A compliant bending probe with integrated FBG sensing and driving for in-situ engine detection and deformation reconstruction algorithm

Abstract

A flexible bending probe and deformation reconstruction algorithm integrating FBG sensing and driving for in-situ detection of an engine, comprising a superelastic shape memory alloy hollow threaded tube and a bending mechanism, wherein a bending mechanism is arranged inside the hollow threaded tube, the bending mechanism is composed of four high-temperature resistant resin rings and superelastic shape memory alloy wires, through holes are arranged on the surface of the high-temperature resistant resin rings, the through holes are distributed at 45 degrees, superelastic shape memory alloy wires are placed inside the through holes, the bending mechanism is completely fitted with the inner wall of the hollow threaded tube, the top surface of the bending mechanism is flush with the upper end surface of the hollow threaded tube, and the bottom surface of the bending mechanism is flush with the lower end surface of the hollow threaded tube. Compared with the prior art, the present invention enables the probe part to realize bending and twisting at any angle through unique structural design and deformation reconstruction algorithm, which is convenient for assembly and disassembly, thereby allowing clearer observation and detection.

Description

Technical Field

[0001] The invention relates to the technical field of aero-engine in-situ detection, in particular to a compliant bending probe and a deformation reconstruction algorithm for integrating FBG sensing and driving for in-situ detection of an engine. Background Art

[0002] Borescope plays a vital role in aircraft damage detection. It can detect abnormal conditions in the engine before they occur, reducing the workload of maintenance and is an important part of maintenance work. At the same time, the borescope can observe places inside the engine that cannot be observed by the naked eye, which increases the observation distance and reduces the difficulty of internal flaw detection.

[0003] The existing borescope includes several parts such as electronic circuits, borescope camera lenses, video adapters, etc. Each single and independent part is interconnected and tightly connected, and there is no way to disassemble the whole. In addition, the existing borescope equipment has poor flexibility, poor accessibility, difficult operation, low work efficiency, and the probe part of the borescope cannot be bent and twisted over a large range.

[0004] Therefore, in order to solve the above problems, the present application proposes a flexible bending probe and deformation reconstruction algorithm that integrates FBG sensing and driving for in-situ detection of engines. Compared with previous borescope equipment, the device is easier to assemble and disassemble, and the probe part can be bent and twisted at any angle, thereby enabling clearer observation and detection. Summary of the invention

[0005] The purpose of the present invention is to fill the gap in the prior art and provide a flexible bending probe and deformation reconstruction algorithm integrating FBG sensing and driving for in-situ detection of engines. Compared with previous borescope equipment, the device is easier to assemble and disassemble, and the probe part can be bent and twisted at any angle, so that clearer observation and detection can be carried out.

[0006] In order to achieve the above-mentioned purpose, the present invention provides a flexible bending probe and deformation reconstruction algorithm for FBG sensing and driving integration for in-situ detection of engines, including a superelastic shape memory alloy hollow threaded tube and a set of bending mechanisms, a set of bending mechanisms is arranged inside the hollow threaded tube, the bending mechanism is composed of four high-temperature resistant resin rings and superelastic shape memory alloy wires, through holes are arranged on the surface of the high-temperature resistant resin rings, the through holes are distributed at 45 degrees, superelastic shape memory alloy wires are placed inside the through holes, the bending mechanism is completely fitted with the inner wall of the hollow threaded tube, the top surface of the bending mechanism is flush with the upper end surface of the hollow threaded tube, and the bottom surface of the bending mechanism is flush with the lower end surface of the hollow threaded tube;

[0007] A high-definition camera lens line is placed at the central axis of the hollow threaded tube. The high-definition camera lens line goes deep into the hollow threaded tube. A high-definition camera lens is installed at one end of the high-definition camera lens line, and the other end of the high-definition camera lens line is connected to a micro display screen.

[0008] The hollow threaded tube and the U-shaped foil are pasted together by an adhesive, and a plurality of fiber optic sensors connected in series are arranged in the U-shaped foil. The U-shaped foil is deformed into an O-shaped tube by high temperature heating, and the fiber optic sensor is completely wrapped by the O-shaped tube. The strain value of the bending mechanism unit is measured by the fiber optic sensor.

[0009] The processing steps of the U-shaped foil are as follows: a shape memory alloy foil with a thickness of 0.5 mm is used to make the shape memory alloy foil into an ultra-thin foil, and the ultra-thin foil is pressed into a U shape by a special mold. The U-shaped ultra-thin foil has a shape memory effect through thermal effect training in a high-temperature furnace, and is converted into an O-type when heated to become an O-type tube; after cooling, the O-type tube can return to the state of the U-shaped foil, and the optical fiber sensor can be taken out.

[0010] The U-shaped foil is tangent to the upper surface of the hollow threaded tube, that is, the hollow threaded tube is horizontally placed on the lower surface of the U-shaped foil, and the U-shaped foil has excellent ductility.

[0011] The micro display screen includes a first video connection line and a second video connection line connected thereto. The first video connection line is in line with the high-definition camera lens line and is away from the bending mechanism. The second video connection line is connected to the high-definition camera lens line and is separated from the first video connection line by a distance without any intersection. At the same time, the second video connection line is away from the bending mechanism.

[0012] The high-definition camera lens line is inserted into the bending mechanism and is tightly adhered and fixed to the hollow threaded tube.

[0013] The first video connection line and the second video connection line are both made of optical fiber material, and both video connection lines are flexible and bendable.

[0014] The HD camera lens line is located at the central axis of the bending mechanism, and there is a certain distance between the HD camera lens line and the through holes in the circular ring of the bending mechanism. The through holes are distributed at 45 degrees. The depth of the through holes is equal to the height of the circular ring in the bending mechanism and is located on the surface of the bending mechanism.

[0015] The connection near the hollow threaded pipe port is smooth and has a certain wall thickness.

[0016] A deformation reconstruction algorithm of a compliant bending probe with integrated FBG sensing and driving for in-situ detection of an engine comprises the following steps:

[0017] S1, a component of equal thickness is bent and deformed, and FBG sensors are attached to its upper and lower surfaces. The relationship between the surface strain value ε(x) and the deflection ω(x) of the component is as follows:

[0018]

[0019] c is the vertical distance from the upper surface to the middle surface of the component with equal thickness, which can be calculated as:

[0020]

[0021] ε t is the surface strain value at a certain point, ε b is the lower surface strain value at the corresponding position, h is the thickness of the hollow threaded tube, and under pure bending deformation, the absolute values ​​of the upper and lower strains at the same position are the same, ε b ≈ε t , convert the above formula into the following formula:

[0022]

[0023] S2, the pasting of n FBGs divides the structure into n-1 segments, and the starting point of segment i With the end point The strain values ​​at i , ε i+1 , the end point of the previous segment is the starting point of the next segment. FBG only obtains the first and last two data on a segment. Through simple linear interpolation, the discrete value becomes continuous, and the strain value of each point on the i-th segment curve is obtained:

[0024]

[0025] S3, the rotation angle of the starting point of the i-th segment on the upper surface of the mechanism and deflection It is known that the i-th section corner The equation can be obtained by integrating the strain expression:

[0026]

[0027] S4, integrating the rotation angle equation, we can get the bending deflection ω:

[0028]

[0029] S5. Through the expression of S4, the expression of the first segment deflection can be obtained, and then the deflection of each segment can be obtained, and then all deflection values ​​can be obtained to reconstruct the shape of the mechanism.

[0030]

[0031] S6, analyzing the mechanical properties of the object, dividing the unit of the problem to be solved into several micro-units, constructing the unit according to the corresponding mechanical model and mechanical equilibrium equation, discretizing the constructed unit, dividing the nodes, and solving the unit stiffness matrix and unit load array;

[0032] S7, calculate the strain field e according to the coordinates of all strain measuring points, assuming that the measured strain field is e ε According to the principle of minimizing the Euclidean norm of the calculated strain field and the measured strain field, the error function Φ = Φ(e, e ε ), Kq = F is derived by finding the minimum value of the error function;

[0033] S8, given the boundary conditions, according to the natural boundary conditions, K and F are processed so that the stiffness matrix K is a full rank matrix, so that K f q=F f , solve

[0034] S9, dividing the outer surface of the bending mechanism (110) into a plurality of node polygonal thin-walled units, wherein the thin-walled units have a plurality of nodes as vertices, and the nodes are numbered in a counterclockwise direction;

[0035] S10, establishing a reference coordinate system in the thin-walled unit, with the origin of the coordinate system located at the centroid of the thin-walled unit, and establishing a global coordinate system, and establishing an algebraic relationship between the reference coordinate system and the global coordinate system through normalization processing;

[0036] S11, FBG strain rosettes are arranged at the centroid of the thin-walled unit to measure the strain values ​​in three directions, including shear strain, tensile strain, and bending strain. The strain rosette arrangement used in the experiment is double-sided arrangement, with part of the strain rosettes arranged on the outer surface of the bending mechanism and part of the strain rosettes arranged on the inner surface of the bending mechanism. The bending mechanism has a certain wall thickness;

[0037] S12, construct the shape function through the mechanical equilibrium relationship, derive the strain matrix, substitute the coordinates of the thin-walled unit nodes into the strain matrix, and obtain three types of strain matrices, namely shear strain matrix, tensile strain matrix and bending strain matrix;

[0038] S13, substitute the strain matrix obtained by S12 into the equation for solving the unit stiffness matrix to obtain the unit stiffness matrix, combine the unit stiffness matrices into a total stiffness matrix, then observe the boundary constraints of the bending mechanism, and then conditionally constrain the total stiffness matrix;

[0039] S14, continue to solve the stress matrix according to the method of solving the total stiffness matrix, and at the same time, limit the boundary conditions and conditionally constrain the stress matrix;

[0040] S15, through the total stiffness matrix of S13 and the above stress matrix, solve the equation through algebraic formula to obtain the required node displacement, and then draw the displacement strain curve through software.

[0041] Compared with the prior art, the present invention enables the probe part to be bent and twisted at any angle through a unique structural design and a deformation reconstruction algorithm, which is convenient for assembly and disassembly, thereby enabling clearer observation and detection. BRIEF DESCRIPTION OF THE DRAWINGS

[0042] Figure 1 It is a schematic cross-sectional structure diagram of a specific embodiment of the present invention;

[0043] Figure 2 is a schematic diagram of the three-dimensional structure of a probe provided in a specific embodiment of the present invention;

[0044] Figure 3 It is a schematic diagram of the structure of a specific embodiment of the present invention;

[0045] Figure 4 It is a structural schematic diagram of a hollow threaded pipe according to a specific embodiment of the present invention;

[0046] Figure 5 is a schematic diagram of a U-shaped foil according to a specific embodiment of the present invention;

[0047] Figure 6 is a schematic diagram of an O-type tube according to a specific embodiment of the present invention;

[0048] Figure 7 It is a schematic diagram of assembling a hollow threaded tube and an O-type tube according to a specific embodiment of the present invention;

[0049] Figure 8 It is a schematic diagram of the top view of the hollow threaded pipe according to a specific embodiment of the present invention;

[0050] Fig. 9 It is a schematic diagram of the solution process of the inverse finite element algorithm of a specific embodiment of the present invention;

[0051] Description of reference numerals:

[0052] 100 is a hollow threaded tube, 110 is a bending mechanism, 120 is a high temperature resistant resin ring, 200 is a high-definition camera lens line, 210 is a high-definition camera lens, 220 is a ring through hole, 300 is a micro display screen, 310 is a first video connecting line, 320 is a second video connecting line, 2 is a shape memory alloy wire, 4 is a U-shaped foil, 5 is an O-shaped tube, 6 is an optical fiber sensor, and 7 is an FBG strain rosette.

[0053] The present invention will now be further described with reference to the accompanying drawings.

[0054] See also Figures 1 to 9 The present invention discloses a flexible bending probe with integrated FBG sensing and driving for in-situ detection of an engine, comprising a hollow threaded tube 100 of superelastic shape memory alloy and a set of bending mechanisms 110. A set of bending mechanisms 110 is arranged inside the hollow threaded tube 100. The bending mechanism 110 is composed of four high-temperature resistant resin rings 120 and a superelastic shape memory alloy wire 2. Through holes 220 are arranged on the surface of the high-temperature resistant resin ring 120. The through holes 220 are distributed at 45 degrees. The superelastic shape memory alloy wire 2 is placed inside the through holes 220. The bending mechanism 110 is completely fitted with the inner wall of the hollow threaded tube 100. The top surface of the bending mechanism 110 is flush with the upper end surface of the hollow threaded tube 100, and the bottom surface of the bending mechanism 110 is flush with the lower end surface of the hollow threaded tube 100.

[0055] A high-definition camera lens line 200 is placed at the central axis of the hollow threaded tube 100. The high-definition camera lens line 200 goes deep into the hollow threaded tube 100. A high-definition camera lens 210 is installed at one end of the high-definition camera lens line 200. The other end of the high-definition camera lens line 200 is connected to a micro display screen 300.

[0056] The hollow threaded tube 100 is pasted to the U-shaped foil 4 by an adhesive, and a plurality of fiber optic sensors 6 connected in series are arranged in the U-shaped foil 4. The U-shaped foil 4 is deformed into an O-shaped tube 5 by high temperature heating, and the fiber optic sensor 6 is completely contained in the O-shaped tube 5. The strain value of the bending mechanism 110 unit is measured by the fiber optic sensor 6.

[0057] The processing steps of the U-shaped foil 4 are as follows: a shape memory alloy foil with a thickness of 0.5 mm is used to make the shape memory alloy foil into an ultra-thin foil, the ultra-thin foil is pressed into a U shape by a special mold, and the U-shaped ultra-thin foil has a shape memory effect through thermal effect training in a high-temperature furnace, and is converted into an O-type when heated to become an O-type tube 5; after cooling, the O-type tube 5 can return to the state of the U-shaped foil 4, and the optical fiber sensor 6 is taken out.

[0058] The U-shaped foil 4 is tangent to the upper surface of the hollow threaded tube 100 , that is, the hollow threaded tube 100 is horizontally placed on the lower surface of the U-shaped foil 4 , and the U-shaped foil 4 has excellent ductility.

[0059] The micro display screen 300 includes a first video connection line 310 and a second video connection line 320 connected thereto. The first video connection line 310 is in line with the high-definition camera lens line 200 and is away from the bending mechanism 110. The second video connection line 320 is connected to the high-definition camera lens line 200 and is separated from the first video connection line 310 by a distance without any intersection. At the same time, the second video connection line 320 is away from the bending mechanism 110.

[0060] The high-definition camera lens line 200 is inserted into the bending mechanism 110 and is tightly adhered and fixed to the hollow threaded tube 100 .

[0061] The first video connection line 310 and the second video connection line 320 are both made of optical fiber materials, and both video connection lines are flexible and bendable.

[0062] The high-definition camera lens line 200 is located at the central axis of the bending mechanism 110, and there is a certain distance between the high-definition camera lens line 200 and the through hole 220 in the circular ring of the bending mechanism 110. The through holes 220 are distributed at 45 degrees. The depth of the through holes 220 is equal to the height of the circular ring in the bending mechanism 110 and is located on the surface of the bending mechanism 110.

[0063] The connection near the port of the hollow threaded tube 100 is smooth and has a certain wall thickness.

[0064] A deformation reconstruction algorithm of a compliant bending probe with integrated FBG sensing and driving for in-situ detection of an engine comprises the following steps:

[0065] S1, a component of equal thickness is bent and deformed, and FBG sensors are attached to its upper and lower surfaces. The relationship between the surface strain value ε(x) and the deflection ω(x) of the component is as follows:

[0066]

[0067] c is the vertical distance from the upper surface to the middle surface of the component with equal thickness, which can be calculated as:

[0068]

[0069] ε t is the surface strain value at a certain point, ε b is the lower surface strain value at the corresponding position, h is the thickness of the hollow threaded tube, and under pure bending deformation, the absolute values ​​of the upper and lower strains at the same position are the same.

[0070] ε b ≈ε t , convert the above formula into the following formula:

[0071]

[0072] S2, the pasting of n FBGs divides the structure into n-1 segments, and the starting point of segment i With the end point The strain values ​​at i , ε i+1 , the end point of the previous segment is the starting point of the next segment. FBG only obtains the first and last two data on a segment. Through simple linear interpolation, the discrete value becomes continuous, and the strain value of each point on the i-th segment curve is obtained:

[0073]

[0074] S3, the rotation angle of the starting point of the i-th segment on the upper surface of the mechanism and deflection It is known that the i-th section corner The equation can be obtained by integrating the strain expression:

[0075]

[0076] S4, integrating the rotation angle equation, we can get the bending deflection ω:

[0077]

[0078] S5. Through the expression of S4, the expression of the first segment deflection can be obtained, and then the deflection of each segment can be obtained, and then all deflection values ​​can be obtained to reconstruct the shape of the mechanism.

[0079]

[0080] S6, analyzing the mechanical properties of the object, dividing the unit of the problem to be solved into several micro-units, constructing the unit according to the corresponding mechanical model and mechanical equilibrium equation, discretizing the constructed unit, dividing the nodes, and solving the unit stiffness matrix and unit load array;

[0081] S7, calculate the strain field e according to the coordinates of all strain measuring points, assuming that the measured strain field is e ε According to the principle of minimizing the Euclidean norm of the calculated strain field and the measured strain field, the error function Φ = Φ(e, e ε ), Kq = F is derived by finding the minimum value of the error function;

[0082] S8, given the boundary conditions, according to the natural boundary conditions, K and F are processed so that the stiffness matrix K is a full rank matrix, so that K f q=F f , solve

[0083] S9, dividing the outer surface of the bending mechanism 110 into a plurality of node polygonal thin-walled units, wherein the thin-walled units have a plurality of nodes as vertices, and the nodes are numbered in a counterclockwise direction;

[0084] S10, establishing a reference coordinate system in the thin-walled unit, with the origin of the coordinate system located at the centroid of the thin-walled unit, and establishing a global coordinate system, and establishing an algebraic relationship between the reference coordinate system and the global coordinate system through normalization processing;

[0085] S11, arranging FBG strain rosettes at the centroid of the thin-walled unit to measure strain values ​​in three directions, including shear strain value, tensile strain value, and bending strain value. The strain rosette arrangement used in the experiment is double-sided arrangement, with a portion of the strain rosettes arranged on the outer surface of the bending mechanism 110, and another portion of the strain rosettes arranged on the inner surface of the bending mechanism 110. The bending mechanism 110 has a certain wall thickness;

[0086] S12, construct the shape function through the mechanical equilibrium relationship, derive the strain matrix, substitute the coordinates of the thin-walled unit nodes into the strain matrix, and obtain three types of strain matrices, namely shear strain matrix, tensile strain matrix and bending strain matrix;

[0087] S13, substituting the strain matrix obtained in S12 into the equation for solving the unit stiffness matrix to obtain the unit stiffness matrix, combining the unit stiffness matrices into a total stiffness matrix, and then observing the boundary constraints of the bending mechanism 110, and then conditionally constraining the total stiffness matrix;

[0088] S14, continue to solve the stress matrix according to the method of solving the total stiffness matrix, and at the same time, limit the boundary conditions and conditionally constrain the stress matrix;

[0089] S15, through the total stiffness matrix of S13 and the above stress matrix, solve the equation through algebraic formula to obtain the required node displacement, and then draw the displacement strain curve through software.

[0090] The above are only preferred embodiments of the present invention, which are only used to help understand the method and core ideas of the present application. The protection scope of the present invention is not limited to the above embodiments. All technical solutions under the concept of the present invention belong to the protection scope of the present invention. It should be pointed out that for ordinary technicians in this technical field, some improvements and modifications without departing from the principle of the present invention should also be regarded as the protection scope of the present invention.

[0091] The present invention solves the problems in the prior art that each single independent part is interconnected and tightly connected, and there is no way to disassemble the whole. The existing borescope equipment has poor flexibility, poor accessibility, difficult operation, low working efficiency, and the probe part of the borescope cannot be bent and twisted over a large range. Through unique structural design and deformation reconstruction algorithm, the probe part can be bent and twisted at any angle, which is convenient for assembly and disassembly, so that clearer observation and detection can be carried out.

Claims

1. A flexible bending probe with integrated FBG sensing and driving for in-situ detection of an engine, characterized in that: The invention comprises a superelastic shape memory alloy hollow threaded tube (100) and a bending mechanism (110), wherein a bending mechanism (110) is arranged inside the hollow threaded tube (100), wherein the bending mechanism (110) is composed of four high temperature resistant resin rings (120) and a superelastic shape memory alloy wire (2), wherein the surface of the high temperature resistant resin ring (120) is provided with through holes (220), wherein the through holes (220) are distributed at 45 degrees, and the superelastic shape memory alloy wire (2) is placed inside the through holes (220), wherein the bending mechanism (110) is completely in contact with the inner wall of the hollow threaded tube (100), wherein the top surface of the bending mechanism (110) is flush with the upper end surface of the hollow threaded tube (100), and wherein the bottom surface of the bending mechanism (110) is flush with the lower end surface of the hollow threaded tube (100); A high-definition camera lens line (200) is placed at the central axis of the hollow threaded tube (100), the high-definition camera lens line (200) penetrates into the hollow threaded tube (100), a high-definition camera lens (210) is installed at one end of the high-definition camera lens line (200), and the other end of the high-definition camera lens line (200) is connected to a micro display screen (300); The hollow threaded tube (100) is adhered to the U-shaped foil (4) by means of an adhesive, a plurality of optical fiber sensors (6) connected in series are arranged in the U-shaped foil (4), the U-shaped foil (4) is deformed into an O-shaped tube (5) by high temperature heating, the optical fiber sensor (6) is completely contained in the O-shaped tube (5), and the strain value of the bending mechanism (110) unit is measured by the optical fiber sensor (6); The processing steps of the U-shaped foil (4) are as follows: using a shape memory alloy foil with a thickness of 0.5 mm, making the shape memory alloy foil into an ultra-thin foil, the ultra-thin foil being pressed into a U shape by a special mold, the U-shaped ultra-thin foil having a shape memory effect through thermal effect training in a high-temperature furnace, and transforming into an O-shaped shape under heating to become an O-shaped tube (5); after cooling, the O-shaped tube (5) can return to the state of the U-shaped foil (4), and the optical fiber sensor (6) can be taken out.

2. The compliant bending probe with integrated FBG sensing and driving for in-situ detection of an engine according to claim 1, characterized in that: The U-shaped foil (4) is tangent to the upper surface of the hollow threaded tube (100), that is, the hollow threaded tube (100) is horizontally placed on the lower surface of the U-shaped foil (4), and the U-shaped foil (4) has excellent ductility.

3. The compliant bending probe with integrated FBG sensing and driving for in-situ detection of an engine according to claim 1, characterized in that: The micro display screen (300) includes a first video connection line (310) and a second video connection line (320) connected thereto, wherein the first video connection line (310) is in line with the high-definition camera lens line (200) and is away from the bending mechanism (110); the second video connection line (320) is connected to the high-definition camera lens line (200) and is separated from the first video connection line (310) by a distance without crossing, and the second video connection line (320) is away from the bending mechanism (110).

4. The compliant bending probe with integrated FBG sensing and driving for in-situ detection of an engine according to claim 3, characterized in that: The high-definition camera lens line (200) is inserted into the interior of the bending mechanism (110) and is tightly adhered and fixed to the hollow threaded tube (100).

5. The compliant bending probe with integrated FBG sensing and driving for in-situ detection of an engine according to claim 3, characterized in that: The first video connection line (310) and the second video connection line (320) are both made of optical fiber material, and both video connection lines are flexible and bendable.

6. The compliant bending probe with integrated FBG sensing and driving for in-situ detection of an engine according to claim 3, characterized in that: The high-definition camera lens line (200) is located at the central axis of the bending mechanism (110), and there is a certain distance between the high-definition camera lens line (200) and the through holes (220) in the circular ring of the bending mechanism (110). The through holes (220) are distributed at 45 degrees, the depth of the through holes (220) is equal to the height of the circular ring in the bending mechanism (110), and the through holes (220) are located on the surface of the bending mechanism (110).

7. The compliant bending probe with integrated FBG sensing and driving for in-situ detection of an engine according to claim 1, characterized in that: The hollow threaded tube (100) is smoothly connected near the port and has a certain wall thickness.

8. A deformation reconstruction algorithm for a compliant bending probe as claimed in claim 1, characterized in that: The following steps are involved: S1, a component of equal thickness is bent and deformed, and FBG sensors are attached to its upper and lower surfaces. The relationship between the surface strain value ε(x) and the deflection ω(x) of the component is as follows: The c is the vertical distance from the upper surface to the middle surface of the component with equal thickness, which can be calculated as: The ε t is the surface strain value at a certain point, ε b is the lower surface strain value at the corresponding position, h is the thickness of the hollow threaded tube, and under pure bending deformation, the absolute values ​​of the upper and lower strains at the same position are the same, ε b ≈ε t , convert the above formula into the following formula: S2, the pasting of n FBGs divides the structure into n-1 segments, and the starting point of segment i With the end point The strain values ​​at i , ε i+1 , the end point of the previous segment is the starting point of the next segment. FBG only obtains the first and last two data on a segment. Through simple linear interpolation, the discrete value becomes continuous, and the strain value of each point on the i-th segment curve is obtained: S3, the rotation angle of the starting point of the i-th segment on the upper surface of the mechanism and deflection It is known that the i-th section corner The equation can be obtained by integrating the strain expression: S4, integrating the rotation angle equation, we can get the bending deflection ω: S5, through the expression of S4, the expression of the first segment deflection can be obtained, and then the deflection of each segment can be obtained, and then all deflection values ​​can be obtained to reconstruct the shape of the mechanism; S6, analyzing the mechanical properties of the object, dividing the unit of the problem to be solved into several micro-units, constructing the unit according to the corresponding mechanical model and mechanical equilibrium equation, discretizing the constructed unit, dividing the nodes, and solving the unit stiffness matrix and unit load array; S7, calculate the strain field e according to the coordinates of all strain measuring points, assuming that the measured strain field is e ε According to the principle of minimizing the Euclidean norm of the calculated strain field and the measured strain field, the error function Φ = Φ(e, e ε ), Kq = F is derived by finding the minimum value of the error function; S8, given the boundary conditions, according to the natural boundary conditions, K and F are processed so that the stiffness matrix K is a full rank matrix, so that K fq =F f , solve S9, dividing the outer surface of the bending mechanism (110) into a plurality of node polygonal thin-walled units, wherein the thin-walled units have a plurality of nodes as vertices, and the nodes are numbered in a counterclockwise direction; S10, establishing a reference coordinate system in the thin-walled unit, with the origin of the coordinate system located at the centroid of the thin-walled unit, and establishing a global coordinate system, and establishing an algebraic relationship between the reference coordinate system and the global coordinate system through normalization processing; S11, arranging a FBG strain rosette at the centroid of the thin-walled unit to measure strain values ​​in three directions, including shear strain value, tensile strain value, and bending strain value. The strain rosette arrangement adopted in the experiment is a double-sided arrangement, with a portion of the strain rosettes arranged on the outer surface of the bending mechanism (110) and another portion of the strain rosettes arranged on the inner surface of the bending mechanism (110). The bending mechanism (110) has a certain wall thickness; S12, constructing a shape function through a mechanical equilibrium relationship, deriving a strain matrix, substituting each coordinate of the thin-walled unit node into the strain matrix, and obtaining three types of strain matrices, namely a shear strain matrix, a tensile strain matrix, and a bending strain matrix; S13, substituting the strain matrix obtained in S12 into the equation for solving the unit stiffness matrix to obtain the unit stiffness matrix, combining the unit stiffness matrices into a total stiffness matrix, and then observing the boundary constraints of the bending mechanism (110), and then conditionally constraining the total stiffness matrix; S14, continue to solve the stress matrix according to the method of solving the total stiffness matrix, and at the same time, limit the boundary conditions and conditionally constrain the stress matrix; S15, using the total stiffness matrix of S13 and the above stress matrix, solving equations through algebraic formulas to obtain the required node displacements, and then drawing the displacement-strain curve through software.

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