Pipe structure inversion method with introduction of angle deviation coefficient and strain field pre-reconstruction

Abstract

This invention discloses a method for inverting the morphology of a tubular structure by introducing an angular deflection coefficient and pre-reconstruction of the strain field, comprising the following steps: Step 1: Spiral arrangement of a high-density weak-reflection grating distributed fiber optic sensor on the surface of a cylindrical tubular structure; Step 2: Strain field inversion of the cylindrical tubular structure based on the introduction of the angular deflection coefficient and the high-density weak-reflection grating distributed fiber optic sensor; Step 3: Inversion of the morphology of the tubular structure based on pre-reconstruction of the strain field; Step 4: Adopting a variable lift angle layout method to further improve the accuracy of the morphology inversion of the cylindrical tubular structure.

Description

Technical Field

[0001] This invention belongs to the field of structural health monitoring based on fiber optic sensors, and specifically proposes a method for inverting the morphology of pipe structures by introducing angular deflection coefficient and strain field prior reconstruction. Background Technology

[0002] Deformation monitoring of circular pipe structures is of great research significance in fields such as flexible pipelines for aerial refueling, wing spars of UAVs, and monitoring of tunnels or highway slopes based on inclinometer tubes. However, current deformation monitoring of circular pipe structures usually adopts paired sensing paths, where each pair of paths can only monitor deformation in one direction. This requires a large number of sensors and cannot provide a comprehensive monitoring of the strain on the surface of the circular pipe.

[0003] Deformation reconstruction of tubular structures based on conventional distributed fiber optic sensors typically requires one or two symmetrically arranged sensing paths for two-dimensional morphological inversion. A single sensing path cannot perform temperature compensation and is easily affected by strain caused by tension and compression, resulting in low accuracy. Furthermore, while symmetrically arranged sensing paths can achieve higher accuracy, to cover as many monitoring areas as possible in different quadrants of the cylindrical surface, more fiber optic sensing paths need to be deployed along the axial direction of the tubular structure, increasing both testing costs and the workload of the demodulation equipment. Moreover, each symmetrically distributed fiber optic sensor group can only perform deformation inversion in one direction, making it impossible to directly extract spatial location information.

[0004] While multi-core optical fibers can achieve three-dimensional deformation inversion of a single path using algorithms such as the Frenet frame or the minimum rotation frame method, the multi-core sensors used in these methods are relatively expensive, and the algorithms are complex and difficult to demodulate.

[0005] For monitoring tubular structural components, such as the use of OFDR sensors with a spiral layout by Tian Hao et al. to monitor the corrosion of reinforcing bars, the spiral layout OFDR sensor is often used to monitor the strain and temperature of tubular structural components, but there are few technologies that use the spiral layout to monitor the deformation of cylindrical tubular structures.

[0006] Kriging interpolation has been applied to strain field inversion on the surface of tubular structures, such as Hu Xitao's scheme for strain field reconstruction and load location identification in cylindrical sections. However, his scheme cannot monitor the deformation of structural components and only achieves strain inversion in a localized part of the cylinder.

[0007] Compared to existing methods that first reconstruct discrete deflection based on discrete strain measurement point information and then perform interpolation fitting, the proposed scheme in this patent, which first reconstructs the strain field and then directly inverts all deflection information, can achieve spatial deformation inversion of the tested pipe structure with temperature compensation along a single sensing path while maintaining high accuracy. This reduces fiber optic consumption and the number of demodulator channels required. Furthermore, this patent introduces the concept of an angle deviation coefficient and utilizes piecewise interpolation to further improve strain inversion accuracy, demonstrating significant practical application value. Summary of the Invention

[0008] Technical problem: The technical problem of this invention is to realize the morphological inversion of a tube structure with temperature compensation using a single OFDR sensor, including strain field inversion and spatial deformation inversion.

[0009] Technical Solution: To solve the above-mentioned technical problems, the present invention provides a method for inverting the morphology of a solid spiral sensor layout circular tube based on strain field prior reconstruction and the introduction of angular deflection coefficient, comprising the following steps:

[0010] Step 1: Arrange high-density, low-reflection grating distributed fiber optic sensors with fixed or variable lift angles spirally on the surface of a cylindrical tubular structure.

[0011] Method 1: Using a fixed angle, a density-low-reflection grating distributed fiber optic sensor is spirally attached to the surface of a single-end fixed cylindrical tubular structure. A cylindrical coordinate system (r, θ, h) is established with the center of the circular section at the fixed end of the tube as the origin, the line connecting the sensor path to this section and the origin as the polar axis, and the tube's axial direction as the vertical axis. Here, h is the vertical coordinate. If the projection of any point in this coordinate system onto the fixed end section is made, then r and θ are the polar radius and polar angle of that point. The sensor installation path in the cylindrical coordinate system satisfies...

[0012]

[0013] Where θ0 is the independent variable, D T L is the outer diameter of the cylindrical tubular structure being measured, and L is the length of the tubular structure. The spiral path angle;

[0014] Method 2: Variable Angle. A density-low-reflection grating distributed fiber optic sensor is spirally attached to the surface of a single-end fixed cylindrical tubular structure. A cylindrical coordinate system (r, θ, h) is established with the center of the circular section at the fixed end of the tube as the origin, the line connecting the sensor path to the origin and the intersection of this section with the origin as the polar axis, and the tube axis as the vertical axis. Here, h is the vertical coordinate. If the projection of any point in this coordinate system onto the fixed end section is made, then r and θ are the polar radius and polar angle of that point. The sensor installation path satisfies the following conditions in the cylindrical coordinate system.

[0015]

[0016]

[0017] Where h N-1 The h coordinate at the end of the (N-1)th cycle. As the initial lift angle, The angle increment is for each circle; the above layout scheme can effectively improve the inversion accuracy of spatial deformation when there are limited costs, limited fiber length, limited demodulation capabilities, limited computing power, or a need for faster computing time.

[0018] Step 2: Conduct strain field inversion of a cylindrical tubular structure based on the introduction of angular deflection coefficients and a high-density weak-reflection grating distributed fiber optic sensor.

[0019] (2-1) The strain measured by the sensor is the strain along the sensor axis, i.e., the strain along the path direction. However, deformation field inversion requires knowledge of the axial strain on the surface of the structural component. If the sensor is at an angle of elevation... The test piece is spirally wound, and a sufficiently short sensor distribution path is arbitrarily chosen as the diagonal on the surface of the test structure. A rectangular micro-element is taken as one side of the radial length dl of the test piece. Then, the length b0 of the other side of the rectangle can be expressed as:

[0020]

[0021] When a structural component bends, if the axial strain at the micro-element is E (E≠0), then the micro-element deforms. The deformed micro-element has side lengths of... A rectangle with a width of (1-μ·E)·dl, where μ is the Poisson's ratio of the structural material.

[0022] Therefore, the diagonal lengths of the infinitesimal element before and after deformation are respectively

[0023]

[0024]

[0025] Then the strain along the sensor axis at this infinitesimal element

[0026]

[0027] Therefore, the axial strain ε1 measured by the high-density, low-reflection grating distributed fiber optic sensor arranged along a spiral has the above functional relationship with the axial strain ε of the cylindrical tubular structure. From its inverse function, the axial strain on the surface of the structural component can be calculated based on the strain along the path direction.

[0028] (2-2) Divide the surface of the pipe fitting to be tested into N T Segment, making the nth segment on the surface of the pipe fitting T +1(0≤nT ≤N T Any point P in segment -1 m (r m ,θ m ,h m )satisfy The centerline of this segment is:

[0029]

[0030] (2-3) Based on optical frequency domain reflectance (OFDR) technology, strain distribution data at several points along the sensing path can be measured. If the nth point... T Given n known strain points measured by sensors in the +1 segment interpolation, calculate the i-th (1≤i≤n) point P. i (r i ,θ i ,h i ) and the j-th (1≤j≤n) point P h (r j ,θ j ,h j The semivariance γ between ) ij γ ij It can be represented as:

[0031]

[0032] Where E is the mathematical expectation, ε i Let ε be the strain value at the i-th sensing point. j Let be the strain value at the j-th sensing point.

[0033] (2-4) Since the strain at any point in the bending deformation satisfies:

[0034]

[0035] Where h is the distance between the point and the neutral layer, and ρ is the radius of curvature of the point, if points A and B are two points on the same cross-section of the surface of the pipe being tested, the x-axis is on the central layer, O is the center of the cross-section, OA is perpendicular to the neutral layer, and the distances of points A and B from the neutral layer are respectively...

[0036] h A =R

[0037] h B =R·cos(Δθ)

[0038] Where Δθ is the angle difference between each point and the centerline of the segment, and R is the outer diameter of the pipe being measured, therefore the ratio of the strains at points A and B is:

[0039]

[0040] Therefore, let the angle deviation coefficient

[0041] (2-5) Definition Let the apparent distance between the i-th point and the j-th point satisfy the following condition:

[0042]

[0043] The r is fitted using the exponential model in the typical semivariogram model. ij and The relationship yields the semi-mutation function r(d) A ), Randomly select a surface of the pipe fitting that satisfies Point P0(r0,θ0,h0) is taken as the point to be estimated. Based on the apparent distance calculation method described above, the apparent distance between each sensing point and the point to be estimated can also be calculated. This leads to the semivariance γ between the known and unknown points. i0 .

[0044] (2-6) Calculate the weight coefficient matrix W = [w1, w2, ..., w n ] T W satisfies

[0045]

[0046] Where w i The weighting coefficients for the i-th known point are used to calculate the strain estimate of the point to be estimated using the traditional Kriging interpolation method. satisfy

[0047]

[0048] By taking a sufficient number of points to be estimated within this interpolation segment and repeating the above process to calculate the strain value at each point, the desired result can be achieved. Strain field inversion within the range, thus enabling the inversion of strain fields within N. T The axial strain field along the surface of the cylindrical tubular structure is reconstructed after segment interpolation.

[0049] Step 3: Reconstruct and invert the morphology of the tube structure based on the strain field.

[0050] According to the method described in step two, the strain field of the cylindrical tubular structure is first reconstructed to obtain high spatial resolution structural strain distribution and response information. Based on the global strain distribution of the monitored object obtained in advance, the morphological inversion of the cylindrical tubular structure is then carried out.

[0051] (3-1) Extract the ε obtained from the inversion in step two. X±∑ ε Y±∑ , where ε X+∑ ε is the strain along the axial direction of the cylindrical tubular structure when θ = 0.X-∑ ε is the strain along the axial direction of the tubular structure when θ = 180°. Y+∑ ε is the strain along the axial direction of the tubular structure when θ = 90°. Y-∑ The strain along the axial direction of the tubular structure is given when θ = 270°.

[0052] (3-2) Temperature self-compensation for a single sensing path is achieved based on the following method.

[0053] Since the temperature difference between any point P(r0,θ0,h0) and point Q(r0,π+θ0,h0) is small, and we have:

[0054] ε Pw -ε Qw =2ε Pw

[0055] Where ε Pw For point P, strain ε is generated due to bending. Qw For point Q, strain occurs due to bending; the ε obtained by the above inversion method... x±∑ ε Y±∑ satisfy

[0056] ε X+∑ =ε X+w +ε F

[0057] ε X-∑ =ε X-w +ε F =-ε X+w +ε F

[0058] ε Y+∑ =ε Y+w +ε F

[0059] ε Y-∑ =ε Y-w +ε F =-ε Y+w +ε F

[0060] Where ε X±w , ε Y±w For bending to produce strain, ε F The spurious strain is caused by temperature, therefore there is

[0061]

[0062]

[0063] (3-3) The strains mentioned above are all functions of the distance h from the fixed support end (i.e., the vertical coordinate). From the relationship between strain, curvature, and displacement, we know that:

[0064]

[0065]

[0066] Where w X w Y The equations for the deflection curves of a cylindrical tubular structure in the X and Y directions are given, respectively, and spatial deformation inversion is achieved based on the strain-curvature-displacement re-integration algorithm.

[0067] The present invention provides a method for inverting the morphology of a circular tube with a 45° rising angle sensor layout based on strain field prior reconstruction and the introduction of angular deflection coefficient, comprising the following steps:

[0068] The spiral path angle described in step one It is 45°;

[0069] Step 2 (2-1): The functional relationship between the axial strain ε1 of the sensor measured by the high-density, low-reflection grating distributed fiber optic sensor arranged along the spiral and the axial strain ε of the cylindrical tubular structure:

[0070]

[0071] An excessively large angle of ascent will reduce inversion accuracy, while an excessively small angle will significantly increase the amount of optical fiber used. A suitable angle is typically found at a certain value. Angle of rise Not only is it within a reasonable range of elevation angles, but it can also simplify the sensor mounting and subsequent calculation steps to a certain extent. Therefore, when there are no special requirements for accuracy and the number of sensors used, a sensor layout with a 45° elevation angle can be given priority.

[0072] The advantages of this invention are: it enables temperature-compensated structural morphology inversion of the tested pipe along a single sensing path, including strain inversion and spatial deformation inversion, reducing fiber consumption and the number of demodulator channels required compared to traditional methods. The fixed-angle spiral layout scheme uses a high-density, low-reflection grating distributed fiber optic sensor for strain sensing, effectively acquiring and utilizing all strain data from the tested pipe surface. Besides spatial deformation inversion, it can also effectively and comprehensively invert the strain field on the tested pipe surface. The variable-angle layout scheme improves the reconstruction accuracy of the strain field near the fixed support end and specifically enhances the inversion accuracy of spatial deformation. Based on finite element simulation, under a certain working condition… The proposed layout uses 1312mm of optical fiber, while the fixed 30° angle layout requires 1323mm. The deformation inversion accuracy of the variable angle layout is significantly improved compared to the fixed angle layout. Therefore, adopting the variable angle layout method is of great significance for further improving the accuracy of morphological inversion of cylindrical tubular structures. This scheme also introduces an angle deviation coefficient, which improves the inversion accuracy of the strain field on the surface of the tested pipe. By reconstructing the axial strain field of the structure through the relationship between the axial strain of the sensor and the axial strain along the structure, spatial deformation inversion can be achieved based on this strain field, which has extremely high practical application value. Attached Figure Description

[0073] Figure 1 The layout scheme for deformation monitoring of tubular structures is shown in (a) and (b), which are commonly used OFDR layout schemes for deformation monitoring of tubular structures; (c) is the OFDR layout scheme for deformation monitoring of the tubular structure in this example.

[0074] Figure 2 The ratio of the strains at points A and B on a certain cross section is:

[0075] Figure 3 The effect of introducing the angular deflection coefficient on the absolute error of strain inversion in an experiment;

[0076] Figure 4 The deformation of any infinitesimal element on the surface of the tested pipe before and after bending;

[0077] Figure 5 A fixed rise angle of 30° layout scheme and a layout scheme with less fiber consumption, starting at a rise angle of 15° and increasing by 5° per turn;

[0078] Figure 6 Figure 5 The relationship between the absolute error of deformation inversion for the two layout schemes shown and the distance from the fixed support end;

[0079] Figure 7 Flowchart of a method for inverting the shape of a circular tube based on strain field prior reconstruction and the introduction of angular deflection coefficient. Detailed Implementation

[0080] The method for inverting the shape of a circular tube with a fixed-angle sensor layout based on strain field prior reconstruction and the introduction of angular deflection coefficient includes the following steps:

[0081] Step 1: Arrange high-density, low-reflection grating distributed fiber optic sensors with fixed or variable lift angles spirally on the surface of a cylindrical tubular structure.

[0082] Method 1: Using a fixed angle, a density-low-reflection grating distributed fiber optic sensor is spirally attached to the surface of a single-end fixed cylindrical tubular structure. A cylindrical coordinate system (r, θ, h) is established with the center of the circular section at the fixed end of the tube as the origin, the line connecting the sensor path to this section and the origin as the polar axis, and the tube's axial direction as the vertical axis. Here, h is the vertical coordinate. If the projection of any point in this coordinate system onto the fixed end section is made, then r and θ are the polar radius and polar angle of that point. The sensor installation path in the cylindrical coordinate system satisfies...

[0083]

[0084] Where θ0 is the independent variable, D T L is the outer diameter of the cylindrical tubular structure being measured, and L is the length of the tubular structure. The spiral path angle;

[0085] Method 2: Variable Angle. A density-low-reflection grating distributed fiber optic sensor is spirally attached to the surface of a single-end fixed cylindrical tubular structure. A cylindrical coordinate system (r, θ, h) is established with the center of the circular section at the fixed end of the tube as the origin, the line connecting the sensor path to the origin and the intersection of this section with the origin as the polar axis, and the tube axis as the vertical axis. Here, h is the vertical coordinate. If the projection of any point in this coordinate system onto the fixed end section is made, then r and θ are the polar radius and polar angle of that point. The sensor installation path satisfies the following conditions in the cylindrical coordinate system.

[0086]

[0087]

[0088] Where h N-1 The h coordinate at the end of the (N-1)th cycle. As the initial lift angle, The angle increment is for each circle; the above layout scheme can effectively improve the inversion accuracy of spatial deformation when there are limited costs, limited fiber length, limited demodulation capabilities, limited computing power, or a need for faster computing time.

[0089] Step 2: Conduct strain field inversion of a cylindrical tubular structure based on the introduction of angular deflection coefficients and a high-density weak-reflection grating distributed fiber optic sensor.

[0090] (2-1) The axial strain ε1 of the high-density weak-reflection grating distributed fiber optic sensor arranged along a spiral has the following corresponding functional relationship with the axial strain ε of the cylindrical tubular structure:

[0091]

[0092] Where μ is Poisson's ratio; using its inverse function, the axial strain distribution information on the surface of the cylindrical structure is calculated based on the strain along the sensing path.

[0093] (2-2) Divide the surface of the pipe fitting to be tested into N T Segment, making the nth segment on the surface of the pipe fitting T +1(0≤n T ≤N T Any point P in segment -1 m (r m ,θ m ,h m )satisfy The centerline of this segment is:

[0094]

[0095] (2-3) Based on optical frequency domain reflectance (OFDR) technology, strain distribution data at several points along the sensing path can be measured.

[0096] If the nth T Given n known strain points measured by sensors in the +1 segment interpolation, calculate the i-th (1≤i≤n) point P. i (r i ,θ i ,h i ) and the j-th (1≤j≤n) point P j (r j ,θ j ,h j The semivariance γ between ) ij γ ij It can be represented as:

[0097]

[0098] Where E is the mathematical expectation, ε i Let ε be the strain value at the i-th sensing point. j Let J be the strain value at the j-th sensing point;

[0099] (2-4) Define k d The angular deviation coefficient can be expressed as:

[0100]

[0101] Where Δθ is the angle difference between each point and the midline of the segment;

[0102] (2-5) Definition Let the apparent distance between the i-th point and the j-th point satisfy the following condition:

[0103]

[0104] The r is fitted using the exponential model in the typical semivariogram model. ij and The relationship yields the semi-mutation function r(d) A ); Randomly select a surface of the pipe fitting that satisfies Point P0(r0,θ0,h0) is taken as the point to be estimated. Based on the apparent distance calculation method described above, the apparent distance between each sensing point and the point to be estimated can also be calculated. This leads to the semivariance γ between the known and unknown points. i0 ;

[0105] (2-6) Calculate the weight coefficient matrix W = [w1, w2, ..., w n ] T W satisfies

[0106]

[0107] Where w i The weighting coefficients for the i-th known point are used to calculate the strain estimate of the point to be estimated using the traditional Kriging interpolation method. satisfy

[0108]

[0109] By taking a sufficient number of points to be estimated within this interpolation segment and repeating the above process to calculate the strain value at each point, the desired result can be achieved. Strain field inversion within the range, thus enabling the inversion of strain fields within N. T The axial strain field along the surface of the cylindrical tubular structure is reconstructed after segment interpolation;

[0110] Step 3: Reconstruct and invert the morphology of the tube structure based on the strain field.

[0111] According to the method described in step two, the strain field of the cylindrical tubular structure is first reconstructed in advance to obtain high spatial resolution structural strain distribution and response information. Based on the global strain distribution of the monitored object obtained in advance, the morphological inversion of the cylindrical tubular structure is then carried out.

[0112] (3-1) Extract the ε obtained from the inversion in step two. X±∑ ε Y±∑ , where ε X+∑ ε is the strain along the axial direction of the cylindrical tubular structure when θ = 0. X-∑ ε is the strain along the axial direction of the tubular structure when θ = 180°. Y+∑ ε is the strain along the axial direction of the tubular structure when θ = 90°. Y-∑ The strain along the axial direction of the tubular structure when θ = 270°;

[0113] (3-2) Temperature self-compensation for a single sensing path is achieved based on the following method.

[0114] Since the temperature difference between any point P(r0,θ0,h0) and point Q(r0,π+θ0,h0) is small, and we have:

[0115] ε Pw -ε Qw =2ε Pw

[0116] Where ε Pw For point P, strain ε is generated due to bending. Qw For point Q, strain occurs due to bending; the ε obtained by the above inversion method... x±∑ ε Y±∑ satisfy

[0117] ε X+∑ =ε X+w +ε F

[0118] ε X-∑ =ε X-w +ε F =-ε X+w +ε F

[0119] ε Y+∑ =ε Y+w +ε F

[0120] ε Y-∑ =ε Y-w +ε F =-ε Y+w +ε F

[0121] Where ε X±w , ε Y±w For bending to produce strain, ε F The spurious strain is caused by temperature, therefore there is

[0122]

[0123]

[0124] (3-3) The strains mentioned above are all functions of the distance h from the fixed support end (i.e., the vertical coordinate). From the relationship between strain, curvature, and displacement, we know that:

[0125]

[0126]

[0127] Where w X w YThe equations for the deflection curves of a cylindrical tubular structure in the X and Y directions are given, respectively, and spatial deformation inversion is achieved based on the strain-curvature-displacement re-integration algorithm.

[0128] 2. The method for inverting the shape of a circular tube with a fixed lifting angle sensor layout based on strain field prior reconstruction and the introduction of angular deflection coefficient as described in claim 1, is characterized by comprising the following processes:

[0129] The spiral path angle described in step one It is 45°;

[0130] Step 2 (2-1): The functional relationship between the axial strain ε1 of the sensor measured by the high-density, low-reflection grating distributed fiber optic sensor arranged along the spiral and the axial strain ε of the cylindrical tubular structure:

[0131]

Claims

1. A method for inverting the morphology of a tube structure by introducing an angular deflection coefficient and prior reconstruction of the strain field, characterized in that, Includes the following steps: Step 1: Arrange high-density, low-reflection grating distributed fiber optic sensors with fixed or variable lift angles spirally on the surface of a cylindrical tubular structure. Method 1: Using a fixed angle, a density-low-reflection grating distributed fiber optic sensor is spirally attached to the surface of a single-end fixed cylindrical tubular structure. A cylindrical coordinate system (r, θ, h) is established with the center of the circular section at the fixed end of the tube as the origin, the line connecting the sensor path to this section and the origin as the polar axis, and the tube's axial direction as the vertical axis. Here, h is the vertical coordinate. If the projection of any point in this coordinate system onto the fixed end section is made, then r and θ are the polar radius and polar angle of that point. The sensor installation path in the cylindrical coordinate system satisfies... Where θ0 is the independent variable, D T L is the outer diameter of the cylindrical tubular structure being measured, and L is the length of the tubular structure. The spiral path angle; Method 2: Variable Angle. A density-low-reflection grating distributed fiber optic sensor is spirally attached to the surface of a single-end fixed cylindrical tubular structure. A cylindrical coordinate system (r, θ, h) is established with the center of the circular section at the fixed end of the tube as the origin, the line connecting the sensor path to the origin and the intersection of this section with the origin as the polar axis, and the tube axis as the vertical axis. Here, h is the vertical coordinate. If the projection of any point in this coordinate system onto the fixed end section is made, then r and θ are the polar radius and polar angle of that point. The sensor installation path satisfies the following conditions in the cylindrical coordinate system. Where h N-1 The h coordinate at the end of the (N-1)th cycle. As the initial lift angle, The angle increment is for each circle; the above layout scheme can effectively improve the inversion accuracy of spatial deformation when there are limited costs, limited fiber length, limited demodulation capabilities, limited computing power, or a need for faster computing time. Step 2: Conduct strain field inversion of a cylindrical tubular structure based on the introduction of angular deflection coefficients and a high-density weak-reflection grating distributed fiber optic sensor. (2-1) The axial strain ε1 of the high-density weak-reflection grating distributed fiber optic sensor arranged along a spiral has the following corresponding functional relationship with the axial strain ε of the cylindrical tubular structure: Where μ is Poisson's ratio; Based on its inverse function and the strain along the sensing path, the axial strain distribution information on the surface of the cylindrical structure is calculated. (2-2) Divide the surface of the pipe fitting to be tested into N T Segment, making the nth segment on the surface of the pipe fitting T +1(0≤n T ≤N T Any point P in segment -1 m (r m ,θ m ,h m )satisfy The centerline of this segment is: (2-3) Based on optical frequency domain reflectance (OFDR) technology, strain distribution data at several points along the sensing path can be measured. If the nth T Given n known strain points measured by sensors in the +1 segment interpolation, calculate the i-th (1≤i≤n) point P. i (r i ,θ i ,h i ) and the j-th (1≤j≤n) point P j (r j ,θ j ,h j The semivariance γ between ) ij γ ij It can be represented as: Where E is the mathematical expectation, ε i Let ε be the strain value at the i-th sensing point. j Let J be the strain value at the j-th sensing point; (2-4) Define k d The angular deviation coefficient can be expressed as: Where Δθ is the angle difference between each point and the midline of the segment; (2-5) Definition Let the apparent distance between the i-th point and the j-th point satisfy the following condition: The r is fitted using the exponential model in the typical semivariogram model. ij and The relationship yields the semi-mutation function r(d) A ); Randomly select a surface of the pipe fitting that satisfies point P0(r0,θ0,h0) is the point to be estimated. Based on the apparent distance calculation method described above, the apparent distance between each sensing point and the point to be estimated can also be calculated. This leads to the semivariance γ between the known and unknown points. i0 ; (2-6) Calculate the weight coefficient matrix W = [w1, w2, ..., w n ] T W satisfies Where w i The weighting coefficients for the i-th known point are used to calculate the strain estimate of the point to be estimated using the traditional Kriging interpolation method. satisfy By taking a sufficient number of points to be estimated within this interpolation segment and repeating the above process to calculate the strain value at each point, the desired result can be achieved. Strain field inversion within the range, thus enabling the inversion of strain fields within N. T The axial strain field along the surface of the cylindrical tubular structure is reconstructed after segment interpolation; Step 3: Reconstruct and invert the morphology of the tube structure based on the strain field. According to the method described in step two, the strain field of the cylindrical tubular structure is first reconstructed in advance to obtain high spatial resolution structural strain distribution and response information. Based on the global strain distribution of the monitored object obtained in advance, the morphological inversion of the cylindrical tubular structure is then carried out. (3-1) Extract the inversion result obtained in step two in Let θ = 0 be the strain along the axial direction of the cylindrical tubular structure. Let be the strain along the axial direction of the tubular structure when θ = 180°. Let θ = 90° be the strain along the axial direction of the tubular structure. The strain along the axial direction of the tubular structure when θ = 270°; (3-2) Temperature self-compensation for a single sensing path is achieved based on the following method. Since the temperature difference between any point P(r0,θ0,h0) and point Q(r0,π+θ0,h0) is small, and we have: e Pw -e Qw =2e Pw Where ε Pw For point P, strain ε is generated due to bending. Qw The strain at point Q due to bending is obtained by the above inversion method. satisfy in For bending to produce strain, ε F The spurious strain is caused by temperature, therefore there is (3-3) The strains mentioned above are all functions of the distance h from the fixed support end (i.e., the vertical coordinate). From the relationship between strain, curvature, and displacement, we know that: Where w X w Y The equations for the deflection curves of a cylindrical tubular structure in the X and Y directions are given, respectively, and spatial deformation inversion is achieved based on the strain-curvature-displacement re-integration algorithm.

2. The method for inverting the morphology of a tube structure by introducing angular deflection coefficients and pre-reconstruction of the strain field according to claim 1, characterized in that... Includes the following processes: The spiral path angle described in step one It is 45°; Step 2 (2-1): The functional relationship between the axial strain ε1 of the sensor measured by the high-density, low-reflection grating distributed fiber optic sensor arranged along the spiral and the axial strain ε of the cylindrical tubular structure:

Images