Steel pipe diameter and out-of-roundness measuring method based on ellipse fitting

Abstract

The invention discloses a steel pipe diameter and out-of-roundness measuring method based on ellipse fitting. The method comprises the following steps: acquiring section contour data of a steel pipe; utilizing an improved ellipse fitting algorithm to obtain an optimal ellipse model and a corresponding local point; reconstructing steel pipe section contour measurement data through a linear interpolation algorithm; and the maximum diameter and the minimum diameter of the steel pipe are calculated by using the reconstructed steel pipe section contour measurement data, so that the out-of-roundness of the steel pipe is determined. On the basis of geometric distribution of data points and high efficiency of an improved ellipse fitting algorithm, steel pipe section contour measurement data can be accurately reconstructed; according to the improved ellipse fitting algorithm, the confocal hyperbolic distance is used for replacing the algebraic distance, the actual geometric distance from the steel pipe section contour data points to the fitting ellipse can be accurately reflected, the fitting ellipse better conforms to the actual section contour of the steel pipe, effective data points are obtained, and the fitting precision is improved. Noise points and outliers generated by a measuring instrument and the environment are eliminated, and the measuring precision is improved.

Description

Technical Field

[0001] The invention belongs to the technical field of machine vision, and in particular relates to a method for measuring the diameter and out-of-roundness of a steel pipe based on ellipse fitting. Background Art

[0002] As the raw material for building oil and gas pipelines, the quality and performance of steel pipes directly affect the safe long-distance transportation of oil and gas resources. With the gradual increase in the strength, diameter, wall thickness and transportation pressure of newly built pipelines, higher requirements are also placed on the quality of steel pipes.

[0003] Diameter and out-of-roundness are the most important geometric dimensions of steel pipes, and are of great significance in ensuring the progress and quality of pipeline construction. If the diameter and out-of-roundness do not meet the requirements, it will be very difficult to weld two steel pipes together. Even if they are barely welded together, a large residual stress will be generated, resulting in a decrease in the mechanical properties of the weld between the two steel pipes, reducing the safety of the pipeline. In the process of oil and gas transportation, the pipeline needs to withstand an internal pressure of dozens or even hundreds of atmospheres. If the mechanical properties of the weld are not good, leakage and explosion accidents are very likely to occur, causing environmental pollution and causing serious economic losses. In order to prevent the above problems, the quality requirements for steel pipes produced by enterprises are extremely strict. In order to be able to screen out qualified pipelines, the diameter and out-of-roundness of the steel pipes must be accurately and strictly tested.

[0004] At present, the circle fitting method is mainly used to measure the diameter and out-of-roundness of steel pipes. Due to the complex on-site environment, it is inevitable that the collected data is interfered by noise. In addition, the steel pipe produced is not an ideal cylinder, and its cross-sectional profile is not an ideal circle. It is difficult to obtain high measurement accuracy using the circle fitting method. How to improve the measurement accuracy of steel pipe diameter and out-of-roundness has become an important issue in the industry. Summary of the invention

[0005] The object of the present invention is to provide a steel pipe diameter and out-of-roundness measurement method based on ellipse fitting, so as to solve the problem of low measurement accuracy of the existing steel pipe diameter and out-of-roundness measurement method based on circle fitting.

[0006] The technical solution adopted by the present invention is: a method for measuring the diameter and out-of-roundness of a steel pipe based on ellipse fitting, and the specific operation steps are as follows: Step 1: Obtain the steel pipe cross-section profile data; Step 2: Use the improved ellipse fitting algorithm to obtain the best ellipse model that best fits the actual cross-sectional profile of the steel pipe and its corresponding in-place points; Step 3: Reconstruct the steel pipe cross-section profile measurement data through a linear interpolation algorithm based on the optimal ellipse model and its corresponding internal points; Step 4: Calculate the maximum and minimum diameters of the steel pipe using the reconstructed steel pipe cross-sectional profile measurement data to determine the out-of-roundness of the steel pipe.

[0007] The present invention is also characterized in that: Step 2 The specific steps are as follows: Step 2.1: Establish an initial steel pipe cross-section profile ellipse model, and assign initial values ​​to the model parameters and algorithm necessary parameters; Step 2.2: Extract n points with medium probability from the steel pipe cross-section profile data. ; Use the least squares method to fit the n extracted point data to obtain 5 geometric parameters , , , , ; ) is the center coordinate, is the semi-major axis of the ellipse, is the semi-minor axis of the ellipse, is the rotation angle, Step 2.3: Determine the number of points in the game :According to the ellipse geometric features obtained in step 2.2, calculate the confocal hyperbolic distance Dh(j) from each data point to the ellipse, where j is the index number of the data point. If Dh(j) is greater than the set distance threshold t, the jth data point is removed and the number of remaining contour points is counted. , these points are called internal points, and the internal points are stored in the set inside; Step 2.3 The method for calculating the confocal hyperbolic distance Dh(j) is: The geometric parameters of the ellipse obtained in step 2.2 , , , , To calculate the confocal hyperbola distance, the specific calculation steps are as follows: Step 2.3.1: Rewrite the ellipse equation by translation and rotation as: , Then passing through any point ( X , Y ) is expressed as: , in, is the semi-major axis of the ellipse, is the semi-minor axis of the ellipse, is the semi-major axis of the hyperbola, is the semi-minor axis of the hyperbola,

[0008] in,( , ) is the coordinate of the data point, ( , ) are the coordinates of the center of the ellipse; Step 2.3.2: Since the ellipse and the hyperbola are confocal, the distance from one focus to the center is , there are the following relations: ; Step 2.3.3: Calculate the orthogonal intersection points of the confocal hyperbola and the ellipse : By using the absolute value function to convert the point coordinates Restricting to the first quadrant shows the correct solution when ,Right now When , orthogonal contact points exist, so no numerical singularity of the circle is imposed, then: If the fitting result of step 2.2 is an ellipse, that is, when hour,

[0009] If the fitting result in step 2.2 is a circle, that is, when hour:

[0010] Step 2.3.4: When , or when and When , the distance function is simplified to the true geometric distance by the following formula: when hour:

[0011] when and hour:

[0012] The confocal hyperbolic distance is then defined in closed form as follows:

[0013] in: is the absolute value function, is the two-dimensional vector of the distance on the XY coordinate plane of translation and rotation, is the L2 norm, i.e. the Euclidean norm.

[0014] Step 2.4: Update the initial ellipse model parameters, the local point set and the number of local points according to the calculation results of steps 2.2-2.3; by comparing the number of local points determined in step 2.3 The number of points inside the initial ellipse model The size of the ellipse model is used to determine the quality of the ellipse model. Greater than , then update the model parameters , , , , , update the model internal point set , the number of points in the game ; Get the best ellipse model under the current number of iterations.

[0015] Step 2.5: Determine the current number of iterations i and the maximum number of iterations N. If i is less than N, perform a new round of calculations and repeat steps 2.2 to 2.4 until the iteration termination condition i>N is met, and the optimal ellipse model parameters that best match the actual cross-sectional profile of the steel pipe are obtained. The optimal ellipse model internal point set ', The points in ' are the effective data after denoising the steel pipe cross-section profile data.

[0016] The initial steel pipe cross-section profile ellipse model parameters and algorithm necessary parameters described in step 2.1 include: number of iterations N, N ≥ 50, , , , , ,in:( ) is the center coordinate, is the semi-major axis, is the semi-minor axis, ' is the rotation angle, and the point set inside the initial ellipse model is , the number of points in the initial ellipse model , the distance threshold is t.

[0017] Step 3 is as follows: Step 3.1: Translation: Subtract the center coordinates of the optimal ellipse from the valid data obtained in step 2 ( ), valid data centered at the origin; Step 3.2: Coordinate transformation: convert the valid data obtained in step 3.1 into polar coordinates; Step 3.3: Linear interpolation and measurement data reconstruction: Take uniformly distributed p Points, calculation p Angle of measuring point °, h is the index number of the measuring point, and then in the valid data obtained in step 3.2, find the angle with the measuring point in the geometric position The two closest data points are located at the measurement point angles. The left and right sides of these two data points are used as the reference angle Linear interpolation is performed to obtain The polar diameter of the angle is finally obtained, and the standardized reconstructed steel pipe cross-section profile measurement data is obtained.

[0018] The specific process of step 4 is: Step 4.1: Coordinate transformation: convert the standardized measurement data points reconstructed in step 3 into rectangular coordinates; Step 4.2: Calculate the diameter: The diameter is obtained by calculating the Euclidean distance between two data points with an angle difference of 180°, that is, the angle is The point and angle are The geometric distance between points of , a total of The value of the bar diameter; Step 4.3: Count the maximum diameter value obtained in step 4.2 and minimum diameter , calculate the out-of-roundness using the maximum and minimum diameter values .

[0019] Step 4.3 The specific method for calculating the out-of-roundness is: .

[0020] The beneficial effects of the present invention are: 1. The steel pipe diameter and out-of-roundness measurement method based on ellipse fitting of the present invention only requires a set of steel pipe cross-sectional profile data. A set of steel pipe cross-sectional profile data provides detailed point information of the steel pipe on a certain plane, including the contour shape, size and deviation of the steel pipe, and can accurately reflect the geometric characteristics of the steel pipe cross section. And through the ellipse fitting method, the main dimensions (such as diameter) and shape characteristics (such as out-of-roundness) of the steel pipe cross section can be accurately extracted. This method is based on the geometric distribution of data points and the high efficiency of the fitting algorithm, and can accurately reconstruct the steel pipe cross-sectional profile measurement data; it can solve the problem of low accuracy of the steel pipe diameter and out-of-roundness measurement method based on circle fitting.

[0021] 2. The original random sampling consistency algorithm uses the algebraic distance from the point to the ellipse when judging the internal point. However, the algebraic distance cannot truly reflect the shortest distance from the point to the ellipse and is easily affected by the curvature change of the ellipse and the normal direction, resulting in the inability to accurately obtain the fitted ellipse. The present invention uses the steps of the random sampling consistency algorithm, performs ellipse fitting by the least squares method, and uses the confocal hyperbola distance instead of the algebraic distance, which can accurately reflect the actual geometric distance from the steel pipe cross-sectional profile data point to the fitted ellipse, so that the fitted ellipse is more consistent with the actual cross-sectional profile of the steel pipe, obtains valid data points, and eliminates noise points and outliers generated by the measuring instrument and the environment. BRIEF DESCRIPTION OF THE DRAWINGS

[0022] Figure 1 It is a flow chart of the steel pipe diameter and out-of-roundness measurement method based on ellipse fitting of the present invention; Figure 2 It is a flow chart of the ellipse fitting algorithm proposed by the present invention. DETAILED DESCRIPTION

[0023] The present invention is described in detail below with reference to the accompanying drawings and specific embodiments.

[0024] Example 1 The present invention uses a steel pipe cross-section profile information acquisition device to obtain two-dimensional profile data of the steel pipe cross-section; uses an ellipse fitting algorithm and a random sampling consistency algorithm to iteratively fit the steel pipe cross-section profile data to obtain the best ellipse model and its corresponding in-line points that best fit the actual cross-section profile of the steel pipe; translates these in-line points so that their centers coincide with the origin of the coordinate system, then converts the rectangular coordinate system into a polar coordinate system, and reconstructs the steel pipe cross-section profile measurement data by means of a linear interpolation algorithm; uses the Euclidean distance between two points to calculate the cross-section diameter of the steel pipe after the data is reconstructed, and uses the maximum diameter and the minimum diameter to calculate the out-of-roundness.

[0025] Example 2 The steel pipe diameter and out-of-roundness measurement method based on ellipse fitting of the present invention is as follows: Figure 1 As shown, the specific implementation steps are as follows: Step 1: Obtain the profile data of the steel pipe cross section, and the obtained profile data is two-dimensional data; Step 2: If Figure 2 As shown, the improved ellipse fitting algorithm is used to obtain the best ellipse model that best fits the actual cross-sectional profile of the steel pipe and its corresponding in-place points; Step 2.1: Parameter initialization: Establish an initial steel pipe cross-section profile ellipse model, and assign initial values ​​to the model parameters and algorithm necessary parameters; The initial steel pipe cross-section profile ellipse model parameters and algorithm necessary parameters include: number of iterations N (generally N ≥ 50), optimal ellipse model parameters , , , , ,in:( ) is the center coordinate, is the semi-major axis, is the semi-minor axis, ' is the rotation angle, the best model internal point set , the number of points in the best model , distance threshold t (t is the distance from the data point to the ellipse, set according to actual conditions); , , , , The initial values ​​are all 0.

[0026] The distance threshold t is used to determine how many data points are valid data that conform to the fitted ellipse, by calculating the confocal hyperbola distance from the data point to the edge of the fitted ellipse. To judge, if If it is greater than t, it is considered that the point is affected by noise or is an outlier. Through continuous iteration, the elliptical model with the most points is retained, which is the model that best fits the contour of the steel pipe. The retained data points are the in-band points, that is, the valid data after denoising.

[0027] Step 2.2: Extract n from the steel pipe cross-section profile data with medium probability ( ) points, and use the least square method to fit the n extracted points to obtain the ellipse's five geometric parameters. , , , , ; Step 2.3: Determine the number of points in the game :According to the ellipse geometric features obtained in step 2.2, calculate the confocal hyperbolic distance Dh(j) from each data point to the ellipse, where j is the index number of the data point. If Dh(j) is greater than the set distance threshold t, the jth data point is removed and the number of remaining contour points is counted. , these points are called internal points, and the internal points are stored in the set inside; Step 2.4: Update the optimal ellipse parameters, the optimal model internal point set and the optimal number of model internal points: by comparing the number of internal points determined in step 2.3 The number of points in the game with the best model The size of the ellipse model is used to determine whether the ellipse model is good or bad. Greater than , then update the optimal ellipse model parameters , , , , , update the best model internal point set , update the number of points in the best model ; Step 2.5: Determine the current number of iterations i and the maximum number of iterations N. If i is less than N, perform a new round of calculations and repeat steps 2.2 to 2.4 until the iteration termination condition (i>N) is met to obtain the optimal elliptical model parameters that best fit the actual cross-sectional profile of the steel pipe. , , , , , the best ellipse model internal point set ', the point set within the optimal ellipse model is the effective data after denoising.

[0028] Step 3: Reconstruct the steel pipe cross-section profile measurement data through a linear interpolation algorithm based on the optimal ellipse model and its corresponding internal points; Step 4: Calculate the maximum and minimum diameters of the steel pipe using the reconstructed steel pipe cross-sectional profile measurement data to determine the out-of-roundness of the steel pipe.

[0029] Example 3 Based on Example 2, step 2.3 is as follows: The ellipse parameters obtained by step 2.2 , , , , To calculate the confocal hyperbola distance, the specific calculation steps are as follows: Step 2.3.1: To simplify the calculation formula, the general form of the ellipse equation can be rewritten as follows through translation and rotation: ( is the semi-major axis of the ellipse, is the semi-minor axis of the ellipse), then the equation of the hyperbola passing through the point (X, Y) is expressed as: ( is the semi-major axis of the hyperbola, is the semi-minor axis of the hyperbola). Where: , ( , ) is the coordinate of the data point, ( , ) are the coordinates of the center of the ellipse.

[0030] Step 2.3.2: Since the ellipse and the hyperbola are confocal, that is, their focal positions are the same, then their focal lengths must also be the same, and the following relationship holds: .

[0031] Step 2.3.3: Calculate the orthogonal intersection points of the confocal hyperbola and the ellipse By simply using the absolute value function Restricting to the first quadrant shows the correct solution. (Right now ), orthogonal contact points exist, so no numerical singularity of the circle is imposed. Then: If the model obtained in step 2.2 is an ellipse, that is, hour,

[0032] If the model obtained in step 2.2 is a circle, then hour:

[0033] Step 2.3.4: When (point on the minor axis), or when and Even though there is no confocal hyperbola technically (a point on the major axis is out of focus), the equation for the intersection point is still determined, and the distance function simplifies to the true geometric distance via the following formula: when hour:

[0034] when and hour:

[0035] The confocal hyperbolic distance can then be defined in closed form as follows:

[0036] in: is the absolute value function, is the two-dimensional vector of the distance on the XY coordinate plane of translation and rotation, is the L2 norm.

[0037] Example 4 Based on Example 3, Step 3.1: Translation: Subtract the center coordinates of the optimal ellipse from the valid data obtained in step 2 ( ), valid data centered at the origin; Step 3.2: Coordinate transformation: convert the valid data obtained in step 3.1 into polar coordinates; Step 3.3: Linear interpolation and measurement data reconstruction: Take uniformly distributedp Points, calculation p Angle of measuring point °, h is the index number of the measuring point, and then in the valid data obtained in step 3.2, find the angle with the measuring point in the geometric position The two closest data points are located at the measurement point angles. The left and right sides of these two data points are used as the reference angle Linear interpolation is performed to obtain The polar diameter of the angle is finally obtained, and the standardized reconstructed steel pipe cross-section profile measurement data is obtained.

[0038] Step 4: Using the reconstructed steel pipe cross-sectional profile measurement data, calculate the maximum diameter and minimum diameter of the steel pipe, thereby determining the out-of-roundness of the steel pipe, as follows: Step 4.1: Coordinate transformation: convert the standardized measurement data points reconstructed in step 3 into rectangular coordinates; Step 4.2: Calculate the diameter: The diameter is obtained by calculating the Euclidean distance between two data points with an angle difference of 180°, that is, the angle is The point and angle are The geometric distance between points of , a total of The value of the bar diameter; Step 4.3: Count the maximum diameter value obtained in step 4.2 and minimum diameter , calculate the out-of-roundness using the maximum and minimum diameters , the specific method for calculating the out-of-roundness is: .

[0039] Example 5 The present invention discloses a method for measuring the diameter and out-of-roundness of a steel pipe based on ellipse fitting. First, the cross-sectional profile data of the steel pipe is obtained. Then, an improved ellipse fitting algorithm is used to obtain the best ellipse model and its corresponding in-line points that conform to the actual cross-sectional profile of the steel pipe. Then, a linear interpolation algorithm is used to reconstruct the cross-sectional profile measurement data of the steel pipe. Finally, the maximum diameter and the minimum diameter of the steel pipe are calculated through the reconstructed cross-sectional profile measurement data of the steel pipe, thereby determining the out-of-roundness of the steel pipe.

[0040] Example 6 Get the profile data of the steel pipe section, taking the center coordinate as , the semi-major axis is 1000, the minor axis is 900, and the rotation angle is 45°. A total of 500 data sets with random noise and discrete points were generated. .

[0041] First, the improved ellipse fitting algorithm of the present invention is used to obtain the data set that meets the requirements. Best ellipse model for: Setting the number of iterations , distance threshold After iterations of steps 2.2 to 2.5, the optimal ellipse model is obtained. , 0. , , , the number of interior points whose distance to the confocal hyperbola of the ellipse is less than 2 , these points are valid data points and are stored in the array middle.

[0042] The dataset of valid points obtained in step 2 , first let each pair Subtract the center coordinates of the optimal ellipse model , get the valid point data centered at the origin ; Then the coordinates of the data points in the rectangular coordinate system Convert to polar coordinates

[0043] Determine the actual number of measurement points , the angles of each actual measurement point are calculated to be , and then use linear interpolation to calculate the ellipse at each Polar diameter on angle ; Assuming that the angle The two polar coordinate points on the left and right that are closest to it are and , then the angle The corresponding polar diameter ; In this way, the polar coordinates of 360 actual measurement points can be obtained ( , ).

[0044] The polar coordinates of the actual measurement point obtained in step 3 ( , ), first convert it into rectangular coordinates ( , ); the diameters of different angles are obtained through the Euclidean distance between two points, and 180 diameters can be obtained, with the maximum value being 1000.39 and the minimum value being 900.50; the out-of-roundness of the data is 99.89.

[0045] The above are only partial implementation schemes of the present invention. For those skilled in the art, several improvements and modifications made to the present invention without departing from the principle of the present invention should also be regarded as the protection scope of the present invention.

Claims

1. A method for measuring the diameter and out-of-roundness of a steel pipe based on ellipse fitting, characterized in that: The specific steps are as follows: Step 1: Obtain the steel pipe cross-section profile data; Step 2: Use the improved ellipse fitting algorithm to obtain the best ellipse model that best fits the actual cross-sectional profile of the steel pipe and its corresponding in-place points; Step 3: Reconstruct the steel pipe cross-section profile measurement data through a linear interpolation algorithm based on the optimal ellipse model and its corresponding internal points; Step 4: Calculate the maximum and minimum diameters of the steel pipe using the reconstructed steel pipe cross-sectional profile measurement data to determine the out-of-roundness of the steel pipe.

2. The method for measuring the diameter and out-of-roundness of a steel pipe based on ellipse fitting according to claim 1, characterized in that: Step 2 The specific steps are as follows: Step 2.1: Establish an initial steel pipe cross-section profile ellipse model, and assign initial values ​​to the model parameters and algorithm necessary parameters; Step 2.2: Extract n points with medium probability from the steel pipe cross-section profile data. ; Use the least squares method to fit the n extracted point data to obtain 5 geometric parameters , , , , ; ) is the center coordinate, is the semi-major axis of the ellipse, is the semi-minor axis of the ellipse, is the rotation angle; Step 2.3: Determine the number of points in the game :According to the ellipse geometric features obtained in step 2.2, calculate the confocal hyperbolic distance Dh(j) from each data point to the ellipse, where j is the index number of the data point. If Dh(j) is greater than the set distance threshold t, the jth data point is removed and the number of remaining contour points is counted. , these points are called internal points, and the internal points are stored in the set inside; Step 2.4: Update the initial steel pipe cross-section profile ellipse model parameters, the local point set and the number of local points according to the calculation results of steps 2.2-2.3; Step 2.5: Determine the current number of iterations i and the maximum number of iterations N. If i is less than N, perform a new round of calculations and repeat steps 2.2 to 2.4 until the iteration termination condition i>N is met, and the optimal ellipse model parameters that best match the actual cross-sectional profile of the steel pipe are obtained. The optimal ellipse model internal point set ', The points in ' are the effective data after denoising the steel pipe cross-section profile data.

3. The method for measuring the diameter and out-of-roundness of a steel pipe based on ellipse fitting according to claim 2, characterized in that: The initial steel pipe cross-section profile ellipse model parameters and algorithm necessary parameters described in step 2.1 include: number of iterations N, N ≥ 50, , , , , ,in:( ) is the center coordinate, is the semi-major axis, is the semi-minor axis, ' is the rotation angle, and the point set inside the initial ellipse model is , the number of points in the initial ellipse model , the distance threshold is t.

4. The method for measuring the diameter and out-of-roundness of a steel pipe based on ellipse fitting according to claim 3, characterized in that: Step 2.3 The method for calculating the confocal hyperbolic distance Dh(j) is: The geometric parameters of the ellipse obtained in step 2.2 , , , , To calculate the confocal hyperbola distance, the specific calculation steps are as follows: Step 2.3.1: Rewrite the ellipse equation by translation and rotation as: , Then passing through any point ( X , Y ) is expressed as: , in, is the semi-major axis of the ellipse, is the semi-minor axis of the ellipse, is the semi-major axis of the hyperbola, is the semi-minor axis of the hyperbola, in,( , ) is the coordinate of the data point, ( , ) are the coordinates of the center of the ellipse; Step 2.3.2: Since the ellipse and the hyperbola are confocal, the distance from one focus to the center is , there are the following relations: ; Step 2.3.3: Calculate the orthogonal intersection points of the confocal hyperbola and the ellipse : By using the absolute value function to convert the point coordinates Restricting to the first quadrant shows the correct solution when ,Right now When , the orthogonal contact point exists, then: If the fitting result of step 2.2 is an ellipse, that is, when hour, If the fitting result in step 2.2 is a circle, that is, when hour: Step 2.3.4: When , or when and When , the distance function is simplified to the true geometric distance by the following formula: when hour: when and hour: The confocal hyperbolic distance is then defined in closed form as follows: in: is the absolute value function, is the two-dimensional vector of the distance on the XY coordinate plane of translation and rotation, is the L2 norm, i.e. the Euclidean norm.

5. The method for measuring the diameter and out-of-roundness of a steel pipe based on ellipse fitting according to claim 3, characterized in that: Step 2.4 is as follows: By comparing the number of points in the game determined in step 2.3 The number of points inside the initial ellipse model The size of the ellipse model is used to determine the quality of the ellipse model. Greater than , then update the model parameters , , , , , update the model internal point set , the number of points in the game ; Get the best ellipse model under the current number of iterations.

6. The method for measuring the diameter and out-of-roundness of a steel pipe based on ellipse fitting according to claim 1, characterized in that: Step 3 is as follows: Step 3.1: Translation: Subtract the center coordinates of the optimal ellipse from the valid data obtained in step 2 ( ), valid data centered at the origin; Step 3.2: Coordinate transformation: convert the valid data obtained in step 3.1 into polar coordinates; Step 3.3: Linear interpolation and measurement data reconstruction: Take uniformly distributed p Points, calculation p Angle of measuring point °, h is the index number of the measuring point, and then in the valid data obtained in step 3.2, find the angle with the measuring point in the geometric position The two closest data points are located at the measurement point angles. The left and right sides of these two data points are used as the reference angle Linear interpolation is performed to obtain The polar diameter of the angle is finally obtained, and the standardized reconstructed steel pipe cross-section profile measurement data is obtained.

7. The method for measuring the diameter and out-of-roundness of a steel pipe based on ellipse fitting according to claim 2, characterized in that: The specific process of step 4 is: Step 4.1: Coordinate transformation: convert the standardized measurement data points reconstructed in step 3 into rectangular coordinates; Step 4.2: Calculate the diameter: The diameter is obtained by calculating the Euclidean distance between two data points with an angle difference of 180°, that is, the angle is The point and angle are The geometric distance between points of , a total of The value of the bar diameter; Step 4.3: Count the maximum diameter value obtained in step 4.2 and minimum diameter , calculate the out-of-roundness using the maximum and minimum diameter values .

8. The method for measuring the diameter and out-of-roundness of a steel pipe based on ellipse fitting according to claim 2, characterized in that: Step 4.3 The specific method for calculating the out-of-roundness is: .

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