CN114413779B - Curved surface double-curvature deformation reconstruction method based on fiber bragg grating strain data - Google Patents
Curved surface double-curvature deformation reconstruction method based on fiber bragg grating strain data Download PDFInfo
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Abstract
The invention discloses a curved surface dual-curvature deformation reconstruction method based on fiber bragg grating strain data, which comprises the following steps of: laying shape memory alloy wires on the curved surface to be detected; respectively acquiring orthogonal curvature components of each shape memory alloy wire at each curvature measuring point by using the fiber bragg grating sensor string, and acquiring coordinates of each measuring point according to the orthogonal curvature components; the measuring point coordinates of the memory alloy wires with different shapes are unified to the same coordinate system by using the memory alloy wires with different shapes which are distributed in an intersecting way; and taking the unified coordinates as coordinates of corresponding scattered points on the curved surface to be measured, and connecting the scattered points by using a grid to complete approximate reconstruction of the curved surface to be measured. The invention unifies the coordinates of each measuring point of each shape memory alloy wire to realize the approximate reconstruction of the curved surface to be measured, improves the reconstruction precision by adjusting the distribution density of the shape memory alloy wires and the interpolation density of curvature data points, and can be used for the real-time deformation calculation of the skin under normal load in the actual assembly situation.
Description
Technical Field
The invention belongs to the technical field of fiber grating shape sensing, and particularly relates to a curved surface double-curvature deformation reconstruction method based on fiber grating strain data.
Background
In recent years, with the development of digitization technology, virtual modeling technology for physical environment has been advanced greatly. In the aspect of manufacturing and assembling products, particularly in the field of aeronautical manufacturing with higher precision and quality requirements, digital manufacturing technologies taking virtual models of components and assemblies as cores are becoming mature. However, the virtual model constructed in the computer at present still mainly is a static ideal design model, and the factors such as dimensional errors, stress deformation and the like of the components in the processing and assembling processes cause the components and the assembly body to have larger differences with the digital model thereof in geometric appearance and mechanical properties, so that the actual product cannot meet the design requirements. Therefore, a high-fidelity dynamic model of the components in the machining and assembling process is established based on the measured data, the incidence relation between the manufacturing quality and the process parameters is researched on the basis, and the realization of the feedback optimization of the process is a future research hotspot.
The existing method for monitoring the curved surface of the flexible structure based on the fiber bragg grating has the following problems in general: (1) The monitored flexible structure object constraint determines (usually one end is fixed and one end is free) (2) the monitored structure is subjected to plane bending in only one direction, and the deformation is single-curvature deformation. In an actual application scenario, a thin-wall structure such as an aircraft skin is subjected to a relatively complex double-curvature small deformation under operations such as drilling and riveting, and the existing curved surface reconstruction method cannot be applied to the situation.
Disclosure of Invention
The invention provides a curved surface double-curvature deformation reconstruction method based on fiber bragg grating strain data, aiming at realizing real-time deformation calculation of a skin under normal load in the actual assembly situation.
In order to realize the purpose, the invention adopts the following technical scheme:
a curved surface double-curvature deformation reconstruction method based on fiber bragg grating strain data comprises the following steps:
step 1: distributing a plurality of non-intersected shape memory alloy wires A on the curved surface to be detected along a certain direction, and distributing a shape memory alloy wire B which is respectively intersected with the shape memory alloy wires A in the other direction; the surface of the shape memory alloy wire is provided with two fiber bragg grating sensor strings which are arranged at 90 degrees along the circumferential direction of the shape memory alloy wire, the number and the interval of fiber optic measuring points on the two fiber bragg grating sensor strings are the same, and the fiber optic measuring points are aligned pairwise along the axial direction of the shape memory alloy wire to form a plurality of curvature measuring points; the curvature measuring points on the shape memory alloy wire B are all positioned at the intersection points of the shape memory alloy wire B and the shape memory alloy wire A;
step 2: respectively acquiring two strain quantities of each shape memory alloy wire A at each curvature measuring point by using the fiber bragg grating sensor string, and calculating two orthogonal curvature components at the curvature measuring points through the strain quantities;
and step 3: respectively interpolating two orthogonal curvature components at each curvature measurement point of the same shape memory alloy wire A to refine curvature data points;
and 4, step 4: based on the orthogonal curvature components at the discrete curvature detection points, respectively reconstructing the coordinates of the shape memory alloy wires A at the curvature data points by utilizing a differential geometry principle;
and 5: acquiring two orthogonal curvature components of the shape memory alloy wire B at each curvature measuring point by using the fiber bragg grating sensor string, deducing the conversion relation of coordinates at curvature data points among different shape memory alloy wires A based on the two orthogonal curvature components, and unifying the coordinates of the shape memory alloy wires A at the curvature data points into the same coordinate system;
step 6: and (3) taking the unified coordinates of the shape memory alloy wires A at the curvature data points as the coordinates of the corresponding scattered points on the curved surface to be measured, and connecting the scattered points by using a grid to complete the approximate reconstruction of the curved surface to be measured.
Further, in step 2, the formula for calculating the curvature K by the strain amount is:
K＝2ε/h，
wherein h is the diameter of the shape memory alloy wire, epsilon is the strain of the shape memory alloy wire at the bending part of the shape memory alloy wire, and epsilon = delta lambda/k 1 λ, λ is the central wavelength of the optical fiber grating sensor grating reflection when the shape memory alloy wire is not bent, Δ λ is the reflection wavelength variation when the shape memory alloy wire is bent, k 1 Is a constant coefficient.
Further, in step 4,
for the same shape memory alloy wire, any two adjacent curvature data points O i And O i+1 The curve segment between is approximated by point O i The arc of curvature in the osculating plane, the arc and the curve being in the plane O i Tangent to point O i And the radius is 1/K i ，K i Is a curve at O i Resultant curvature of the point, K i From the obtained O i Orthogonal curvature component K of a point ix And K iy Synthesizing; at point O i The tangent line, the main normal line and the auxiliary normal line of the curve are respectively used as the Z axis, the X axis and the Y axis to establish O i Point Fliner frame, denoted as { X Fi Y Fi Z Fi }；
Respectively with O i The direction vectors of the orthogonal curvature components of the points are X-axis and Y-axis, and the curve is in O i Is the Z axis at O i The points are set up into a rectangular coordinate system, which is called as O i Parallel frames of points, denoted as { X i Y i Z i Like this, establish O i+1 Parallel frame of points { X i+1 Y i+1 Z i+1 }, then { X i+1 Y i+1 Z i+1 From (c) } to (X) i Y i Z i The homogeneous transformation matrix of
Comprises the following steps:
wherein alpha is i Is K i Curvature vector of and K ix Angle of curvature vector of theta i Is O i And O i+1 Angle of rotation, L, of an approximate arc of a curve between two points i Is arc-long and has
According to the homogeneous conversion matrix between the parallel frames of adjacent points, selecting one end point of the shape memory alloy wire as a reconstruction datum point, using the parallel frame as a global reference coordinate system, and calculating in turn by recursionGlobal coordinates of the rest curvature data points, and a position vector of the ith point under a parallel frame of the reference point
Is composed of
t i Representing parallel frames { X i Y i Z i To { X } i+1 Y i+1 Z i+1 The translation vector of }:
further, in step 5, the arrangement direction of each shape memory alloy wire a is u, the arrangement direction of each shape memory alloy wire B is v, the curve formed by the shape memory alloy wires a is referred to as a u-direction curve, the curve formed by the shape memory alloy wires B is referred to as a v-direction curve, and the intersection point C between the v-direction curve and the jth u-direction curve is defined as a v-direction curve j Here, the Ferner shelf and the parallel shelf of the v-directional curve are respectively denoted as { X } vF Y vF Z vF And { X } v Y v Z v The Ferna frames and parallel frames of the u-direction curves are respectively marked as { X } uF Y uF Z uF And { X } u Y u Z u }；
Rotation matrix from parallel frame of u-direction curve to parallel frame of v-direction curve at intersection point
Comprises the following steps:
the conversion matrix from the u-direction curve parallel frame to the v-direction curve parallel frame at the intersection point is as follows:
wherein alpha is u And alpha v Respectively an included angle between the X axes of the fleiner frames of the v-directional curve and the u-directional curve and an included angle between the X axes of the parallel frames, and
K vx and K vy Is the orthogonal curvature component of the v-curve at the intersection point, K ux And K uy Is the orthogonal curvature component of the u-curve at the intersection point;
jth u-directional curve A j At the intersection point C with the v-direction curve j Parallel frame of (A) j The transformation matrix of the parallel frame for reconstructing the reference points is as follows:
v-direction curve at intersection point C j To its first intersection point C 1 The transformation matrix of the parallel frame is:
wherein i is the intersection C j At A j The subscripts in the various points of the curve,
is A j Transition matrix, T, of parallel frames between adjacent points of the curve B Is a conversion matrix of parallel frames between adjacent points of the v-direction curve;
thus, curve A is obtained j Parallel frame to v-curve at its reconstructed reference point at point C 1 The transformation matrix of the parallel frame is:
is the point of intersection C j A transformation matrix from the u-direction curve parallel frame to the v-direction curve parallel frame according to
Coordinates of the shape memory alloy wires A at the curvature data points are unified into the same coordinate system.
The invention has the beneficial effects that:
the invention unifies the coordinates of each measuring point of each shape memory alloy wire A through the shape memory alloy wires B which are distributed in an intersecting way so as to realize the approximate reconstruction of the curved surface to be measured, improves the reconstruction precision by adjusting the distribution density of the shape memory alloy wires A and the interpolation density of curvature data points, and can be used for the real-time deformation calculation of the skin under normal load in the actual assembly situation.
Drawings
FIG. 1 is a schematic flow diagram of the process of the present invention;
FIG. 2 is a schematic structural diagram of a fiber grating sensor string according to the present invention;
FIG. 3 is a schematic layout view of shape memory alloy wires;
FIG. 4 is a schematic diagram of the parallel frames and the Ferner frame of the present invention;
FIG. 5 is a schematic diagram of the rotational transformation between the parallel frames of adjacent points of the curve according to the present invention;
FIG. 6 shows an intersection C with a curve B of alloy wires arranged in the v direction in the present invention j Alloy wire A arranged in the u direction j A schematic diagram of the geometric relationship between the parallel frame of the curve and the fleiner frame;
FIG. 7 shows an alloy wire A laid in the u direction in the present invention j Intersection point C of the curves j A geometrical relation schematic diagram of a parallel frame and a Flenar frame of the alloy wire B curve arranged in the v direction;
FIG. 8 is a schematic diagram illustrating the arrangement of shape memory alloy wires on a double-curvature curved surface to be measured in the embodiment;
fig. 9 is a reconstruction result of the dual-curvature curved surface to be measured.
Detailed Description
The present invention will now be described in further detail with reference to the accompanying drawings.
The invention aims to provide a curved surface double-curvature small-deformation reconstruction method based on fiber bragg grating strain measurement, which aims at realizing real-time deformation calculation of a skin under normal load in an actual assembly situation. As shown in fig. 1, the method of the present invention comprises:
s1: preparation and layout of the sensor:
preparing a plurality of shape memory alloy wires (SMA), wherein two fiber bragg grating strings arranged at 90 degrees in the circumferential direction are mounted on the surface of each SMA, the number and the interval of grating measuring points of the two fiber bragg grating strings are the same, and the two fiber bragg grating strings are aligned in pairs in the axial direction to form a plurality of curvature measuring points of the axis of the SMA, as shown in FIG. 2; a plurality of shape memory alloy wires A are arranged on the curved surface to be measured at equal intervals in parallel along a certain direction 1 A 2 A 3 8230and an alloy wire B with the direction orthogonal to the alloy wires B. The curvature measuring points of the axis of the alloy wire B on the curved surface are all positioned at the same position as the alloy wire A 1 A 2 A 3 Intersection point C of 1 C 2 C 3 8230am made of natural plant materials.
S2: and (3) performing deformation reconstruction on the axis of each alloy wire:
1. curvature information acquisition
The fiber grating sensor takes optical fiber as a light transmission medium, grating measuring points which are specially processed by the optical fiber and can reflect light waves are discretely distributed on the fiber grating sensor, and the reflection wavelength is related to the length of the grating. When the temperature changes or the optical fiber is axially pulled and pressed, the length of a grating measuring point is changed, and the reflection wavelength is changed. By demodulating the reflection wavelength, the strain or ambient temperature of the grating measuring point can be obtained. The strain ε and the temperature change Δ T, in general, follow a linear coupling relationship with the reflection wavelength change Δ λ as follows:
where λ is the center wavelength of the grating reflection when ε and Δ T are zero, k 1 And k 2 The coefficient is constant, and when the monitoring time is short and the variation of the environmental temperature is not significant, the following are approximated:
when each micro-segment of the alloy wire is bent towards any direction, the axis of the base material becomes a space curve, and each measuring point of the two fiber bragg grating sensors can respectively sense the bending strain components of each micro-segment of the alloy wire in two orthogonal directions. By combining the pure bending theory of material mechanics, two orthogonal curvature components of the axis of the base material can be calculated, namely K =2 epsilon/h, h is the diameter of the shape memory alloy wire, and epsilon is the strain quantity of the shape memory alloy wire at the bending position.
After the fiber grating sensor obtains two orthogonal curvature components of the axis of the alloy wire at each measuring point, curvature interpolation is carried out among the measuring points to refine the curvature data point of the axis, and linear interpolation and cubic spline interpolation are commonly used as interpolation methods. Based on the orthogonal curvature of each discrete point, the coordinate of each point on the axis can be reconstructed by utilizing the differential geometry principle.
2. The space curve reconstruction algorithm based on the orthogonal curvature comprises the following steps:
according to the differential geometry principle, for two points O on an arbitrary space curve i And O i+1 When O is present i+1 Approach to O i When the curve segment between two points can be approximated as point O i A circular arc of curvature in the osculating plane, the circular arc and the curve being in the plane O i Tangent to point O i And has a radius of
Wherein K i Is a curve at O i The resultant curvature of the dots. Point O on the space curve i Establishing Frenet Frame (Frenet Frame) with curve tangent, main normal and auxiliary normal as Z axis, X axis and Y axis, and recording as { X Fi Y Fi Z Fi }; then, the grating is used to measure the point at O i The direction vectors of two curvature vectors corresponding to the two orthogonal bending curvatures are respectively taken as an X axis and a Y axis, a curve tangent is taken as a Z axis, and the curve tangent is O i Establishing a rectangular coordinate system by points, namely the coordinate system is a Parallel Frame (Parallel Transport Frame or Parallel Frame) and is marked as { X } i Y i Z i As in fig. 4.
In FIG. 4, P i Is O i Center of point curvature circle, O i To P i Is a distance of
I.e. radius of curvature R i Equal to the resultant curvature K i Reciprocal of (2), Q i Is the i +1 th data point O i+1 To the coordinate plane X i -O i -Y i Is in the foot. K ix And K iy Are each O i Two orthogonal curvature components at the point. Resultant curvature of K i Its curvature vector follows the principal normal vector of the curve. Alpha is alpha i Is K i Curvature vector of and K ix The included angle of the curvature vectors of (1), namely the included angle between the X axis of the Flrenar frame and the X axis of the parallel frame; theta i Is O i And O i+1 Angle of rotation, L, of an approximate arc of a curve between two points i Arc length, is a known quantity.
Following the geometric relationships of FIG. 4, the following derivation is made in the coordinate system { X } i Y i Z i Lower O i+1 Coordinates of points and coordinate system { X } i+1 Y i+ 1 Z i+1 To { X } i Y i Z i Homogeneous transformation matrix of }:
K i from orthogonal curvature components K ix And K iy Synthesizing:
for alpha i Comprises the following steps:
for theta i Comprises the following steps:
point P i To point Q i The distance to is:
point O i+1 To point Q i The distance of (a) is:
point O i To point Q i The distance of (a) is:
then point O i+1 At point O i Coordinate system of { X i Y i Z i The three coordinates below are:
is then O i Coordinate system of { X i Y i Z i O to i+1 Coordinate system of { X } i+1 Y i+1 Z i+1 The translation vector of is:
from a coordinate system { X i Y i Z i The orientation of the device is rotated to the coordinate system X i+1 Y i+1 Z i+1 The rigid body transforms in azimuth: { X i Y i Z i Around O i Sub-normal rotation of point θ i Obtaining coordinatesIs { X } i+1 Y i+1 Z i+1 This transform can be further decomposed into:
①{X i Y i Z i around Z i Rotation of the shaft alpha i To the frainer shelf { X } Fi Y Fi Z Fi }
②{X Fi Y Fi Z Fi Wind Y Fi Rotation theta i To obtain { X Fi ’Y Fi ’Z Fi ’}
③{X Fi ’Y Fi ’Z Fi ' } around Z Fi ' rotational-alpha i To obtain { X i+1 Y i+1 Z i+1 }
As shown in fig. 5.
FIG. 5 shows a point O i Parallel frame { XiYiZi } to point O i+1 Rotation transformation schematic diagram of 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:
note that the above transformation is an orbital rotation, then the rotation matrix of { Xi +1Yi +1Zi +1} to { XiYI Zi }, is
From a matrix R 1 R 2 R 3 And sequentially right multiplying to obtain:
thus, X can be constructed i+1 Y i+1 Z i+1 From (c) } to (X) i Y i Z i The homogeneous transformation matrix of
In the formula (2.15), α i And theta i Determined by the formulae (2.2) and (2.3), respectively.
And (5) calculating a homogeneous conversion matrix between the parallel frames of all adjacent points on the space curve according to the formula (2.15). And selecting one end point of the curve as a reconstruction datum point, taking the parallel frame as a global reference coordinate system, and sequentially calculating the global coordinates of the rest points in a recursion manner. The position vector of the ith point under the parallel frame of the 1 st point (reference point)
Comprises the following steps:
and (3) calculating the coordinates of all points of the curve in the same coordinate system according to the formula (2.16), wherein the data points are dense enough after the curve interpolation, and a smooth approximate curve can be obtained by connecting the points by using a straight-line segment to complete the reconstruction of the curve.
S3, a small-deformation double-curvature curve reconstruction method based on curve scatter points comprises the following steps:
as shown in FIG. 3, a plurality of alloy wires A are marked on a curved surface at equal intervals in parallel 1 A 2 A 3 8230the laying direction is u, and the laying direction of the alloy wires B orthogonal to the u is v.
The curvature measuring points and measuring point intervals of A1, A2 and A3 \8230arethe same, and a measuring point array is formed on the curved surface. According to the curve reconstruction method of S2, the deformation curve of the sensors A1, A2 and A3 \8230iscalculated to obtain the scattered point coordinates on the curve. The point coordinates are located under the parallel frames of the reconstructed reference points of each curve, and the conversion relation of the parallel frames needs to be searched for unifying the scattered point coordinate systems.
When the curved surface is slightly deformed, the orthogonality of the orthogonal curve on the curved surface is unchanged. By using the characteristic, the rotation relation of the parallel frame of the u-direction curve of the sensors A1, A2 and A3 at the intersection points C1 and C2 \8230wherethe parallel frame of the v-direction curve of the sensor B is orthogonal can be obtained. A matrix expression for this rotation relationship is derived as follows:
v-direction curve and u-direction curve at intersection point C j The geometrical relationships of the grid and the parallel grid are shown in FIGS. 6 and 7, respectively, where the grid and the parallel grid of the v-directional curve are denoted by { X vF Y vF Z vF And { X } v Y v Z v }; the Ferner frame and the parallel frame of the u-direction curve are respectively marked as { X uF Y uF Z uF And { X } u Y u Z u }。
The transformation of the fleiner shelf of the v-direction curve to the fleiner shelf of the u-direction curve at the intersection point is a 90 degree counterclockwise rotation about the X-axis. The rotation matrix of this transformation is:
the rotation matrix of the fleiner frame of the v-directional curve to its parallel frame is:
the transformation matrix from the parallel frame of the u-direction curve to its fleiner frame is:
then the rotation matrix from the parallel frame of the u-direction curve to the parallel frame of the v-direction curve at the intersection point is:
in the formula alpha u And alpha v The included angles of the two curved flener frames and the x axis of the parallel frame are determined by the orthogonal curvature acquired by the sensor at the intersection point:
then the conversion matrix from the u-direction curve parallel frame to the v-direction curve parallel frame at the intersection point is:
and: sensor A with the formula 2.16 u direction j The curve is at the intersection point C with the curve of the sensor B in the v direction j Parallel frame of (A) j The conversion matrix of the parallel frame of the curve reconstruction reference point is as follows:
wherein i is the intersection C j In A j The subscripts in the various points of the curve,
is A j And (3) a conversion matrix of parallel frames between adjacent points of the curve.
The v-curve of sensor B is at intersection point C j To its first intersection point C 1 The transformation matrix of the parallel frame is:
in the formula T B Parallel frames between adjacent points of B curveAnd converting the matrix.
Thus sensor A j Parallel frame-to-sensor B curve of the curve at its reconstructed reference point at point C 1 The transformation matrix of the parallel frame is:
in the formula (I), the compound is shown in the specification,
is the point of intersection C j Conversion matrix from u-direction curve parallel frame to v-direction curve parallel frame
Therefore, the parallel frames of the reconstructed reference points of each u-direction curve are unified
After the coordinates of the scattered points on the curved surface are unified, when the scattered points become dense enough through curvature interpolation, the grid is used for connecting the scattered points to complete approximate reconstruction of the curved surface.
Simulation verification:
as shown in FIG. 8, 7 curves A1 and A2 \8230andA 7 are selected along the u direction on A1/4 ellipsoid with the major semi-axis of 2 and the minor semi-axis of 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 point, the normal vector direction of the u-direction curve is the same as that of the v-direction curve, and the tangent vector direction is vertical. The spherical coordinate equation of the sampling ellipsoid is:
the curvatures of 6 curvature sampling points of 7 curves in the u direction are as follows: 2,1.2767,0.68247,0.4383,0.328569 and 0.276, wherein the interval of sampling points is 0.3672566, the number of curvature interpolation points of adjacent measuring points of each curve is 10, and the interpolation method is linear interpolation. The curvatures of 7 sampling points of a curve B in the v direction are all 0.5, the measuring point interval is 1.0472, the curvature interpolation points of adjacent sampling points are 10, and the interpolation method is linear interpolation. By using the double curvature surface reconstruction method based on the curve scatter points, which is provided by the patent, the ellipsoid is reconstructed by using curvature data of the scatter points, and the reconstruction result is shown in fig. 9. At the moment, the reconstruction curved surface and the sampling curved surface have no obvious error, so that the method for reconstructing the double-curvature curved surface based on the curve scatter points, which is provided by the patent, has theoretical feasibility and can accurately reconstruct the curved surface according to curvature data of the curve scatter points.
The above are only preferred embodiments of the present invention, and the scope of the present invention is not limited to the above examples, and all technical solutions that fall under the spirit of the present invention belong to the scope of the present invention.
Claims (4)
1. A curved surface double-curvature deformation reconstruction method based on fiber grating strain data is characterized by comprising the following steps:
step 1: distributing a plurality of non-intersected shape memory alloy wires A on the curved surface to be detected along a certain direction, and distributing a shape memory alloy wire B which is respectively intersected with the shape memory alloy wires A in the other direction; the surface of the shape memory alloy wire is provided with two fiber bragg grating sensor strings which are arranged at 90 degrees along the circumferential direction of the shape memory alloy wire, the number and the interval of fiber optic measuring points on the two fiber bragg grating sensor strings are the same, and the fiber optic measuring points are aligned pairwise along the axial direction of the shape memory alloy wire to form a plurality of curvature measuring points; the curvature measuring points on the shape memory alloy wire B are all positioned at the intersection points of the shape memory alloy wire B and the shape memory alloy wire A;
step 2: respectively acquiring two strain quantities of each shape memory alloy wire A at each curvature measurement point by using the fiber bragg grating sensor string, and calculating two orthogonal curvature components at the curvature measurement points through the strain quantities;
and step 3: respectively interpolating two orthogonal curvature components at each curvature measurement point of the same shape memory alloy wire A to refine curvature data points;
and 4, step 4: based on the orthogonal curvature components at the discrete curvature detection points, respectively reconstructing the coordinates of the shape memory alloy wires A at the curvature data points by utilizing a differential geometry principle;
and 5: acquiring two orthogonal curvature components of the shape memory alloy wire B at each curvature measuring point by using the fiber bragg grating sensor string, deducing the conversion relation of coordinates at curvature data points among different shape memory alloy wires A based on the two orthogonal curvature components, and unifying the coordinates of the shape memory alloy wires A at the curvature data points into the same coordinate system;
and 6: and (3) taking the unified coordinates of the shape memory alloy wires A at the curvature data points as the coordinates of corresponding scattered points on the curved surface to be measured, and connecting the scattered points by using a grid to complete the approximate reconstruction of the curved surface to be measured.
2. The method for reconstructing curved surface dual-curvature deformation based on fiber bragg grating strain data as claimed in claim 1, wherein in the step 2, the formula for calculating the curvature K through the strain amount is as follows:
K＝2ε/h，
wherein h is the diameter of the shape memory alloy wire, epsilon is the strain quantity of the shape memory alloy wire at the bending part of the shape memory alloy wire, and epsilon = delta lambda/k 1 λ, λ is the central wavelength of the optical fiber grating sensor grating reflection when the shape memory alloy wire is not bent, Δ λ is the reflection wavelength variation when the shape memory alloy wire is bent, k 1 Is a constant coefficient.
3. The method for reconstructing curved surface dual-curvature deformation based on fiber bragg grating strain data according to claim 1, wherein in the step 4,
for the same shape memory alloy wire, any two adjacent curvature data points O i And O i+1 The curve segment between is approximated by point O i A circular arc of curvature in the osculating plane, the circular arc and the curve being in the plane O i Is tangent to point O i And the radius is 1/K i ，K i Is a curve at O i Resultant curvature of point, K i From the obtained O i Orthogonal curvature component K of a point ix And K iy Synthesizing; at point O i The tangent line, the main normal line and the auxiliary normal line of the curve are respectively used as the Z axis, the X axis and the Y axis to establish O i Point Fliner frame, noted { X Fi Y Fi Z Fi }；
Are each independently of O i The direction vectors of the orthogonal curvature components of the points are X-axis and Y-axis, and the curve is in O i The tangent of (A) is the Z axisIn O of i The point establishes a rectangular coordinate system, which is called as O i Parallel frames of points, denoted as { X i Y i Z i Like this, establish O i+1 Parallel frame of points { X i+1 Y i+1 Z i+1 }, then { X i+1 Y i+1 Z i+1 To { X } i Y i Z i The homogeneous transformation matrix of
Comprises the following steps:
wherein alpha is i Is K i Curvature vector of and K ix Angle of curvature vector of theta i Is O i And O i+1 Angle of rotation of an approximate arc of a curve between two points, L i Is arc-long and has
According to a homogeneous conversion matrix between the parallel frames of adjacent points, selecting an end point of the shape memory alloy wire as a reconstruction reference point, using the parallel frame as a global reference coordinate system, sequentially calculating the global coordinates of the rest curvature data points in a recursion manner, and calculating the position vector of the ith point under the parallel frame of the reference point
Is composed of
t i Parallel frame of representation { X i Y i Z i From (c) } to (X) i+1 Y i+1 Z i+1 Translation vector of }:
4. the method for reconstructing curved surface double-curvature deformation based on fiber bragg grating strain data as claimed in claim 3, wherein in the step 5, the arrangement direction of each shape memory alloy wire A is u, the arrangement direction of each shape memory alloy wire B is v, the curve formed by the shape memory alloy wires A is called a u-direction curve, the curve formed by the shape memory alloy wires B is called a v-direction curve, and the intersection point C between the v-direction curve and the jth u-direction curve is set as a v-direction curve j Here, the Ferner shelf and the parallel shelf of the v-directional curve are respectively denoted as { X vF Y vF Z vF And { X } v Y v Z v The Ferna frames and parallel frames of the u-direction curves are respectively marked as { X } uF Y uF Z uF And { X } u Y u Z u }；
Rotation matrix from parallel frame of u-direction curve to parallel frame of v-direction curve at intersection point
Comprises the following steps:
the conversion matrix from the u-direction curve parallel frame to the v-direction curve parallel frame at the intersection point is as follows:
wherein alpha is u And alpha v Respectively an included angle between the X axes of the fleiner frames of the v-directional curve and the u-directional curve and an included angle between the X axes of the parallel frames, and
K vx and K vy At the intersection point for the v-direction curveOf the orthogonal curvature component, K ux And K uy Is the orthogonal curvature component of the u-direction curve at the intersection point;
jth u-direction curve A j At the intersection point C with the v-direction curve j To A of a parallel frame j The transformation matrix of the parallel frame for reconstructing the reference points is as follows:
v-direction curve at intersection point C j To its first intersection point C 1 The transformation matrix of the parallel frame is:
wherein i is the intersection C j At A j The subscripts in the various points of the curve,
is A j Transition matrix, T, of parallel frames between adjacent points of the curve B Is a conversion matrix of parallel frames between adjacent points of the v-direction curve;
thus, curve A is obtained j Parallel frame to v-curve at its reconstructed reference point at point C 1 The transformation matrix of the parallel frame is:
is the point of intersection C j A transformation matrix from the u-direction curve parallel frame to the v-direction curve parallel frame according to
Coordinates of the shape memory alloy wires A at the curvature data points are unified into the same coordinate system.
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