Ancient building cylindrical structure inclination measurement method considering irregular surface and measurement error

Abstract

The invention discloses a historic building cylindrical structure inclination measurement method considering irregular surfaces and measurement errors, and the method comprises the steps: measuring the three-dimensional coordinates of measurement points at different section heights of a historic building wood structure cylinder with a cutting or irregular surface; determining an optimal solution after a certain error is removed from the coordinates of the circle center of the section by adopting a self-adaptive random sampling consistency algorithm, then obtaining the central axis of the cylinder according to principal component analysis, and calculating the included angle of the earth normal vector of the central axis of the cylinder, namely the inclination angle of the historic building wood structure cylinder. By using the algorithm, the influence of cutting or irregular surfaces and measurement errors on historic building wood structure cylinder inclination measurement can be eliminated, and the reliability and the accuracy of a measurement result are effectively improved.

Description

Technical Field

[0001] The present invention relates to the technical fields of civil engineering monitoring and engineering surveying, and particularly to a method for measuring the inclination of ancient building column structures considering irregular surfaces and measurement errors. Background Art

[0002] The inclination deformation of ancient building wooden structures is an important index for identifying their damaged points and reliability levels. However, there are some difficulties in the current measurement of inclination deformation: Trees naturally have large and small ends, and it is impossible to directly measure the upper and lower inclination amounts with a total station. The currently commonly used method is to use the least squares method to fit the center coordinates of the cross-section through the measuring points on the column surface, and then calculate the axis vector of the cylinder. However, the irregular cross-sections caused by cutting during the processing of round wooden columns, as well as defects such as cracking and rotten knots during service, will reduce the accuracy of inclination measurement.

[0003] In the existing traditional ancient building measurements, there is a lack of a method that can automatically eliminate the influence of irregular cutting of the cylinder itself, material defects, and manual measurement errors. Summary of the Invention

[0004] In view of this, the purpose of the present invention is to propose a method for measuring the inclination of ancient building column structures considering irregular surfaces and measurement errors, which is reliable in implementation, high in measurement accuracy, and convenient in measurement.

[0005] In order to achieve the above technical purpose, the technical solution adopted by the present invention is as follows:

[0006] A method for measuring the inclination of ancient building column structures considering irregular surfaces and measurement errors, which includes:

[0007] S01. Divide the column structure of the ancient building to be measured into n cross-sectional heights from bottom to top, and arrange M observation measuring points along the circumference for each cross-section (the measuring point numbers are m i , where i = 1 to n); among them, the divided cross-sectional heights and the arranged measuring points should be as evenly distributed as possible along the column height and circumference;

[0008] S02. According to the on-site situation of the column to be measured, set up a total station at a suitable position, and use the total station to measure the observation measuring points at n cross-sectional heights of the column structure to obtain the spatial three-dimensional coordinates corresponding to the M observation measuring points on each cross-section; to make the measurement results as accurate as possible, select a transfer station at an appropriate position to ensure that the measuring points are arranged in a circumferential loop around the round wooden column. If it is not allowed due to actual conditions such as enclosure structure obstruction, the measuring points should cover as much of the circumference as possible;

[0009] S03. Perform noise reduction processing on the spatial three-dimensional coordinates corresponding to the M observation measuring points on each obtained cross-section, and then solve the center coordinates of the corresponding plane of each cross-section;

[0010] S04. Based on the center coordinates corresponding to n cross-sectional planes, the axis of the column body is obtained through principal component analysis, and then the normal angle between the axis of the column body and the plane where the bottom of the cylindrical structure of the ancient building to be measured is located is calculated, that is, the inclination angle of the cylindrical structure of the ancient building to be measured.

[0011] As a possible implementation, further, in this solution S01, the cylindrical structure is evenly divided into n cross-sectional heights from bottom to top; M observation measurement points are evenly arranged along the circumference of each cross-section, where M is an integer greater than 1.

[0012] As a possible implementation, further, in this solution S03, the denoising process includes removing the measurement points located on the cutting surface and irregular surface of the cylinder for each cross-section, as well as the spatial three-dimensional coordinates with error deviations exceeding the preset range caused by manual measurement errors.

[0013] As a better implementation option, preferably, in this solution S03, the spatial three-dimensional coordinates corresponding to the M observation measurement points obtained for each cross-section are denoised through the adaptive random sample consensus algorithm, and then the center coordinates of the planes corresponding to each cross-section are solved, which includes:

[0014] S031. Assume that the initial value [d In of the threshold is equal to the error of the measuring instrument itself; select a cross-section plane without cutting and irregular surface near the half-column height of the cylindrical structure of the ancient building to be measured, and evenly arrange m i measurement points (i = 2 to n - 1) along the circumference of the cross-section plane to form a measurement point data set, and set the coordinates of each measurement point in the cross-section plane as P i (x i , y i ); then calculate the center of the circle by taking any three points among the measurement points of this cross-section plane. Each process of calculating the center of the circle is an iteration, and assume the number of iterations is k; each time an iteration is performed, randomly select 3 points P1, P2, and P3 from all the measurement points, and their corresponding coordinates are P1(x1, y1), P2(x2, y2), and P3(x3, y3). Solve the following center coordinate formula to obtain the center coordinate (x pc， y pc ) of the p-th iteration;

[0015] (x pc - x1) 2 + (y pc - y1) 2 = r p 2

[0016] (x pc - x2) 2 + (y pc - y2) 2 = rp 2

[0017] (x pc - x3) 2 +(y pc - y3) 2 =r p 2

[0018] S032. For each iteration, for the remaining measurement points P4 to P in the measurement point dataset mi Calculate the distance d from it to the center of the circle. The formula is as follows

[0019]

[0020] where x c , y c are the coordinates of the center of the circle, and x and y are the coordinates of the measurement point in the x and y coordinate systems respectively;

[0021] Compare the calculated distance d from the center of the circle with [d In . If d ≥ [d In , then define this measurement point as an outlier. Otherwise, define this point as an inlier, and then count the number of inliers a;

[0022] S033. Use [d In as the initial value for adjustment and trial calculation. Take the [d i when a is closest to the true number m of measurement points on the cutting plane In as the threshold [d f required for calculating the center coordinates of the wooden column;

[0023] S034. Use [d f as the threshold for solving the center of the cutting plane. After k iterations of the measurement points within the cutting plane, determine the iteration number with the largest number of inliers. Take the center coordinates calculated in this iteration as the optimal solution of the center of the cutting plane; then sequentially solve the optimal solutions of the center coordinates (x ic , y ic , z ic )(i = 1 to n) of each cutting plane height to obtain the center coordinates of the corresponding planes of each cutting plane.

[0024] As a preferred implementation option, preferably, in this solution S04, based on the center coordinates corresponding to n cross-sectional planes, the axis of the column body is obtained through principal component analysis, and then the normal angle between the axis of the column body and the plane where the bottom of the cylindrical structure of the ancient building to be measured is located is calculated, including:

[0025] S041. Fit the three-dimensional space coordinates of the center points of n cross-sections to find the average value of the three-dimensional space coordinates of the center points of n cross-sections. The formula is defined as follows:

[0026]

[0027] Among them, x ic , y ic , z ic are the coordinate values of the center points of n cross-sections in the x, y, and z coordinate systems respectively; are the average coordinate values of the center points of n cross-sections fitted in the x, y, and z coordinate systems respectively;

[0028] S042. Construct the coordinate matrix after data centralization:

[0029]

[0030] Calculate the covariance matrix C:

[0031]

[0032] Define I as the identity matrix, solve the characteristic equation of the covariance matrix C, λ is its eigenvalue, and its definition is as follows:

[0033] |C - λI| = 0

[0034] Solve for the three eigenvalues and arrange them in descending order, i.e., λ1 ≥ λ2 ≥ λ3; for each eigenvalue λ, calculate its corresponding eigenvector v:

[0035] Cv i = λ i v i

[0036] Through the eigenvector v i , construct the eigenvector matrix V:

[0037] V = [v1 v2 v3]

[0038] Assume that the normal vector of the ground plane is n = (0, 0, 1), then calculate the angle θ between the eigenvector v1 corresponding to the largest eigenvalue λ1 and the normal vector n:

[0039]

[0040] Adopting the above technical solution, compared with the prior art, the beneficial effects of the present invention are as follows: This solution measures the three-dimensional space coordinates of the measuring points on different column height cross-sections through a total station, then eliminates the error measuring points and the measuring points located on the cutting or irregular surfaces through the adaptive random sampling consensus algorithm, obtains the center coordinates of each cross-section height, calculates the cylindrical axis direction vector passing through the center coordinates through principal component analysis, and solves the included angle between it and the earth normal direction, realizing the inclination measurement of the ancient wooden structure columns. It is not only reliable in implementation, but also convenient in operation and has good measurement accuracy. Brief Description of the Drawings

[0041] In order to more clearly illustrate the technical solutions in the embodiments of the present invention or the prior art, the following will briefly introduce the drawings required for the description of the embodiments or the prior art. Obviously, the drawings in the following description are only some embodiments of the present invention. For those of ordinary skill in the art, without creative efforts, other drawings can be obtained based on these drawings.

[0042] Figure 1 It is a flowchart of the method for measuring the inclination rate of ancient building columns in the embodiments of the present invention.

[0043] Figure 2 It is a schematic diagram of the total station measurement of the ancient building wooden structure columns in the embodiments of the present invention.

[0044] Figure 3 It is a schematic diagram of the method for calculating the inclination angle through the measurement points of the ancient building wooden structure columns in the embodiments of the present invention. Detailed Embodiment

[0045] The present invention will be further described in detail below in conjunction with the drawings and embodiments. It should be specifically noted that the following embodiments are only used to illustrate the present invention, but do not limit the scope of the present invention. Similarly, the following embodiments are only partial embodiments of the present invention rather than all embodiments. All other embodiments obtained by those of ordinary skill in the art without creative efforts fall within the scope of protection of the present invention.

[0046] An inclination measurement method for ancient building column structures considering irregular surfaces and measurement errors, which includes:

[0047] S01. Divide the column structure of the ancient building to be measured into n cross-sectional heights from bottom to top, and arrange M observation measurement points along the circumference for each cross-section (the measurement point numbers are m i , where i = 1 to n); among them, the divided cross-sectional heights and arranged measurement points should be as evenly distributed as possible along the column height and circumference;

[0048] S02. According to the on-site situation of the column to be measured, set up a total station at a suitable position, and use the total station to measure the observation measurement points at n cross-sectional heights of the column structure to obtain the three-dimensional spatial coordinates corresponding to the M observation measurement points on each cross-section; in order to make the measurement results as accurate as possible, select a transfer station at an appropriate position to ensure that the measurement points are arranged around the circular wooden column for one week. If it is not allowed due to actual conditions such as the enclosure structure blocking, the measurement points should cover as much of the circumference as possible;

[0049] S03. Denoise the three-dimensional spatial coordinates corresponding to the M observation measurement points on each obtained cross-section, and then solve the center coordinates of the corresponding plane of each cross-section;

[0050] S04. Based on the center coordinates corresponding to n cross-sectional planes, the axis of the column body is obtained through principal component analysis, and then the normal angle between the axis of the column body and the plane where the bottom of the cylindrical structure of the ancient building to be measured is located is calculated, that is, the inclination angle of the cylindrical structure of the ancient building to be measured.

[0051] As a possible implementation, further, in S01 of this solution, the cylindrical structure is evenly divided into n cross-sectional heights from bottom to top; M observation measurement points are evenly arranged along the circumference of each cross-section, where M is an integer greater than 1.

[0052] As a possible implementation, further, in S03 of this solution, the denoising process includes removing the measurement points located on the cylindrical cutting surface and irregular surfaces of each cross-section, as well as the spatial three-dimensional coordinates of the error deviations caused by artificial measurement errors that exceed the preset range.

[0053] As a better implementation option, preferably, in S03 of this solution, the spatial three-dimensional coordinates corresponding to the M observation measurement points obtained on each cross-section are denoised through the adaptive random sample consensus algorithm, and then the center coordinates of the planes corresponding to each cross-section are solved, which includes:

[0054] S031. Assume that the initial value of the threshold [d In is equal to the error of the measuring instrument itself; select a cross-sectional plane without cutting and irregular surfaces near half of the column height of the cylindrical structure of the ancient building to be measured, and evenly arrange m i measurement points (i = 2 to n - 1) along the circumference of the cross-sectional plane to form a measurement point data set, and set the coordinates of each measurement point in the cross-sectional plane as P i (x i , y i ); then select any three points from the measurement points of this cross-sectional plane to calculate its center. Each process of calculating the center is an iteration, and let the number of iterations be k; each time an iteration is performed, randomly select 3 points P1, P2, and P3 from all the measurement points, and their corresponding coordinates are P1(x1, y1), P2(x2, y2), and P3(x3, y3). Solve the following center coordinate formula simultaneously to obtain the center coordinates (x pc， y pc ) of the pth iteration;

[0055] (x pc - x1) 2 + (y pc - y1) 2 = r p 2

[0056] (x pc - x2) 2 + (y pc - y2)2 = r p 2

[0057] (x pc - x3) 2 +(y pc - y3) 2 = r p 2

[0058] S032. For each iteration, for the remaining measuring points P4 to P in the measuring point dataset mi Calculate the distance d from it to the center of the circle. The formula is as follows

[0059]

[0060] where x c , y c are the coordinates of the center of the circle, and x and y are the coordinates of the measuring point in the x and y coordinate systems respectively;

[0061] Compare the calculated distance d from the center of the circle with [d In . If d ≥ [d In , then define this measuring point as an outlier. Otherwise, define this point as an inlier, and then count the number of inliers a;

[0062] S033. Use [d In as the initial value and repeat steps S031 to S032 for iterative calculation. When the a obtained in a certain iterative calculation is closest to the true number m of measuring points on the cutting plane i at this time, then [d In is the threshold [d f required for calculating the center coordinates of the wooden column;

[0063] S034. Use [d f as the threshold for solving the center of the cutting plane. After k iterations of the measuring points in the cutting plane, determine the iteration number with the largest number of inliers, and take the center coordinates calculated in this iteration as the optimal solution of the center of the cutting plane; then sequentially solve the optimal solutions of the center coordinates (x ic , y ic , z ic )(i = 1 to n) of each cutting plane height to obtain the center coordinates of the corresponding planes of each cutting plane.

[0064] As a preferred implementation option, preferably, in step S04 of this solution, based on the center coordinates corresponding to n cross-sectional planes, the axis of the column is obtained by principal component analysis, and then the normal angle between the axis of the column and the plane where the bottom of the cylindrical structure of the ancient building to be measured is located is calculated, including:

[0065] S041. Fit the three-dimensional spatial coordinates of the center points of n cross-sections, and calculate the average value of the three-dimensional spatial coordinates of the center points of n cross-sections. Its formula is defined as follows:

[0066]

[0067] Among them, x ic , y ic , z ic are the coordinate values of the center points of n cross-sections in the x, y, and z coordinate systems respectively; are the coordinate means of the center points of the n cross-sections fitted in the x, y, and z coordinate systems respectively;

[0068] S042. Construct a coordinate matrix after data centralization:

[0069]

[0070] Calculate the covariance matrix C:

[0071]

[0072] Define I as the identity matrix, solve the characteristic equation of the covariance matrix C, and λ is its eigenvalue, which is defined as follows:

[0073] |C - λI| = 0

[0074] Solve for the three eigenvalues and sort them in descending order, i.e., λ1 ≥ λ2 ≥ λ3; for each eigenvalue λ, calculate its corresponding eigenvector v i :

[0075] Cv i = λ i v i

[0076] Construct an eigenvector matrix V through the eigenvector v i :

[0077] V = [v1 v2 v3]

[0078] Assume that the normal vector of the ground plane is n = (0, 0, 1), then calculate the angle θ between the eigenvector v1 corresponding to the largest eigenvalue λ1 and the normal vector n:

[0079]

[0080] Combined with Figures 1 to 3 One of the following, the present solution will be elaborated with an implementation example; a method for measuring the inclination of an ancient building column structure considering irregular surfaces and measurement errors, which includes:

[0081] Step 1: Assume an ancient wooden structure cylindrical column to be measured, with the height / base column diameter ratio of 10:1 and the upper and lower taper of 1 / 100. Take a round wooden column with a column height H = 5m and bottom / top diameters D = 500 / 450mm as an example. The inclination amount refers to the local structural inclination limit value Δ = H / 250 (inclination angle θ = 0.0040°) in the current appraisal standard. Divide the column from the bottom to the top into 5 cross-sectional heights, and try to ensure equal-spacing division; for each height cross-section of the circle, arrange 20 observation measuring points around its circumference, and the arranged measuring points should be evenly distributed along the circumference as much as possible;

[0082] Step 2: Set up a total station at a suitable position on the construction site, and use the total station to measure the three-dimensional spatial coordinates of the measuring points arranged at each cross-sectional height of the ancient wooden structure cylindrical column; the measurement should try to cover the entire cross-section of the circumference. In case of occlusion or limited vision, transfer station measurement can be carried out through point transfer;

[0083] Step 3: In actual projects, if the column inclination rate is not large and the cross-section of the inclined column can still be regarded as a circle, then the center of each of the above-mentioned cross-sectional heights is the center of the circle;

[0084] Step 4: Assume an initial threshold value [d In , whose value is equal to the instrument's own error. For example, if a total station is used, the threshold value [d In can be tentatively set to 2mm;

[0085] Step 5: Select a cross-sectional plane without cutting and irregular surfaces near half of the height of the cylindrical column to be measured, and evenly arrange 20 measuring points around the circumference of the cross-sectional plane. The coordinates of each measuring point in the cross-sectional plane are P i (x i , y i ); Select any three points from all the measuring points in this cross-sectional plane to calculate its center of the circle. Each process of calculating the center of the circle is called "iteration". Let the total number of iterations be k. Since the number of measuring points is not large in actual projects, k = 100 can be set. Then, each iteration randomly selects 3 measuring points from all the measuring points, namely 3 points P1, P2, and P3, with corresponding coordinates P1(x1, y1), P2(x2, y2), and P3(x3, y3). Solve the following center coordinate formula simultaneously to obtain the center coordinates (x pc， y pc ) of the p-th iteration:

[0086] (x pc - x1) 2 + (y pc - y1) 2 = r p 2

[0087] (x pc - x2) 2 + (y pc-y2) 2 = r p 2

[0088] (x pc -x3) 2 +(y pc -y3) 2 = r p 2

[0089] Step 6: Calculate the distance d between the center coordinates of the circle at each iteration of the cross-section and the remaining measuring points on the cross-section plane. For the p-th iteration, the distance d from the remaining measuring points on the cross-section plane to the calculated center of the circle is as follows: p :

[0090]

[0091] Step 7: Define a point as an "outlier" when d p ≥ [d In , and define the point as an "inlier" otherwise. Count the number a of "inliers".

[0092] Step 8: Take [d In = 2 mm as the initial value, and repeat Steps 5 to 7 by incrementing or decrementing by 0.1 near it. When [d In is taken as 2.8 mm, the calculated number of inliers "a" = 20, which is closest to the true number of measuring points 20 on the plane. Then take [d f = 2.8 mm;

[0093] Step 9: Take [d f = 2.8 mm as the threshold for solving the center of the circle of the column, and repeat Steps 5 to 8 to solve the optimal solution of the center coordinates of the 5 cross-section planes. By attaching the heights of the 5 cross-sections, the three-dimensional space coordinates can be obtained as = (1.166, 4.82, 0); (10.008, 7.614, 2500); (15.142, 16.889, 5000); (24.187, 24.234, 7500); (32.521, 31.393, 10000).

[0094] Step 10: Calculate the average value of the three-dimensional coordinates of the centers of each cross-section plane respectively:

[0095]

[0096]

[0097] Step 11: Construct a coordinate matrix after data centering for the centers of each cross-section plane:

[0098]

[0099] Step 12, calculate the covariance matrix C of the coordinate matrix:

[0100]

[0101] Step 13, define I as the identity matrix, solve the characteristic equation of the covariance matrix C, and sort the eigenvalues λ, such that λ1 ≥ λ2 ≥ λ3.

[0102] |C - λI| = 0

[0103] Step 14, calculate the eigenvector v corresponding to each eigenvalue λ i and the eigenvector matrix V

[0104] Cv i = λ i v i

[0105]

[0106] Step 15, calculate the angle θ between the eigenvector v1 = (0.0028, 0.0029, 1.0000) corresponding to λ1 and the normal vector n = (0, 0, 1) of the ground plane, which is the inclination angle of the ancient building wooden structure column to be measured:

[0107]

[0108] In summary, in this solution, the three-dimensional coordinates of the measurement points at different cross-section heights of the ancient building wooden structure column with a cut or irregular surface are measured, and the adaptive random sampling consensus algorithm is used to determine the optimal solution of the cross-section center coordinates after removing certain errors. Then, the central axis of the column is obtained according to the principal component analysis, and the angle between its normal vector to the ground is calculated, which is the inclination angle of the ancient building wooden structure column. By using the above algorithm, the influence of the cut or irregular surface and measurement errors on the inclination measurement of the ancient building wooden structure column can be removed, effectively improving the reliability and accuracy of the measurement results.

[0109] The above are only some embodiments of the present invention, and thus do not limit the protection scope of the present invention. Any equivalent device or equivalent process transformation made by using the content of the specification and drawings of the present invention, or directly or indirectly applied in other related technical fields, shall be equally included in the patent protection scope of the present invention.

Claims

1. A method for measuring the inclination of cylindrical structures of ancient buildings taking into account irregular surfaces and measurement errors, characterized in that: It includes: S01. Divide the cylindrical structure of the ancient building to be measured into n cross-sectional heights from bottom to top, and arrange M observation points along the circumference of each cross-sectional height; S02. Use a total station to measure the observation points at the height of n sections on the cylindrical structure to obtain the spatial three-dimensional coordinates corresponding to the M observation points on each section; S03, performing denoising processing on the spatial three-dimensional coordinates corresponding to the M observation points on each cross section, and then solving the coordinates of the center of the plane corresponding to each cross section; S04. Based on the coordinates of the center of the circle corresponding to the n cross-sectional planes, the axis of the column body is obtained through principal component analysis, and then the normal angle between the axis of the column body and the plane where the bottom of the cylindrical structure of the ancient building to be measured is located is calculated, that is, the inclination angle of the cylindrical structure of the ancient building to be measured.

2. The method for measuring the inclination of an ancient building cylindrical structure taking into account irregular surfaces and measurement errors as claimed in claim 1, characterized in that: In S01, the cylindrical structure is evenly divided into n cross-sectional heights from bottom to top; each cross-sectional height is evenly distributed with M observation points along the circumference, where M is an integer greater than 1.

3. The method for measuring the inclination of an ancient building cylindrical structure taking into account irregular surfaces and measurement errors as claimed in claim 1, characterized in that: In S03, the denoising process includes eliminating the measurement points on the cylindrical cutting surface and irregular surface on each cross section, as well as the spatial three-dimensional coordinates whose error deviations caused by manual measurement errors exceed the preset range.

4. The method for measuring the inclination of an ancient building cylindrical structure taking into account irregular surfaces and measurement errors as claimed in claim 3, characterized in that: In S03, the spatial three-dimensional coordinates corresponding to the M observation points on each cross section are denoised by an adaptive random sampling consistency algorithm, and then the center coordinates of the plane corresponding to each cross section are solved, which includes: S031, assuming the initial value of the threshold [d In ] is equal to the error of the measuring instrument itself; select a section plane without cutting and irregular surface near half the column height of the cylindrical structure of the ancient building to be measured, and evenly arrange m i measuring points (i = 2 to n-1) to form a measuring point data set. The coordinates of each measuring point in the measuring point data set in the section plane are set as P i (x i ,y i ); then take any three points from the measurement points of the section plane to calculate its center. Each process of calculating the center is an iteration, and the number of iterations is k; in each iteration, three points P1, P2 and P3 are randomly selected from all the measurement points, and their corresponding coordinates are P1(x1, y1), P2(x2, y2) and P3(x3, y3). The following formula for the center coordinate is used to solve the center coordinates of the pth iteration (x pc， y pc ); (x pc -x1) 2 +(y pc -y1) 2 =r p 2 (x pc -x2) 2 +(y pc -y2) 2 =r p 2 (x pc -x3) 2 +(y pc -y3) 2 =r p 2 S032. For each iteration, the remaining measurement points P4 to P mi Calculate the distance d from the center of the circle as follows: Among them, x c ,y c are the coordinates of the center of the circle, x and y are the coordinates of the measuring point in the x and y coordinate systems respectively; The calculated center distance d and [d In ] for comparison, such as d≥[d In ] then define the measuring point as an external point, otherwise define the point as an internal point, and then count the number of internal points a; S033, with [d In ] is used as the initial value for adjustment and trial calculation, and a is taken as the number of actual measurement points m closest to the section plane. i When [d In ] is the threshold value required for calculating the center coordinates of the wooden column [d f ]; S034, with [d f ] as the threshold for solving the center of the cutting plane. After k iterations of the measuring points in the cutting plane, the iteration number with the largest number of internal points is determined, and the center coordinates calculated by this iteration are taken as the optimal solution of the center of the cutting plane. Then, the center coordinates (x ic ,y ic ,z ic )(i=1~n), and obtain the center coordinates of the plane corresponding to each cross section.

5. The method for measuring the inclination of an ancient building cylindrical structure taking into account irregular surfaces and measurement errors as claimed in any one of claims 1 to 4, characterized in that: S04. Based on the coordinates of the center of the circle corresponding to the n cross-sectional planes, the axis of the column shaft is obtained by principal component analysis, and then the normal angle between the axis of the column shaft and the plane where the bottom of the cylindrical structure of the ancient building to be measured is located is calculated, including: S041. Fit the three-dimensional spatial coordinates of the center points of n cross sections to find the average value of the three-dimensional spatial coordinates of the center points of n cross sections. The formula is defined as follows: Among them, x ic ,y ic 、z ic are the coordinate values ​​of the center points of the n cross sections in the x, y, and z coordinate systems respectively; are the mean values ​​of the center points of the fitted n cross sections in the x, y, and z coordinate systems respectively; S042. Construct the coordinate matrix after data centering: Calculate the covariance matrix C: Define I as the identity matrix and solve the characteristic equation of the covariance matrix C. λ is its eigenvalue, which is defined as follows: |C-λI|=0 Solve the three eigenvalues ​​and arrange them in descending order, that is, λ1≥λ2≥λ3; for each eigenvalue λ, calculate its corresponding eigenvector v i : Cv i =λ i v i Through the feature vector v i , construct the eigenvector matrix V: V=[v1 v2 v3] Define the normal line of the geodesic plane as n = (0,0,1), and calculate the angle θ between the eigenvector v1 corresponding to the maximum eigenvalue λ1 and the normal line n:

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