A method for surface reconstruction based on tafel curve load positioning and curvature correction

Abstract

The application discloses a kind of based on Tafel curve load positioning and curvature correction's surface reconstruction method.The method comprises: firstly according to strain sensor, obtains strain data, then the curvature of sensing point is calculated from strain data and interpolation is acquired continuous curvature data;Curvature data is used to calculate the position of loading point;Then using loading point position and reconstruction curve distance information, curvature correction function is used to correct curvature;Using curvature data, reconstruction curve is obtained from the both ends of curve respectively and is weighted to obtain modified curve;Finally, the modified curve is obtained by interpolation to reconstruct the surface.The application adopts a kind of based on Tafel curve load positioning and curvature correction's surface reconstruction method, the algorithm can judge the position of loading point, and correct the curvature data obtained near the point, and make the end point of the final reconstructed surface on fixed point, improve shape reconstruction precision, can be used in the scene of four around fixed single-end loading surface deformation reconstruction.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of optical fiber shape sensing, and particularly relates to a curved surface reconstruction method based on Tafel curve load positioning and curvature correction. BACKGROUND

[0002] In the field of aerospace, the four-around fixing plate is widely used in key parts and systems such as spacecraft cabin structure, propulsion system, thermal control system, solar cell panel and instrument equipment support structure, and bears important structural functions and tasks. In the long-term operation of the spacecraft, once the structures such as cracks, deformation and loosening occur, the normal operation of the spacecraft will be threatened, and even serious accidents will occur. Therefore, monitoring the structural performance of the four-around fixing plate is of great significance to the normal and safe operation of the spacecraft. The fiber Bragg grating sensor has the advantages of strong anti-interference ability, high precision, small size and light weight, so the fiber grating shape sensor has great application potential in the field of deformation monitoring of spacecraft plate structures. Therefore, how to use the strain information measured by the fiber grating to reconstruct the curved surface has become a hot issue.

[0003] The existing curved surface reconstruction method based on fiber grating has defects in the case of single-point loading of the four-around fixing plate.

[0004] The algorithm cannot give a high-precision reconstructed curved surface for different loading point positions. For example, the curved surface reconstruction algorithm proposed by Yan Jie et al. only uses the center point of the four-around fixing plate as the load loading point to reconstruct the curved surface deformation. In this application scenario, the plate deformation is completely symmetrical, and only one quarter of the plate surface needs to be reconstructed. However, the fixed loading point limits the application range of the algorithm. (Yan Jie, Li Wei, Jiang Mingshun, et al. Shape perception and three-dimensional reconstruction technology of plate structure based on fiber grating sensor [J]. China Laser, 2020, 47(11): 231-240.)

[0005] Although the algorithm combines boundary conditions to correct the reconstruction results, the correction method only considers the boundary error, and similar corrections will be given for the same boundary error when the loading point position is different, resulting in a larger error in the correction results. (Zhang Jiaming, Wang Wenrui, Lu Yu. Elastic thin plate deformation field reconstruction method based on strain measurement [J]. Laboratory Research and Exploration, 2021, 40(11): 14-19.)

[0006] The problems existing in the current curved surface reconstruction method based on fiber grating are mainly as follows: only the boundary conditions provided by the four-around fixing plate are considered, and the influence of the loading point position on the reconstruction error is not considered, which will lead to an increase in the reconstruction error after the curved surface is calibrated according to the boundary conditions; the correction function is single, and cannot give a correction function according to the change of the loading point position. SUMMARY

[0007] The application aims to provide a curved surface reconstruction method based on Tafel curve load positioning and curvature correction.

[0008] The application achieves the above-mentioned purpose by the following technical solutions.

[0009] A curved surface reconstruction method based on Tafel curve load positioning and curvature correction comprises the following steps.

[0010] Step 1: Obtain basic position parameters of all sensing points in a non-deformed state according to the structure and arrangement of the sensor; obtain strain values of each sensing point when the curved surface is deformed, and obtain the curvature κ of the sensor bend in combination with the geometric model of the sensor;

[0011] Step 2: Obtain more curvature data by interpolation to make the curvature data continuous;

[0012] Step 3: Determine the range of the load point position using the curvature data, assume the load point position one by one in the range, compensate the curvature at the assumed position using the Tafel curve according to the curvature variation law at the load point, and find the load point closest to the curvature on the x-direction and y-direction curves in the range, which is the determination position result;

[0013] Step 4: Determine the distance between the load point position and the reconstructed curve, and correct the curvature using two curvature correction functions according to the curvature variation law under different distances;

[0014] Step 5: Use the reconstruction algorithm to obtain two reconstructed curves, and determine the main curve and the secondary curve according to the load point information; the reconstructed curve far from the starting point of the load point position is the main curve, and the other is the secondary curve; the reconstructed result from the starting point to the load point in the result of the main curve is retained, and the main curve and the secondary curve are used for weighted average in the interval from the load point to the end point of the main curve;

[0015] Step 6: Obtain the coordinates of the multiple curves by reconstructing the sensor data, and perform spline interpolation on the coordinates to obtain a continuous and smooth curved surface.

[0016] Further, the sensor in step 1 is arranged in the x and y directions of the curved surface respectively, divides the curved surface into a certain number of grids, and is arranged on the grid points; the curvature data is obtained by pressing the four surrounding fixed plates from a single arbitrary load point to obtain strain data at the sensor arrangement point.

[0017] Further, in step 3, the Tafel curve function is used to compensate the curvature peak value according to the curvature variation law at the load point, and the function expression is as follows:

[0018] f(x) = a + b*lg(n-x).

[0019] Further, the loading point in step three is positioned as line positioning and surface positioning; the line positioning determines the position of the loading point on the curve in x and y directions respectively, and the surface positioning further judges the curve closest to the loading point in x and y directions, and the line positioning results of the two curves are the accurate positioning values of the surface loading point.

[0020] Further, the specific steps of step three are as follows:

[0021] (1) Obtain continuous curvature data;

[0022] (2) Obtain the maximum point of the curvature data as the possible position of the loading point on the curve in x and y directions;

[0023] (3) Determine the range of the loading point on the surface from the possible position of the loading point in x and y directions;

[0024] (4) Determine whether the curves contained in the range in x and y directions are less than 2, if less than, go to the next step; if greater than, further limit the positioning range of the possible loading point positioning result of the multiple curves contained in the range, and return to (3);

[0025] (5) The curve closest to the approximate range is used for the positioning result of the loading point as the determination result.

[0026] Further, after determining the position of the loading point in step four, the position of the loading point from the curve is determined, and the closer the loading point is to the curve, the greater the degree of curvature change; when the loading point is on the curve, the curvature correction function used is the Tafel curve; when the loading point is within the range of 3 cm on both sides of the curve, the exponential function f(x) = a*x b is used for correction; if it is beyond the range, no correction function is used, and the correction process is exited; finally, the curvature data near the loading point is obtained through the correction function.

[0027] Further, the specific steps of step four are as follows:

[0028] (1) Obtain the positioning position of the loading point;

[0029] (2) Calculate the distance L of the positioning position from the reconstructed curve;

[0030] (3) L = 0 uses the Tafel curve to correct the curvature, 0 < L < 3 cm uses the exponential function to correct the curvature, and L > 3 cm does not correct the curvature, and exits the correction process;

[0031] (4) The curvature peak value obtained after correction is added to the curvature data set;

[0032] (5) The curvature at the loading point is a segment point, and the curvature data is divided into two segments before and after the segment point; independent interpolation processing is performed on the curvature data of each segment, and finally the curvature data is spliced to obtain a complete curve curvature.

[0033] Further, the spline function is used to independently interpolate each segment of curvature data, the curvature change trend near the loading point is maintained, and the curvature at the loading point is continuous.

[0034] Further, the reconstruction algorithm in step five is a coordinate recursive algorithm, a two-dimensional coordinate system is established with the first point as the origin, the curvatures of the points calculated based on the previous steps are used for coordinate transformation by using a matrix, and the coordinates of the next point in the two-dimensional coordinate system are calculated one by one; and the coordinates are connected to obtain the entire reconstructed curve.

[0035] Further, the weighted average method in step five is that the closer to the loading point, the greater the weight of the main curve, at the loading point, the weight of the main curve is 1, the closer to the end point of the main curve, the greater the weight of the secondary curve, at the end point, the weight of the secondary curve is 1, the main curve and the secondary curve are added to obtain the reconstructed curve l, and the specific formula is as follows:

[0036]

[0037] l=m1l1+m2l2

[0038] In the formula, n1 is the position coordinate of the end point of the main curve, and x is the position distance from the start point of the main curve.

[0039] The beneficial effects of the present application are as follows:

[0040] The present application can effectively process the reconstruction problem of a deformed curved surface with four fixed points and a single loading point. By judging the position of the loading point and the curvature change near the loading point, correcting the curvature, and correcting the position of the end point after surface reconstruction, the present application can obtain a high-precision surface deformation shape under the condition of four fixed points and a single loading point, and improve the shape reconstruction precision.

[0041] The present application automatically judges the position of the loading point according to the curvature data; the present application uses different curvature correction functions to correct the obtained curvature according to the distance of the loading point from the curve, to improve the accuracy of the curvature data; the present application uses a main-secondary curve weighted method to obtain a reconstructed curve, so that the reconstructed curve is continuous and smooth, and the end point of the reconstructed curve is at a fixed position, and finally the reconstruction precision of the surface shape obtained by interpolation is improved. BRIEF DESCRIPTION OF DRAWINGS

[0042] Figure 1 is the algorithm flowchart of the present application;

[0043] Figure 2 is the loading point positioning flowchart of the present application;

[0044] Figure 3 is the flow chart of curvature correction of the present application;

[0045] Figure 4 is the schematic diagram of the arrangement of fiber grating sensor array in the present application;

[0046] Figure 5 is the schematic diagram of Tafel function;

[0047] Figure 6 is the schematic diagram of the principle of determining the range where the loading point is located in the present application;

[0048] Figure 7 is the schematic diagram of the change of curvature of different curves with the distance of loading point;

[0049] Figure 8 is the curvature acquisition result before and after curvature correction in the present application;

[0050] Figure 9 is the schematic diagram of the curved surface shape in the embodiment;

[0051] Figure 10 is the comparison diagram of the curved surface reconstruction result of the present application and the general method;

[0052] Figure 11 is the comparison diagram of the curved surface reconstruction error of the present application and the general method. DETAILED DESCRIPTION

[0053] The present application will be further described below in combination with the drawings.

[0054] The present application is a curved surface reconstruction method based on Tafel curve load positioning and curvature correction, according to Figure 1 , the specific steps are as follows:

[0055] Step one: according to the structure and arrangement mode of the sensor, the basic position parameters of all sensing points in the non-deformation state are obtained; the strain values of each sensing point are obtained when the curved surface is deformed, and the curvature κ of the sensor bend is obtained in combination with the geometric model of the sensor;

[0056] Step two: more curvature data are obtained through interpolation to make the curvature data continuous;

[0057] Step three: the approximate range of the loading point position is determined by using the curvature data, in which range, the loading point position is assumed one by one, and according to the curvature variation law at the loading point, the Tafel curve is used to compensate the curvature at the assumed position, and the loading point on the x direction and y direction curves closest to the curvature in the range is found out, which is the assumed loading point, and the assumed loading point is the determination position result;

[0058] Step four: judging the distance between the loading point position and the reconstructed curve, using two kinds of curvature correction functions to obtain the peak value data of the loading point and update the curvature data set according to the change rule of the curve curvature under different distances, and using the loading point as a segmentation point, using the spline function to interpolate the front and rear two segments, and finally splicing the curvature data to form a complete curve curvature.

[0059] Step five: using the reconstruction algorithm to reconstruct the two ends of the curve respectively, and then judging the main curve and the auxiliary curve according to the loading point information, the reconstructed curve far from the starting point of the loading point position is the main curve, and the other is the auxiliary curve. The reconstructed result from the starting point to the loading point in the result of the main curve is retained, and the main and auxiliary curves are used for weighted average in the interval from the loading point to the end point of the main curve.

[0060] Step six: after reconstructing the coordinates of multiple curves using sensor data, the coordinates are spline interpolated to obtain a continuous and smooth surface.

[0061] The sensors in step one are arranged in the x and y directions of the surface respectively, dividing the surface into a certain number of grids, and the sensors are arranged on the grid points. The specific arrangement is as shown in Figure 4 The curvature data is obtained by pressing the four surrounding fixed thin plates from a single arbitrary loading point to obtain the strain data of the sensor arrangement point.

[0062] In step three, according to the change rule of the curvature at the loading point, the Tafel curve function is used to compensate the curvature peak value, and the function change is as shown in Figure 5 The function expression is:

[0063] f(x)=a+b*lg(n-x)

[0064] Wherein, a, b are to be determined coefficients, and n is the Tafel function symmetry axis, that is, the position of the curvature peak value to be fitted.

[0065] In step three, the positioning of the loading point is divided into two steps, namely line positioning and surface positioning, and the principle of judging the range of the loading point is as shown in Figure 6

[0066] The line positioning determines the position of the loading point on the x and y direction curves, which can be divided into two steps: first, the coarse positioning of the loading point is obtained by obtaining the maximum point of the curvature data as the approximate position of the loading point. Then, near this position, every point is assumed to be a loading point at an interval of 1 cm, and the curvature splicing is performed using the curvature correction function. After removing the end point data in the loading point interval, the spliced curvature is compared with the actual curvature, and the variance is calculated to determine the point with the minimum variance as the accurate loading point position.

[0067] ​The surface positioning can also be divided into two steps: firstly, the line loading point positioning is performed on the curves in the x direction and the y direction, and the approximate range of the loading point is determined according to the positioning result. Then, the curves closest to the range are found, and the line positioning result of the two curves is the accurate value of the surface measurement point positioning.

[0068] In the third step, the loading point positioning process is as shown in Figure 2 , and the specific process is as follows:

[0069] 1) Obtain the continuous curvature data;

[0070] 2) Analyze the possible positions of the loading point on the curves in the x direction and the y direction;

[0071] 3) Determine the possible range of the loading point on the surface from the possible positions of the loading point in the x direction and the y direction;

[0072] 4) Determine whether the curves contained in the range in the x direction and the y direction are less than 2, if less than, enter the next step; if greater than, further limit the positioning range of the possible loading point positioning result of the multiple curves contained in the range, and return to 3);

[0073] 5) The loading point positioning result of the curve closest to the approximate range is taken as the determination result.

[0074] In the fourth step, after the position of the loading point is determined, the position of the loading point from the curve is determined. The curvature change on different curves is different due to the different distances from the loading point, and the specific change is as shown in Figure 7 . The closer the distance from the loading point, the greater the degree of change of the curvature of the curve, so the distance is divided into two cases, and different curvature correction functions are used to obtain the curvature peak value at the loading point.

[0075] The curvature correction function used when the loading point is on the curve is the Tafel function, the exponential function f(x) = a*x b is used when the loading point is within the range of 3 cm on both sides of the curve, and no correction function is used when the distance from the curve is more than 3 cm. After obtaining the curvature at the loading point position, the spline function is used for piecewise interpolation Figure 8 to maintain the curvature change trend near the loading point and ensure the continuity of the curvature at the loading point. The corrected curvature is as shown in

[0076] In the fourth step, the curvature correction process is as shown in Figure 3 , and the specific process is as follows:

[0077] 1) Obtain the loading point positioning position;

[0078] 2) Calculate the distance L of the positioning position from the reconstructed curve;

[0079] 3) L=0 using Lattes curve to correct curvature, 0

[0080] 4) using the corrected curvature peak to add the curvature data set;

[0081] 5) loading point curvature is a segmented point, and the curvature data is divided into two segments. The curvature data of each segment is independently interpolated, and finally the curvature data is spliced to obtain a complete curve curvature.

[0082] The reconstruction algorithm in step five is a coordinate recursive algorithm. A two-dimensional coordinate system is established with the first point as the origin. Based on the curvature of each point calculated in the previous steps, the coordinates of the next point in the two-dimensional coordinate system are calculated one by one by using matrix coordinate transformation. The coordinates of the curve are connected to obtain the entire reconstructed curve.

[0083] The weighted average method in step five is: the closer to the loading point position n, the greater the weight m1 of the main curve l1. At the loading point, the weight of the main curve is 1. The closer to the end point of the main curve, the greater the weight m2 of the secondary curve l2. At the end point, the weight of the secondary curve is 1. The main and secondary curves are added to obtain the reconstructed curve l, and the specific formula is as follows:

[0084]

[0085] l = m1l1 + m2l2

[0086] In the formula, n1 is the position coordinate of the end point of the main curve, and x is the position distance from the start point of the main curve.

[0087] Figure 9 is the reconstructed target surface image, Figure 10 is the reconstruction result of the general method and the reconstruction result of the method of the application, Figure 11 is the reconstruction error of the general method and the reconstruction error of the method of the application. As can be seen from the figure, the reconstruction method of the application can more accurately reconstruct the shape of the measured surface, and it can be verified that the surface reconstruction method based on Lattes curve load positioning and curvature correction proposed in the patent has theoretical feasibility and can accurately reconstruct the surface according to the discrete curvature data of the surface.

[0088] The above only describes the preferred embodiments of the application and is not intended to limit the application. For those skilled in the art, the application can have various modifications and changes. Any modification, equivalent replacement, improvement, etc. made within the spirit and principles of the application shall be included in the protection scope of the application.

Claims

1. A surface reconstruction method based on Tafel curve load positioning and curvature correction, characterized in that: Includes the following steps: Step 1: Based on the structure and arrangement of the sensors, obtain the basic position parameters of all sensing points in the undeformed state; The strain values ​​at each sensing point are obtained during surface deformation, and the curvature of the sensors at the grid points is obtained by combining the sensor's geometric model. ; Step 2: Obtain more curvature data through interpolation to make the curvature data continuous; Step 3: Use curvature data to determine the range of loading point locations. Within the range, assume loading point locations one by one. Based on the curvature change pattern at the loading point, use the Tafel curve to perform peak compensation on the curvature at the assumed location. Find the loading point with the closest curvature on the x and y direction curves within the range, which is the result of the location determination. Step 4: Determine the distance between the loading point and the curve. Based on the pattern of curve curvature change at different distances, use two curvature correction functions to correct the curvature. Step 5: Apply the reconstruction algorithm to both ends of the curve to obtain two reconstructed curves. Then, determine the main curve and the sub-curve based on the loading point information. The reconstructed curve whose loading point is farther from the reconstruction starting point is the main curve, and the other is the sub-curve. The reconstruction result from the starting point to the loading point is retained in the result of the main curve. The interval from the loading point to the end point of the main curve is weighted and averaged using the main and sub-curves. Step 6: After reconstructing the coordinates of multiple curves using sensor data, perform spline interpolation on the coordinates to obtain a continuous and smooth surface.

2. The surface reconstruction method based on Tafel curve load positioning and curvature correction according to claim 1, characterized in that: In step one, the sensors are arranged in the x and y directions of the curved surface, and the curved surface is divided into a certain number of grids. The sensors are arranged at the grid points. The curvature data is obtained by applying pressure to the surrounding fixed thin plate at a single arbitrary loading point and calculating the strain data at the sensor arrangement point.

3. The surface reconstruction method based on Tafel curve load positioning and curvature correction according to claim 1, characterized in that: In step three, based on the curvature variation pattern at the loading point, the Tafel curve function is used to compensate for the peak curvature. The expression of this function is: ； in, For coefficients, The axis of symmetry of the Tafel function is the location of the peak curvature that needs to be fitted.

4. The surface reconstruction method based on Tafel curve load positioning and curvature correction according to claim 1, characterized in that: In step three, the loading point is located by line positioning and surface positioning. Line positioning determines the position of the loading point on the curves in the x and y directions, respectively. Surface positioning further determines the curves closest to the loading point in the x and y directions. The line positioning results of these two curves are the accurate values ​​of the surface loading point positioning.

5. The surface reconstruction method based on Tafel curve load positioning and curvature correction according to claim 4, characterized in that: The specific steps are as follows: (1) Obtain continuous curvature data; (2) Obtain the maximum value of the curvature data as the possible location of the loading point on the curve in the x and y directions; (3) Determine the range of the loading point on the surface based on the possible positions of the loading point in the x and y directions; (4) Determine whether there are fewer than 2 curves in the x and y directions within the range. If there are fewer, proceed to the next step. If there are more, further limit the positioning range of the possible loading point positioning results of the multiple curves within the range, and return to (3). (5) The loading point location result of the curve closest to this range is used as the judgment result.

6. The surface reconstruction method based on Tafel curve load positioning and curvature correction according to claim 1, characterized in that: After determining the loading point location in step four, the distance between the loading point and the curve is judged. The closer the loading point is to the curve, the greater the change in curvature. When the loading point is on the curve, the curvature correction function used is the Tafel curve. When the loading point is within 3 cm on both sides of the curve, the exponential function is used. Perform correction; if the value exceeds the range, do not use the correction function and exit the correction process; finally, obtain the curvature data near the loading point through the correction function.

7. The surface reconstruction method based on Tafel curve load positioning and curvature correction according to claim 6, characterized in that: The specific steps are as follows: (1) Obtain the location of the loading point; (2) Calculate the distance between the positioning location and the reconstructed curve. ; (3) 0. Curvature correction is performed using Tafel curves. Curvature is corrected using an exponential function. Do not correct the curvature, and exit the correction process; (4) Use the corrected curvature peaks to add to the curvature dataset; (5) The curvature at the loading point is the segmentation point, and the curvature data is divided into two segments. The curvature data of each segment is interpolated independently, and finally the curvature data is spliced ​​together to obtain the complete curve curvature.

8. The surface reconstruction method based on Tafel curve load positioning and curvature correction according to claim 7, characterized in that: The spline function is used to interpolate each segment of curvature data independently, preserving the curvature change trend near the loading point while ensuring curvature continuity at the loading point.

9. The surface reconstruction method based on Tafel curve load positioning and curvature correction according to claim 1, characterized in that: The reconstruction algorithm in step five is a coordinate recursive algorithm. It establishes a two-dimensional coordinate system with the first point as the origin, and uses a matrix to perform coordinate transformation based on the curvature of each point calculated in the previous steps to calculate the coordinates of the next point in the two-dimensional coordinate system one by one. The coordinate curves are then connected to obtain the entire reconstruction curve.

10. The surface reconstruction method based on Tafel curve load positioning and curvature correction according to claim 1, characterized in that: The weighted averaging method in step five is as follows: the closer to the loading point, the greater the weight of the principal curve; at the loading point, the weight of the principal curve is 1. The closer to the end point of the principal curve, the greater the weight of the secondary curve; at the end point, the weight of the secondary curve is 1. The principal and secondary curves are added together to obtain the reconstructed curve. The specific formula is as follows: ； ； ； In the formula, Here are the coordinates of the endpoint of the main curve, where x is the distance from the starting point of the main curve. Main curve, The weight of the main curve, sub-curve, For the weight of the sub-curve, The axis of symmetry of the Tafel function is the location of the peak curvature that needs to be fitted.

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