A method and system for online measurement of flexible skin deformation based on FBG strain sensor

Abstract

The invention discloses an online measurement method and system for flexible skin deformation based on FBG strain sensors. The method comprises: discretizing the flexible skin into a plurality of flexible hoses, calculating the curvature and azimuth of discrete points of the neutral axis of the flexible hoses, fitting the curvature and azimuth that change in real time as a function of arc length, calculating the local coordinates of the origin of each motion coordinate system in the previous motion coordinate system by integration on each section, converting them into a fixed coordinate system by coordinate transformation, and performing cubic spline fitting, thereby performing real-time deformation monitoring on the flexible skin; the system is used to implement the method. The online measurement method provided by the invention more realistically reflects the shape of the flexible skin after deformation, improves the accuracy of the flexible skin deformation measurement, and has a high calculation speed.

Description

Technical Field

[0001] The invention belongs to the technical field of online measurement of flexible skin deformation, and in particular relates to an online measurement method and system for flexible skin deformation based on an FBG strain sensor. Background Art

[0002] At present, large aircraft, tethered balloons and low-altitude airships in near-space usually adopt multi-airbag structures. This design plays a vital role in improving load-bearing capacity and overall stability. Since the airbag structure is affected by complex environmental factors during flight, such as airflow disturbances, temperature changes and external loads, its shape and internal pressure change dynamically. These changes further cause the flexible skin covering the surface of the airbag to deform accordingly, which may affect the aerodynamic performance, structural integrity and other key functions of the aircraft.

[0003] In order to ensure the stability of the flexible skin in harsh service environments, especially the robustness in electromagnetic performance, real-time deformation monitoring of the flexible skin is particularly important. Accurate monitoring of the deformation state of the flexible skin not only helps to evaluate the operation of the airbag structure, but also provides important data support for the health management, structural optimization and fault warning of the aircraft. Therefore, researching and developing high-precision and high-response speed flexible skin deformation monitoring technology is of great significance for improving the reliability and long-term service capability of aircraft in complex environments such as near-space.

[0004] The curvature method has been widely used in three-dimensional imaging and deformation monitoring because of its advantages such as its adaptability to complex geometric shapes, applicability to surfaces of various materials, and intuitive operation. At present, when using the curvature method to measure the shape of a curve, the data is usually expanded by interpolation, and the entire curve is processed in segments, assuming that the curvature and azimuth angle in each segment are constant. Although this segmentation and constant assumption simplifies the calculation process, it ignores the continuous change characteristics of the curvature and azimuth angle, resulting in the loss of local detail information, especially in areas with large curvature changes. The interpolation error will be further amplified. Especially in the curve shape measurement based on fiber Bragg grating, the existing curvature method cannot meet the deformation monitoring accuracy of flexible skin. Summary of the invention

[0005] In order to overcome the shortcomings of the above-mentioned prior art, the purpose of the invention is to provide an online measurement method and system for flexible skin deformation based on FBG strain sensors, discretize the flexible skin into multiple flexible hoses, calculate the curvature and azimuth of discrete points on the neutral axis of the flexible hose, fit the curvature and azimuth that change in real time as a function of the arc length, and calculate the local coordinates of the origin of each motion coordinate system in the previous motion coordinate system in each segment by integration, and then convert them into a fixed coordinate system by coordinate transformation, so as to perform real-time deformation monitoring of the flexible skin, more realistically reflect the deformed shape of the flexible skin, improve the accuracy of the flexible skin deformation measurement, and improve the calculation speed due to the small number of segments.

[0006] In order to achieve the above object, the technical solution adopted by the present invention is as follows:

[0007] An online measurement method for deformation of a flexible skin based on an FBG strain sensor discretizes the flexible skin into a plurality of flexible hoses, comprising the following steps:

[0008] Step 1: Install several FBG strain sensors at equal intervals on the surface of the flexible hose, and measure the central wavelength offset of the FBG strain sensor. Calculate the curvature of the neutral axis of a flexible hose at discrete points and direction angle ;

[0009] Step 2: The curvature of the discrete points on the neutral axis of the flexible hose is calculated using the cubic spline fitting algorithm. and direction angle Fitting is performed to obtain the function of curvature with respect to arc length and direction angle as a function of arc length ;

[0010] Step 3: The curvature obtained from the fitting is a function of the arc length , calculate the function of the central angle of a circle with respect to the arc length ; Based on the function of the central angle of a circle with respect to the arc length And the function of the direction angle obtained by fitting about the arc length , solve Motion coordinate system of the neutral axis of the flexible hose at each cross section Origin In the previous motion coordinate system The local coordinates in ;

[0011] Step 4: Discrete point direction angles according to the neutral axis of the flexible hose and the central angle as a function of arc length , calculate the Motion coordinate system of the neutral axis of the flexible hose at each cross section To a fixed coordinate system The rotation matrix ;

[0012] Step 5: According to Motion coordinate system of the neutral axis of the flexible hose at each cross section Fixed coordinate system The rotation matrix and Motion coordinate system of the neutral axis of the flexible hose at each cross section Origin In the previous motion coordinate system The local coordinates in , the motion coordinate system Origin The coordinates are converted to a fixed coordinate system In the Motion coordinate system of the neutral axis of the flexible hose at each cross section Origin In a fixed coordinate system Coordinates in ;

[0013] Step 6: Use the cubic spline fitting algorithm to fit the Motion coordinate system of the neutral axis of the flexible hose at each cross section Origin In a fixed coordinate system Coordinates in The curve of the neutral axis of the deformed flexible hose is obtained by fitting, that is, the shape of the deformed flexible hose; and the deformed shapes of all the flexible hoses are then fitted to obtain the deformed shape of the flexible skin.

[0014] It is assumed that during the deformation process, the flexible hose only undergoes pure bending deformation.

[0015] In step 1, the curvature of the hose neutral axis discrete points and direction angle The expressions are as follows:

[0016] (1.4)

[0017] (1.5)

[0018] In the formula, Respectively represent The central wavelength offset measured by three FBG strain sensors at each cross section is: is the strain sensitivity of the FBG strain sensor, is the radius of the flexible hose.

[0019] In step 3, the function of the curvature obtained by fitting with respect to the arc length is Perform integral calculation to obtain the function of the central angle of each arc with respect to the arc length , the expression is as follows:

[0020] (3.1)

[0021] In the formula, is the integration variable, Indicates the upper limit of the integral;

[0022] Then calculate the The neutral axis of the flexible hose at each cross section Origin In the previous motion coordinate system The local coordinates in , the expression is as follows:

[0023] (3.2)

[0024] In the formula, is the integration variable, is the function of the direction angle obtained by fitting with respect to the arc length;

[0025] The Taylor polynomials are used to expand equation (3.2) as follows:

[0026] exist The third-order Taylor expansion polynomial at is:

[0027]

[0028] exist The third-order Taylor expansion polynomial at is:

[0029]

[0030] exist The third-order Taylor expansion polynomial at is:

[0031]

[0032] exist The third-order Taylor expansion polynomial at is:

[0033]

[0034] Substitute the Taylor expansion polynomial into equation (3.2) and integrate to obtain The motion coordinate system of the neutral axis of the hose at each cross section Origin In the previous motion coordinate system The local coordinates in .

[0035] The calculation process of step 4 is as follows:

[0036] Place the neutral axis of the flexible hose Arc length at each cross section Substitute The function of the central angle of the arc segment with respect to the arc length , that is, Motion coordinate system of the neutral axis of the flexible hose at each cross section Central angle of rotation for:

[0037] (4.1)

[0038] In the formula, is the integration variable;

[0039] Assume motion coordinate system Origin The coordinates of the point are , then the motion coordinate system Fixed coordinate system The rotation matrix , the expression is:

[0040] (4.2)

[0041] The motion coordinate system Around Axis Positive axis direction Axis positive direction of rotation , so that the rotated The positive direction of the axis coincides with the bending direction, and the motion coordinate system after the first rotation is obtained. , so the motion coordinate system To the coordinate system after the first rotation The rotation matrix , the expression is:

[0042] (4.3)

[0043] The rotated motion coordinate system Around Axis Positive axis direction Axis positive direction of rotation , so that the rotated The positive direction of the axis points to the motion coordinate system The tangent direction of the rotation The positive direction of the axis points to the motion coordinate system The bending direction of the second rotation is obtained. , so the motion coordinate system To the coordinate system after the second rotation The rotation matrix , the expression is:

[0044] (4.4)

[0045] The rotated motion coordinate system Around Axis Positive axis direction Axis positive direction of rotation , so that the rotated The positive direction of the axis points to the motion coordinate system of Axis positive direction, after rotation The positive direction of the axis points to the motion coordinate system of The positive direction of the axis, get the motion coordinate system after the third rotation , so the motion coordinate system To the coordinate system after the third rotation The rotation matrix , the expression is:

[0046] (4.5)

[0047] Therefore, the motion coordinate system Coordinate system of motion The rotation matrix , the expression is:

[0048] (4.6)

[0049] According to equations (4.2), (4.3), (4.4), (4.5) and (4.6), we can get Motion coordinate system of the neutral axis of the flexible hose at each cross section Fixed coordinate system The rotation matrix , the expression is:

[0050] (4.7)

[0051] In the formula, Represents the motion coordinate system Fixed coordinate system The rotation matrix of Represents the motion coordinate system Coordinate system of motion The rotation matrix of .

[0052] In step 5, Motion coordinate system of the neutral axis of the flexible hose at each cross section Origin In a fixed coordinate system Coordinates in , the expression is as follows:

[0053] (5.1)

[0054] In the formula, The motion coordinate system In a fixed coordinate system The coordinates in The motion coordinate system Rotate to a fixed coordinate system The rotation matrix of The motion coordinate system Origin In the motion coordinate system The coordinates in .

[0055] The present invention also provides an online measurement system for flexible skin deformation based on FBG strain sensors, comprising:

[0056] The first calculation module: install several FBG strain sensors at equal intervals on the surface of the flexible hose, and calculate the central wavelength offset measured by the FBG strain sensors. Calculate the curvature of the neutral axis of a flexible hose at discrete points and direction angle ;

[0057] The first fitting module: the curvature of the discrete points of the neutral axis of the flexible hose is calculated based on the cubic spline fitting algorithm. and direction angle Fitting is performed to obtain the function of curvature with respect to arc length and direction angle as a function of arc length ;

[0058] The second calculation module: the function of the curvature obtained by fitting with respect to the arc length , calculate the function of the central angle of a circle with respect to the arc length ; Based on the function of the central angle of a circle with respect to the arc length And the function of the direction angle obtained by fitting about the arc length , solve Motion coordinate system of the neutral axis of the flexible hose at each cross section Origin In the previous motion coordinate system The local coordinates in ;

[0059] The third calculation module: according to the direction angle of the discrete points of the neutral axis of the flexible hose and the central angle as a function of arc length , calculate the Motion coordinate system of the neutral axis of the flexible hose at each cross section To a fixed coordinate system The rotation matrix ;

[0060] The fourth calculation module: Motion coordinate system of the neutral axis of the flexible hose at each cross section Fixed coordinate system The rotation matrix and Motion coordinate system of the neutral axis of the flexible hose at each cross section Origin In the previous motion coordinate system The local coordinates in , the motion coordinate system Origin The coordinates are converted to a fixed coordinate system In the Motion coordinate system of the neutral axis of the flexible hose at each cross section Origin In a fixed coordinate system Coordinates in ;

[0061] The second fitting module: According to the cubic spline fitting algorithm, Motion coordinate system of the neutral axis of the flexible hose at each cross section Origin In a fixed coordinate system Coordinates in The curve of the neutral axis of the deformed flexible hose is obtained by fitting, that is, the shape of the deformed flexible hose; and the deformed shapes of all the flexible hoses are then fitted to obtain the deformed shape of the flexible skin.

[0062] Compared with the prior art, the present invention has the following beneficial effects:

[0063] 1. In order to more realistically reflect the deformed shape of the flexible hose, the present invention fully considers various situations and can reflect the deformed shape of the flexible hose to the greatest extent through real-time changes in curvature and direction angle.

[0064] 2. For the curvature and azimuth of discrete points, the prior art uses interpolation to expand the curvature and azimuth, while the present invention uses cubic spline fitting to process the curvature and azimuth, which can more accurately reflect the changes in the curvature and azimuth, and improve the fitting accuracy of the curvature and azimuth.

[0065] 3. Regarding the calculation of the local coordinates of the moving coordinate system, compared with the calculation method using constant curvature and direction angle in the prior art, the present invention proposes a method for calculating the local coordinates using variable curvature and direction angle, and uses Taylor's formula to expand it into a polynomial form for integral calculation, thereby improving the calculation accuracy of the local coordinates.

[0066] 4. For calculating the rotation matrix from a moving coordinate system to a fixed coordinate system, the prior art uses a fixed curvature and a corresponding arc length to multiply the center angle of each arc length, while the present invention proposes using an integral method to calculate the center angle of each arc length, thereby improving the accuracy of the rotation matrix.

[0067] To sum up, in the prior art, when calculating the coordinates of the hose, a whole hose is divided into multiple segments, and it is believed that the curvature and the azimuth are constant in each segment, but in fact they are not constant. Therefore, the present invention discretizes the flexible skin into multiple flexible hoses, and expresses the curvature and azimuth that change in real time as a function of the arc length, calculates its local coordinates by integration, and when integrating, it is expanded into a polynomial form integral by Taylor expansion, and then converted into a fixed coordinate system by coordinate transformation, thereby performing real-time deformation monitoring of the flexible skin, more realistically reflecting the deformed shape of the flexible skin, improving the accuracy of the flexible skin deformation measurement, and because the number of segments is small, the calculation speed is improved. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 The present invention is a flow chart of the method for online measurement of flexible skin deformation based on FBG strain sensor.

[0069] Figure 2 A pure bending model of the flexible hose provided by the present invention.

[0070] Figure 3 This is a schematic diagram of the installation of the FBG strain sensor at the cross section of the flexible hose provided by the present invention.

[0071] Figure 4 A schematic diagram of the origin of the motion coordinate system corresponding to the arc length on the entire flexible hose provided by the present invention.

[0072] Figure 5 This is a coordinate solution diagram of the origin of the adjacent local coordinate system of the flexible hose provided by the present invention. DETAILED DESCRIPTION

[0073] The technical solution of the present invention is further described below in conjunction with the accompanying drawings.

[0074] When the flexible skin is being monitored for deformation, the present invention discretizes it into a plurality of flexible hoses, firstly completes the deformation monitoring of the plurality of flexible hoses, and finally completes the deformation monitoring of the flexible skin.

[0075] like Figure 1 As shown, a method for online measurement of flexible skin deformation based on FBG strain sensor comprises the following steps:

[0076] Step 1: Install several FBG (Fiber Bragg Grating) strain sensors at equal intervals on the surface of the flexible hose. Calculate the curvature of the neutral axis of a flexible hose at discrete points and direction angle ;

[0077] Generally, when a flexible hose is bent, it is subjected to the combined effects of pressure and tension to form an arc; however, at this time, the neutral axis is stress-free, that is, it will not be contracted or stretched. Assuming that the flexible hose is deformed during the deformation process, the effect of torsion is ignored and only pure bending deformation occurs, such as Figure 2 As shown;

[0078] Several FBG strain sensors are installed at equal intervals on the entire surface of the flexible hose. Every three FBG strain sensors are installed at the same cross section of the flexible hose at equal intervals of 120°. FBG1, FBG2, and FBG3 represent three FBG strain sensors. Direction angle of the neutral axis discrete points of the flexible hose at each cross section As an indicator for obtaining direction information, the direction from the center of the flexible hose to the second FBG strain sensor (FBG2) is Axis positive direction, the tangent direction of the neutral axis of the flexible hose is Positive direction of the axis, determined by the right-hand screw rule Axis positive direction, such as Figure 3 As shown;

[0079] Since the angle between the three FBG strain sensors is 120° and the distance from the three FBG strain sensors to the neutral axis is a constant, The surface strain of the flexible hose at the three FBG strain sensors corresponding to the cross section and the curvature of the discrete points of the neutral axis of the flexible hose and direction angle The relationship between them is:

[0080] (1.1)

[0081] In the formula, ( ) are respectively The surface strain of the flexible hose measured by three FBG strain sensors at each cross section is For the The tensile strain on the flexible hose surface measured by three FBG strain sensors at each cross section is For the The curvature of the neutral axis discrete points of the flexible hose at each cross section, is the radius of the flexible hose, For the The direction angle of the discrete points of the neutral axis of the flexible hose at each cross section;

[0082] The said The relationship between the central wavelength offset, strain change, and temperature change measured by the three FBG strain sensors at each cross section is as follows:

[0083] (1.2)

[0084] In the formula, Respectively represent The central wavelength offset measured by three FBG strain sensors at each cross section is: is the strain sensitivity of the FBG strain sensor, Respectively represent The strain variation of discrete points on the flexible hose surface corresponding to the three FBG strain sensors at each cross section, is the temperature sensitivity of the FBG strain sensor, is the temperature change of the FBG strain sensor;

[0085] When the flexible hose is bent, The strain variation of discrete points on the surface of the flexible hose at the three FBG strain sensors corresponding to each cross section has the following relationship:

[0086] (1.3)

[0087] Combining formulas (1.1), (1.2) and (1.3), we can obtain the curvature of the discrete points of the neutral axis of the flexible hose: and direction angle , the expressions are as follows:

[0088] (1.4)

[0089] (1.5)

[0090] Step 2: The curvature of the discrete points of the neutral axis of the flexible hose in step 1 is calculated using the cubic spline fitting algorithm. and direction angle Fitting is performed to obtain the function of curvature with respect to arc length and direction angle as a function of arc length ;

[0091] In actual measurement, due to the influence of the number of grating measurement points of the FBG strain sensor and the number of channels of the fiber Bragg grating demodulator, the measured curvature data and azimuth angle data are discrete; the present invention adopts a cubic spline fitting algorithm, which can not only ensure the smoothness of the fitting curve, but also better retain its local characteristics;

[0092] The first The arc length of the neutral axis of the flexible hose at each cross section is expressed as , according to step 1 Curvature of the neutral axis of the flexible hose at discrete points in each cross section and direction angle , we get the curvature as a function of arc length for:

[0093] (2.1)

[0094] In the formula, Respectively represent part The coefficient of

[0095] The function of the direction angle with respect to the arc length for:

[0096] (2.2)

[0097] In the formula, Respectively represent part The coefficient of

[0098] Step 3: The function of the curvature obtained from step 2 with respect to the arc length , calculate the function of the central angle of a circle with respect to the arc length ; Based on the function of the central angle of a circle with respect to the arc length The function of the direction angle obtained by fitting in step 2 about the arc length , solve Motion coordinate system of the neutral axis of the flexible hose at each cross section Origin In the previous motion coordinate system The local coordinates in ;

[0099] like Figure 4 As shown, The points on the neutral axis of the flexible hose at each cross section are used as the motion coordinate system of the flexible hose. Origin , motion coordinate system Coordinate axis direction: Motion coordinate system of the flexible hose Origin Pointing to the second FBG strain sensor (FBG2) Axis positive direction, the tangent direction of the neutral axis of the flexible hose is Positive direction of the axis, determined by the right-hand screw rule Axis positive direction;

[0100] The function of the curvature obtained from step 2 with respect to the arc length Perform integral calculation to obtain the function of the central angle of each arc with respect to the arc length , the expression is as follows:

[0101] (3.1)

[0102] In the formula, is the integration variable, Indicates the upper limit of the integral;

[0103] like Figure 5 As shown, according to the function of the central angle of each arc with respect to the arc length The function of the direction angle obtained by fitting in step 2 about the arc length , calculate the neutral axis of the flexible hose in the motion coordinate system Origin In the previous motion coordinate system The local coordinates in , the expression is as follows:

[0104] (3.2)

[0105] In the formula, is the integration variable;

[0106] However, due to yes The quartic function of yes The cubic function of , , There is no specific expression for the original function, so Taylor polynomials are used to expand equation (3.2), as follows:

[0107] exist The third-order Taylor expansion polynomial at is:

[0108]

[0109] exist The third-order Taylor expansion polynomial at is:

[0110]

[0111] exist The third-order Taylor expansion polynomial at is:

[0112]

[0113] exist The third-order Taylor expansion polynomial at is:

[0114]

[0115] Substitute the Taylor expansion polynomial into equation (3.2) and integrate to obtain Motion coordinate system of the neutral axis of the flexible hose at each cross section Origin In the previous motion coordinate system The local coordinates in ;

[0116] Step 4: Discrete point direction angles based on the neutral axis of the flexible hose in step 1 and the function of the central angle with respect to the arc length in step 3 , calculate the Motion coordinate system of the neutral axis of the flexible hose at each cross section To a fixed coordinate system The rotation matrix ;

[0117] Place the neutral axis of the flexible hose Arc length at each cross section Substitute The function of the central angle of the arc segment with respect to the arc length , that is, Motion coordinate system of the neutral axis of the flexible hose at each cross section Central angle of rotation for:

[0118] (4.1)

[0119] In the formula, is the integration variable;

[0120] A fixed coordinate system is a coordinate system whose position and direction do not change. The coordinates finally calculated are all coordinates in the fixed coordinate system.

[0121] Assume motion coordinate system Origin The coordinates of the point are , due to the fixed coordinate system Origin and motion coordinate system Origin coincide with each other, and the directions of the two coordinate systems are consistent, so we know that the rotation matrix is the unit matrix, then the motion coordinate system Fixed coordinate system The rotation matrix , the expression is:

[0122] (4.2)

[0123] The motion coordinate system Around Axis Positive axis direction Axis positive direction of rotation , so that the rotated The positive direction of the axis coincides with the bending direction, and the motion coordinate system after the first rotation is obtained. , so the motion coordinate system To the coordinate system after the first rotation The rotation matrix , the expression is:

[0124] (4.3)

[0125] The rotated motion coordinate system Around Axis Positive axis direction Axis positive direction of rotation , so that the rotated The positive direction of the axis points to the motion coordinate system The tangent direction of the rotation The positive direction of the axis points to the motion coordinate system The bending direction of the second rotation is obtained. , so the motion coordinate system To the coordinate system after the second rotation The rotation matrix , the expression is:

[0126] (4.4)

[0127] The rotated motion coordinate system Around Axis Positive axis direction Axis positive direction of rotation , so that the rotated The positive direction of the axis points to the motion coordinate system of Axis positive direction, after rotation The positive direction of the axis points to the motion coordinate system of The positive direction of the axis, get the motion coordinate system after the third rotation , so the motion coordinate system To the coordinate system after the third rotation The rotation matrix , the expression is:

[0128] (4.5)

[0129] Therefore, the motion coordinate system Coordinate system of motion The rotation matrix , the expression is:

[0130] (4.6)

[0131] According to equations (4.2), (4.3), (4.4), (4.5) and (4.6), we can get Motion coordinate system of the neutral axis of the flexible hose at each cross section Fixed coordinate system The rotation matrix , the expression is:

[0132] (4.7)

[0133] Step 5: According to the step 4 Motion coordinate system of the neutral axis of the flexible hose at each cross section Fixed coordinate system The rotation matrix and step 3 Motion coordinate system of the neutral axis of the flexible hose at each cross section Origin In the previous motion coordinate system The local coordinates in , the motion coordinate system Origin The coordinates are converted to a fixed coordinate system In the Motion coordinate system of the neutral axis of the flexible hose at each cross section Origin In a fixed coordinate system Coordinates in ;

[0134] According to the motion coordinate system set in step 4 Origin The coordinates of the point are , get a fixed coordinate system Origin for ,origin Corresponding motion coordinate system , so the origin Corresponding motion coordinate system ; According to the fixed coordinate system Origin , get the Motion coordinate system of the neutral axis of the flexible hose at each cross section Origin In a fixed coordinate system Coordinates in , the expression is as follows:

[0135] (5.1)

[0136] In the formula, The motion coordinate system In a fixed coordinate system The coordinates in The motion coordinate system Rotate to a fixed coordinate system The rotation matrix of The motion coordinate system Origin In the motion coordinate system The coordinates in ;

[0137] Step 6: Use the cubic spline fitting algorithm to fit the Motion coordinate system of the neutral axis of the flexible hose at each cross section Origin In a fixed coordinate system Coordinates in Fitting is performed to obtain the curve of the neutral axis of the deformed flexible hose, that is, the shape of the deformed flexible hose; then, the deformed shapes of all the flexible hoses are fitted with cubic splines to obtain the deformed shape of the flexible skin;

[0138] Coordinate system of motion within each arc length segment Origin In a fixed coordinate system Coordinates in The expressions are as follows:

[0139]

[0140] In the formula, For the section The coefficient of

[0141]

[0142] In the formula, For the section The coefficient of .

[0143] In this way, the deformed shape of a flexible hose is obtained. Finally, the deformed shape of all flexible hoses only needs to be fitted to obtain the deformed shape of the flexible skin.

[0144] The present invention also provides an online measurement system for flexible skin deformation based on FBG strain sensors, comprising:

[0145] The first calculation module: install several FBG strain sensors at equal intervals on the surface of the flexible hose, and calculate the central wavelength offset measured by the FBG strain sensors. Calculate the curvature of the neutral axis of a flexible hose at discrete points and direction angle ;

[0146] The first fitting module: the curvature of the discrete points of the neutral axis of the flexible hose is calculated based on the cubic spline fitting algorithm. and direction angle Fitting is performed to obtain the function of curvature with respect to arc length and direction angle as a function of arc length ;

[0147] The second calculation module: the function of the curvature obtained by fitting with respect to the arc length , calculate the function of the central angle of a circle with respect to the arc length ; Based on the function of the central angle of a circle with respect to the arc length And the function of the direction angle obtained by fitting about the arc length , solve Motion coordinate system of the neutral axis of the flexible hose at each cross section Origin In the previous motion coordinate system The local coordinates in ;

[0148] The third calculation module: according to the direction angle of the discrete points of the neutral axis of the flexible hose and the central angle as a function of arc length , calculate the Motion coordinate system of the neutral axis of the flexible hose at each cross section To a fixed coordinate system The rotation matrix ;

[0149] The fourth calculation module: Motion coordinate system of the neutral axis of the flexible hose at each cross section Fixed coordinate system The rotation matrix and Motion coordinate system of the neutral axis of the flexible hose at each cross section Origin In the previous motion coordinate system The local coordinates in , the motion coordinate system Origin The coordinates are converted to a fixed coordinate system In the Motion coordinate system of the neutral axis of the flexible hose at each cross section Origin In a fixed coordinate system Coordinates in ;

[0150] The second fitting module: According to the cubic spline fitting algorithm, Motion coordinate system of the neutral axis of the flexible hose at each cross section Origin In a fixed coordinate system Coordinates in The curve of the neutral axis of the deformed flexible hose is obtained by fitting, that is, the shape of the deformed flexible hose; and the deformed shapes of all the flexible hoses are then fitted to obtain the deformed shape of the flexible skin.

Claims

1. An online measurement method for deformation of a flexible skin based on an FBG strain sensor, wherein the flexible skin is discretized into a plurality of flexible hoses, characterized in that: The following steps are involved: Step 1: Install several FBG strain sensors at equal intervals on the surface of the flexible hose, and measure the central wavelength offset of the FBG strain sensor. Calculate the curvature of the neutral axis of a flexible hose at discrete points and direction angle ; Step 2: The curvature of the discrete points on the neutral axis of the flexible hose is calculated using the cubic spline fitting algorithm. and direction angle Fitting is performed to obtain the function of curvature with respect to arc length and direction angle as a function of arc length ; Step 3: The curvature obtained from the fitting is a function of the arc length , calculate the function of the central angle of a circle with respect to the arc length ; Based on the function of the central angle of a circle with respect to the arc length And the function of the direction angle obtained by fitting about the arc length , solve Motion coordinate system of the neutral axis of the flexible hose at each cross section Origin In the previous motion coordinate system The local coordinates in ; Step 4: Discrete point direction angles according to the neutral axis of the flexible hose and the central angle as a function of arc length , calculate the Motion coordinate system of the neutral axis of the flexible hose at each cross section To a fixed coordinate system The rotation matrix ; Step 5: According to Motion coordinate system of the neutral axis of the flexible hose at each cross section Fixed coordinate system The rotation matrix and Motion coordinate system of the neutral axis of the flexible hose at each cross section Origin In the previous motion coordinate system The local coordinates in , the motion coordinate system Origin The coordinates are converted to a fixed coordinate system In the Motion coordinate system of the neutral axis of the flexible hose at each cross section Origin In a fixed coordinate system Coordinates in ; Step 6: Use the cubic spline fitting algorithm to fit the Motion coordinate system of the neutral axis of the flexible hose at each cross section Origin In a fixed coordinate system Coordinates in The curve of the neutral axis of the deformed flexible hose is obtained by fitting, that is, the shape of the deformed flexible hose; and the deformed shapes of all the flexible hoses are then fitted to obtain the deformed shape of the flexible skin.

2. The method for online measurement of flexible skin deformation based on FBG strain sensor according to claim 1, characterized in that: It is assumed that during the deformation process, the flexible hose only undergoes pure bending deformation.

3. The method for online measurement of flexible skin deformation based on FBG strain sensor according to claim 1 is characterized in that: In step 1, the curvature of the discrete points of the neutral axis of the flexible hose and direction angle The expressions are as follows: (1.4) (1.5) In the formula, Respectively represent The central wavelength offset measured by three FBG strain sensors at each cross section is: is the strain sensitivity of the FBG strain sensor, is the radius of the flexible hose.

4. The method for online measurement of flexible skin deformation based on FBG strain sensor according to claim 1 is characterized in that: In step 3, the function of the curvature obtained by fitting with respect to the arc length is Perform integral calculation to obtain the function of the central angle of each arc with respect to the arc length , the expression is as follows: (3.1) In the formula, is the integration variable, Indicates the upper limit of the integral; Then calculate the The neutral axis of the flexible hose at each cross section Origin In the previous motion coordinate system The local coordinates in , the expression is as follows: (3.2) In the formula, is the integration variable, is the function of the direction angle obtained by fitting with respect to the arc length; Taylor polynomials are used to expand equation (3.2) as follows: exist The third-order Taylor expansion polynomial at is: exist The third-order Taylor expansion polynomial at is: exist The third-order Taylor expansion polynomial at is: exist The third-order Taylor expansion polynomial at is: Substitute the Taylor expansion polynomial into equation (3.2) and integrate to obtain Motion coordinate system of the neutral axis of the flexible hose at each cross section Origin In the previous motion coordinate system The local coordinates in .

5. The method for online measurement of flexible skin deformation based on FBG strain sensor according to claim 1 is characterized in that: The calculation process of step 4 is as follows: Place the neutral axis of the flexible hose Arc length at each cross section Substitute The function of the central angle of the arc segment with respect to the arc length , that is, Motion coordinate system of the neutral axis of the flexible hose at each cross section Central angle of rotation for: (4.1) In the formula, is the integration variable; Assume motion coordinate system Origin The coordinates of the point are , then the motion coordinate system Fixed coordinate system The rotation matrix , the expression is: (4.2) The motion coordinate system Around Axis Positive axis direction Axis positive direction of rotation , so that the rotated The positive direction of the axis coincides with the bending direction, and the motion coordinate system after the first rotation is obtained. , so the motion coordinate system To the coordinate system after the first rotation The rotation matrix , the expression is: (4.3) The rotated motion coordinate system Around Axis Positive axis direction Axis positive direction of rotation , so that the rotated The positive direction of the axis points to the motion coordinate system The tangent direction of the rotation The positive direction of the axis points to the motion coordinate system The bending direction of the second rotation is obtained. , so the motion coordinate system To the coordinate system after the second rotation The rotation matrix , the expression is: (4.4) The rotated motion coordinate system Around Axis Positive axis direction Axis positive direction of rotation , so that the rotated The positive direction of the axis points to the motion coordinate system of Axis positive direction, after rotation The positive direction of the axis points to the motion coordinate system of The positive direction of the axis, get the motion coordinate system after the third rotation , so the motion coordinate system To the coordinate system after the third rotation The rotation matrix , the expression is: (4.5) Therefore, the motion coordinate system Coordinate system of motion The rotation matrix , the expression is: (4.6) According to equations (4.2), (4.3), (4.4), (4.5) and (4.6), we can get Motion coordinate system of the neutral axis of the flexible hose at each cross section Fixed coordinate system The rotation matrix , the expression is: (4.7) In the formula, Represents the motion coordinate system Fixed coordinate system The rotation matrix of Represents the motion coordinate system Coordinate system of motion The rotation matrix of .

6. The method for online measurement of flexible skin deformation based on FBG strain sensor according to claim 1 is characterized in that: In step 5, Motion coordinate system of the neutral axis of the flexible hose at each cross section Origin In a fixed coordinate system Coordinates in , the expression is as follows: (5.1) In the formula, The motion coordinate system In a fixed coordinate system The coordinates in The motion coordinate system Rotate to a fixed coordinate system The rotation matrix of The motion coordinate system Origin In the motion coordinate system The coordinates in .

7. A flexible skin deformation online measurement system based on FBG strain sensor, characterized in that: include: The first calculation module: install several FBG strain sensors at equal intervals on the surface of the flexible hose, and calculate the central wavelength offset measured by the FBG strain sensors. Calculate the curvature of the neutral axis of a flexible hose at discrete points and direction angle ; The first fitting module: the curvature of the discrete points of the neutral axis of the flexible hose is calculated based on the cubic spline fitting algorithm. and direction angle Fitting is performed to obtain the function of curvature with respect to arc length and direction angle as a function of arc length ; The second calculation module: the function of the curvature obtained by fitting with respect to the arc length , calculate the function of the central angle of a circle with respect to the arc length ; Based on the function of the central angle of a circle with respect to the arc length And the function of the direction angle obtained by fitting about the arc length , solve Motion coordinate system of the neutral axis of the flexible hose at each cross section Origin In the previous motion coordinate system The local coordinates in ; The third calculation module: according to the direction angle of the discrete points of the neutral axis of the flexible hose and the central angle as a function of arc length , calculate the Motion coordinate system of the neutral axis of the flexible hose at each cross section To a fixed coordinate system The rotation matrix ; The fourth calculation module: Motion coordinate system of the neutral axis of the flexible hose at each cross section Fixed coordinate system The rotation matrix and Motion coordinate system of the neutral axis of the flexible hose at each cross section Origin In the previous motion coordinate system The local coordinates in , the motion coordinate system Origin The coordinates are converted to a fixed coordinate system In the Motion coordinate system of the neutral axis of the flexible hose at each cross section Origin In a fixed coordinate system Coordinates in ; The second fitting module: According to the cubic spline fitting algorithm, Motion coordinate system of the neutral axis of the flexible hose at each cross section Origin In a fixed coordinate system Coordinates in The curve of the neutral axis of the deformed flexible hose is obtained by fitting, that is, the shape of the deformed flexible hose; and the deformed shapes of all the flexible hoses are then fitted to obtain the deformed shape of the flexible skin.

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