Arch axis fitting method of railway stone arch bridge

Abstract

The present application relates to the technical fields of bridge engineering, and discloses an arch axis fitting method of a railway stone arch bridge, which comprises the following steps: collecting three-dimensional coordinates of each measuring point on the arch bottom surface; collecting three-dimensional coordinates of each measuring point on the upper edge of the arch side surface and three-dimensional coordinates of each measuring point on the lower edge of the arch side surface; respectively carrying out denoising treatment on the three-dimensional coordinates of each measuring point on the arch bottom surface, the three-dimensional coordinates of each measuring point on the upper edge of the arch side surface and the three-dimensional coordinates of each measuring point on the lower edge of the arch side surface; calculating the geometric center of the arch bottom surface according to the denoised three-dimensional coordinate data of the arch bottom surface, and converting the denoised three-dimensional coordinate data of the upper and lower edges of the arch side surface into a three-dimensional rectangular coordinate system with the geometric center as the coordinate origin to generate the three-dimensional coordinate data of the upper and lower edges of the arch side surface in unified coordinates; selecting the corresponding curve equation of the railway stone arch bridge according to the type of the railway stone arch bridge, and adopting the least square method to carry out parameter fitting on the three-dimensional coordinate data of the upper and lower edges of the arch side surface in unified coordinates to generate the arch axis of the railway stone arch bridge; and the present application improves the fitting precision of the arch axis.

Description

Technical Field

[0001] The invention relates to the technical field of bridge engineering, and in particular to an arch axis fitting method for a railway stone arch bridge. Background Art

[0002] During the inspection and maintenance of railway stone arch bridges, accurate acquisition of the arch axis is crucial for assessing the safety of the bridge structure. Existing arch structure alignment methods, while highly accurate, can only capture the arch bottom alignment and fail to fully understand the overall arch structure. While arch side profile testing can capture the upper and lower edge alignments to provide a comprehensive understanding of the overall shape, the long distance between the measurement points and the arch side leads to significant data acquisition errors. Furthermore, due to limitations in the arch ring shape and testing conditions, it is difficult to fully capture the spatial position information of key components of railway stone arch bridges. Consequently, the data foundation provided for arch axis fitting is unreliable, impacting the accuracy of arch axis fitting.

[0003] In addition, the existing methods are targeted at specific types of railway stone arch bridges (such as only applicable to one of the circular arch bridges or parabolic arch bridges), and lack the ability to flexibly cope with different types and working conditions of railway stone arch bridges by adjusting the curve equation and the parameters to be fitted. When the type or working condition of the arch bridge changes, it is difficult to achieve high-precision arch axis fitting, which has great limitations in application scenarios. Summary of the Invention

[0004] In response to the above-mentioned deficiencies in the prior art, the present invention provides a method for fitting the arch axis of a railway stone arch bridge, which is used to solve the problem that it is difficult to balance the test accuracy and test range in the existing linear detection method of the arch structure, that is, the overall shape of the arch structure cannot be fully obtained, resulting in low detection accuracy and low arch axis fitting accuracy.

[0005] In order to achieve the above-mentioned object of the invention, the technical solution adopted by the present invention is:

[0006] A method for fitting an arch axis of a railway stone arch bridge comprises the following steps:

[0007] S1. Set several measuring points on the arch bottom surface and collect the three-dimensional coordinates of each measuring point on the arch bottom surface by deploying high-precision total stations;

[0008] S2, setting a number of measuring points on the upper edge and the lower edge of the arch side surface, and collecting the three-dimensional coordinates of each measuring point on the upper edge of the arch side surface and the three-dimensional coordinates of each measuring point on the lower edge of the arch side surface by deploying a three-dimensional laser scanner;

[0009] S3, using a statistical filtering method to perform denoising on the three-dimensional coordinates of each measuring point on the arch bottom surface, the three-dimensional coordinates of each measuring point on the upper edge of the arch side surface, and the three-dimensional coordinates of each measuring point on the lower edge of the arch side surface, to generate denoised three-dimensional coordinate data of the arch bottom surface and three-dimensional coordinate data of the upper and lower edges of the arch side surfaces;

[0010] S4. According to the denoised three-dimensional coordinate data of the arch bottom surface, the geometric center of the arch bottom surface is calculated, a three-dimensional rectangular coordinate system with the geometric center as the coordinate origin is established, and the three-dimensional coordinate data of the upper and lower edges of the arch side surface in the denoised state is converted to the three-dimensional rectangular coordinate system with the geometric center as the coordinate origin, to generate the three-dimensional coordinate data of the upper and lower edges of the arch side surface in the unified coordinates.

[0011] S5. According to the type of the railway stone arch bridge, a corresponding curve equation of the railway stone arch bridge is selected.

[0012] S6. Based on the corresponding curve equation of the railway stone arch bridge, the least square method is used to perform parameter fitting on the three-dimensional coordinate data of the upper and lower edges of the arch side surface in the unified coordinates, to generate the arch axis of the railway stone arch bridge.

[0013] The present application has the following beneficial effects:

[0014] 1. The arch axis fitting method of the railway stone arch bridge provided by the present application can collect three-dimensional coordinates of arch bottom surface measuring points through a high-precision total station and collect three-dimensional coordinates of upper and lower edge measuring points of the arch side surface through a three-dimensional laser scanner, so as to accurately and comprehensively obtain spatial position information of each key part of the railway stone arch bridge, thereby providing reliable data basis for arch axis fitting and improving the accuracy of the fitted arch axis.

[0015] 2. The present application is suitable for railway stone arch bridges of different types and under different working conditions. Whether it is a circular arch bridge or a parabolic arch bridge, high-precision arch axis fitting can be achieved by adjusting the curve equation and the parameters to be fitted, and it has strong versatility and adaptability. BRIEF DESCRIPTION OF DRAWINGS

[0016] Figure 1 The flowchart of the arch axis fitting method of the railway stone arch bridge provided by the present application. DETAILED DESCRIPTION

[0017] The specific embodiments of the present application are described below to facilitate understanding of the present application by those skilled in the art, but it should be clear that the present application is not limited to the scope of the specific embodiments. For those skilled in the art, it is obvious that various changes are within the spirit and scope of the present application as defined in the appended claims, and all inventions utilizing the concept of the present application are within the scope of protection.

[0018] As shown in Figure 1 A method for fitting the arch axis of a railway stone arch bridge, comprising the following steps S1-S6:

[0019] S1. Set a plurality of measuring points on the arch bottom surface, and collect three-dimensional coordinates of each measuring point on the arch bottom surface by arranging a high-precision total station.

[0020] Specifically, step S1 specifically comprises:

[0021] At the arch bottom surface, a plurality of measuring points are divided according to a predicted interval, and a high-precision total station is arranged to collect three-dimensional coordinates of each measuring point of the arch bottom surface; the three-dimensional coordinates of each measuring point of the arch bottom surface are , wherein, , , , and , respectively represent the , , axis coordinates of the i-th measuring point of the arch bottom surface, , and n represents the total number of measuring points of the arch bottom surface.

[0022] In this embodiment, the arch bottom surface is the lower surface of the arch ring of a railway stone arch bridge, which is of great significance in bridge stress, load bearing and shape presentation. In actual measurement, a plurality of measuring points are usually preset according to a certain interval (generally 1-2 meters) along the arch bottom surface, and then high-precision total station is used to obtain the three-dimensional coordinates of these measuring points, so as to obtain a plurality of three-dimensional coordinate data of the arch bottom surface.

[0023] S2, a plurality of measuring points on the upper edge and the lower edge of the arch side surface are set, and a three-dimensional laser scanner is arranged to collect three-dimensional coordinates of each measuring point on the upper edge of the arch side surface and three-dimensional coordinates of each measuring point on the lower edge of the arch side surface.

[0024] Specifically, step S2 specifically includes:

[0025] Taking the left arch side surface or the right arch side surface, a plurality of measuring points are divided on the upper edge and the lower edge of the arch side surface according to a preset distance, respectively, and a three-dimensional laser scanner is arranged to collect three-dimensional coordinates of each measuring point on the upper edge of the arch side surface and three-dimensional coordinates of each measuring point on the lower edge of the arch side surface; the three-dimensional coordinates of each measuring point on the upper edge of the arch side surface are , wherein, , , , and , respectively represent the , , axis coordinates of the i-th measuring point of the arch side surface, , and n represents the total number of measuring points on the upper edge of the arch side surface; the three-dimensional coordinates of each measuring point on the lower edge of the arch side surface are , wherein, , , , and , respectively represent the , , axis coordinates of the i-th measuring point of the arch side surface, , and n represents the total number of measuring points on the lower edge of the arch side surface.

[0026] In this embodiment, the arch side is the side of the arch ring, that is, the side part of the arch ring in the transverse direction (perpendicular to the length direction of the bridge), which is closely related to the bridge structure and stress characteristics; the upper edge of the arch side is the upper boundary of the arch side, and the lower edge of the arch side is the lower boundary of the arch side; since only the data of a certain place on the arch side is collected, the actual shape of the arch ring cannot be fully reflected, therefore, only by obtaining the three-dimensional coordinate data of the upper edge and the lower edge, the profile of the arch ring in the side direction can be outlined based on these data, and then combined with the arch bottom surface data, the high-precision fitting of the arch axis shape of the entire railway stone arch bridge can be realized in the subsequent steps.

[0027] In addition, since the railway stone arch bridge is symmetrical, when measuring the three-dimensional coordinates of the arch side, that is, the left side and the right side of the railway stone arch bridge, only the data of one side can be considered, and the other side can not be considered, so as to reduce the amount of calculation; and when laying the three-dimensional laser scanner, the scanning position is determined to be on any side of the railway stone arch bridge, and a position with a vertical distance of 2-5 meters from the arch bottom surface is selected, and the position should have an open view without trees, buildings and other obstructions; such a distance can not only ensure that the scanner completely covers the arch side area, but also reduce the measurement blind area caused by too close distance and the measurement error caused by too far distance. For example, for a stone arch bridge with a relatively low arch ring and a relatively open surrounding environment, the scanner can be set at a distance of 2 meters from the arch bottom surface; if the bridge is relatively high or there are interference factors nearby, the scanner can be set at a distance of 5 meters; and the scanning angle is adjusted to ensure that the three-dimensional laser scanner is erected on a stable tripod, and the instrument is in a horizontal state through the level; the scanning direction is aligned as vertically as possible to the arch side through the aiming function of the scanner; before scanning, a test scanning can be performed, and whether the upper and lower edges of the arch side are within the scanning range can be observed through the preview function of the instrument; if there are some areas that are not scanned, the horizontal and vertical angles of the scanner can be adjusted until the upper and lower edges of the entire arch side can be clearly and completely displayed in the scanning field of view; finally, the measurement stations are arranged reasonably according to the length of the bridge; for a railway stone arch bridge with a relatively short length (less than 50 meters), one measurement station can be arranged at each end of the bridge, and the scanning ranges of the two stations need to have a certain overlap, and the overlapping part generally accounts for 10%-20% of the total scanning range, so as to ensure the integrity and continuity of the data; for a bridge with a relatively long length (more than 50 meters), a measurement station can be arranged every 30-50 meters, and there also needs to be enough overlapping area between adjacent stations.

[0028] S3, respectively, the three-dimensional coordinates of each measurement point on the arch bottom surface, the three-dimensional coordinates of each measurement point on the upper edge of the arch side, and the three-dimensional coordinates of each measurement point on the lower edge of the arch side are denoised by using a statistical filtering method to generate denoised arch bottom surface three-dimensional coordinate data, arch side upper and lower edge three-dimensional coordinate data.

[0029] Specifically, step S3 specifically includes:

[0030] Calculate the mean and standard deviation of the three-dimensional coordinates of each measuring point on the bottom surface of the arch, the three-dimensional coordinates of each measuring point on the upper edge of the arch side, and the three-dimensional coordinates of each measuring point on the lower edge of the arch side, and set the filtering threshold. The filtering threshold is times the standard deviation, centered around the mean, times the standard deviation is the radius, which will deviate from the mean by more than The filtering threshold is set to K times the standard deviation. The K value is determined by experiments and is usually 2 to 3 to balance the denoising effect and data retention requirements.

[0031] In this embodiment, by deviating from the mean by more than Points with a value greater than or equal to times the standard deviation are considered noise points and eliminated, ultimately obtaining the denoised three-dimensional coordinate data of the arch bottom surface and the three-dimensional coordinate data of the upper and lower edges of the arch side surfaces. This method is simple and fast, can reduce the amount of calculation, and is suitable for processing obvious outlier noise points in the data.

[0032] S4. Calculate the geometric center of the arch bottom surface based on the denoised three-dimensional coordinate data of the arch bottom surface, establish a three-dimensional rectangular coordinate system with the geometric center as the coordinate origin, and convert the denoised three-dimensional coordinate data of the upper and lower edges of the arch side surface into a three-dimensional rectangular coordinate system with the geometric center as the coordinate origin to generate unified three-dimensional coordinate data of the upper and lower edges of the arch side surface.

[0033] Specifically, step S4 includes S41-S43:

[0034] S41. Calculate the mean of the denoised arch bottom surface three-dimensional coordinate data and use it as the geometric center of the arch bottom surface.

[0035] S42. With the horizontal direction of the railway stone arch bridge as the x-axis, the vertical direction as the y-axis, and the vertical direction of the arch bottom as the z-axis, a three-dimensional rectangular coordinate system is established with the geometric center as the coordinate origin.

[0036] S43, by calculating the reflection transformation matrix, converting the denoised three-dimensional coordinate data of the upper and lower edges of the arch side surface into a three-dimensional rectangular coordinate system with the geometric center as the coordinate origin, to generate unified coordinate three-dimensional coordinate data of the upper and lower edges of the arch side surface, specifically:

[0037] Obtain the denoised 3D coordinate data of the upper edge of the arch side or the lower edge of the arch side, and generate the translation matrix by the translation vectors in the x-axis, y-axis, and z-axis directions, namely:

[0038]

[0039] in, Represents the translation vector in the x-axis, y-axis, and z-axis directions 、 、 The translation matrix of .

[0040] Obtain the denoised 3D coordinate data of the upper edge of the arch side or the lower edge of the arch side, and generate the rotation matrix by the rotation angles around the x-axis, y-axis, and z-axis, namely:

[0041]

[0042] in, 、 、 Represents the rotation angles around the x-axis, y-axis, and z-axis respectively 、 、 The rotation matrix of 、 、 、 、 、 are intermediate variables. represents the cosine function, Represents the sine function.

[0043] Calculate the reflection transformation matrix based on the translation matrix and rotation matrix ,Right now:

[0044] .

[0045] Assume that the denoised 3D coordinate data of the upper edge of the arch side or the lower edge of the arch side is , and convert it to homogeneous coordinates , is the transpose operation.

[0046] Based on the reflection transformation matrix and homogeneous coordinates, calculate the transformed homogeneous coordinates ,Right now:

[0047] ;

[0048] Finally, take the transformed homogeneous coordinates The first three dimensions are obtained to obtain the three-dimensional coordinate data of the upper and lower edges of the arch side with unified coordinates.

[0049] In this embodiment, the reflection transformation matrix is ​​a 4×4 homogeneous coordinate matrix, which is used to describe operations such as translation and rotation in coordinate transformation. Therefore, the reflection transformation matrix is ​​used to convert the denoised three-dimensional coordinate data of the upper and lower edges of the arch side surface into a three-dimensional rectangular coordinate system with the geometric center as the coordinate origin, which is not only convenient but also fast to calculate.

[0050] S5. According to the type of railway stone arch bridge, select the curve equation corresponding to the railway stone arch bridge.

[0051] Specifically, the railway stone arch bridge type in step S5 includes a circular arch bridge and a parabolic arch bridge.

[0052] In the embodiment, a suitable curve equation can accurately describe the shape of the arch ring of the railway stone arch bridge; whether it is a circular arch bridge or a parabolic arch bridge, the arch ring shape is complex and has a specific geometric rule, and the corresponding curve equation can express this rule in mathematical language, providing a basis for subsequent arch axis fitting, structure analysis and the like; therefore, the present application considers that the railway stone arch bridge includes various types, such as a circular arch bridge, a parabolic arch bridge and the like, thereby improving the accuracy of subsequent parameter fitting of the arch bottom surface three-dimensional coordinate data, the arch side surface upper and lower edge three-dimensional coordinate data and the arch side surface upper and lower edge curve equation.

[0053] S6, based on the curve equation corresponding to the railway stone arch bridge, using the least square method to perform parameter fitting on the arch side surface upper edge three-dimensional coordinate data of the unified coordinate, to generate the arch axis of the railway stone arch bridge.

[0054] Specifically, step S6 specifically includes S61-S65:

[0055] S61, the curve equation corresponding to the railway stone arch bridge is , , respectively represent independent variables in a three-dimensional rectangular coordinate system, that is, the horizontal coordinate, the vertical coordinate and the point, represent dependent variables, that is, the vertical coordinates of the corresponding points, represent parameters to be fitted.

[0056] In the embodiment, since the curve equations corresponding to different types of railway stone arch bridges are different, the curve equation corresponding to the railway stone arch bridge is simplified here, that is, defined as ; for example, when the railway stone arch bridge is a parabolic arch bridge, the curve equation corresponding to the railway stone arch bridge is a quadratic curve equation, and its general form is , , , , , respectively are parameters to be fitted, that is, the corresponding , and , , , correspond to , , correspond to ; for example, when the railway stone arch bridge is a circular arch bridge, the curve equation corresponding to the railway stone arch bridge is , , , , are the parameters to be fitted (i.e., center coordinates and radius), which correspond to ,and 、 、 They are the independent variables (horizontal coordinate, vertical coordinate, and vertical coordinate) in the three-dimensional rectangular coordinate system, that is, they correspond to 、 、 Therefore, in practical applications, the equation can be deformed or simplified according to specific circumstances. For example, if the projection center and radius of the circular arch bridge in a certain plane (such as the xy plane) are known, the equation form can be further determined for operations such as curve fitting. That is, it can also be applied to two dimensions, and only projection and conversion to a two-dimensional rectangular coordinate system are required.

[0057] S62. Assume that the three-dimensional coordinate data of the upper edge of the arch side surface of the unified coordinate is , the three-dimensional coordinate data of the lower edge of the arch side with unified coordinates is , 、 、 They represent the upper edge of the arch side with unified coordinates. The three-dimensional coordinates of the points, 、 、 They represent the lower edge of the arch side with unified coordinates. The three-dimensional coordinates of the points, Indicates the total number of data points on the upper edge of the arch side after unified coordinates, Represents the total number of data points on the lower edge of the arch side with unified coordinates.

[0058] S63. Use the unified coordinate three-dimensional coordinate data of the upper and lower edges of the arch side surface as the input of the least square method, and construct a minimization objective function, namely:

[0059]

[0060] in, Indicates taking the minimum value, represents the objective function.

[0061] S64, minimizing the objective function with respect to the parameters to be fitted After finding the partial derivative and setting it to 0, the optimal parameters to be fitted are obtained by solving it.

[0062] S65. Substitute the optimal parameters to be fitted into the curve equation corresponding to the railway stone arch bridge to generate the arch axis of the railway stone arch bridge.

[0063] In this embodiment, if the railway stone arch bridge type is a parabolic arch bridge, the corresponding curve equation of the railway stone arch bridge is selected as a quadratic curve equation, i.e., taking the quadratic curve equation as an example, the effectiveness of the method is verified, and specifically:

[0064] Let the general equation of the quadratic curve equation be ;

[0065] Then, the three-dimensional coordinate data coordinates of the uniform coordinates on the upper edge of the arch side are taken as the input of the least square method, and a minimization objective function is constructed, i.e.:

[0066]

[0067] The objective function represents the average error of the fitting curve and the upper and lower edge data points in the direction, so by minimizing the objective function, the best fitting curve can be determined; at the same time, when the objective function is minimized, the partial derivatives of the objective function with respect to the parameters , , , , are solved, and the partial derivatives are set to 0, then a five-element linear equation group can be established; for example, for the parameter , there is:

[0068]

[0069] By solving the equation, the optimal parameter can be obtained, and similarly, the optimal parameters , , , can be obtained, so that the optimal , , , , is substituted into the original equation , and the arch axis of the railway stone arch bridge is obtained; similarly, if it is other types of railway stone arch bridges, the operation method is the same, only the corresponding curve equation needs to be substituted.

[0070] In summary, the arch axis fitting method of the railway stone arch bridge provided by the present application firstly proposes a multi-source data acquisition method combining a total station and a three-dimensional laser scanner, accurately arranges the position of the instrument and collects data according to the specification, records the instrument parameters and environmental information, and provides rich information for subsequent data processing. Compared with the traditional single data acquisition method, the railway stone arch bridge structure data can be more comprehensively and accurately obtained. Secondly, the statistical filtering method is used for denoising to eliminate noise interference in the collected data, so that the three-dimensional coordinate data of the upper and lower edges of the arch bottom surface and the arch side surface is more accurate, and the reliability of subsequent calculation and analysis is ensured to improve the accuracy of the fitted arch axis. Then, a three-dimensional rectangular coordinate system is established with the geometric center of the arch bottom surface as the origin, and the coordinates are converted to make the data of different parts under the unified space reference, which is convenient for subsequent analysis and calculation based on the overall structure. Finally, according to the type of the railway stone arch bridge, the corresponding curve equation is selected, the three-dimensional coordinate data of the upper and lower edges of the arch side surface is fitted by the least square method, the actual geometric characteristics of the structure are fully considered, the influence of data error is effectively reduced, the arch axis is accurately determined, and the shape of the arch ring of the railway stone arch bridge is accurately reflected, thereby providing key basis for evaluating the safety of the structure, analyzing the diseases and carrying out maintenance and reinforcement (that is, the accurate arch axis fitting result provides a reliable basis for the safety evaluation of the railway stone arch bridge. By combining the analysis of the structure parameters, potential problems of the bridge structure such as deformation and stress concentration can be found in time to ensure the safety of railway transportation). In addition, the present application is suitable for railway stone arch bridges of different types and under different working conditions. Whether it is a circular arch bridge or a parabolic arch bridge, high-precision arch axis fitting can be realized by adjusting the curve equation and fitting parameters, which has strong universality and adaptability. Not only the arch axis information can be obtained, but also the structure parameters of each section of the bridge such as the cross-sectional height and the arch ring thickness can be calculated through the fitted arch bottom surface equation and the upper and lower edge equations of the arch side, thereby providing rich data support for the comprehensive detection of the bridge structure.

[0071] The principles and implementation manners of the present application are described in the specific embodiments in the present application, and the above embodiment descriptions are only used to help understand the method of the present application and its core idea; meanwhile, for those skilled in the art, according to the idea of the present application, the specific implementation manners and application ranges can be changed, and the above descriptions should not be understood as limitations of the present application.

[0072] Those skilled in the art will appreciate that the embodiments described herein are presented for the purpose of understanding the principles of the present application and should be understood as not limiting the protection scope of the present application. Those skilled in the art can make various other specific modifications and combinations according to the technical inspirations disclosed in the present application without departing from the essence of the present application, and these modifications and combinations are still within the protection scope of the present application.

Claims

1. A method for fitting the arch axis of a railway stone arch bridge, characterized by: S1. Setting a number of measuring points on the arch bottom surface and collecting the three-dimensional coordinates of each measuring point on the arch bottom surface; dividing the arch bottom surface into a number of measuring points according to the predicted spacing, and collecting the three-dimensional coordinates of each measuring point on the arch bottom surface by deploying high-precision total stations; The three-dimensional coordinates of each measuring point on the arch bottom are , 、 、 Represent the arch bottom No. measuring points 、 、 Axis coordinates, Indicates the total number of measuring points on the arch bottom surface; S2, collecting the three-dimensional coordinates of each measuring point on the upper edge and lower edge of the arch side surface; setting a number of measuring points on the upper edge and lower edge of the arch side surface, and collecting the three-dimensional coordinates of each measuring point on the upper edge of the arch side surface and the three-dimensional coordinates of each measuring point on the lower edge of the arch side surface by deploying a three-dimensional laser scanner; Take the left or right arch side surface, divide a number of measuring points at the upper edge and lower edge of the arch side surface according to preset distances, and deploy a three-dimensional laser scanner to collect the three-dimensional coordinates of each measuring point on the upper edge of the arch side surface and the three-dimensional coordinates of each measuring point on the lower edge of the arch side surface; The three-dimensional coordinates of each measuring point on the upper edge of the arch side are , 、 、 Respectively represent the side of the arch No. measuring points 、 、 Axis coordinates, Indicates the total number of points on the upper edge of the arch side; The three-dimensional coordinates of each measuring point on the lower edge of the arch side are , 、 、 Indicates the arch side measuring points 、 、 Axis coordinates, Indicates the side of the arch The total number of points on the lower edge; S3, using statistical filtering method to perform denoising on the three-dimensional coordinates of each measuring point on the arch bottom surface, the upper edge mark of the arch side surface, and the lower edge of the arch side surface, to generate denoised three-dimensional coordinate data of the arch bottom surface and the upper and lower edges of the arch side surface; calculating the mean and standard deviation of the three-dimensional coordinates of each measuring point on the arch bottom surface, the three-dimensional coordinates of each measuring point on the upper edge of the arch side surface, and the three-dimensional coordinates of each measuring point on the lower edge of the arch side surface, and setting a filtering threshold, and the filtering threshold is times the standard deviation, centered around the mean, times the standard deviation is the radius, which will deviate from the mean by more than Eliminate all measurement points with a value greater than or equal to the standard deviation; S4. Calculate the geometric center of the arch bottom surface based on the denoised three-dimensional coordinate data of the arch bottom surface, establish a three-dimensional rectangular coordinate system with the geometric center as the coordinate origin, convert the denoised three-dimensional coordinate data of the upper and lower edges of the arch side surface into the three-dimensional rectangular coordinate system with the geometric center as the coordinate origin, and generate unified coordinate three-dimensional coordinate data of the upper and lower edges of the arch side surface; S5. Select the curve equation corresponding to the railway stone arch bridge according to the type of the railway stone arch bridge; S6. Based on the curve equation corresponding to the railway stone arch bridge, the least squares method is used to perform parameter fitting on the three-dimensional coordinate data of the upper and lower edges of the arch side surface with unified coordinates to generate the arch axis of the railway stone arch bridge.

2. The arch axis fitting method of a railway stone arch bridge according to claim 1, characterized in that: Step S4 specifically includes: S41, calculating the mean of the denoised arch bottom surface three-dimensional coordinate data, and using the mean as the geometric center of the arch bottom surface; S42, establishing a three-dimensional rectangular coordinate system with the geometric center as the coordinate origin, with the horizontal direction of the railway stone arch bridge as the x-axis, the vertical direction as the y-axis, and the vertical direction of the arch bottom as the z-axis; S43, by calculating the reflection transformation matrix , the denoised three-dimensional coordinate data of the upper and lower edges of the arch side surface are converted into a three-dimensional rectangular coordinate system with the geometric center as the coordinate origin, and the three-dimensional coordinate data of the upper and lower edges of the arch side surface with unified coordinates are generated.

3. The arch axis fitting method of a railway stone arch bridge according to claim 2, characterized in that: Step S43 specifically includes: Obtain the denoised 3D coordinate data of the upper edge of the arch side or the lower edge of the arch side, and generate the translation matrix by the translation vectors in the x-axis, y-axis, and z-axis directions, namely: ； in, Represents the translation vector in the x-axis, y-axis, and z-axis directions 、 、 The translation matrix of Obtain the denoised 3D coordinate data of the upper edge of the arch side or the lower edge of the arch side, and generate the rotation matrix by the rotation angles around the x-axis, y-axis, and z-axis, namely: ； in, 、 、 Represents the rotation angles around the x-axis, y-axis, and z-axis respectively 、 、 The rotation matrix of 、 、 、 、 、 are intermediate variables. represents the cosine function, represents the sine function; Calculate the reflection transformation matrix based on the translation matrix and rotation matrix ,Right now: ； Assume that the denoised 3D coordinate data of the upper edge of the arch side or the lower edge of the arch side is , and convert it to homogeneous coordinates , is the transpose operation; Based on the reflection transformation matrix With homogeneous coordinates, calculate the transformed homogeneous coordinates ,Right now: ； Finally, take the transformed homogeneous coordinates The first three dimensions are obtained to obtain the three-dimensional coordinate data of the upper and lower edges of the arch side with unified coordinates.

4. The arch axis fitting method of a railway stone arch bridge according to claim 3, characterized in that: In step S5, the types of railway stone arch bridges include but are not limited to circular arch bridges, parabolic arch bridges and catenary arch bridges, and the curve equation is adjusted to adapt to different bridge types.

5. The arch axis fitting method of a railway stone arch bridge according to claim 4, characterized in that: Step S6 specifically includes: S61. Assume that the curve equation corresponding to the railway stone arch bridge is , 、 Respectively represent the independent variables in the three-dimensional rectangular coordinate system, that is, the horizontal coordinate and vertical coordinate of the point, represents the dependent variable, that is, the vertical coordinate of the corresponding point, represents the parameters to be fitted; S62. Assume that the three-dimensional coordinate data of the upper edge of the arch side surface of the unified coordinate is , the three-dimensional coordinate data of the lower edge of the arch side with unified coordinates is , 、 、 They represent the upper edge of the arch side with unified coordinates. The three-dimensional coordinates of the points, 、 、 They represent the lower edge of the arch side with unified coordinates. The three-dimensional coordinates of the points, Indicates the total number of data points on the upper edge of the arch side after unified coordinates, Indicates the total number of data points on the lower edge of the arch side in unified coordinates; S63. Use the unified coordinate three-dimensional coordinate data of the upper and lower edges of the arch side surface as the input of the least square method, and construct a minimization objective function, namely: ； in, Indicates taking the minimum value, represents the objective function; S64, minimizing the objective function with respect to the parameters to be fitted After finding the partial derivative and setting it to 0, the optimal parameters to be fitted are obtained by solving it; S65. Substitute the optimal parameters to be fitted into the curve equation corresponding to the railway stone arch bridge to generate the arch axis of the railway stone arch bridge.

6. A non-volatile storage medium, characterized in that: The non-volatile storage medium includes a stored program, wherein when the program is executed, the device where the non-volatile storage medium is located is controlled to execute the method according to any one of claims 1 to 5.

7. A terminal device, characterized in that: The terminal device includes: a processor, a memory, a communication interface and a bus; the processor, the memory and the communication interface are connected through the bus and communicate with each other; the memory stores executable program code; the processor runs a program corresponding to the executable program code by reading the executable program code stored in the memory, so as to execute the method as described in any one of claims 1 to 5 above.

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