Contact type displacement sensor calibration tool and complex curved surface contour measurement method

Abstract

The invention relates to a contact type displacement sensor calibration tool and a complex curved surface contour measurement method. The method comprises the steps of performing coaxial calibration of two contact type displacement sensors based on a calibration tool; based on a contact type displacement sensor, collecting and processing measurement data of the complex curved surface contour; according to the local slope and the local curvature change, obtaining segmentation nodes, and according to the segmentation nodes, carrying out segmentation processing on the complex curved surface contour to obtain a corrected fitting curve; performing polynomial fitting on each segment in the complex curved surface contour to obtain a fitting error term of each segment; based on the segment node of each segment, constructing a regularization item so as to enable the segments to be in smooth transition; based on the corrected fitting curve, the fitting error term and the regularization term, constructing a target function of the complex curved surface contour fitting curve; and obtaining a curve fitting result of the complex curved surface contour based on the objective function. According to the invention, a high-precision contour fitting effect is realized.

Description

Technical Field

[0001] The invention relates to the field of precision measurement technology, in particular to a contact displacement sensor calibration tool and a complex curved surface profile measurement method. Background Art

[0002] The measurement of complex curved surface contours is a key process to determine the machining allowance before grinding and polishing of complex curved surface parts, and to inspect the machining quality after grinding and polishing. The current mainstream measurement method is to use three-coordinate measuring equipment to measure the complex curved surface contours, but the three-coordinate measuring equipment cannot perform online measurement. If the test result is unqualified, it needs to be re-processed online. In addition, the three-coordinate measuring equipment itself is too expensive and requires a constant temperature, constant humidity and seismic isolation operating environment, resulting in low three-coordinate measurement efficiency and high measurement costs.

[0003] Existing public patents: A blade profile measurement method, device and system based on a line laser sensor, patent publication number CN111504223B, discloses a blade measurement method, device and system based on a line laser sensor, the line laser sensor measures partial contour data points of a complex surface, and then fits and splices the data points into a complete cross-sectional profile. This type of measurement method has certain limitations, such as water stains or grinding dust on complex surfaces that affect measurement accuracy; complex surfaces have a weak mirror effect after grinding and polishing, causing reflected light to scatter, resulting in the sensor being unable to collect reflected light; the large curvature of the complex surface causes the light reflection angle to be too large, which also causes the receiver to be unable to collect reflected light, seriously affecting measurement accuracy.

[0004] A contact displacement sensor is a sensor that directly contacts the object being measured and is used to measure the contour changes on the surface of the object. It has the advantages of high precision, good stability, simple structure and low cost. Existing public patents: an adjustment device, an optical device and a detection system, patent publication number CN221079022U, discloses an adjustment device, an optical device and a detection system, which designs a tooling for laser measurement sensors, with movement in three directions and rotation in two directions, and can adjust the installation posture of the laser measurement sensor at multiple angles for calibration. However, this tooling needs to be used with the calibration software that comes with the laser sensor to complete the calibration of the sensor measurement position, and cannot be used for the calibration of two independent contact displacement sensors.

[0005] During the measurement process, the measurement data generated a lot of noise due to the influence of burrs, grinding dust and roughness on the complex surface, and there was an error between the fitted profile and the actual profile. Since the contact displacement sensor probe was in contact with the complex surface for a long time, the probe was worn and the measurement accuracy decreased. And due to the different surface profiles, the surface and the contact sensor had different contact areas, resulting in different degrees of wear in different areas of the contact sensor probe. Therefore, adopting a suitable data fitting method and compensating the measurement results during the measurement process have become key technical points to improve and ensure the accuracy of blade profile measurement.

[0006] In addition, the commonly used methods for measuring data fitting include linear regression, least squares method, polynomial regression, neural network and support vector machine regression. Existing public patent: A data processing method, device, equipment and medium based on linear fitting, patent publication number CN118484915A, discloses a data processing method, device, equipment and medium based on linear fitting. A three-layer loop single variable successive search strategy is proposed, and a prediction vector is generated by linear fitting to search for the optimal density difference and depth more finely, and linear fitting is introduced in the innermost layer to improve the solution efficiency and accuracy. Linear regression algorithm and least squares method are often used to capture the linear relationship of data, and perform poorly when facing nonlinear data distribution. Although polynomial regression can handle nonlinear relationships, when the polynomial order is too high, the model is prone to overfitting the training data, resulting in insufficient generalization ability for new data. In addition, polynomial regression requires a function that can fit complex curves, but the contour of complex surfaces is complex, and there is a characteristic that the contour changes with the cross-sectional position, and the contours of different parts are quite different, which is difficult to accurately fit with a single function.

[0007] Although neural networks are powerful nonlinear models that are good at handling complex pattern recognition and fitting problems, they require a large amount of data and computing resources. In addition, the internal structure of neural networks is complex, and the decision-making process and prediction results are difficult to explain, making it impossible to achieve high-precision measurements of complex surfaces. The performance of support vector machine regression is highly dependent on hyperparameters (such as the selection of parameters such as the kernel function γ). The parameter adjustment process is complex and requires a large amount of cross-experimental verification to determine the optimal parameters. In addition, in unbalanced data sets, the support vector machine regression method tends to favor the majority class and ignores the minority class, resulting in inaccurate fitting.

[0008] Considering the diversity and complexity of the surface profile functions to be measured, the errors between the actual surface and the theoretical model, and the requirement of high-precision measurement, there is an urgent need to design a lightweight and adaptive data fitting algorithm that can adapt to different surface profiles in order to effectively process the collected complex surface profile measurement data. Summary of the invention

[0009] To this end, the present invention provides a contact displacement sensor calibration tool and a complex surface contour measurement method. The calibration tool is used to achieve precise adjustment of the sensor position and posture, ensuring that two contact displacement sensors are coaxially installed to improve measurement accuracy. And for different complex surface contours, adaptive segmented fitting, compensation and smooth transition strategies are adopted to achieve high-precision contour fitting effects.

[0010] In order to solve the above technical problems, the present invention provides a contact displacement sensor calibration tool, comprising: Based on the contact displacement sensor calibration fixture, coaxial calibration of two contact displacement sensors is performed; Based on the contact displacement sensor, collecting measurement data of complex curved surface contours; Performing denoising and filtering processing on the measurement data to obtain processed measurement data; Based on the processed measurement data, segmentation nodes are obtained according to changes in local slope and local curvature, and segmentation processing is performed on the complex surface contour according to the segmentation nodes; Based on the processed measurement data, an initial fitting curve and residuals are obtained, polynomial fitting is performed on the residuals to obtain a polynomial form, a design matrix is ​​constructed based on the polynomial form, polynomial coefficients are obtained based on the design matrix, a compensation polynomial is obtained based on the polynomial coefficients, and a modified fitting curve is obtained based on the compensation polynomial and the initial fitting curve; Perform polynomial fitting on each segment in the complex surface profile to obtain the fitting error term of each segment; Based on the segment nodes of each segment, a regularization term is constructed to make a smooth transition between segments; Based on the corrected fitting curve, the fitting error term and the regularization term, an objective function of the complex surface profile fitting curve is constructed, and based on the objective function, a curve fitting result of the complex surface profile is obtained; Wherein, the contact displacement sensor calibration tool comprises: Base; An adjustment seat, adjustably connected to the base along a first direction; A main bracket is pivoted on the adjustment seat with the second direction as an axis; A secondary support, adjustably connected to the main support along the second direction; A sensor mounting plate, pivoted on the sub-bracket with the first direction as an axis, the sensor mounting plate being used to mount a contact displacement sensor, the probe of the contact displacement sensor being adjustable to extend along a third direction; The first direction, the second direction and the third direction are perpendicular to each other.

[0011] In one embodiment of the present invention, it further includes a first support shaft, a second support shaft, and a first adjustment spring; The first support shaft is installed on the base, the adjustment seat is slidably connected to the base through the first support shaft along the first direction, two first adjustment springs are sleeved on the first support shaft, and two ends of each first adjustment spring are limited by the adjustment seat and the base respectively; A first locking member capable of abutting against the first supporting shaft is connected to the adjusting seat along the third direction to lock the relative position of the adjusting seat and the base; The second support shaft is installed on the adjustment seat along the second direction, and the main bracket is rotatably connected to the adjustment seat through the second support shaft; A first adjusting member connected to the second supporting shaft is connected to the middle end surface of the adjusting seat along the second direction to adjust the angle between the main support and the adjusting seat.

[0012] In one embodiment of the present invention, it further includes a third support shaft and a second adjustment spring; The third support shaft is installed on the main support, the auxiliary support is slidably connected to the third support shaft along the second direction, and the second adjustment spring is sleeved on the third support shaft and its two ends are respectively limited by the auxiliary support and the main support; The main bracket is connected to a second adjusting member along the second direction to abut against the auxiliary bracket so as to adjust the relative position between the auxiliary bracket and the main bracket; The main bracket is connected with a second locking piece along the first direction and abuts against the auxiliary bracket to lock the relative position between the auxiliary bracket and the main bracket.

[0013] In one embodiment of the present invention, it further includes a fourth support shaft and a rotation adjustment block; The fourth support shaft is installed on the auxiliary bracket along the first direction, and the sensor mounting plate is rotatably connected to the auxiliary bracket through the fourth support shaft; The rotation adjustment block is connected to the auxiliary bracket, and is connected to a third adjustment member capable of abutting against the sensor mounting plate to adjust the angle between the sensor mounting plate and the auxiliary bracket.

[0014] In one embodiment of the present invention, coaxial calibration of two contact displacement sensors is performed, including: Place the calibration block in the middle of the two contact displacement sensors so that the probes of the contact displacement sensors on both sides extend along the x-axis and contact the calibration block; Rotate and adjust each contact displacement sensor around the y-axis to minimize its measured value; Rotate and adjust each contact displacement sensor around the z-axis so that its measured value reaches the minimum again, and make the probe axes of the two contact displacement sensors parallel to the reference plane of the calibration block; Place the calibration ball in the middle of the two contact displacement sensors, move the probes of each contact displacement sensor horizontally along the y-axis direction, and find the minimum value on the same horizontal plane; Move the probes of each contact displacement sensor along the z-axis direction to find the minimum value in different height directions, so that the probe axes of the two contact displacement sensors are coaxial.

[0015] After the adjustment is completed, fix the positions of the two contact displacement sensors.

[0016] In one embodiment of the present invention, based on the processed measurement data, segmentation nodes are obtained according to the local slope and local curvature changes, and segmentation processing is performed on the complex surface contour according to the segmentation nodes, including: Calculating the slope of each data point in the processed measurement data, and obtaining the slope difference between the slopes of adjacent data points; If the slope difference is greater than a preset slope change threshold, the corresponding data point is used as a segmentation node; calculating the curvature of each data point in the processed measurement data; If the curvature is greater than a preset curvature change threshold, the corresponding data point is also used as a segmentation node; Wherein, the slope is calculated as follows: , The slope difference is calculated as follows: , The curvature is calculated as follows: , in, is the slope of the ith data point, and are the ordinate and abscissa of the point, respectively. and are the ordinate and abscissa of the next point respectively, and They are the ordinate and abscissa of the next data point respectively.

[0017] In one embodiment of the present invention, based on the processed measurement data, an initial fitting curve and a residual are obtained, a polynomial fitting is performed on the residual to obtain a polynomial form, a design matrix is ​​constructed based on the polynomial form, polynomial coefficients are obtained based on the design matrix, a compensation polynomial is obtained based on the polynomial coefficients, and a modified fitting curve is obtained based on the compensation polynomial and the initial fitting curve, including: The residual of each data point in the processed measurement data is calculated, that is, the difference between the actual value and the fitted value, wherein the residual is defined as: , in, is the actual data point, and are the ordinate and abscissa of the data point, respectively. is the initial fitting curve At the point The value at which the initial fitting curve Fitting by spline interpolation; Residual Perform polynomial fitting, for each data point , the polynomial form is: , n is a positive integer; For m data points, construct the design matrix X, specifically: , Calculate polynomial coefficients , specifically: , in, ; T is the transpose of the matrix; Generate the compensation polynomial: , in, , ..., are polynomial coefficients, n is a positive integer; Correction of fitting curve is the initial fitting curve With compensation polynomial The superposition of: .

[0018] In one embodiment of the present invention, a polynomial fitting is performed on each segment in the complex curved surface profile to obtain a fitting error term for each segment, including: In each segment, the least squares method is used to solve the coefficients of the polynomial, gradually increasing the order of the polynomial and calculating the fitting error at each order. ; The mean square error (MSE) is used as the evaluation criterion, and the fitting starts from a low-order polynomial until the error decreases to no more than a preset threshold, where: , in, n is the number of data points, is the fitting error term.

[0019] In one embodiment of the present invention, the expression of the objective function is: , in, is the regularization term; and The kth and k+1th segments are at the boundary points The derivative at ; K is a positive integer; is the fitting error term; is the preset regularization strength, which is used to control the balance between the fitting error term and the regularization term; when When it is small, the fitting error term dominates and the curve is closer to the data point; When it is larger, the regularization term dominates and the curve is smoother.

[0020] The above technical solution of the present invention has the following advantages compared with the prior art: The contact displacement sensor calibration fixture and complex surface profile measurement method described in the present invention adjust the positions and angles of two contact displacement sensors through the calibration fixture and corresponding calibration steps to achieve a coaxial installation state, so that the theoretical measurement point coincides with the actual measurement point. An adaptive piecewise fitting method is proposed, which uses an adaptive piecewise polynomial interpolation algorithm combined with a regularization algorithm to fit the measurement data, and based on the error between the actual profile of the complex surface and the fitted profile, the measurement result is adaptively compensated to improve the accuracy and stability of complex surface profile measurement.

[0021] The present invention adaptively divides the overall data set into multiple curves that can be represented by different polynomial functions according to the slope variation of the measured data in different areas. Based on the error between the actual contour and the fitted contour, a polynomial compensation function is used to provide a bias for the measured data on the basis of the initial fitting function to compensate for the measurement error caused by the wear of the sensor probe. A polynomial interpolation algorithm is used to fit the data in each segment, and the least squares method is used to solve the polynomial coefficients to ensure local fitting accuracy. A regularization term is introduced between each segment of the curve, and the fitting error term and the regularization term are combined to construct the objective function, so as to achieve a balance between smooth transition and closeness to the actual measured data, and achieve a high-precision contour fitting effect. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] In order to make the contents of the present invention more clearly understood, the present invention is further described in detail below based on specific embodiments of the present invention in conjunction with the accompanying drawings.

[0023] Figure 1 It is a schematic diagram of the overall structure of the contact displacement sensor calibration tooling of the present invention.

[0024] Figure 2 It is a schematic diagram of the exploded structure of the contact displacement sensor calibration tooling of the present invention.

[0025] Figure 3 It is an adjustment direction diagram of the contact displacement sensor calibration tooling of the present invention.

[0026] Figure 4 It is a flow chart of the complex curved surface profile measurement method of the present invention.

[0027] Figure 5 This is a schematic diagram of the contact displacement sensor when it is installed on different axes.

[0028] Figure 6 It is a schematic diagram of the coaxial calibration (using calibration block) of the contact displacement sensor.

[0029] Figure 7 It is a schematic diagram of the coaxial calibration (using a calibration ball) of a contact displacement sensor.

[0030] Description of the Figures in the Specification: 1. Base; 11. First support shaft; 12. First adjustment spring; 13. First hole position; 2. Adjustment seat; 21. Second support shaft; 22. Second hole position; 3. Main bracket; 31. Third support shaft; 32. Second adjustment spring; 33. Third hole position; 34. Fourth hole position; 4. Auxiliary bracket; 41. Fourth support shaft; 5. Sensor mounting plate; 6. Rotate the adjustment block; 61. The fifth hole position. DETAILED DESCRIPTION

[0031] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments so that those skilled in the art can better understand the present invention and implement it, but the embodiments are not intended to limit the present invention.

[0032] In the present invention, if directions (up, down, left, right, front and back) are described, it is only for the convenience of describing the technical solution of the present invention, and does not indicate or imply that the technical features referred to must have a specific orientation, be constructed and operate in a specific orientation. Therefore, it cannot be understood as a limitation of the present invention.

[0033] In the present invention, "several" means one or more, "multiple" means more than two, "greater than", "less than", "exceed" and the like are understood to exclude the number itself; "above", "below", "within" and the like are understood to include the number itself. In the description of the present invention, if there is a description of "first" or "second", it is only used for the purpose of distinguishing technical features, and cannot be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features or implicitly indicating the order of the indicated technical features.

[0034] In the present invention, unless otherwise clearly defined, the words "set", "install", "connect" and the like should be understood in a broad sense, for example, they can be directly connected or indirectly connected through an intermediate medium; they can be fixedly connected or detachably connected or integrally formed; they can be mechanically connected or electrically connected or able to communicate with each other; they can be the internal connection of two elements or the interaction relationship between two elements. Those skilled in the art can reasonably determine the specific meanings of the above words in the present invention in combination with the specific content of the technical solution.

[0035] Reference Figures 1 to 3 As shown, a contact displacement sensor calibration tool comprises: Base 1; An adjustment seat 2, adjustably connected to the base 1 along a first direction; The main bracket 3 is pivoted on the adjustment seat 2 with the second direction as the axis; A secondary bracket 4, adjustably connected to the main bracket 3 along the second direction; A sensor mounting plate 5 is pivoted on the auxiliary bracket 4 with the first direction as an axis, and the sensor mounting plate 5 is used to mount a contact displacement sensor, and the probe of the contact displacement sensor can be adjusted to extend along the third direction; The first direction, the second direction and the third direction are perpendicular to each other.

[0036] Specifically, it also includes a first support shaft 11, a second support shaft 21, and a first adjustment spring 12; The first support shaft 11 is installed on the base 1, the adjustment seat 2 is slidably connected to the base 1 through the first support shaft 11 along the first direction, two first adjustment springs 12 are sleeved on the first support shaft 11, and two ends of each first adjustment spring 12 are respectively limited by the adjustment seat 2 and the base 1; A first locking member capable of abutting against the first supporting shaft 11 is connected to the adjusting seat 2 (on the first hole 13) along the third direction to lock the relative position of the adjusting seat 2 and the base 1; the first locking member may be a screw; The second support shaft 21 is installed on the adjustment seat 2 along the second direction, and the main bracket 3 is rotatably connected to the adjustment seat 2 through the second support shaft 21; A first adjusting member connected to the second support shaft 21 is connected to the middle end surface of the adjusting seat 2 (on the second hole 22) along the second direction to adjust the angle between the main bracket 3 and the adjusting seat 2. The first adjusting member can be a bolt; Specifically, it also includes a third support shaft 31 and a second adjustment spring 32; The third support shaft 31 is installed on the main support 3, the auxiliary support 4 is slidably connected to the third support shaft 31 along the second direction, and the second adjustment spring 32 is sleeved on the third support shaft 31 and its two ends are respectively limited by the auxiliary support 4 and the main support 3; The main bracket 3 (on the third hole 33) is connected with a second adjusting member abutting against the auxiliary bracket 4 along the second direction to adjust the relative position between the auxiliary bracket 4 and the main bracket 3; the second adjusting member may be a bolt; The main bracket 3 (on the fourth hole 34) is connected with a second locking member abutting against the auxiliary bracket 4 along the first direction to lock the relative position between the auxiliary bracket 4 and the main bracket 3; the second locking member may be a screw; Specifically, it also includes a fourth support shaft 41 and a rotation adjustment block 6; The fourth support shaft 41 is installed on the auxiliary bracket 4 along the first direction, and the sensor mounting plate 5 is rotatably connected to the auxiliary bracket 4 through the fourth support shaft 41; The rotation adjustment block 6 is connected to the auxiliary bracket 4, and the rotation adjustment block 6 (on the fifth hole 61) is connected with a third adjustment member capable of abutting against the sensor mounting plate 5 to adjust the angle between the sensor mounting plate 5 and the auxiliary bracket 4. The third adjustment member can be a bolt, and two bolts are provided, which are respectively installed on both sides of the rotation adjustment block 6 in the rotation direction of the sensor mounting plate 5.

[0037] It should be noted that, in this embodiment, the first direction, the second direction and the third direction are the y-axis, the z-axis and the x-axis respectively.

[0038] Reference Figure 4 As shown, this embodiment also provides a complex curved surface profile measurement method, which measures the complex curved surface profile based on the coaxial relative installation of two contact displacement sensors, including: S1. Based on the contact displacement sensor calibration tool, coaxial calibration of two contact displacement sensors is performed.

[0039] Reference Figure 5 As shown in the figure, since two independent contact displacement sensors are used for measurement, the coaxial installation of the sensors cannot be guaranteed by relying solely on processing and installation accuracy, resulting in a position deviation between the theoretical measurement point and the actual measurement point. Therefore, it is necessary to calibrate the position and posture of the two measurement sensors to improve the measurement accuracy.

[0040] Reference Figure 6 , Figure 7 As shown, the calibration steps include: Place the calibration block in the middle of the two contact displacement sensors so that the probes of the contact displacement sensors on both sides extend along the x-axis and contact the calibration block; Rotate and adjust each contact displacement sensor around the y-axis to minimize its measured value; Rotate and adjust each contact displacement sensor around the z-axis so that its measured value reaches the minimum again, and make the probe axes of the two contact displacement sensors parallel to the reference plane of the calibration block; Place the calibration ball in the middle of the two contact displacement sensors, move the probes of each contact displacement sensor horizontally along the y-axis direction, and find the minimum value on the same horizontal plane; Move the probes of each contact displacement sensor along the z-axis direction to find the minimum value in different height directions, so that the probe axes of the two contact displacement sensors are coaxial.

[0041] After the adjustment is completed, fix the positions of the two contact displacement sensors.

[0042] S2. Based on the contact displacement sensor, collect measurement data of complex curved surface contour.

[0043] It should be noted that the complex surface only needs to make a simple linear movement between two contact displacement sensors. The contact displacement sensor's probe contacts different positions of the complex surface, and according to the change in contour amplitude, the probe expands and contracts and floats within the measurement range, so that the contour of the complex surface can be measured and the measurement data can be obtained.

[0044] S3, performing denoising and filtering on the measurement data to obtain processed measurement data. Specifically including: First, the mean filtering method is used to clean the measurement data to remove abnormal values ​​or noise. The denoising window size is set to δ , calculate each data point around δ The average value within is given by the following formula: , in, is the processed data. Use a low-pass filter to filter the measured data to remove high-frequency noise. The formula is as follows: , in, is the transfer function of the filter, is the frequency, is the cutoff frequency, is the order of the filter.

[0045] S4. Determine the number of segments of the overall contour and the initial node of each segment according to the distribution characteristics of the processed measurement data. Specifically, based on the processed measurement data, obtain segment nodes according to the local slope and local curvature changes, and perform segment processing on the complex surface contour according to the segment nodes.

[0046] More specifically, it includes: Calculate the local slope, that is, calculate the slope of each data point in the processed measurement data, and reflect the change trend of the curve through the slope. If the slope changes significantly, it means that the curve may have a mutation point or a transition point in this area; Set the slope change threshold , by traversing the slope sequence, the slope difference between the slopes of adjacent data points is obtained; If the slope difference is greater than the preset slope change threshold , it is considered that there is a significant trend change at this point, and the corresponding data point is used as a segmentation node. Then, set k i is the curvature at point i, setting the curvature change threshold ; Calculate the curvature of each data point in the processed measurement data ; If the curvature Greater than the preset curvature change threshold , indicating that there is a significant geometric shape change in the area, and the corresponding data points are also used as segmentation nodes; Wherein, the slope is calculated as follows: , The slope difference is calculated as follows: , The curvature is calculated as follows: , in, is the slope of the ith data point, and are the ordinate and abscissa of the point, respectively. and are the ordinate and abscissa of the next point respectively, and They are the ordinate and abscissa of the next data point respectively.

[0047] It should be noted that the starting point of each segment is the end point of the previous segment, and the end point is the next segment node or curve end point detected.

[0048] S5. Due to the diversity of complex curved surfaces, different areas of the probe have different degrees of wear when measuring, so data compensation is required. The specific steps are: based on the processed measurement data, an initial fitting curve and residuals are obtained, a polynomial fitting is performed on the residuals to obtain a polynomial form, based on the polynomial form, a design matrix is ​​constructed, based on the design matrix, polynomial coefficients are obtained, based on the polynomial coefficients, a compensation polynomial is obtained, and based on the compensation polynomial and the initial fitting curve, a modified fitting curve is obtained.

[0049] More specifically, it includes: The residual of each data point in the processed measurement data is calculated, that is, the difference between the actual value and the fitted value, wherein the residual is defined as: , in, is the actual data point, is the initial fitting curve at point The initial fitting curve is fitted by spline interpolation. Residual Perform polynomial fitting, for each data point , the polynomial form is: , n is a positive integer; For m data points, construct the design matrix: , Calculate polynomial coefficients , specifically: , in, ; Generate the compensation polynomial: , in, , ..., are polynomial coefficients, n is a positive integer; Correction of fitting curve is the initial fitting curve With the compensation polynomial The superposition of: .

[0050] S6. Perform segmented polynomial differential interpolation on the obtained correction curve F(x). Use a polynomial to fit each segment. Use the least squares method to solve the polynomial coefficients in each segment to ensure local fitting accuracy. Calculate the fitting error in each segment, start fitting from a low-order polynomial, and gradually increase the order until the error is no longer significantly reduced. The polynomial order selected at this time can avoid overfitting while ensuring fitting accuracy.

[0051] Specifically, a polynomial fitting is performed on each segment in the complex surface profile to obtain the fitting error term of each segment, including: In each segment, the least square method is used to solve the coefficients of the polynomial, the order of the polynomial is gradually increased, and the fitting error at each order is calculated; The mean square error (MSE) is used as the evaluation criterion, and the fitting starts from a low-order polynomial until the error decreases to no more than a preset threshold, where: , in, n is the number of data points, is the fitting error term. When the MSE decreases no longer significantly, we can stop increasing the polynomial order. The standard for no longer being significant is set manually as a parameter.

[0052] S7. Based on the segment nodes of each segment, construct a regularization term to achieve a smooth transition between segments.

[0053] A regularization term is added to the objective function to control the smoothness of the entire fitting curve. The regularization term can be based on the first-order or second-order derivative of the curve, and the smoothing effect is achieved by penalizing excessive derivative changes. Among them, the regularization term is based on the regularization of the first-order derivative to limit the slope change of the curve, ensuring that the fitting curve is not too steep or changes drastically. Its function is: , In the formula, and The kth and k+1th segments are at the boundary points The regularization term penalizes the sudden change of the derivative at the segment boundary, so that the fitting curve maintains a smooth transition between segments.

[0054] S8. Based on the corrected fitting curve, the fitting error term and the regularization term, an objective function of the complex surface profile fitting curve is constructed, and based on the objective function, a curve fitting result of the complex surface profile is obtained.

[0055] Specifically, the expression of the objective function is: , in, is the regularization term; and The kth and k+1th segments are at the boundary points The derivative at ; is the fitting error term; is the preset regularization strength, which is used to control the balance between the fitting error term and the regularization term; when When it is small, the fitting error term dominates and the curve is closer to the data point; When it is larger, the regularization term dominates and the curve is smoother. For the objective function, an iterative optimization method (such as gradient descent or quadratic optimization algorithm) can be used to solve it.

[0056] This objective function achieves a balance between fitting accuracy and curve smoothness. The fitting error term and the regularization term are combined to ensure that the fitting curve is close to the actual measured data and has a smooth transition on the segment boundaries.

[0057] This measurement method adjusts the sensor position and posture through calibration tooling, realizes coaxial installation measurement of two contact displacement sensors, and improves measurement accuracy; and based on different complex surface contours, uses adaptive segmented fitting, compensation and smooth transition methods for measurement data to achieve high-precision contour fitting effects.

[0058] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present application may adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program codes.

[0059] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0060] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0061] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0062] Finally, it should be noted that the above specific implementation methods are only used to illustrate the technical solution of the present invention rather than to limit it. Although the present invention has been described in detail with reference to examples, those skilled in the art should understand that the technical solution of the present invention can be modified or replaced by equivalents without departing from the spirit and scope of the technical solution of the present invention, which should be included in the scope of the claims of the present invention.

Claims

1. A complex surface profile measurement method, characterized in that: include: Based on the contact displacement sensor calibration fixture, coaxial calibration of two contact displacement sensors is performed; Based on the contact displacement sensor, collecting measurement data of complex curved surface contours; Performing denoising and filtering processing on the measurement data to obtain processed measurement data; Based on the processed measurement data, segmentation nodes are obtained according to changes in local slope and local curvature, and segmentation processing is performed on the complex surface contour according to the segmentation nodes; Based on the processed measurement data, an initial fitting curve and residuals are obtained, polynomial fitting is performed on the residuals to obtain a polynomial form, a design matrix is ​​constructed based on the polynomial form, polynomial coefficients are obtained based on the design matrix, a compensation polynomial is obtained based on the polynomial coefficients, and a modified fitting curve is obtained based on the compensation polynomial and the initial fitting curve; Perform polynomial fitting on each segment in the complex surface profile to obtain the fitting error term of each segment; Based on the segment nodes of each segment, a regularization term is constructed to make a smooth transition between segments; Based on the corrected fitting curve, the fitting error term and the regularization term, an objective function of the complex surface profile fitting curve is constructed, and based on the objective function, a curve fitting result of the complex surface profile is obtained; Wherein, the contact displacement sensor calibration tool comprises: Base (1); An adjustment seat (2) adjustably connected to the base (1) along a first direction; A main bracket (3) is pivoted on the adjustment seat (2) with the second direction as an axis; A secondary support (4) adjustably connected to the main support (3) along the second direction; A sensor mounting plate (5) is pivoted on the auxiliary bracket (4) with the first direction as an axis, the sensor mounting plate (5) being used to mount a contact displacement sensor, the probe of the contact displacement sensor being capable of being adjusted to extend along a third direction; The first direction, the second direction and the third direction are perpendicular to each other.

2. A complex curved surface profile measurement method according to claim 1, characterized in that: It also includes a first support shaft (11), a second support shaft (21), and a first adjustment spring (12); The first support shaft (11) is mounted on the base (1); the adjustment seat (2) is slidably connected to the base (1) along the first direction via the first support shaft (11); two first adjustment springs (12) are sleeved on the first support shaft (11), and two ends of each first adjustment spring (12) are respectively limited by the adjustment seat (2) and the base (1); A first locking member capable of abutting against the first supporting shaft (11) is connected to the adjustment seat (2) along the third direction to lock the relative position of the adjustment seat (2) and the base (1); The second support shaft (21) is mounted on the adjustment seat (2) along the second direction, and the main bracket (3) is rotatably connected to the adjustment seat (2) via the second support shaft (21); A first adjustment member connected to the second support shaft (21) is connected to the middle end surface of the adjustment seat (2) along the second direction to adjust the angle between the main support (3) and the adjustment seat (2).

3. A complex curved surface profile measurement method according to claim 1, characterized in that: It also includes a third support shaft (31) and a second adjustment spring (32); The third support shaft (31) is mounted on the main support (3), the auxiliary support (4) is slidably connected to the third support shaft (31) along the second direction, and the second adjustment spring (32) is sleeved on the third support shaft (31) and has two ends respectively limited by the auxiliary support (4) and the main support (3); The main support (3) is connected to a second adjusting member along the second direction and abuts against the auxiliary support (4) so ​​as to adjust the relative position between the auxiliary support (4) and the main support (3); The main bracket (3) is connected to a second locking piece along the first direction and abuts against the auxiliary bracket (4) so ​​as to lock the relative position between the auxiliary bracket (4) and the main bracket (3).

4. A complex surface profile measurement method according to claim 1, characterized in that: It also includes a fourth supporting shaft (41) and a rotation adjustment block (6); The fourth support shaft (41) is mounted on the auxiliary bracket (4) along the first direction, and the sensor mounting plate (5) is rotatably connected to the auxiliary bracket (4) via the fourth support shaft (41); The rotation adjustment block (6) is connected to the auxiliary bracket (4), and the rotation adjustment block (6) is connected to a third adjustment member capable of abutting against the sensor mounting plate (5) so as to adjust the angle between the sensor mounting plate (5) and the auxiliary bracket (4).

5. The complex surface profile measurement method according to claim 1, characterized in that: Perform a coaxial calibration of two contact displacement sensors, including: Place the calibration block in the middle of the two contact displacement sensors so that the probes of the contact displacement sensors on both sides extend along the x-axis and contact the calibration block; Rotate and adjust each contact displacement sensor around the y-axis to minimize its measured value; Rotate and adjust each contact displacement sensor around the z-axis so that its measured value reaches the minimum again, and make the probe axes of the two contact displacement sensors parallel to the reference plane of the calibration block; Place the calibration ball in the middle of the two contact displacement sensors, move the probes of each contact displacement sensor horizontally along the y-axis direction, and find the minimum value on the same horizontal plane; Move the probes of each contact displacement sensor along the z-axis direction to find the minimum value in different height directions, so that the probe axes of the two contact displacement sensors are coaxial; After the adjustment is completed, fix the positions of the two contact displacement sensors.

6. A complex surface profile measurement method according to claim 1, characterized in that: Based on the processed measurement data, segmentation nodes are obtained according to the local slope and local curvature changes, and segmentation processing is performed on the complex surface contour according to the segmentation nodes, including: Calculating the slope of each data point in the processed measurement data, and obtaining the slope difference between the slopes of adjacent data points; If the slope difference is greater than a preset slope change threshold, the corresponding data point is used as a segmentation node; calculating the curvature of each data point in the processed measurement data; If the curvature is greater than a preset curvature change threshold, the corresponding data point is also used as a segmentation node; Wherein, the slope is calculated as follows: ； The slope difference is calculated as follows: ； The curvature is calculated as follows: ； in, is the slope of the ith data point, and are the ordinate and abscissa of the point, respectively. and are the ordinate and abscissa of the next point respectively; and They are the ordinate and abscissa of the next data point respectively.

7. A complex curved surface profile measurement method according to claim 6, characterized in that: Based on the processed measurement data, an initial fitting curve and a residual are obtained, a polynomial fitting is performed on the residual to obtain a polynomial form, a design matrix is ​​constructed based on the polynomial form, polynomial coefficients are obtained based on the design matrix, a compensation polynomial is obtained based on the polynomial coefficients, and a modified fitting curve is obtained based on the compensation polynomial and the initial fitting curve, including: The residual of each data point in the processed measurement data is calculated, that is, the difference between the actual value and the fitted value, wherein the residual is defined as: ； in, is the actual data point, is the initial fitting curve at point The initial fitting curve is fitted by spline interpolation. Residual Perform polynomial fitting, for each data point , the polynomial form is: , n is a positive integer; For m data points, construct the design matrix X, specifically: ； Calculate polynomial coefficients , specifically: ； in, ; T is the transpose of the matrix; Generate the compensation polynomial: ； in, , ..., are polynomial coefficients, n is a positive integer; Correction of fitting curve is the initial fitting curve With the compensation polynomial The superposition of: 。 8. A complex curved surface profile measurement method according to claim 7, characterized in that: Perform polynomial fitting on each segment in the complex surface profile to obtain the fitting error term of each segment, including: In each segment, the least squares method is used to solve the coefficients of the polynomial, gradually increasing the order of the polynomial and calculating the fitting error at each order. ; The mean square error (MSE) is used as the evaluation criterion, and the fitting starts from a low-order polynomial until the error decreases to no more than a preset threshold, where: ； in, n is the number of data points, is the fitting error term.

9. A complex surface profile measurement method according to claim 8, characterized in that: The expression of the objective function is: ； in, is the regularization term; and The kth and k+1th segments are at the boundary points The derivative at ; k is a positive integer; is the fitting error term; is the preset regularization strength, which is used to control the balance between the fitting error term and the regularization term; when When it is small, the fitting error term dominates and the curve is closer to the data point; When it is larger, the regularization term dominates and the curve is smoother.

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