Methods for sensing two-dimensional acceleration using a sensing device

Abstract

This invention discloses a method for sensing two-dimensional acceleration using a sensing device. The sensing device utilizes a single-mode optical fiber and fiber sheath in a special configuration to form a Fabry-Perot resonant cavity within its fiber optic probe. Signal processing is achieved using a spectral analysis device based on the fiber optic Fabry-Perot resonant cavity principle, enabling real-time sensing of two-dimensional acceleration in conjunction with a mass block. This sensing device offers advantages such as simple structure, high sensitivity, temperature self-compensation, electromagnetic interference resistance, pollution-free operation, good durability, and real-time monitoring. It is particularly suitable for applications requiring long-term operation, explosion-proof, waterproof, corrosion-resistant, miniaturized, and electromagnetic interference-resistant sensing devices, particularly in fields such as marine engineering construction and marine structural health monitoring.

Description

Technical Field

[0001] This invention belongs to the field of measurement, specifically relating to a sensing device and a method for sensing two-dimensional acceleration. Background Technology

[0002] Ocean currents are primarily horizontal, and the load on structures is closely related to the flow velocity. Under long-term, continuous horizontal water loads, the materials of marine structures experience fatigue and even failure. In certain specialized engineering fields, accurately obtaining the fine flow field of the water is crucial. Therefore, it is necessary to strengthen the monitoring of water flow velocity to analyze the load characteristics borne by structures. For situations where the water flow velocity exceeds the design range of the structure, immediate detection and handling are required. Real-time monitoring of ocean current velocity is beneficial for improving the rationality of marine structure design, operational safety, and the timeliness of problem detection and resolution. Furthermore, multi-point monitoring of ocean current velocity is also helpful for analyzing local ocean current characteristics, providing monitoring tools for basic scientific research related to ocean currents.

[0003] There are three main existing methods for measuring current velocity: first, on-site monitoring methods, such as drop-out profiling instruments; second, remote sensing monitoring methods, such as high-frequency ground wave radar; and third, traditional physical methods, such as dyeing methods. The first method primarily uses electronic sensors, which typically require strict waterproofing and corrosion resistance, generating electrochemical noise and reducing sensing accuracy. The second method mainly monitors the movement of the ocean surface and cannot obtain the velocity distribution in deeper layers. The third method is time-consuming, labor-intensive, and has a significant impact on the ecological environment.

[0004] In addition to flow velocity, a detailed understanding of the relative motion requires the sensing of acceleration. An accelerometer's structure mainly includes a mass, damper, elastic element, and sensing element. Its principle is based on the inertial force acting on the mass and Newton's second law to obtain the acceleration of the measured object. Based on the sensing element, accelerometers currently on the market include capacitive, inductive, strain gauge, piezoresistive, and piezoelectric types. These electronic sensing devices can generate certain electrochemical noise under certain conditions, leading to signal distortion and affecting the accuracy of the measurement signal; furthermore, their sensitivity has certain limitations. Summary of the Invention

[0005] Purpose of the invention: In order to overcome the shortcomings of the prior art, the present invention provides a sensing device and a method for sensing two-dimensional acceleration.

[0006] Technical solution: The sensing device of the present invention includes:

[0007] An optical fiber probe includes a flexible, circularly shaped optical fiber sheath and four single-mode optical fibers. The optical fiber sheath has four blind holes extending inward from its end face along its length. The four blind holes are symmetrically arranged at equal intervals around the central axis of the optical fiber sheath. The bottom surface of each blind hole forms a reflective surface, and all four reflective surfaces are located on the same plane perpendicular to the central axis. The four single-mode optical fibers are coaxially inserted into the blind holes one by one, with gaps between them and the reflective surfaces to form a Fabry-Perot resonant cavity.

[0008] The fixing part, which is connected to the optical fiber sheath, is used to fix the optical fiber probe to the object being measured;

[0009] The spectral analysis device emits broadband light into the four single-mode optical fibers and receives and analyzes the signals transmitted by the four single-mode optical fibers.

[0010] In one embodiment, the fixing part is a protective sleeve, which is fitted over the four single-mode optical fibers and sealed to the end face of the optical fiber sheath where the blind hole is opened; the protective sleeve is provided with a scale for measuring water depth. Sealing the optical fiber sheath with the protective sleeve protects the optical fiber probe, preventing water from seeping into the device and affecting its use, and also provides feedback on the sensed depth, making it particularly suitable for measuring water flow velocity.

[0011] In one embodiment, the optical probe further includes a mass block attached to the bottom of the optical fiber sheath. By adding the mass block, two-dimensional acceleration sensing can be achieved.

[0012] Preferably, the mass block is detachably connected to the bottom of the fiber optic sheath. When the mass block is removed, it can be used to sense two-dimensional flow velocity; when the mass block is connected, it can be used to sense two-dimensional acceleration.

[0013] Specifically, the reflective surface is coated with a reflective coating, which has a reflectivity greater than 0.04 for light with a wavelength of 1550nm.

[0014] Specifically, the wavelength of the broadband light is between 200 and 1590 nm.

[0015] Corresponding to the aforementioned sensing device, the present invention provides a method for sensing two-dimensional flow velocity, characterized by comprising the following steps:

[0016] (1) Place the fiber optic probe in the water;

[0017] (2) The water flow causes the fiber optic probe to bend and deform, which in turn causes the gap between the single-mode fiber and the reflective surface to change.

[0018] (3) The cavity length of each Fabry-Perot resonator is analyzed in real time using a spectral analysis device to obtain the deformation state and the flow direction of the water.

[0019] (4) The flow velocity of the water relative to the fiber optic probe is obtained by the relationship between the flow velocity and the deformation state of the fiber optic probe.

[0020] In step (3), when the neutral surface of the device bends does not pass through the center of any single-mode fiber, two single-mode fibers are in the compression zone, and the other two single-mode fibers are in the tension zone. The direction passing through the center of the fiber sheath cross-section, pointing towards the compression zone, and parallel to the line connecting the centers of two adjacent single-mode fibers whose cavity length changes are negative, is defined as the reference direction. The angle α between the water flow direction and the reference direction is:

[0021]

[0022] Where, k = r1 / r2, r1 is the distance between the center of the first single-mode fiber that is closer to the neutral plane in the tension zone and the neutral plane, and r2 is the distance between the center of the second single-mode fiber that is adjacent to the first single-mode fiber in the compression zone and the neutral plane.

[0023] When the neutral surface of the device bends and passes through the center of any single-mode fiber, the direction of water flow is from the single-mode fiber with the longer cavity length to the single-mode fiber with the shorter cavity length.

[0024] In step (4), the fiber optic probe is approximated as an elastic rod with a uniform cross-section, and the load applied by the fluid is equivalent to a uniformly distributed load. According to the Morrison equation, ignoring the influence of horizontal inertial force, the expression for the relationship between the flow velocity u and the cavity length of the Fabry-Perot resonator is obtained:

[0025]

[0026] Among them, l fi Let l be the length of the i-th single-mode fiber inside the fiber sheath. 0i Let Δl be the cavity length of the i-th single-mode fiber before deformation. ti Let r be the cavity length change corresponding to the i-th single-mode fiber, where i is the single-mode fiber number, i = 1, 2, 3, 4. i Let E be the distance between the center of single-mode fiber i and the neutral plane, and let C be the elastic modulus of the fiber probe. D ρ is the drag force coefficient, ρ is the seawater density, and d is the outer diameter of the optical fiber sheath.

[0027] Furthermore, the present invention provides a method for sensing two-dimensional acceleration, comprising the following steps:

[0028] (1) Securely attach the fiber optic probe to the object being measured and keep the probe suspended vertically.

[0029] (2) The end mass block causes the fiber optic probe to bend and deform under the action of inertial force, which in turn causes the gap between the single-mode fiber and the reflective surface to change.

[0030] (3) The cavity length of each Fabry-Perot resonator is analyzed in real time using a spectral analysis device to obtain the deformation state and acceleration direction;

[0031] (4) The acceleration of the object under test is obtained by the relationship between the acceleration of the object under test and the deformation state of the fiber optic probe.

[0032] In step (3), when the neutral plane of the device bends does not pass through the center of any single-mode fiber, two single-mode fibers are in the compression zone, and the other two single-mode fibers are in the tension zone. The direction passing through the center of the fiber sheath cross-section, pointing towards the compression zone, and parallel to the line connecting the centers of two adjacent single-mode fibers whose cavity length changes are negative, is defined as the reference direction. The angle α between the acceleration direction and the reference direction is:

[0033]

[0034] Where, k = r1 / r2, r1 is the distance between the center of the first single-mode fiber that is closer to the neutral plane in the tension zone and the neutral plane, and r2 is the distance between the center of the second single-mode fiber that is adjacent to the first single-mode fiber in the compression zone and the neutral plane.

[0035] When the neutral plane of the device bends through the center of any single-mode fiber, the direction of acceleration is from the single-mode fiber with the longer cavity length to the single-mode fiber with the shorter cavity length.

[0036] In step (4), the sensing device is approximately a weightless elastic rod with a uniform cross-section. The mass block at the end generates an inertial force, thus obtaining the expression for the relationship between the acceleration a of the measured object and the cavity length of the Fabry-Perot resonant cavity:

[0037]

[0038] Among them, l fi Let l be the length of the i-th single-mode fiber inside the fiber sheath. 0i Let Δl be the cavity length of the i-th single-mode fiber before deformation. ti Let r be the cavity length change corresponding to the i-th single-mode fiber, where i is the single-mode fiber number, i = 1, 2, 3, 4. i Let E be the distance between the center of single-mode fiber i and the neutral plane, and let E be the elastic modulus of the fiber probe. s The mass of the mass block.

[0039] Beneficial effects: Compared with existing technologies, this sensing device forms a Fabry-Perot resonant cavity through the cooperation of blind holes in the optical fiber and the optical fiber sheath. Based on the fiber optic Fabry-Perot resonant cavity, it can realize real-time sensing of two-dimensional acceleration with a mass block. It has the advantages of simple structure, high sensitivity, temperature self-compensation, anti-electromagnetic interference, no pollution, good durability and real-time monitoring. It is particularly suitable for applications requiring long-term operation, explosion-proof, waterproof, corrosion-resistant, miniaturized and anti-electromagnetic interference, such as marine engineering construction and marine structural health monitoring. Attached Figure Description

[0040] Figure 1 This is a schematic diagram of the sensing device structure according to Embodiment 1 of the present invention;

[0041] Figure 2 This is a schematic diagram of the fiber optic probe in Example 1;

[0042] Figure 3 This is a schematic diagram of the sensing device according to Embodiment 2 of the present invention;

[0043] Figure 4 This is a schematic diagram of the fiber optic probe in Example 2;

[0044] Figure 5 This is a top view of the fiber optic probe;

[0045] Figure 6 This is a schematic diagram of the propagation paths of reflected and incident light;

[0046] Figure 7 This is a schematic diagram of the fiber optic probe subjected to a uniformly distributed load in Example 1;

[0047] Figure 8 This is a schematic diagram of the force applied to the fiber optic probe in Example 2;

[0048] Figure 9 This is a schematic diagram showing the bending direction of the fiber optic probe and the calculation of the distance from each single-mode fiber to the neutral plane. Detailed Implementation

[0049] The present invention will now be described in further detail with reference to the accompanying drawings.

[0050] like Figure 1-2 As shown, the sensing device of Embodiment 1 is used to sense two-dimensional flow velocity, and its main components include an optical fiber probe 1, a fixing part 2, and a spectral analysis device 3.

[0051] The fiber optic probe 1 includes a fiber optic sheath 11 and four single-mode optical fibers 12. The fiber optic sheath 11 is made of polymer or gel, is cylindrical, with an outer diameter between 500 micrometers and 5 millimeters, and a length between 5 millimeters and 10 centimeters. Four blind holes 13 are formed along its length from its end face, with diameters between 130 micrometers and 200 micrometers, and depths determined according to the dimensions of the fiber optic sheath 11. (Please refer to...) Figure 5 Four blind apertures 13 are symmetrically arranged at equal intervals around the central axis of the optical fiber sheath 11. The center of each blind aperture 13 lies on a concentric circle, the center of which is located on the central axis of the optical fiber sheath 11. The bottom surface of each blind aperture 13 is polished smooth and coated with a reflective coating to form a reflective surface 14. This reflective coating is required to have a reflectivity greater than 0.04 for light with wavelengths of 1550 nm and near. All four reflective surfaces 14 are located on the same plane perpendicular to the central axis.

[0052] The diameter of the four single-mode optical fibers 12 is slightly smaller than that of the blind holes 13. The cut surfaces at their ends are polished flat and smooth. They are coaxially inserted into the four blind holes 13 respectively, leaving a gap of 50 micrometers to 1 millimeter between them and the reflecting surface 14. The cavity formed by this gap is the Fabry-Perot resonant cavity.

[0053] The insertion port of blind hole 13 is bonded and sealed with epoxy resin or other adhesives that have bonding and sealing properties.

[0054] To protect the optical fiber and ensure a tight seal to prevent internal water leakage, in this embodiment, the fixing part 2 is a cylindrical steel casing, which is coaxially connected to the optical fiber sheath 11. The connection is also sealed with adhesive. The single-mode optical fiber 12 is inserted into the casing and connected to the spectral analysis device 3. The surface of the casing is marked with length graduations to monitor water depth.

[0055] The spectral analysis device 3 emits broadband light into four single-mode optical fibers 12, receives and analyzes the signals transmitted by the four single-mode optical fibers 12. The wavelength of the broadband light is between 200 and 1590 nm, and the signals are processed using an analysis method based on the fiber Fabry-Perot resonator principle.

[0056] The installation method of this sensing device is as follows: Connect the fiber optic probe 1 to a marine structure, ship hull, or other structure using a protective sleeve, and place it vertically. Initially connect the receiving ends of the four single-mode optical fibers 12 to the spectral analysis device 3 for initial calibration. Disconnect the fiber optic receiving ends from the spectral analysis device 3, and position the probe 1 using the length-scaled protective sleeve, ensuring it is fully immersed in the designated location of the seawater to be measured, and then fix it in place. Connect the receiving ends of the four single-mode optical fibers 1 to the spectral analysis device 3 to complete the installation.

[0057] This sensing device monitors the deformation of the fiber optic probe 1 by monitoring the cavity length of the Fabry-Perot resonator, thereby monitoring the flow velocity of the water relative to the fiber optic probe 1. Since each single-mode fiber 12 is fixed only at the insertion end within the fiber sheath 11, and there is no bonding between them inside the sheath 11, they can deform relatively freely. Therefore, when the fiber optic probe 1 bends, the cavity length corresponding to each fiber changes. Because the size and stiffness of the fiber are smaller than those of the flexible polymer sheath 11, the fiber optic probe 1 is approximated as a solid polymer with the same outer diameter and height during fluid flow, and the load applied by the fluid relative to it is approximated as a uniformly distributed load. The deformation of the fiber optic probe 1 is analyzed using a cantilever beam model under a uniformly distributed load. Since there is no bonding between the single-mode fiber and the sheath, the change in fiber length when the fiber optic probe 1 bends is negligible. By analyzing the cavity length corresponding to each fiber in real time, the deformation curve and direction of the fiber optic probe are obtained. By analyzing the relationship between flow velocity and the deformation state of the fiber optic probe, the flow velocity of seawater relative to the fiber optic probe (including magnitude and direction) can be obtained, i.e., the flow velocity of seawater relative to the structure.

[0058] Specifically, the steps of its sensing method are as follows:

[0059] (1) Place the fiber optic probe vertically in the water;

[0060] (2) The water flow causes the fiber optic probe to bend and deform, which in turn causes the gap between the single-mode fiber and the reflective surface to change.

[0061] (3) The cavity length of each Fabry-Perot resonator is analyzed in real time using a spectral analysis device to obtain the deformation state and the flow direction of the water.

[0062] (4) The flow velocity of the water relative to the fiber optic probe is obtained by the relationship between the flow velocity and the deformation state of the fiber optic probe.

[0063] like Figure 6 As shown, the probe light (E) inc At the end of the single-mode fiber 12, light exits from the fiber core and enters the cavity air, with some light (E)... refl,1 The light is reflected at the core-air interface and re-enters the core; another portion of the light (E) is reflected back into the core. laun Light transmitted from the fiber core-air interface into the air becomes transmitted light. The transmitted light continues to propagate in the air (E... circ When light reaches the air-reflective coating interface, it is reflected, and its propagation direction is opposite to that before reflection, becoming the reflected light (E). b-circ The reflected light continues to propagate to the air-core interface, where a portion of the light (E) RT The emitted light propagates again towards the reflective coating, while another portion of the light (E) is emitted and propagates back towards the reflective coating. backThe light enters the fiber core through this interface. Since the light reflected from the two interfaces is parallel to each other, and the light propagates perpendicular to these two interfaces, multiple reflections occur. Considering the light propagation equation and boundary conditions, as well as the interference condition between the transmitted light from the interface and the reflected light, the electric field of the reflected light is:

[0064]

[0065] Where, r ab Let t be the reflectance of the interface between material a and material b. ab Let φ be the transmittance of the interface between material a and material b, where a = 1, 2 or 3 and b = 1, 2 or 3; subscripts 1, 2, and 3 represent single-mode fiber, air, and reflective coating (reflective surface), respectively; j is the imaginary unit; φ = 2πl0n0 / λ0; l0 is the cavity length of the Fabry-Perot resonator; n0 is the refractive index of air, which can be approximated as 1; λ0 is the wavelength of the probe light in vacuum.

[0066] From equation (1), we know that the electric field intensity of the reflected light is a quasi-periodic function of the wavelength. Taking the derivative of equation (1) and setting it equal to 0, we get:

[0067]

[0068] Where λ0l m is the extreme point in the distribution image of reflected photoelectric field intensity as a function of wavelength; m is the modulus of each extreme point. From formula (2), it can be seen that for the same modulus, each extreme point in the distribution image of reflected photoelectric field intensity as a function of wavelength has a linear relationship with the cavity length, and its slope is 4n0 / m. Therefore, by monitoring the wavelength of each extreme point in the reflection spectrum corresponding to each optical fiber, the corresponding cavity length can be monitored, and its sensitivity is 4n0 / m.

[0069] Because the size and stiffness of optical fibers are much smaller than those of fiber polymer or gel sleeves, the sensing device can be approximated as a uniform cross-section elastic rod during the deformation process caused by fluid flow relative to the sensing device, and the load applied by the fluid is a uniformly distributed load. Figure 7 Based on the above approximation, the deformation of the sensing device can be analyzed using a cantilever beam model under uniformly distributed load. Under uniformly distributed load, the bending moment distribution along the axial direction of the cantilever beam is as follows:

[0070]

[0071] Where x is the distance from the calculation point to the fixed end; q is the uniformly distributed load applied by the fluid to the sensing device; and L is the length of the sensing device from the fixed end. Considering the sensing device has a circular cross-section, its strain distribution is as follows:

[0072]

[0073] Where r is the distance from the calculation point to the neutral plane; E is the elastic modulus of the sensing element; and d is the outer diameter of the fiber polymer or gel sleeve. Integrating equation (4) along the rod length yields the axial deformation of the sensing device. Since there is no bonding between the fiber and the fiber sheath, the change in fiber length when the sensing device bends is negligible. Let the length of the i-th fiber inside the fiber sheath be l. fi Distance from neutral surface r i The cavity length before deformation is l 0i The subscript 'i' indicates the fiber number. The change in cavity length Δl... ti The magnitude of the uniformly distributed load q is derived as follows:

[0074]

[0075] According to Morrison's equation, the formula for a unit column height q at any height z of a vertical column is:

[0076]

[0077] Equation (6) neglects the influence of horizontal inertial force. C D ρ is the drag force coefficient, ρ is the seawater density, and u is the seawater velocity.

[0078] Therefore, the formula for calculating seawater flow velocity can be obtained as follows:

[0079]

[0080] To determine the flow direction of the fluid and the distance of each optical fiber from the neutral plane, we will first discuss the general case. For example... Figure 9 As shown, when the neutral plane does not pass through the center of any single-mode fiber, due to the equidistant and symmetrical arrangement of the four single-mode fibers, two fibers must be in the compression zone, and the other two fibers must be in the tension zone. Fibers 111-114 represent the centers of the four fibers, the solid great circle represents the outer contour of the fiber optic probe, and the dashed line passing through the center of the circle represents the neutral plane of the bent fiber optic probe. Assume fibers 112 and 114 are in the compression zone, with their cavity lengths decreasing; fibers 111 and 113 are in the tension zone, with their cavity lengths increasing. The changes in the cavity lengths of the four fibers can be determined through spectral analysis. Therefore, a reference direction can be defined as the direction passing through the center of the circle, pointing towards the compression zone, and parallel to the line connecting the centers of the two adjacent fibers whose cavity length changes are negative. By determining the angle between the neutral plane and the reference direction, the flow direction of the fluid can be determined. Figure 9 The solid arrow in the center line points to the reference direction in this example, and the solid line passing through the center of the circle is perpendicular to the reference direction. The dashed arrow is perpendicular to the neutral plane and represents the deformation direction of the fiber optic probe, i.e., the flow direction of the fluid. The distances of the fibers numbered 111 to 114 from the neutral plane are denoted as r1 to r4, respectively.

[0081] Let α be the angle between the dashed arrow (the direction of fluid flow) and the solid arrow (the reference direction).

[0082]

[0083] Where k = r1 / r2, r1 is the distance between the center of the first single-mode fiber closer to the neutral plane in the tension zone and the neutral plane, and r2 is the distance between the center of the second single-mode fiber adjacent to the first single-mode fiber in the compression zone and the neutral plane; thus, the flow direction of the fluid relative to the sensing device has been determined.

[0084] Considering a special case, when the neutral plane passes through the center point of two optical fibers, fibers numbered 111 and 113 must be non-adjacent fibers, and the line connecting their centers passes through the center of the sensing device. In this case, the distance between these two fibers and the neutral plane is 0, while the distance between the other two fibers and the neutral plane is... When α = 0, the direction of water flow is from a single-mode fiber with a longer cavity to a single-mode fiber with a shorter cavity.

[0085] In general, the distances of all four single-mode fibers from the neutral plane are readily available, but only the distance from one fiber to the neutral plane is needed to determine the uniformly distributed load. Therefore, the values ​​of the other three fibers are redundant, and theoretically, substituting these four values ​​should yield a consistent uniformly distributed load. However, in practical applications, due to various errors and interference, the four uniformly distributed load values ​​may differ slightly. Therefore, in practical applications, the average of the four values ​​can be taken to reduce errors.

[0086] In special cases, since the two single-mode fibers pass through the neutral plane, their distance from the neutral plane and the cavity length change are both zero, which is reflected in the above formula as zero in terms of both the molecule and the distribution. Therefore, the values ​​of these two fibers cannot be used. Instead, the correlation values ​​of the two fibers that do not pass through the neutral plane are used to solve for the magnitude of the uniformly distributed load, and the average value of the results is taken.

[0087] The sensing device in Example 2 is used to sense two-dimensional acceleration, such as Figure 3 and Figure 4 As shown, its structure is roughly the same as that of Embodiment 1. The difference is that when underwater operation is not required, the fixing part 2 can be directly made of a patch made of metal or non-metal sheet with strong bending resistance and not easily reacting with the environment, and is also installed at the end of the fiber optic sheath 11 with the blind hole 13.

[0088] A counterweight 15 is connected to the bottom of the fiber optic sheath 11. Of course, the counterweight 15 can be made into a detachable structure and can be installed on the fiber optic sheath 11 when it is necessary to measure two-dimensional acceleration.

[0089] Furthermore, for measuring two-dimensional acceleration, the gap between the single-mode fiber 12 and the reflecting surface 14 is set to approximately 1 mm, the outer diameter of the fiber sheath 11 is 5 mm, the length is 10 cm, and the diameter of the blind aperture is preferably around 200 μm. Correspondingly, the height of the control mass block 15 is 5 mm, and the material is a high-density material that is not easily reactive with the environment; generally, metals such as lead or high-density non-metals can be selected.

[0090] The steps of its sensing method are as follows:

[0091] (1) Securely attach the fiber optic probe to the object being measured and keep the probe suspended vertically.

[0092] (2) The end mass block causes the fiber optic probe to bend and deform under the action of inertial force, which in turn causes the gap between the single-mode fiber and the reflective surface to change.

[0093] (3) The cavity length of each Fabry-Perot resonator is analyzed in real time using a spectral analysis device to obtain the deformation state and acceleration direction;

[0094] (4) The acceleration of the object under test is obtained by the relationship between the acceleration a of the object under test and the deformation state of the fiber optic probe.

[0095] like Figure 6 As shown, the probe light (E) inc At the end of the single-mode fiber 12, light exits from the fiber core and enters the cavity air, with some light (E) refl,1 The light is reflected at the core-air interface and re-enters the core; another portion of the light (E) is reflected back into the core. laun Light transmitted from the fiber core-air interface into the air becomes transmitted light. The transmitted light continues to propagate in the air (E... circ When light reaches the air-reflective coating interface, it is reflected, and its propagation direction is opposite to that before reflection, becoming the reflected light (E). b-circ The reflected light continues to propagate to the air-core interface, where a portion of the light (E)... RT The emitted light propagates again towards the reflective coating, while another portion of the light (E) is emitted and propagates back towards the reflective coating. back The light enters the fiber core through this interface. Since the light reflected from the two interfaces is parallel to each other, and the light propagates perpendicular to these two interfaces, multiple reflections occur. Considering the light propagation equation and boundary conditions, as well as the interference condition between the transmitted light from the interface and the reflected light, the electric field of the reflected light is:

[0096]

[0097] Where, r ab Let t be the reflectance of the interface between material a and material b. abLet be the transmittance of the interface between material a and material b, where a = 1, 2, or 3 and b = 1, 2, or 3; subscripts 1, 2, and 3 represent single-mode fiber, air, and reflective coating (reflective surface), respectively; j is the imaginary unit; φ = 2πl0n0 / λ0; l0 is the cavity length of the Fabry-Perot resonator; n0 is the refractive index of air, which can be approximated as 1; λ0 is the wavelength of the probe light in vacuum. From equation (1), it can be seen that the electric field intensity of the reflected light is a quasi-periodic function of the wavelength. Taking the derivative of equation (1) and setting it equal to 0, we get:

[0098]

[0099] Where λ0l m is the extreme point in the distribution image of reflected photoelectric field intensity as a function of wavelength; m is the modulus of each extreme point. From formula (2), it can be seen that for the same modulus, each extreme point in the distribution image of reflected photoelectric field intensity as a function of wavelength has a linear relationship with the cavity length, and its slope is 4n0 / m. Therefore, by monitoring the wavelength of each extreme point in the reflection spectrum corresponding to each optical fiber, the corresponding cavity length can be monitored, and its sensitivity is 4n0 / m.

[0100] Because the size and stiffness of optical fibers are much smaller than those of fiber polymer or gel sleeves, the sensing device can be approximated as a uniform cross-section elastic rod during deformation relative to the sensing device. The inertial force generated by the end mass block is equivalent to a concentrated load F( Figure 8 Based on the above approximation, the deformation of the sensing device can be analyzed using a cantilever beam model under load F. Under concentrated load, the axial distribution of the bending moment of the cantilever beam is as follows:

[0101] M(x)=F(Lx)(3)

[0102] Where x is the distance from the calculation point to the fixed end; F is the concentrated load applied to the sensing device; and L is the length of the sensing device from the fixed end. Considering the sensing device has a circular cross-section, its strain distribution is as follows:

[0103]

[0104] Where r is the distance from the calculation point to the neutral plane; E is the elastic modulus of the sensing component; and d is the outer diameter of the fiber polymer or gel sleeve. Integrating equation (4) along the rod length yields the axial deformation of the sensing device. Since there is no bonding between the fiber and the fiber sleeve, the change in fiber length when the sensing device bends is negligible. Let the length of the i-th fiber inside the fiber sleeve be l. fi Distance from neutral surface r i The cavity length before deformation is l 0i The subscript 'i' indicates the fiber number. The change in cavity length Δl... ti The magnitude of the concentrated load F is derived as follows:

[0105]

[0106] Therefore, the formula for calculating acceleration can be obtained as follows:

[0107]

[0108] To determine the distance between each fiber and the neutral plane, we will first discuss the general case. For example... Figure 9 As shown, when the neutral plane does not pass through the center of any single-mode fiber, due to the equidistant and symmetrical arrangement of the four single-mode fibers, two fibers must be in the compression region, and the other two fibers must be in the tension region. Fibers 111-114 represent the centers of the four fibers, the solid great circle represents the outer contour of the fiber optic probe, and the dashed line passing through the center of the circle represents the neutral plane of the fiber optic probe's bend. Assume fibers 112 and 114 are in the compression region, with their cavity lengths shortening; fibers 111 and 113 are in the tension region, with their cavity lengths lengthening. The changes in the cavity lengths of the four fibers can be determined through spectral analysis. Therefore, a negative direction passing through the center of the circle, pointing towards the compression region, and parallel to the line connecting the centers of the two adjacent fibers with varying cavity lengths can be defined as the reference direction. By determining the angle between the neutral plane and the reference direction, the direction of the acceleration of the measured object can be determined. Figure 9 The solid arrow points to the reference direction in this example, and the solid line passing through the center is perpendicular to the reference direction. The dashed arrow is perpendicular to the neutral plane and represents the deformation direction of the fiber optic probe, which is the acceleration direction. The distances of the fibers numbered 111 to 114 from the neutral plane are denoted as r1 to r4, respectively. The angle between the dashed arrow (acceleration direction) and the solid arrow (reference direction) is denoted as α.

[0109]

[0110] Where k = r1 / r2, r1 is the distance between the center of the first single-mode fiber closer to the neutral plane in the tension zone and the neutral plane, and r2 is the distance between the center of the second single-mode fiber adjacent to the first single-mode fiber in the compression zone and the neutral plane; thus, the direction of acceleration has been determined.

[0111] Considering a special case, when the neutral plane passes through the center point of two optical fibers, fibers numbered 111 and 113 must be non-adjacent fibers, and the line connecting their centers passes through the center of the sensing device. In this case, the distance between these two fibers and the neutral plane is 0, while the distance between the other two fibers and the neutral plane is... α = 0, the direction of acceleration is from the single-mode fiber with increasing cavity length to the single-mode fiber with decreasing cavity length.

[0112] In general, the distances of all four single-mode fibers to the neutral plane are readily available, but only the distance of one fiber to the neutral plane is needed to determine F. Therefore, the values ​​of the other three fibers are redundant, and theoretically, substituting these four values ​​should yield a consistent F. However, in practical applications, due to various errors and interference, the calculated values ​​of the four concentrated loads may differ slightly. Therefore, in practical applications, the average of the four values ​​can be taken to reduce errors.

[0113] In special cases, since the two single-mode fibers pass through the neutral plane, their distance from the neutral plane and the cavity length change are both zero, which is reflected in the above formula as zero in terms of both the molecule and the distribution. Therefore, the values ​​of these two fibers cannot be used. Instead, the correlation values ​​of the two fibers that do not pass through the neutral plane are used to solve for the magnitude of the uniformly distributed load, and the average value of the results is taken.

Claims

1. A method for sensing two-dimensional acceleration using a sensing device, characterized in that, The sensing device includes an optical fiber probe (1), which includes a flexible optical fiber sheath (11) with a circular cross-section and four single-mode optical fibers (12); the optical fiber sheath (11) is provided with four blind holes (13) extending inward from its end face along the length direction, the four blind holes (13) are symmetrically arranged at equal intervals around the central axis of the optical fiber sheath (11), the bottom surface of the blind holes (13) forms a reflective surface (14), and the four reflective surfaces (14) are all located on the same plane perpendicular to the central axis; the four single-mode optical fibers (12) are coaxially inserted into the blind holes (13) one by one, and a gap is left between them and the reflective surfaces (14) to form a Fabry-Perot resonant cavity; The fixing part (2) is connected to the optical fiber sheath (11) and is used to fix the optical fiber probe (1) to the object being measured. The spectral analysis device (3) emits broadband light into the four single-mode optical fibers (12), and receives and analyzes the signals transmitted by the four single-mode optical fibers (12). The method for sensing two-dimensional acceleration includes the following steps: (1) Securely attach the fiber optic probe to the object being measured and keep the probe suspended vertically. (2) The end mass block causes the fiber optic probe to bend and deform under the action of inertial force, which in turn causes the gap between the single-mode fiber and the reflective surface to change. (3) The cavity length of each Fabry-Perot resonator is analyzed in real time using a spectral analysis device to obtain the deformation state and acceleration direction; (4) The acceleration of the object under test is obtained by the relationship between the acceleration of the object under test and the deformation state of the fiber optic probe. In step (3), when the neutral plane of the device bends does not pass through the center of any single-mode fiber, two single-mode fibers are in the compression zone, and the other two single-mode fibers are in the tension zone; the direction passing through the center of the cross-section of the fiber sheath, pointing towards the compression zone, and parallel to the line connecting the centers of two adjacent single-mode fibers whose cavity length changes are negative is defined as the reference direction. Then the angle α between the acceleration direction and the reference direction is: Where, k = r1 / r2, r1 is the distance between the center of the first single-mode fiber that is closer to the neutral plane in the tension zone and the neutral plane, and r2 is the distance between the center of the second single-mode fiber that is adjacent to the first single-mode fiber in the compression zone and the neutral plane. When the neutral plane of the device bends through the center of any single-mode fiber, the direction of acceleration is from the single-mode fiber with the longer cavity length to the single-mode fiber with the shorter cavity length. In step (4), the sensing device is approximately a weightless elastic rod with a uniform cross-section. The mass block at the end generates an inertial force, thus obtaining the expression for the relationship between the acceleration a of the measured object and the cavity length of the Fabry-Perot resonant cavity: Among them, l fi Let l be the length of the i-th single-mode fiber inside the fiber sheath. 0i Let Δl be the cavity length of the i-th single-mode fiber before deformation. ti Let r be the cavity length change corresponding to the i-th single-mode fiber, where i is the single-mode fiber number, i = 1, 2, 3, 4. i Let be the distance between the center of single-mode fiber i and the neutral plane, and E be the elastic modulus of the fiber probe, m. s The mass of the mass block.

2. The method for sensing two-dimensional acceleration using the sensing device according to claim 1, characterized in that, The fiber optic probe (1) also includes a mass block (15), which is connected to the bottom of the fiber optic sheath (11).

3. The method for sensing two-dimensional acceleration using the sensing device according to claim 2, characterized in that, The mass block is detachably connected to the bottom of the optical fiber sheath (11).

4. The method for sensing two-dimensional acceleration using the sensing device according to claim 1, characterized in that, The reflective surface (14) is coated with a reflective coating that has a reflectivity greater than 0.04 for light with a wavelength of 1550 nm.

5. The method for sensing two-dimensional acceleration using the sensing device according to claim 1, characterized in that, The wavelength of the broadband light is between 200 and 1590 nm.

Images