CN114413779B - Curved surface double-curvature deformation reconstruction method based on fiber bragg grating strain data - Google Patents

Abstract

The invention discloses a curved surface hyperbolic deformation reconstruction method based on fiber grating strain data, comprising the steps of: arranging shape memory alloy wires on a curved surface to be measured; Orthogonal curvature component at the measuring point, and obtain the coordinates of each measuring point accordingly; use the intersecting shape memory alloy wires to unify the coordinates of the measuring points belonging to different shape memory alloy wires into the same coordinate system; As the coordinates of the corresponding scatter points on the surface to be measured, each scatter point is connected with a grid to complete the approximate reconstruction of the surface to be measured. The invention realizes the approximate reconstruction of the curved surface to be measured by unifying the coordinates of each measuring point of each shape memory alloy wire, and can improve the reconstruction accuracy by adjusting the layout density of the shape memory alloy wire and the interpolation density of the curvature data points , which can be used for real-time deformation calculation of skin under normal load in actual assembly scenarios.

Description

A Method for Reconstructing Surface Hyperbolic Deformation Based on Fiber Bragg Grating Strain Data

technical field

The invention belongs to the technical field of optical fiber grating shape sensing, and in particular relates to a curved surface hyperbolic deformation reconstruction method based on optical fiber grating strain data.

Background technique

In recent years, with the development of digital technology, the virtual modeling technology of physical environment has made great progress. In terms of product manufacturing and assembly, especially in the aerospace manufacturing field with higher precision and quality requirements, the digital manufacturing technology centered on virtual models of components and assemblies is becoming more and more mature. However, the virtual models currently constructed in the computer are still mainly static ideal design models. Factors such as dimensional error and force deformation of components in the process of processing and assembling make components, assemblies and their digital models in geometric shape, mechanical There is a big difference in performance, so that the actual product cannot meet the design requirements. Therefore, it is a future research hotspot to establish a high-fidelity dynamic model of components in the process of processing and assembling based on the measured data, and to study the relationship between manufacturing quality and process parameters based on this.

The existing monitoring methods of flexible structures based on fiber gratings generally have the following problems: (1) The monitored flexible structure objects are constrained (often fixed at one end and free at one end) (2) The monitoring structure only occurs in one direction The plane is bent, and the deformation is a single curvature deformation. In practical application scenarios, thin-walled structures such as aircraft skins undergo a relatively complex hyperbolic small deformation under operations such as drilling and riveting, and the existing surface reconstruction methods are not suitable for such situations.

SUMMARY OF THE INVENTION

Aiming at the deficiencies in the prior art, the present invention provides a curved surface hyperbolic deformation reconstruction method based on fiber grating strain data, aiming at realizing real-time deformation calculation of skin under normal load for actual assembly scenarios.

To achieve the above object, the present invention adopts the following technical solutions:

A method for reconstruction of curved surface hyperbolic deformation based on fiber grating strain data, comprising the following steps:

Step 1: Arrange several disjoint shape memory alloy wires A along a certain direction on the curved surface to be measured, and arrange a shape memory alloy wire B that intersects the shape memory alloy wire A in the other direction; Two bundles of fiber grating sensor strings arranged at 90° in the circumferential direction are installed on the surface. The number and interval of optical fiber measuring points on the two bundles of fiber grating sensor strings are the same, and they are formed by aligning the shape memory alloy wires in pairs in the axial direction. Several curvature measuring points; the curvature measuring points on the shape memory alloy wire B are all located at the intersection point with the shape memory alloy wire A;

Step 2: using the fiber grating sensor string to obtain two strain quantities of each shape memory alloy wire A at each curvature measuring point respectively, and calculating the two orthogonal curvature components at the curvature measuring points through the strain quantities;

Step 3: Interpolate the two orthogonal curvature components at each curvature measurement point of the same shape memory alloy wire A to refine the curvature data points;

Step 4: Based on the orthogonal curvature components at the discrete curvature detection points, the coordinates of each shape memory alloy wire A at each of its curvature data points are reconstructed by using the principle of differential geometry;

Step 5: Use the fiber grating sensor string to obtain the two orthogonal curvature components of the shape memory alloy wire B at each curvature measurement point, and deduce the transformation relationship between the coordinates of the curvature data points between different shape memory alloy wires A based on this , unify the coordinates of each shape memory alloy wire A at its curvature data point into the same coordinate system;

Step 6: Take the unified coordinates of each shape memory alloy wire A at each curvature data point as the coordinates of the corresponding scattered points on the surface to be measured, and connect the scattered points with a grid to complete the approximate reconstruction of the surface to be measured.

Further, in step 2, the formula for calculating the curvature K by the strain variable is:

K=2ε/h,

where h is the diameter of the shape memory alloy wire, ε is the strain amount of the shape memory alloy wire at its bend and ε=Δλ/k ₁ λ, λ is the center wavelength of the reflection of the fiber grating sensor grating when the shape memory alloy wire is not bent , Δλ is the reflection wavelength change when the shape memory alloy wire is bent, and k ₁ is a constant coefficient.

Further, in step 4,

For the same shape memory alloy wire, the curve segment between any two adjacent curvature data points O _i and O _i+1 is approximately the curvature arc in the close plane of the point O _{i .} The tangent line is tangent to the point O _i and the radius is 1/K _i , K _i is the resultant curvature of the curve at the point O _i , and K _i is composed of the orthogonal curvature components K _ix and K _iy of the point O _i obtained; At _i , the tangent of the curve, the main normal and the secondary normal are used as the Z axis, the X axis and the Y axis to establish the Freiner frame of the point O _i , which is denoted as {X _Fi Y _Fi Z _Fi };

为：Taking the direction vector of the orthogonal curvature component of the point O _i as the X axis and the Y axis, and taking the tangent of the curve at O _i as the Z axis, a Cartesian coordinate system is established at the point O _i , which is called the coordinate system of the point O _i . Parallel frame, denoted as {X _i Y _i Z _i }, in the same way, to establish the parallel frame of O _i+1 point {X _i+1 Y _i+1 Z _i+1 }, then {X _i+1 Y Homogeneous transformation matrix from _i+1 Z _i+1 } to {X _i Y _i Z _i }

for:

Among them, α _i is the angle between the curvature vector of K _i and the curvature vector of K _ix , θ _i is the approximate arc angle of the curve between the two points O _i and O _i+1 , L _i is the arc length, and there are

为

t_i表示平行标架{X_iY_iZ_i}到{X_i+1Y_i+1Z_i+1}的平移向量：According to the homogeneous transformation matrix between the parallel frames of adjacent points, one end point of the shape memory alloy wire is selected as the reconstruction reference point, and its parallel frame is used as the global reference coordinate system, and the rest of the curvature data points are calculated recursively in turn. The global coordinates of , the potential vector of the i-th point under the parallel frame of the reference point

for

t _i represents the translation vector of the parallel frame {X _i Y _i Z _i } to {X _i+1 Y _i+1 Z _i+1 }:

Further, in step 5, the layout direction of each shape memory alloy wire A is set as u, and the layout direction of the shape memory alloy wire B is v, the curve formed by the shape memory alloy wire A is called the u-direction curve, and the shape The curve formed by the memory alloy wire B is called the v-direction curve. At the intersection point C _j of the v-direction curve and the jth u-direction curve, the Freiner frame and the parallel frame of the v-direction curve are respectively marked as {X _vF Y _vF Z _vF } and {X _v Y _v Z _v }, the Freiner frame and parallel frame of the u-direction curve are marked as {X _uF Y _uF Z _uF } and {X _u Y _u Z _u };

为：Rotation matrix from the u-direction curve-parallel frame to the v-direction curve-parallel frame at the intersection

for:

The transformation matrix from the u-direction curve-parallel frame to the v-direction curve-parallel frame at the intersection is:

K_vx和K_vy为v向曲线在交点处的正交曲率分量，K_ux和K_uy为u向曲线在交点处的正交曲率分量；where α _u and α _v are the angle between the X-axis of the Freiner frame of the v-direction curve and the u-direction curve and the angle between the X-axis of the parallel frame, and

K _vx and K _vy are the orthogonal curvature components of the v-direction curve at the intersection, and _Kux and _Kuy are the orthogonal curvature components of the u-direction curve at the intersection;

v向曲线在交点C_j的平行标架到其在第一个交点C₁处的平行标架的转换矩阵为：

其中，i是交点C_j在A_j曲线各点中的下标，

是A_j曲线相邻点间平行标架的转换矩阵，T_B是v向曲线相邻点间平行标架的转换矩阵；The transformation matrix from the parallel frame of the jth u-direction curve A _j at the intersection point C _j of the v-direction curve to the parallel frame of the reconstructed reference point of A _j is:

The transformation matrix of the parallel frame of the v-direction curve at the intersection point C _j to its parallel frame at the first intersection point C ₁ is:

Among them, i is the subscript of the intersection point C _j in each point of the curve A _j ,

is the transformation matrix of the parallel frame between the adjacent points of the A _j curve, and T _B is the transformation matrix of the parallel frame between the adjacent points of the v-direction curve;

是交点C_j处u向曲线平行标架到v向曲线平行标架的转换矩阵，根据

将各形状记忆合金丝A在各曲率数据点处的坐标统一到同一坐标系中。Thus, the transformation matrix from the parallel frame of the curve A _j at its reconstructed reference point to the parallel frame of the v-direction curve at the point C ₁ is:

is the transformation matrix from the u-direction curve-parallel frame to the v-direction curve-parallel frame at the intersection C _j , according to

The coordinates of each shape memory alloy wire A at each curvature data point are unified into the same coordinate system.

The beneficial effects of the present invention are:

The invention unifies the coordinates of each measuring point of each shape memory alloy wire A through the intersecting shape memory alloy wires B, so as to realize the approximate reconstruction of the curved surface to be measured, and can adjust the layout density of the shape memory alloy wire A and The interpolation density of curvature data points improves reconstruction accuracy and can be used for real-time deformation calculations of skins under normal loads in actual assembly scenarios.

Description of drawings

Fig. 1 is the schematic flow chart of the method of the present invention;

2 is a schematic structural diagram of a fiber grating sensor string in the present invention;

Fig. 3 is the layout schematic diagram of shape memory alloy wire;

Fig. 4 is the establishment schematic diagram of parallel frame and Freighter frame in the present invention;

Fig. 5 is a schematic diagram of rotation transformation between parallel frames of adjacent points of a curve in the present invention;

6 is a schematic diagram of the geometric relationship between the parallel frame of the alloy wire A _j curve laid in the u direction and the Freiner frame at the intersection point C _j of the alloy wire B curve laid in the v direction in the present invention;

7 is a schematic diagram of the geometric relationship between the parallel frame of the alloy wire B curve arranged in the v direction and the Freiner frame at the intersection point C _j of the alloy wire A _j curve arranged in the u direction in the present invention;

8 is a schematic diagram of the layout of shape memory alloy wires on the hyperbolic curved surface to be measured in the embodiment;

FIG. 9 is the reconstruction result of the hyperbolic curved surface to be measured.

Detailed ways

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

The purpose of the present invention is to provide a curved surface hyperbolic small deformation reconstruction method based on fiber grating strain measurement, which can realize the real-time deformation calculation of the skin under the normal load for the actual assembly scenario. As shown in Figure 1, the method of the present invention comprises:

S1: Preparation and layout of the sensor:

Prepare a plurality of shape memory alloy wires (SMA), and each alloy wire has two fiber grating strings arranged at 90 degrees in the circumferential direction. A number of curvature measuring points, which are aligned in two to form the axis of the alloy wire, are shown in Figure 2; a plurality of such shape memory alloy wires A ₁ A ₂ A ₃ ... are arranged in parallel and at equal intervals along a certain direction on the surface to be measured, and one Alloy wire B whose direction is orthogonal to them. The curvature measuring points of the axis of the alloy wire B on the curved surface are all located at the intersection points C ₁ C ₂ C ₃ ... with the alloy wires A ₁ A ₂ A ₃ and so on.

S2: Deformation and reconstruction of the axis of each alloy wire:

1. Acquisition of curvature information

The fiber grating sensor uses optical fiber as the light transmission medium, on which there are discretely distributed grating measuring points that can reflect light waves specially processed by the optical fiber, and the reflected wavelength is related to the length of the grating. When the temperature changes or the fiber is subjected to axial tension and compression, the length of the grating measuring point changes, causing the reflected wavelength to change. By demodulating the reflected wavelength, the strain or ambient temperature of the grating measuring point can be obtained. The strain ε and the temperature change ΔT usually follow the following linear coupling relationship with the reflected wavelength change Δλ:

In the formula, λ is the center wavelength of the grating reflection when ε and ΔT are zero, k ₁ and k ₂ are constant coefficients, when the monitoring time is short and the ambient temperature change is not significant, the approximation is:

When each micro-segment of the alloy wire is bent in any direction so that the axis of the substrate becomes a spatial curve, each measuring point of the two bundles of fiber grating sensors can sense the bending strain components in two orthogonal directions of each micro-segment of the alloy wire respectively. Combined with the pure bending theory of material mechanics, the two orthogonal curvature components of the axis of the substrate can be calculated, namely K=2ε/h, h is the diameter of the shape memory alloy wire, and ε is the deformation of the shape memory alloy wire at its bending position. variable.

After the fiber grating sensor obtains the two orthogonal curvature components of the alloy wire axis at each measuring point, curvature interpolation is performed between the measuring points to refine the curvature data points of the axis. The commonly used interpolation methods include linear interpolation and cubic spline interpolation. Based on the orthogonal curvature of each discrete point, the coordinates of each point on the axis can be reconstructed by using the principle of differential geometry.

2. Spatial curve reconstruction algorithm based on orthogonal curvature:

其中K_i为曲线在O_i点的合曲率。在空间曲线上的点O_i处分别以曲线切线、主法线和副法线为Z轴、X轴和Y轴建立弗莱纳标架(Frenet Frame)，记为{X_FiY_FiZ_Fi}；再以光栅测点在O_i获取的两个正交弯曲曲率对应的两个曲率向量的方向向量分别作为X轴Y轴，以曲线切线作为Z轴，在O_i点建立一个直角坐标系，称此坐标系为平行标架(Parallel Transport Frameor Parallel Frame)，记为{X_iY_iZ_i}，如图4。According to the principle of differential geometry, for two points O _i and O _i+1 on any space curve, when O _i+1 approaches O _i , the curve segment between the two points can be approximated as the curvature circle in the approximation plane of the point O _i The arc, the tangent of this arc and the curve at O _i is tangent to the point O _i and the radius is

where K _i is the resultant curvature of the curve at the point O _i . At the point O _i on the space curve, take the curve tangent, main normal and secondary normal as the Z-axis, X-axis and Y-axis respectively to establish a Frenet Frame (Frenet Frame), denoted as {X _Fi Y _Fi Z _Fi }; Then take the direction vectors of the two curvature vectors corresponding to the two orthogonal bending curvatures obtained by the grating measuring point at O _i as the X axis and the Y axis respectively, and take the curve tangent as the Z axis, and establish a Cartesian coordinate system at the O _i point , this coordinate system is called Parallel Transport Frame or Parallel Frame, marked as {X _i Y _i Z _i }, as shown in Figure 4.

即曲率圆半径R_i，等于合曲率K_i的倒数，Q_i是第i+1个数据点O_i+1到坐标平面X_i-O_i-Y_i的垂足。K_ix和K_iy分别是O_i点处两个正交曲率分量。合曲率为K_i，其曲率向量沿曲线的主法矢。α_i为K_i的曲率向量与K_ix的曲率向量的夹角，即弗莱纳标架X轴与平行标架X轴的夹角；θ_i为O_i与O_i+1两点间曲线的近似圆弧的转角，L_i为弧长，是已知量。In Figure 4, P _i is the center of the curvature circle at the point O _i , and the distance from O _i to P _i

That is, the radius of curvature R _i is equal to the reciprocal of the resultant curvature K _i , and Q _i is the foot of the i+1th data point O _i+1 to the coordinate plane X _i -O _i -Y _i . K _ix and K _iy are the two orthogonal curvature components at the O _i point, respectively. The resultant curvature is K _i , whose curvature vector is along the principal normal of the curve. α _i is the angle between the curvature vector of _Ki and the curvature vector of K _ix , that is, the angle between the X-axis of the Freiner frame and the X-axis of the parallel frame; θ _i is the curve between the two points of O _i and O _i+1 The approximate arc angle of , _Li is the arc length, which is a known quantity.

According to the geometric relationship in Figure 4, the coordinates of the point O _i+1 in the coordinate system {X _i Y _i Z _i } and the coordinate system {X _i+1 Y _{i+ 1} Z _i+1 } to {X _i Y _i are deduced below Homogeneous transformation matrix for Z _i }:

K _i is composed of orthogonal curvature components K _ix and K _iy :

For α _i we have:

For θ _i we have:

The distance from point _Pi to point _Qi is:

The distance from point O _{i +1} to point Qi is:

The distance from point O _i to point Qi is _:

So the three coordinates of the point O _{i +1} under the coordinate system {X _i Y _i Z _i } of the point O i are:

So the translation vector from the coordinate system of O _i {X _i Y _i Z _i } to the coordinate system of O _i+1 {X _i+1 Y _i+1 Z _i+1 } is:

The rigid body transformation from the orientation of the coordinate system {X _i Y _i Z _i } to the orientation of the coordinate system {X _i+1 Y _i+1 Z _i+1 } is: {X _i Y _i Z _i } around the point O _i The binormal of θ _i is rotated to obtain the coordinate system {X _i+1 Y _i+1 Z _i+1 }, and this transformation can be further decomposed into:

①{X _i Y _i Z _i } rotate α _i around the Z _i axis to the Freiner frame {X _Fi Y _Fi Z _Fi }

②{X _Fi Y _Fi Z _Fi } rotate around Y _Fi by θ _i to get {X _Fi 'Y _Fi 'Z _Fi '}

③{X _Fi 'Y _Fi 'Z _Fi '} rotate around Z _Fi '-α _i to get {X _i+1 Y _i+1 Z _i+1 }

As shown in Figure 5.

FIG. 5 is a schematic diagram of the rotation transformation from the point O _i parallel frame {XiYiZi} to the point O _i+1 parallel frame {Xi+1Yi+1Zi+1}

The matrix corresponding to the rotation transformation ① is:

The matrix corresponding to the rotation transformation ② is:

The matrix corresponding to the rotation transformation ③ is:

由矩阵R₁R₂R₃依次右乘得到：Note that the above transformation is an orbital system rotation, then the rotation matrix from {Xi+1Yi+1Zi+1} to {XiYiZi}

Multiply by the matrix R ₁ R ₂ R ₃ to the right to get:

Then the homogeneous transformation matrix from {X _i+1 Y _i+1 Z _i+1 } to {X _i Y _i Z _i } can be constructed

In formula (2.15), α _i and θ _i are determined by formulas (2.2) and (2.3), respectively.

为：Calculate the homogeneous transformation matrix between the parallel frames of all adjacent points on the space curve according to formula (2.15). An end point of the curve is selected as the reconstruction reference point, and its parallel frame is used as the global reference coordinate system, and the global coordinates of the remaining points are calculated recursively. The potential vector of the i-th point under the parallel frame of the first point (reference point)

for:

According to formula (2.16), the coordinates of all points of the curve in the same coordinate system are calculated. After the curvature interpolation, the data points are dense enough. Connecting each point with a straight line segment can obtain a smooth enough approximate curve to complete the reconstruction of the curve.

S3. Small deformation hyperbolic surface reconstruction method based on curve scatter points:

As shown in Fig. 3, the layout direction of a plurality of parallel and equally spaced alloy wires A ₁ A ₂ A ₃ . . . on the curved surface is u, and the layout direction of the alloy wires B orthogonal to them is v.

A1, A2, A3... have the same number of curvature measuring points and interval between measuring points, forming a measuring point array on the curved surface. According to the curve reconstruction method of S2, the deformation curves of the sensors A1, A2, A3 . . . are calculated, and the scatter coordinates on the curves are obtained. The coordinates of these points are located under the parallel frame of the reconstructed reference point of each curve, and it is necessary to find the transformation relationship of these parallel frames to unify the scatter coordinate system.

The orthogonality of orthogonal curves on the surface does not change when the surface is deformed by a small amount. Using this characteristic, at the intersection points C1, C2, . The matrix expression for this rotation relationship is derived as follows:

The geometrical relationship of the Freiner frame and the parallel frame of the v-direction curve and the u-direction curve at the intersection point C _j are shown in Figs. {X _vF Y _vF Z _vF } and {X _v Y _v Z _v }; the Freighter frame and parallel frame of the u-direction curve are denoted as {X _uF Y _uF Z _uF } and {X _u Y _u Z _u respectively }.

The transformation from the Freiner frame of the v-direction curve to the Freiner frame of the u-direction curve at the intersection point is to rotate 90 degrees counterclockwise around the X-axis. The rotation matrix for this transformation is:

The rotation matrix of the Freiner frame of the v-direction curve to its parallel frame is:

The transformation matrix from the parallel frame of the u-direction curve to its Freiner frame is:

Then the rotation matrix from the u-direction curve-parallel frame to the v-direction curve-parallel frame at the intersection is:

where α _u and α _v are the angles between the two curved Freiner frames and the x-axis parallel to the frame, respectively, which can be determined by the orthogonal curvature obtained by the sensor at the intersection point:

Then the transformation matrix from the u-direction curve-parallel frame to the v-direction curve-parallel frame at the intersection is:

Also: from Equation 2.16, the transformation matrix from the parallel frame of the sensor A _j curve in the u direction at the intersection point C _j of the sensor B curve in the v direction to the parallel frame of the reconstructed reference point of the A _j curve is:

是A_j曲线相邻点间平行标架的转换矩阵。where i is the subscript of the intersection point C _j in each point of the curve A _j ,

is the transformation matrix of the parallel frame between adjacent points of the A _j curve.

The transformation matrix from the parallel frame of sensor B's v-curve at intersection C _j to its parallel frame at the first intersection C ₁ is:

where T _B is the transformation matrix of the parallel frame between adjacent points of the B curve.

Then the transformation matrix from the parallel frame of the curve of sensor A _j at its reconstructed reference point to the parallel frame of the curve of sensor B at point C ₁ is:

是交点C_j处u向曲线平行标架到v向曲线平行标架的转换矩阵In the formula,

is the transformation matrix from the u-direction curve-parallel frame to the v-direction curve-parallel frame at the intersection C _j

In this way, the parallel frames of the reconstructed reference points of each u-curve are unified.

After the coordinates of the scattered points on the surface are unified, when the scattered points become dense enough through curvature interpolation, the approximate reconstruction of the surface is completed by connecting the scattered points with a grid.

Simulation:

As shown in Figure 8, 7 curves A1, A2...A7 are selected along the u direction on the 1/4 ellipsoid with the major semi-axis being 2 and the minor semi-axis being 1, and each curve has 6 curvature sampling points. The 7 curves and the v-direction B curve intersect at 7 curvature sampling points respectively. At the intersection, the normal vector direction of the u-direction curve and the v-direction curve are the same, and the tangent vector direction is perpendicular. The spherical coordinate equation of the sampling ellipsoid is:

The curvatures of the 6 curvature sampling points of the 7 curves in the u direction are: 2, 1.2767, 0.68247, 0.4383, 0.328569, 0.276, the sampling point interval is 0.3672566, and the number of curvature interpolation points of adjacent measurement points of each curve is 10 , the interpolation method is linear interpolation. The curvature of the 7 sampling points of the v-direction B curve is 0.5, the measuring point interval is 1.0472, the number of curvature interpolation points of adjacent sampling points is 10, and the interpolation method is linear interpolation. Using the hyperbolic surface reconstruction method based on curve scatter points proposed in this patent, the ellipsoid surface is reconstructed by using the curvature data of the scatter points, and the reconstruction result is shown in FIG. 9 . At this time, there is no obvious error between the reconstructed surface and the sampled surface. It can be verified that the hyperbolic surface reconstruction method based on curve scatter points proposed in this patent is theoretically feasible, and the curved surface can be reconstructed more accurately according to the surface scatter point curvature data. .

The above are only preferred embodiments of the present invention, and the protection scope of the present invention is not limited to the above-mentioned embodiments, and all technical solutions that belong to the idea of the present invention belong to the protection scope of the present invention.

Claims (4)

1. a curved surface hyperbolic deformation reconstruction method based on fiber grating strain data, is characterized in that, comprises the following steps: Step 1: Arrange several disjoint shape memory alloy wires A along a certain direction on the curved surface to be measured, and arrange a shape memory alloy wire B that intersects the shape memory alloy wire A in the other direction; Two bundles of fiber grating sensor strings arranged at 90° in the circumferential direction are installed on the surface. The number and interval of optical fiber measuring points on the two bundles of fiber grating sensor strings are the same, and they are formed by aligning the shape memory alloy wires in pairs in the axial direction. Several curvature measuring points; the curvature measuring points on the shape memory alloy wire B are all located at the intersection point with the shape memory alloy wire A; Step 2: using the fiber grating sensor string to obtain two strain quantities of each shape memory alloy wire A at each curvature measuring point respectively, and calculating the two orthogonal curvature components at the curvature measuring points through the strain quantities; Step 3: Interpolate the two orthogonal curvature components at each curvature measurement point of the same shape memory alloy wire A to refine the curvature data points; Step 4: Based on the orthogonal curvature components at the discrete curvature detection points, the coordinates of each shape memory alloy wire A at each of its curvature data points are reconstructed by using the principle of differential geometry; Step 5: Use the fiber grating sensor string to obtain the two orthogonal curvature components of the shape memory alloy wire B at each curvature measurement point, and deduce the transformation relationship between the coordinates of the curvature data points between different shape memory alloy wires A based on this , unify the coordinates of each shape memory alloy wire A at its curvature data point into the same coordinate system; Step 6: Take the unified coordinates of each shape memory alloy wire A at each curvature data point as the coordinates of the corresponding scattered points on the surface to be measured, and connect the scattered points with a grid to complete the approximate reconstruction of the surface to be measured. 2. a kind of curved surface hyperbolic deformation reconstruction method based on fiber grating strain data as claimed in claim 1 is characterized in that, in step 2, the formula for calculating curvature K by strain variable is: K=2ε/h, where h is the diameter of the shape memory alloy wire, ε is the strain amount of the shape memory alloy wire at its bend and ε=Δλ/k ₁ λ, λ is the center wavelength of the reflection of the fiber grating sensor grating when the shape memory alloy wire is not bent , Δλ is the reflection wavelength change when the shape memory alloy wire is bent, and k ₁ is a constant coefficient. 3. a kind of curved surface hyperbolic deformation reconstruction method based on fiber grating strain data as claimed in claim 1 is characterized in that, in step 4, For the same shape memory alloy wire, the curve segment between any two adjacent curvature data points O _i and O _i+1 is approximately the curvature arc in the close plane of the point O _{i .} The tangent line is tangent to the point O _i and the radius is 1/K _i , K _i is the resultant curvature of the curve at the point O _i , and K _i is composed of the orthogonal curvature components K _ix and K _iy of the point O _i obtained; At _i , the tangent of the curve, the main normal and the secondary normal are used as the Z axis, the X axis and the Y axis to establish the Freiner frame of the point O _i , which is denoted as {X _Fi Y _Fi Z _Fi }; Taking the direction vector of the orthogonal curvature component of the point O _i as the X axis and the Y axis, and taking the tangent of the curve at O _i as the Z axis, a Cartesian coordinate system is established at the point O _i , which is called the coordinate system of the point O _i . Parallel frame, denoted as {X _i Y _i Z _i }, in the same way, to establish the parallel frame of O _i+1 point {X _i+1 Y _i+1 Z _i+1 }, then {X _i+1 Y Homogeneous transformation matrix from _i+1 Z _i+1 } to {X _i Y _i Z _i }

for:

Among them, α _i is the angle between the curvature vector of K _i and the curvature vector of K _ix , θ _i is the approximate arc angle of the curve between the two points O _i and O _i+1 , L _i is the arc length, and there are

According to the homogeneous transformation matrix between the parallel frames of adjacent points, one end point of the shape memory alloy wire is selected as the reconstruction reference point, and its parallel frame is used as the global reference coordinate system, and the rest of the curvature data points are calculated recursively in turn. The global coordinates of , the potential vector of the i-th point under the parallel frame of the reference point

for

t _i represents the translation vector of the parallel frame {X _i Y _i Z _i } to {X _i+1 Y _i+1 Z _i+1 }:

4. A method for reconstructing curved surface hyperbolic deformation based on fiber grating strain data as claimed in claim 3, wherein in step 5, the layout direction of each shape memory alloy wire A is set to be u, and the shape memory alloy wire A is set as u. The laying direction of the wire B is v, the curve formed by the shape memory alloy wire A is called the u-direction curve, and the curve formed by the shape memory alloy wire B is called the v-direction curve. At the intersection point C _j of the u-direction curve, the Freiner frame and the parallel frame of the v-direction curve are marked as {X _vF Y _vF Z _vF } and {X _v Y _v Z _v }, respectively, and the Freiner frame of the u-direction curve The frame and parallel frame are marked as {X _uF Y _uF Z _uF } and {X _u Y _u Z _u }; Rotation matrix from the u-direction curve-parallel frame to the v-direction curve-parallel frame at the intersection

for:

The transformation matrix from the u-direction curve-parallel frame to the v-direction curve-parallel frame at the intersection is:

where α _u and α _v are the angle between the X-axis of the Freiner frame of the v-direction curve and the u-direction curve and the angle between the X-axis of the parallel frame, and

K _vx and K _vy are the orthogonal curvature components of the v-direction curve at the intersection, and _Kux and _Kuy are the orthogonal curvature components of the u-direction curve at the intersection; The transformation matrix from the parallel frame of the jth u-direction curve A _j at the intersection point C _j of the v-direction curve to the parallel frame of the reconstructed reference point of A _j is:

The transformation matrix of the parallel frame of the v-direction curve at the intersection point C _j to its parallel frame at the first intersection point C ₁ is:

Among them, i is the subscript of the intersection point C _j in each point of the curve A _j ,

is the transformation matrix of the parallel frame between the adjacent points of the A _j curve, and T _B is the transformation matrix of the parallel frame between the adjacent points of the v-direction curve; Thus, the transformation matrix from the parallel frame of the curve A _j at its reconstructed reference point to the parallel frame of the v-direction curve at the point C ₁ is:

is the transformation matrix from the u-direction curve-parallel frame to the v-direction curve-parallel frame at the intersection C _j , according to

The coordinates of each shape memory alloy wire A at each curvature data point are unified into the same coordinate system.

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