensor plane, a planar static equilibrium equation is constructed. Gravity is bidirectionally decomposed along the parallel and perpendicular directions of the dominant grating. Based on the differential result of the center wavelength change of sensing fiber optic grating 4, a system of equations is established to first calculate the local tilt direction. The tilt direction is then obtained by superimposing the local tilt direction with the fixed placement angle of the dominant grating. Finally, by simultaneously solving the two sets of force equilibrium equations, the tilt angle of the sensor plane can be obtained.

[0033] Figure 4 , Figure 5 , Figure 6 As shown, Figure 4 This is a schematic diagram of the planar region division and tilt direction, and local tilt direction of a two-dimensional fiber optic tilt sensor according to the present invention. Figure 5 , Figure 6 This invention provides a schematic diagram of the tilt angle and static equilibrium forces during the operation of a two-dimensional fiber Bragg grating tilt sensor. The plane containing the three sensing fiber Bragg gratings 4 is denoted as the sensor plane. The three sensing fiber Bragg gratings 4 are labeled FBG1, FBG2, and FBG3 in counterclockwise order, respectively. The angle between the projection of the gravity direction of the mass sphere 5 onto the sensor plane and FBG1 is the tilt angle direction. On the sensor plane, when When FBG1 rotates counterclockwise within the range of 0° to 180°, it takes a positive value. The value is negative when FBG1 rotates clockwise from 0° to 180°; the angle between the sensor plane and the horizontal plane is the tilt angle. ; On the sensor plane, the radial direction of FBG1 is selected as the initial zero-position reference for the tilt direction, and the tilt direction of the three sensing fiber optic gratings 4 is determined: the angle between FBG1 and the initial zero-position reference for the tilt direction is 0°, i.e. The angle between FBG2 and the initial zero-position reference in the tilt direction is 120°, that is... The angle between FBG3 and the initial zero-position reference in the tilt direction is -120°, that is... ; The tilt direction region within the sensor plane is determined as follows: The sensor plane is divided into six regions with a span of 60° each. Starting from FBG1, rotate counterclockwise and define each 60° span as region A, region B, region C, region D, region E, and region F. When the ambient temperature remains constant, the change in center wavelength of the sensing fiber grating 4 is negative when it is compressed and positive when it is stretched. The changes in center wavelength of the three sensing fiber gratings 4 are dynamically sorted from smallest to largest. The sensing fiber grating 4 with the smallest change in wavelength is the dominant grating, the sensing fiber grating 4 with the second smallest change in wavelength is the first auxiliary grating, and the sensing fiber grating 4 with the largest change in wavelength is the second auxiliary grating. Among them, mass sphere 5 exerts the greatest pressure on the dominant grating, and the projection of the gravity direction of mass sphere 5 onto the sensor plane is closest to the dominant grating; the angle between the projection of the gravity of mass sphere 5 onto the sensor plane and the dominant grating is the local tilt angle direction. ;when The value is positive when the dominant grating rotates counterclockwise from 0° to 60°. Negative values ​​are taken within the clockwise range of 0° to 60° of the dominant grating; based on the local tilt angle direction. In the area where it is located, calculate the dip direction. value.

[0034] The temperature self-compensation processing in step S3 includes: since the three sensing fiber gratings 4 are in the same temperature environment and are made of the same material, their temperature sensitivity coefficients... Consistent, the temperature effect is eliminated by subtracting the changes in center wavelength pairwise:

[0035] In formula (0), The initial center wavelength of sensing fiber optic grating 4; The strain sensitivity coefficient of the fiber Bragg grating 4; The Young's modulus of the sensing fiber grating 4; The radius of the sensing fiber optic grating is 4. This is the difference between the center wavelength change of FBG1 and the center wavelength change of FBG2. This is the difference between the center wavelength change of FBG1 and the center wavelength change of FBG3. This is the difference between the center wavelength change of FBG2 and the center wavelength change of FBG3. This is compared to the change in the center wavelength of FBG1 when the sensor tilt angle is 0°. This is compared to the change in the center wavelength of FBG2 when the sensor tilt angle is 0°. This is the change in the center wavelength of FBG3 compared to when the sensor tilt angle is 0°; The axial tensile force of FBG1, The axial tensile force of FBG2 This refers to the axial tensile force of FBG3.

[0036] Furthermore, the horizontal zero-tilt condition includes: the center wavelength changes of FBG1, FBG2, and FBG3 satisfying... At this time, the tilt angle of the sensor is 0°, the sensor is placed horizontally, and there is no tilt direction.

[0037] Furthermore, the measurement conditions for the six tilt directions include: Condition A: The center wavelength changes of FBG1, FBG2, and FBG3 satisfy... Then, using FBG1 as the dominant grating, FBG2 as the first auxiliary grating, and FBG3 as the second auxiliary grating, the local tilt direction is determined. Located in area A; The static modeling and solution are as follows: The components of the gravity of mass sphere 5 in the sensor plane satisfy the following equation:

[0038]

[0039] In formulas (1) and (2), Let be the component of the gravitational force on mass sphere 5 in the sensor plane. For a mass sphere of mass 5, For local gravitational acceleration, For mass sphere 5, the material density is... For a mass sphere with a volume of 5, For a mass sphere with a radius of 5, For the sensor tilt angle, Decomposed into the parallel and perpendicular directions of the dominant grating, we obtain:

[0040] In formula (3), for The component in the direction parallel to the dominant grating for The component in the vertical direction of the dominant grating The direction of the local tilt angle; in the sensor, the sensing fiber grating 4 is always in a straight state, and the displacement of the mass sphere 5 during the tilting process is negligible relative to the size of the entire sensor and the mass sphere 5. Therefore, the force direction of each sensing fiber grating 4 is along its initial arrangement direction, thus establishing a static equilibrium model:

[0041]

[0042] Substituting formula (3) into formulas (4) and (5) respectively, and dividing formula (5) by formula (4) to obtain the local tilt direction. :

[0043] As can be determined by the tilt direction, the tilt direction is the sum of the local tilt direction and the position of the dominant grating in the corresponding tilt direction:

[0044] Substituting formula (0) into formulas (6) and (7), the local tilt direction is calculated. ; This is the difference between the center wavelength change of FBG3 and the center wavelength change of FBG2. This is the difference between the center wavelength change of FBG2 and the center wavelength change of FBG1. This is the difference between the center wavelength change of FBG3 and the center wavelength change of FBG1. Inclination direction ; From formulas (3), (4), and (5), we get:

[0045] By taking the square root of both sides of the equation, rearranging the terms, and taking the arcsine of both sides, we obtain the angle of inclination:

[0046] Substituting formula (0) into formula (9), the inclination angle is obtained. ; Condition B: The center wavelength changes of FBG1, FBG2, and FBG3 satisfy... Then, using FBG2 as the dominant grating, FBG1 as the first auxiliary grating, and FBG3 as the second auxiliary grating, the local tilt direction is determined. Located in region B; the static modeling and solution steps are the same as for case A; the local tilt direction is obtained from the solution. , Inclination direction ;inclination ; Condition C: The center wavelength changes of FBG1, FBG2, and FBG3 satisfy... Then, using FBG2 as the dominant grating, FBG3 as the first auxiliary grating, and FBG1 as the second auxiliary grating, the local tilt direction is determined. Located in region C; the static modeling and solution steps are the same as for case A; the local tilt direction is obtained from the solution. , Inclination direction ;inclination ; Condition D: The center wavelength changes of FBG1, FBG2, and FBG3 satisfy... Then, using FBG3 as the dominant grating, FBG2 as the first auxiliary grating, and FBG1 as the second auxiliary grating, the local tilt direction is determined. Located in region D; the static modeling and solution steps are the same as for case A; the local tilt direction is obtained from the solution. , Inclination direction ;inclination ; Operating condition E: The center wavelength changes of FBG1, FBG2, and FBG3 satisfy... Then, using FBG3 as the dominant grating, FBG1 as the first auxiliary grating, and FBG2 as the second auxiliary grating, the local tilt direction is determined. Located in region E; the static modeling and solution steps are the same as for case A; the local tilt direction is obtained from the solution. , Inclination direction ;inclination ; Condition F: The center wavelength changes of FBG1, FBG2, and FBG3 satisfy... Then, using FBG1 as the dominant grating, FBG3 as the first auxiliary grating, and FBG2 as the second auxiliary grating, the local tilt direction is determined. Located in region F; the static modeling and solution steps are the same as for case A; the local tilt direction is obtained from the solution. , Inclination direction ;inclination .

[0047] Furthermore, the six critical operating conditions at regional boundaries include: Operating condition a: The center wavelength changes of FBG1, FBG2, and FBG3 satisfy... FBG1 is used as the dominant grating, and FBG2 and FBG3 are used as auxiliary gratings; the local tilt direction is determined. Located on the boundary line between region F and region A, i.e., in the direction of the dip angle. 0°; Static modeling to solve for the tilt angle The procedure is the same as in condition A; tilt angle ; Condition b: The center wavelength changes of FBG1, FBG2, and FBG3 satisfy... FBG1 and FBG2 are used as the dominant gratings, and FBG3 is used as the auxiliary grating; the local tilt direction is determined. Located on the boundary line between region A and region B, i.e., in the direction of the dip angle. The angle is 60°; static modeling is used to solve the tilt angle. The procedure is the same as in condition A; tilt angle ; c. Operating condition: The center wavelength changes of FBG1, FBG2, and FBG3 satisfy... FBG2 is used as the dominant grating, and FBG3 and FBG1 are used as auxiliary gratings; the local tilt direction is determined. Located on the boundary line between region B and region C, i.e., in the direction of the dip angle. The angle is 120°; static modeling is used to solve the tilt angle. The procedure is the same as in condition A; tilt angle ; Operating condition d: The center wavelength changes of FBG1, FBG2, and FBG3 satisfy... FBG2 and FBG3 are used as the dominant gratings, and FBG1 is used as the auxiliary grating; the local tilt direction is determined. Located on the boundary line between region C and region D, i.e., in the direction of the dip angle. 180°; Static modeling to solve for the tilt angle The procedure is the same as in condition A; tilt angle ; e-condition: The center wavelength changes of FBG1, FBG2, and FBG3 satisfy... FBG3 is used as the dominant grating, and FBG1 and FBG2 are used as auxiliary gratings; the local tilt direction is determined. Located on the boundary line between region D and region E; i.e., in the direction of the dip angle. -120°; Static modeling to calculate the tilt angle The procedure is the same as in condition A; tilt angle ; Operating condition f: The center wavelength changes of FBG1, FBG2, and FBG3 satisfy... FBG1 and FBG3 are used as the dominant gratings, and FBG2 is used as the auxiliary grating; the local tilt direction is determined. Located on the boundary line between region E and region F, i.e., in the dip direction. -60°; Static modeling to calculate the tilt angle The procedure is the same as in condition A; tilt angle .

[0048] Furthermore, the change in the center wavelength of the sensing fiber optic grating 4 in this invention The calculation method is as follows:

[0049] in, This represents the change in the center wavelength of the sensing fiber optic grating 4. The effective elastic coefficient of the sensing fiber grating 4. To sense the four-axis strain of the fiber Bragg grating. The initial center wavelength of sensing fiber optic grating 4 is given. is the coefficient of thermal expansion of the sensing fiber grating 4. The thermo-optic coefficient of sensing fiber grating 4. This refers to the change in ambient temperature. The axial strain of the three sensing fiber gratings 4 satisfies the following relationship:

[0050] in, For sensing the 4-axis tensile force of the fiber Bragg grating, The Young's modulus of the sensing fiber grating 4. This represents the net cross-sectional area of ​​the sensing fiber optic grating 4. The radius of the sensing fiber optic grating is 4. Let the strain sensitivity coefficient of the fiber optic grating 4 be Temperature sensitivity coefficient is Substituting formula (10) into formula (11) yields formula (12);

[0051] Under constant ambient temperature, when the sensing fiber optic grating 4 is subjected to pressure, When the sensing fiber grating 4 is under tension, ; The aforementioned algorithm fully covers all operating conditions of the sensor at zero horizontal tilt, six tilt direction zones, and six regional boundary critical lines. It distinguishes measurement scenarios solely by numerically sorting the four wavelength changes of the three sensing fiber optic gratings, without requiring switching between temperature compensation and mechanical solution models throughout the process. It can simultaneously achieve full-range calculations for tilt directions [-180°, 180°] and tilt directions [0°, 90°].

[0052] Without causing conflict, those skilled in the art can freely combine and use the above-mentioned additional technical features.

[0053] The above description is only a preferred embodiment of the present invention. Any technical solution that achieves the purpose of the present invention by essentially the same means is within the protection scope of the present invention.

Claims

1. A two-dimensional fiber Bragg grating tilt sensor, characterized in that: The sensor includes an annular base, a mass sphere, three sensing fiber optic gratings, a fiber optic fixing base, and a fiber optic loose tube. Optical fiber fixing seats are fixedly installed on the annular base at 120° angular intervals, that is, the optical fiber fixing seats are fixedly distributed at the edges of the annular base in the 0°, 120° and -120° directions; small holes for optical fiber pigtails to pass through are opened on the three optical fiber fixing seats along the radial direction of the annular base. The mass sphere is positioned at the center of the annular base. The two ends of three equal-length sensing fiber gratings with the same center wavelength are fixed to the surface of the mass sphere and the fiber optic mounting base, respectively. The three sensing fiber gratings are symmetrically distributed in a trident shape at equal angles of 120°, and all are pre-stressed with the same pre-tension force to bear the gravitational components of the mass sphere in each direction in the plane where the sensing fiber grating is located when tilting occurs. The pigtails of the three sensing fiber optic gratings pass through the small holes in the fiber optic fixing base and exit the annular base. The pigtails of the sensing fiber optic gratings are protected by fiber optic loose tubes, coated with glue and cured before being led out. The sensor also includes an annular protective shell. The outer ring of the upper end face of the annular base is provided with an arc-shaped stepped assembly and bonding surface. The arc-shaped stepped assembly and bonding surface is located between every two fiber optic fixing seats. At the same time, each fiber optic fixing seat is provided with an assembly screw hole. The outer contour of the annular protective shell matches the outer contour of the annular base; the annular protective shell has through holes corresponding to the positions of each mounting screw hole; the annular protective shell covers the upper end face of the annular base; the lower end face of the annular protective shell is pressed against the arc-shaped step mounting surface of the annular base to achieve assembly; after the mounting screw holes are aligned with the through holes on the annular protective shell, locking bolts are inserted to fasten and lock the annular protective shell and the annular base, forming a sealed protective cavity.

2. A method for calculating the tilt angle of a two-dimensional fiber optic grating sensor, characterized in that: Using the two-dimensional fiber optic grating tilt sensor as described in claim 1, the method for calculating the tilt angle and tilt direction of the sensor includes the following steps: S1. Place the sensors horizontally to monitor and record the initial center wavelength of each sensing fiber optic grating. ; S2. Collect the change in the center wavelength of the three sensing fiber optic gratings; When the sensor is tilted, the mass ball is in a state of force equilibrium. The resultant force of the component of the mass ball's gravity on the sensor plane and the axial tension of the three sensing fiber optic gratings is zero. The change in axial tension of the sensing fiber grating causes axial strain in the sensing fiber grating, and the change in the center wavelength of the three sensing fiber gratings under axial strain is collected in real time. S3. Perform temperature self-compensation processing on the collected changes in the center wavelength of the three sensing fiber optic gratings. The three sensing fiber gratings are in the same temperature field and have the same temperature sensitivity coefficient. The pairwise difference operation is performed on the change in the center wavelength of the three sensing fiber gratings to completely eliminate the wavelength drift introduced by the ambient temperature. S4. Determining the direction of the tilt angle; The three sensing fiber optic gratings are sorted in ascending order of their center wavelength changes, with the one with the smallest wavelength change value defined as the dominant grating. The other two are designated as the first and second auxiliary gratings, respectively, in ascending order of their center wavelength changes. Based on the relationship between the three values, the tilt direction is divided into a horizontal zero tilt direction, six tilt direction zone measurement conditions, and six regional boundary critical conditions. S5. Solve the tilt direction and tilt angle of the sensor using static modeling; Static modeling and solution: Based on the component of gravity of the mass sphere in the sensor plane, a planar static equilibrium equation is constructed. Gravity is bidirectionally decomposed along the directions parallel and perpendicular to the dominant grating. Based on the differential result of the change in the center wavelength of the sensing fiber optic grating, a system of equations is solved to first determine the local tilt direction. The tilt direction is then obtained by superimposing the local tilt direction with the fixed placement angle of the dominant grating. Finally, by simultaneously solving the two sets of force equilibrium equations, the tilt angle of the sensor plane can be obtained.

3. The solution method according to claim 2, characterized in that: In step S4, the sensor tilt direction region is determined as follows: The plane containing the three sensing fiber Bragg gratings is denoted as the sensor plane. The three sensing fiber Bragg gratings are labeled FBG1, FBG2, and FBG3 in counterclockwise order, respectively. The angle between the projection of the mass sphere's gravitational force onto the sensor plane and FBG1 is the tilt angle direction. On the sensor plane, when When FBG1 rotates counterclockwise within the range of 0° to 180°, it takes a positive value. The value is negative when FBG1 rotates clockwise from 0° to 180°; the angle between the sensor plane and the horizontal plane is the tilt angle. ; On the sensor plane, the radial direction of FBG1 is selected as the initial zero-position reference for the tilt direction, and the tilt directions of the three sensing fiber optic gratings are determined: the angle between FBG1 and the initial zero-position reference for the tilt direction is 0°, i.e. The angle between FBG2 and the initial zero-position reference in the tilt direction is 120°, that is... The angle between FBG3 and the initial zero-position reference in the tilt direction is -120°, that is... ; The sensor plane is divided into six regions with a span of 60° each. Starting from FBG1, the regions are rotated counterclockwise, and the ranges of each 60° span are region A, region B, region C, region D, region E, and region F, respectively. Under constant ambient temperature, the change in center wavelength of the sensing fiber grating is negative when it is compressed and positive when it is stretched. The center wavelength changes of the three sensing fiber gratings are dynamically sorted from smallest to largest. The sensing fiber grating with the smallest wavelength change is the dominant grating, the sensing fiber grating with the second smallest wavelength change is the first auxiliary grating, and the sensing fiber grating with the largest wavelength change is the second auxiliary grating. Among them, the mass sphere exerts the greatest pressure on the dominant grating, and the projection of the mass sphere's gravity direction onto the sensor plane is closest to the dominant grating; the angle between the projection of the mass sphere's gravity onto the sensor plane and the dominant grating is the local tilt angle direction. ,when The value is positive when the dominant grating rotates counterclockwise from 0° to 60°. Negative values ​​are taken within the clockwise range of 0° to 60° of the dominant grating; based on the local tilt angle direction. The region in which the dip angle is calculated. value.

4. The solution method according to claim 3, characterized in that: In step S3, the temperature self-compensation processing includes: since the three sensing fiber optic gratings are in the same temperature environment and are made of the same material, their temperature sensitivity coefficients... Consistent, the temperature effect is eliminated by subtracting the changes in center wavelength pairwise: ； In formula (0), The initial center wavelength of the sensing fiber optic grating; The strain sensitivity coefficient of the fiber optic grating; The Young's modulus of the sensing fiber optic grating; The radius of the sensing fiber optic grating cross section; This is the difference between the center wavelength change of FBG1 and the center wavelength change of FBG2. This is the difference between the center wavelength change of FBG1 and the center wavelength change of FBG3. This is the difference between the center wavelength change of FBG2 and the center wavelength change of FBG3. This is compared to the change in the center wavelength of FBG1 when the sensor tilt angle is 0°. This is compared to the change in the center wavelength of FBG2 when the sensor tilt angle is 0°. This is the change in the center wavelength of FBG3 compared to when the sensor tilt angle is 0°; The axial tensile force of FBG1, The axial tensile force of FBG2 This refers to the axial tensile force of FBG3.

5. The solution method according to claim 4, characterized in that: The horizontal zero-tilt condition includes: the center wavelength changes of FBG1, FBG2, and FBG3 satisfying the following conditions. At this time, the tilt angle of the sensor is 0°, the sensor is placed horizontally, and there is no tilt direction.

6. The solution method according to claim 4, characterized in that: The six tilt direction zone measurement conditions include: Condition A: The center wavelength changes of FBG1, FBG2, and FBG3 satisfy... Then, using FBG1 as the dominant grating, FBG2 as the first auxiliary grating, and FBG3 as the second auxiliary grating, the local tilt direction is determined. Located in area A; The static modeling and solution are as follows: The components of the mass sphere's gravity in the sensor plane satisfy the following equation: ； ； In formulas (1) and (2), Let be the component of the mass sphere's gravity on the sensor plane. For the mass of the ball, For local gravitational acceleration, For the mass of the sphere material, Let the mass of the sphere be the volume. Let be the radius of the mass sphere. For the sensor tilt angle, Decomposed into the parallel and perpendicular directions of the dominant grating, we obtain: ； In formula (3), for The component in the direction parallel to the dominant grating for The component in the vertical direction of the dominant grating The direction of the local tilt angle; in the sensor, the sensing fiber grating is always in a straight state, and the displacement of the mass sphere during the tilting process is negligible relative to the size of the entire sensor and the mass sphere. Therefore, the force direction of each sensing fiber grating is along its initial arrangement direction, thus establishing a static equilibrium model: ； ； Substituting formula (3) into formulas (4) and (5) respectively, and dividing formula (5) by formula (4) to obtain the local tilt direction. : ； As can be determined by the tilt direction, the tilt direction is the sum of the local tilt direction and the position of the dominant grating in the corresponding tilt direction: ； Substituting formula (0) into formulas (6) and (7), the local tilt direction is calculated. ; This is the difference between the center wavelength change of FBG3 and the center wavelength change of FBG2. This is the difference between the center wavelength change of FBG2 and the center wavelength change of FBG1. It is the difference between the center wavelength change of FBG3 and the center wavelength change of FBG1; Inclination direction ; From formulas (3), (4), and (5), we get: ； By taking the square root of both sides of the equation, rearranging the terms, and taking the arcsine of both sides, we obtain the angle of inclination: ； Substituting formula (0) into formula (9), the inclination angle is obtained. ; Condition B: The center wavelength changes of FBG1, FBG2, and FBG3 satisfy... Then, using FBG2 as the dominant grating, FBG1 as the first auxiliary grating, and FBG3 as the second auxiliary grating, the local tilt direction is determined. Located in region B; the static modeling and solution steps are the same as for case A; the local tilt direction is obtained from the solution. , Inclination direction ;inclination ; Condition C: The center wavelength changes of FBG1, FBG2, and FBG3 satisfy... Then, using FBG2 as the dominant grating, FBG3 as the first auxiliary grating, and FBG1 as the second auxiliary grating, the local tilt direction is determined. Located in region C; the static modeling and solution steps are the same as for case A; the local tilt direction is obtained from the solution. , Inclination direction ;inclination ; Condition D: The center wavelength changes of FBG1, FBG2, and FBG3 satisfy... Then, using FBG3 as the dominant grating, FBG2 as the first auxiliary grating, and FBG1 as the second auxiliary grating, the local tilt direction is determined. Located in region D; the static modeling and solution steps are the same as for case A; the local tilt direction is obtained from the solution. , Inclination direction ;inclination ; Operating condition E: The center wavelength changes of FBG1, FBG2, and FBG3 satisfy... Then, using FBG3 as the dominant grating, FBG1 as the first auxiliary grating, and FBG2 as the second auxiliary grating, the local tilt direction is determined. Located in region E; the static modeling and solution steps are the same as for case A; the local tilt direction is obtained from the solution. , Inclination direction ;inclination ; Condition F: The center wavelength changes of FBG1, FBG2, and FBG3 satisfy... Then, using FBG1 as the dominant grating, FBG3 as the first auxiliary grating, and FBG2 as the second auxiliary grating, the local tilt direction is determined. Located in region F; the static modeling and solution steps are the same as for case A; the local tilt direction is obtained from the solution. , Inclination direction ;inclination .

7. The solution method according to claim 6, characterized in that: The six critical operating conditions at regional boundaries include: Operating condition a: The center wavelength changes of FBG1, FBG2, and FBG3 satisfy... FBG1 is used as the dominant grating, and FBG2 and FBG3 are used as auxiliary gratings; the local tilt direction is determined. Located on the boundary line between region F and region A, i.e., in the direction of the dip angle. 0°; Static modeling to solve for the tilt angle The procedure is the same as in condition A; tilt angle ; Condition b: The center wavelength changes of FBG1, FBG2, and FBG3 satisfy... FBG1 and FBG2 are used as the dominant gratings, and FBG3 is used as the auxiliary grating; the local tilt direction is determined. Located on the boundary line between region A and region B, i.e., in the direction of the dip angle. The angle is 60°; static modeling is used to solve the tilt angle. The procedure is the same as in condition A; tilt angle ; c. Operating condition: The center wavelength changes of FBG1, FBG2, and FBG3 satisfy... FBG2 is used as the dominant grating, and FBG3 and FBG1 are used as auxiliary gratings; the local tilt direction is determined. Located on the boundary line between region B and region C, i.e., in the direction of the dip angle. The angle is 120°; static modeling is used to solve the tilt angle. The procedure is the same as in condition A; tilt angle ; Operating condition d: The center wavelength changes of FBG1, FBG2, and FBG3 satisfy... FBG2 and FBG3 are used as the dominant gratings, and FBG1 is used as the auxiliary grating; the local tilt direction is determined. Located on the boundary line between region C and region D, i.e., in the direction of the dip angle. 180°; Static modeling to solve for the tilt angle The procedure is the same as in condition A; tilt angle ; e-condition: The center wavelength changes of FBG1, FBG2, and FBG3 satisfy... FBG3 is used as the dominant grating, and FBG1 and FBG2 are used as auxiliary gratings; the local tilt direction is determined. Located on the boundary line between region D and region E; i.e., in the direction of the dip angle. -120°; Static modeling to calculate the tilt angle The procedure is the same as in condition A; tilt angle ; Operating condition f: The center wavelength changes of FBG1, FBG2, and FBG3 satisfy... FBG1 and FBG3 are used as the dominant gratings, and FBG2 is used as the auxiliary grating; the local tilt direction is determined. Located on the boundary line between region E and region F, i.e., in the dip direction. -60°; Static modeling to calculate the tilt angle The procedure is the same as in condition A; tilt angle .

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