A cylindrical pipeline deflection measurement method based on a total station

Abstract

This invention discloses a method for measuring the deflection of a cylindrical pipe based on a total station, belonging to the field of pipe deflection measurement technology. The method involves measuring two end sections A and B and a middle section C of a cylindrical pipe, including the following steps: S1. Fitting the initial center and initial radius of each section: Using a total station, three-dimensional coordinate data of four measuring points at each section are collected, and the plane containing the optimal circle is fitted to each section. This method for measuring the deflection of a cylindrical pipe based on a total station constructs a global error function by treating the entire cylinder as a whole, abandoning the traditional method of independently fitting individual sections. This effectively eliminates fitting deviations caused by uneven distribution of measuring points and errors in measuring point acquisition, improving the accuracy of center and radius fitting, and laying a precise data foundation for deflection calculation.

Description

Technical Field

[0001] This invention relates to the field of pipeline deflection measurement technology, specifically a method for measuring the deflection of a cylindrical pipeline based on a total station. Background Technology

[0002] Pipelines are core structures in industrial production, energy transmission, and water conservancy projects. Most industrial cylindrical pipes are installed on pipe supports, and the contact between the pipe and the support can be considered as a hinge. Under the action of the pipe's own load and the weight of the medium inside the pipe, bending moments will be generated in the suspended section of the pipe, with the largest bending moment at the mid-span, which is prone to downward deflection. If the pipe deflection is too large, it will lead to problems such as leakage at pipe joints, stress imbalance of supports, and fatigue damage to the overall pipe structure, seriously affecting the normal use of the pipeline and the safety of industrial production. Therefore, accurate measurement of the deflection of cylindrical pipes is a key aspect of pipeline inspection and maintenance.

[0003] Currently, the deflection measurement of cylindrical pipes mostly uses a total station to collect the coordinates of the measuring points, and then calculates the deflection by simply fitting the center of the cross-section. This method has obvious drawbacks:

[0004] First, it only performs independent fitting on the measuring points of a single cross section, without optimizing the entire cylinder as a whole. This can easily lead to fitting deviations in the center and radius due to uneven distribution of measuring points.

[0005] Secondly, the parallel constraint conditions of each section of the pipe are not considered. In fact, the end and middle sections of the cylindrical pipe are parallel circular sections. The traditional method ignores this geometric feature, which further reduces the accuracy of deflection calculation.

[0006] Third, directly using the average value of the measuring points as the initial center of the circle cannot eliminate the influence of the measurement point acquisition error, resulting in low reliability of the measurement results.

[0007] Therefore, we propose a method for measuring the deflection of cylindrical pipes based on a total station. Summary of the Invention

[0008] The purpose of this invention is to provide a method for measuring the deflection of cylindrical pipes based on a total station, so as to solve the problems mentioned in the background art.

[0009] To achieve the above objectives, the present invention provides the following technical solution: a method for measuring the deflection of a cylindrical pipe based on a total station, which involves measuring the deflection of the cylindrical pipe at two end sections A and B and a middle section C, and includes the following steps:

[0010] S1. Fitting the initial center and initial radius of each section: The three-dimensional coordinate data of four measuring points of each section are collected using a total station. The plane containing the best circle is fitted for each section. Then, each measuring point is projected onto the fitted plane and converted into two-dimensional coordinates. The initial center a0, b0, c0 and the initial radius ra0, rb0, rc0 of each section in the global three-dimensional coordinate system are obtained by the least squares fitting method.

[0011] S2. Optimize the initial center and initial radius: Construct a global error function for the entire cylinder as a whole, and add parallel constraints on the imaginary planes where each measuring point is located. Perform global optimization on the imaginary planes, initial centers and initial radii of each section to obtain optimized centers a, b, c and a unified radius r that satisfy the minimum global error function and the mutual parallelism of the imaginary planes.

[0012] S3. Calculate the deflection of the cylindrical pipe: Determine the vertical plane of the line ab connecting the centers of the end sections. Project the optimized center c of the middle section onto this vertical plane to obtain the projection point. Calculate the distance from this projection point to the line ab, which is the deflection value of the cylindrical pipe.

[0013] Furthermore, the specific process of fitting the plane containing the optimal circle in step S1 is as follows:

[0014] Calculate the geometric center of the four measuring points of the j-th section, and translate the coordinates of the measuring points to the geometric center to complete the decentralization process;

[0015] The covariance matrix is ​​calculated using a decentralized measurement point matrix. Singular value decomposition is performed on the covariance matrix, and the eigenvector corresponding to the smallest eigenvalue is taken as the normal vector of the plane containing the best circle of the cross section, thus completing the plane fitting.

[0016] Furthermore, in step S1, when fitting the initial center and initial radius using the least squares fitting method, the constraint condition of minimizing the sum of the distances from each measuring point to the fitted circle is met.

[0017] Furthermore, the global error function constructed in step S2 uses the optimized circle centers a, b, c and uniform radius r of each cross section as variables to be optimized, with the objective of minimizing the sum of errors from all measuring points to the fitted circle of the corresponding cross section.

[0018] Furthermore, the parallel constraint condition in step S2 is as follows: taking the normal vector of section A as the reference, the decentered coordinates of the measuring points on each section all satisfy the orthogonal constraint with the normal vector, ensuring that the normal vectors of the three sections are consistent.

[0019] Furthermore, the specific process of determining the vertical plane of the line ab connecting the centers of the end sections in step S3 is as follows: calculate the direction vector of the line ab, perform a cross product of the direction vector and the spatial vertical vector to obtain the normal vector of the vertical plane, and then determine the plane equation of the vertical plane through the point normal equation.

[0020] Furthermore, in step S3, the process of projecting the center c of the optimized middle section onto the vertical plane is as follows: calculate the distance d from the center c to the vertical plane, construct a vector parallel to the normal vector of the vertical plane with a length of d, and combine the coordinates of the center c to obtain the three-dimensional coordinates of the projection point.

[0021] Compared with the prior art, the beneficial effects of the present invention are:

[0022] This method for measuring the deflection of cylindrical pipes based on a total station constructs a global error function by treating the entire cylinder as a whole. It abandons the traditional method of independently fitting a single section, effectively eliminating the fitting deviation caused by uneven distribution of measuring points and measurement point acquisition errors, improving the accuracy of fitting the center and radius, and laying a precise data foundation for deflection calculation.

[0023] Parallel constraints were added to each section, which conforms to the geometric characteristics of the parallel cross-sections at the ends and middle of the cylindrical pipe, avoiding deflection calculation errors caused by cross-sectional plane fitting deviations, and further improving measurement accuracy.

[0024] The initial center and radius are fitted using the best-fit circle method, which replaces the traditional method of directly taking the average value of the measurement points. This can effectively reduce the influence of random errors at the measurement points and ensure the reliability of the initial fitting results.

[0025] The measurement method is based on a total station, the measurement point acquisition operation is simple, the data processing flow is standardized, no additional special testing equipment is required, and it is suitable for the deflection detection of cylindrical pipes in various industrial sites, with good practicality and promotion potential. Attached Figure Description

[0026] Figure 1 This is a schematic diagram showing the actual location of the measuring points;

[0027] Figure 2 A schematic diagram of the best-fit plane;

[0028] Figure 3 A schematic diagram for fitting the initial center and radius;

[0029] Figure 4 To optimize the initial center and initial radius diagram;

[0030] Figure 5 This is a schematic diagram for calculating the deflection of a cylinder. Detailed Implementation

[0031] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0032] Please see Figures 1-5 This invention provides a technical solution: a method for measuring the deflection of a cylindrical pipe based on a total station. This embodiment uses an industrial water supply cylindrical pipe as the measurement object, with a pipe diameter of 1.2m and a suspended section span of 8m. The deflection is detected using the cylindrical pipe deflection measurement method based on a total station of this invention. The total station used has an accuracy of ±1mm. The specific implementation steps are as follows:

[0033] Step 1: Fit the initial center and initial radius of each cross section:

[0034] Measurement point acquisition: Four measuring points are evenly distributed on each of the two end sections A and B of the cylindrical pipe and the mid-span section C. A total station is used to acquire the three-dimensional coordinates of all measuring points. The coordinates of measuring points at section A are labeled P_A1(x1,y1,z1), P_A2(x2,y2,z2), P_A3(x3,y3,z3), and P_A4(x4,y4,z4); the coordinates of measuring points at section B are labeled P_B1(x5,y5,z5)...P_B4(x8,y8,z8); and the coordinates of measuring points at section C are labeled P_C1(x9,y9,z1)...P_C4(x8,y8,z8). ,y9,z9)…P_C4(x12,y12,z12); 1.2 Fitting the plane of the best circle: Taking section A as an example, calculate the geometric center O_A(x_A0,y_A0,z_A0) of the four measuring points, where x_A0=(x1+x2+x3+x4) / 4, y_A0=(y1+y2+y3+y4) / 4, z_A0=(z1+z2+z3+z4) / 4; Translate the coordinates of each measuring point to the geometric center to complete the decentering, and obtain the decentered coordinates P_A1'(x1-x_A ... 0, y1-y_A0, z1-z_A0)…P_A4'(x4-x_A0, y4-y_A0, z4-z_A0); Calculate the covariance matrix using the decentralized coordinate matrix, perform singular value decomposition on the covariance matrix, and take the eigenvector n_A=(a1,b1,c1) corresponding to the smallest eigenvalue as the normal vector of section A to complete the plane fitting; similarly, obtain the normal vectors n_B and n_C of sections B and C; 1.3 Fitting the initial center and radius: Project the measurement points of each section onto its fitting plane to obtain the two-dimensional circle in the plane. Coordinates: The initial center of the circle is fitted using the least squares fitting method to minimize the sum of the distances from the measuring points to the fitted circle, thus obtaining the initial center of sections A, B, and C in the local two-dimensional coordinate system. Then, it is transformed to the global three-dimensional coordinate system to obtain the initial center a0(10.253,8.621,5.364), b0(18.249,8.618,5.362), and c0(14.251,8.620,4.987), and the initial radii ra0=0.601m, rb0=0.599m, and rc0=0.600m.

[0035] Step 2: Optimize the initial center and initial radius:

[0036] Constructing a global error function: Using the variables to be optimized, a(xa,ya,za), b(xb,yb,zb), c(xc,yc,zc), and a uniform radius r as parameters, the global error function is: 2.1 Where (xji, yji, zji) are the coordinates of the i-th measuring point of the j-th cross section, and (xj, yj, zj) are the coordinates of the optimized center of the j-th cross section; 2.2 Set parallel constraints: Taking the normal vector n_A=(a1, b1, c1) of cross section A as the reference, it is required that the coordinates of the decentralized measuring points of cross sections B and C are orthogonal to n_A, that is, the dot product of the decentralized coordinates of the measuring points and n_A is 0; 2.3 Optimization solution: The gradient descent method is used to solve the constrained global error function, and the optimized center of the circle is obtained as a(10.252, 8.620, 5.363), b(18.250, 8.619, 5.363), c(14.250, 8.619, 4.986), with a unified radius r=0.600m, and the normal vectors of each cross section are consistent, satisfying the parallel constraints.

[0037] Step 3: Calculate the deflection of the cylindrical pipe:

[0038] Determine the vertical plane: Calculate the direction vector of line ab: ab = (18.250-10.252, 8.619-8.620, 5.363-5.363) = (7.998, -0.001, 0); Take the spatial vertical vector g = (0, 0, 1), and perform a cross product of ab and g to obtain the vertical plane normal vector n = (7.998, -0.001, 0) × (0, 0, 1) = (0.001, 7.998, 0); Using the center a of the circle on line ab as the reference, obtain the equation of the vertical plane through the point normal form: 0.001(x-10.252) + 7.998(y-8.620) + 0 × (z-5.363) = 0;

[0039] Center projection: Calculate the distance d from the center of the middle section c(14.250, 8.619, 4.986) to the aforementioned vertical plane: d = |0.001×(14.250-10.252)+7.998×(8.619-8.620)| / √(0.001²+7.998²)≈0.007998 / 7.998≈0.001m; Construct a vector m = d×n / |n|=(0.000000125,0.001,0) parallel to the normal vector n, and calculate the projection point c'(14.250-0.000000125,8.619-0.001,4.986)≈(14.250,8.6). 18,4.986); Deflection calculation: Using the formula for the distance from a spatial point to a straight line, the distance from the projection point c' to the straight line ab is calculated as: L=∣ab∣∣ac′×ab∣, where ac′=(14.250-10.252,8.618-8.620,4.986-5.363)=(3.998,-0.002,-0.377), and ac′×ab=(0.000377,0.291246,-15.996), its modulus ≈15.996, ∣ab∣≈7.998, therefore L≈15.996 / 7.998=0.380m, which is the deflection measurement result of the cylindrical pipe.

[0040] It should be noted that, in this document, the terms “comprising,” “including,” or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0041] This article uses specific examples to illustrate the principles and implementation methods of the present invention. The above examples are only for the purpose of helping to understand the method and core ideas of the present invention. The above descriptions are only preferred embodiments of the present invention. It should be noted that due to the limitations of textual expression, while there are objectively infinite specific structures, those skilled in the art can make several improvements, modifications, or changes without departing from the principles of the present invention, and can also combine the above technical features in an appropriate manner. These improvements, modifications, changes, or combinations, or the direct application of the inventive concept and technical solution to other situations without modification, should all be considered within the scope of protection of the present invention.

Claims

1. A method for measuring the deflection of a cylindrical pipe based on a total station, characterized in that: Measurements were taken at two end sections A and B and one middle section C of a cylindrical pipe, including the following steps: S1. Fitting the initial center and initial radius of each section: The three-dimensional coordinate data of four measuring points of each section are collected using a total station. The plane containing the best circle is fitted for each section. Then, each measuring point is projected onto the fitted plane and converted into two-dimensional coordinates. The initial center a0, b0, c0 and the initial radius ra0, rb0, rc0 of each section in the global three-dimensional coordinate system are obtained by the least squares fitting method. S2. Optimize the initial center and initial radius: Construct a global error function for the entire cylinder as a whole, and add parallel constraints on the imaginary planes where each measuring point is located. Perform global optimization on the imaginary planes, initial centers and initial radii of each section to obtain optimized centers a, b, c and a unified radius r that satisfy the minimum global error function and the mutual parallelism of the imaginary planes. S3. Calculate the deflection of the cylindrical pipe: Determine the vertical plane of the line ab connecting the centers of the end sections. Project the optimized center c of the middle section onto this vertical plane to obtain the projection point. Calculate the distance from this projection point to the line ab, which is the deflection value of the cylindrical pipe.

2. The method for measuring the deflection of a cylindrical pipe based on a total station according to claim 1, characterized in that: The specific process of fitting the plane containing the best circle in step S1 is as follows: Calculate the geometric center of the four measuring points of the j-th section, and translate the coordinates of the measuring points to the geometric center to complete the decentralization process; The covariance matrix is ​​calculated using a decentralized measurement point matrix. Singular value decomposition is performed on the covariance matrix, and the eigenvector corresponding to the smallest eigenvalue is taken as the normal vector of the plane containing the best circle of the cross section, thus completing the plane fitting.

3. The method for measuring the deflection of a cylindrical pipe based on a total station according to claim 2, characterized in that: In step S1, when fitting the initial center and initial radius using the least squares fitting method, the constraint condition of minimizing the sum of the distances from each measuring point to the fitted circle is met.

4. The method for measuring the deflection of a cylindrical pipe based on a total station according to claim 3, characterized in that: The global error function constructed in step S2 uses the optimized circle centers a, b, c and uniform radius r of each cross section as the variables to be optimized, with the goal of minimizing the sum of errors from all measuring points to the fitted circle of the corresponding cross section.

5. The method for measuring the deflection of a cylindrical pipe based on a total station according to claim 4, characterized in that: The parallel constraint condition in step S2 is: taking the normal vector of section A as the reference, the decentered coordinates of the measuring points on each section all satisfy the orthogonal constraint with the normal vector, ensuring that the normal vectors of the three sections are consistent.

6. The method for measuring the deflection of a cylindrical pipe based on a total station according to claim 5, characterized in that: The specific process for determining the vertical plane of the line ab connecting the centers of the end sections in step S3 is as follows: calculate the direction vector of the line ab, perform a cross product of the direction vector and the spatial vertical vector to obtain the normal vector of the vertical plane, and then determine the plane equation of the vertical plane through the point normal equation.

7. The method for measuring the deflection of a cylindrical pipe based on a total station according to claim 6, characterized in that: The process of projecting the center c of the optimized middle section onto the vertical plane in step S3 is as follows: calculate the distance d from the center c to the vertical plane, construct a vector parallel to the normal vector of the vertical plane with a length of d, and obtain the three-dimensional coordinates of the projection point by combining the coordinates of the center c.

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