A spatial sphere node measurement method, system and structure stress evaluation method

Abstract

The application discloses a kind of space spherical node determination method, system and structure stress evaluation method, by establishing good space measurement control network to carry out space spherical node measurement positioning, to obtain multiple spherical coordinates, according to multiple spherical coordinates indirect adjustment error equation set is established, and the spherical center coordinates and spherical radius of space spherical node are solved to obtain, the fitting accuracy of spherical center coordinates and spherical radius is calculated and iterative optimization is carried out, to finally obtain optimized spherical center coordinates and optimized spherical radius, to realize high-precision positioning to space spherical node. Meanwhile, the optimized spherical center coordinates are converted into the coordinates under target coordinates, to facilitate subsequent structural deformation evaluation to space spherical node. For the space measurement control network established, the total station equipment used is simple and easy to operate, while reducing the requirements for measurement personnel and equipment, the space spherical node determination method of the embodiment of the application also improves the measurement efficiency, realizes contactless measurement positioning.

Description

Technical Field

[0001] This invention relates to the field of surveying and mapping technology, and in particular to a method, system, and structural stress assessment method for determining the nodes of a space sphere. Background Technology

[0002] Large-span spatial structures, with their aesthetic appeal, magnificent architecture, and spaciousness, are widely used in modern civil engineering structures and have become an important indicator of a country's construction industry development level. However, large-span spatial grid structures undergo significant deformation with increasing service life, leading to performance degradation, reduced safety, and decreased durability. Specifically, bolted or welded spheres, as key nodes, connect converging members and transfer loads. They also serve as critical positioning control points in the entire grid measurement system; their spatial displacement directly causes uneven distribution of internal forces, resulting in buckling of localized compression members and failure of tension members leading to force redistribution, ultimately causing overall failure. Therefore, measuring the deformation of existing spatial structures requires first measuring the coordinates of each node and comparing them with the coordinates at the time of design and initial construction to obtain the node deformation, and then conducting a stress assessment of the entire large-span spatial structure.

[0003] Current methods for spatial node positioning measurements include: the cup-and-loop method, the plumb line method, the laser scanning method, and the prism-free method. Among these, the cup-and-loop method and the plumb line method are contact measurements, requiring specialized external tools or devices and involving high-altitude work, making accuracy difficult to guarantee; they are only suitable for simple spatial sphere positioning measurements. Laser scanning and photogrammetry are more advanced, but these methods also have drawbacks at present: they require specialized imaging measurement equipment, the measurement process is complex, the establishment of a digital model of the target is complex, and the measurement cycle is long, making them unsuitable for real-time rapid measurements. The prism-free method can maximize the advantages of a prism-free total station, avoiding high-altitude work, reducing workload, and improving the degree of automation in measurement; however, the fitting solution of the sphere's center coordinates is crucial, directly affecting the accuracy of coordinate positioning.

[0004] Therefore, existing spatial node positioning and measurement technologies struggle to accurately determine the spatial positions of bolted balls, welded balls, and steel pipe truss nodes when dealing with large-span structural spherical nodes in complex shapes and environments. Summary of the Invention

[0005] This invention aims to at least solve one of the technical problems existing in the prior art. To this end, this invention proposes a method for determining the spatial location of a sphere node, solving the problem of the difficulty in accurately determining the spatial position of a sphere node in the prior art.

[0006] The present invention also provides a space sphere node measurement system, a method for evaluating the stress on a space sphere node structure, and a computer-readable storage medium.

[0007] A method for determining the nodes of a spatial sphere according to a first aspect of the present invention, the method comprising the following steps:

[0008] Multiple spherical coordinates of a spatial spherical node are obtained, and the multiple spherical coordinates are obtained by measuring and locating the spatial spherical node using a pre-established spatial measurement and control network;

[0009] An indirect adjustment error equation system is established based on multiple spherical coordinates, wherein the parameters to be solved in the indirect adjustment error equation system include at least the center coordinates of the spatial sphere nodes.

[0010] Based on the least squares principle, the indirect adjustment error equations are adjusted to obtain at least the center coordinates of the spatial sphere nodes.

[0011] The fitting accuracy is calculated based on the center coordinates of the spatial sphere nodes, and optimization is performed based on the fitting accuracy to output the optimized center coordinates of the spatial sphere nodes.

[0012] Based on the Euler coordinate transformation principle, the optimized sphere center coordinates are transformed to obtain the target sphere center coordinates in the target coordinate system.

[0013] The spatial sphere node determination method according to embodiments of the present invention has at least the following beneficial effects:

[0014] By establishing a spatial measurement control network for the measurement and positioning of spatial spherical nodes, multiple spherical coordinates are obtained. Based on these coordinates, an indirect adjustment error equation system is established, and the coordinates of the sphere's center and radius are solved to obtain the sphere's center coordinates and radius. The fitting accuracy of the sphere's center coordinates and radius is calculated and iteratively optimized to ultimately obtain optimized sphere's center coordinates and radius, thus achieving high-precision positioning of the spatial spherical nodes. Simultaneously, the optimized sphere's center coordinates are converted to coordinates in the target coordinate system of the construction design, facilitating subsequent structural deformation assessment of the spatial spherical nodes. The established spatial measurement control network utilizes a simple and easy-to-operate total station, reducing the requirements for surveyors and equipment. Furthermore, the spatial spherical node determination method of this invention improves measurement efficiency and achieves non-contact measurement and positioning.

[0015] According to some embodiments of the present invention, before establishing the indirect adjustment error equation system based on the plurality of spherical coordinates, the spatial sphere node determination method further includes the following steps:

[0016] When the radius of the sphere of the spatial sphere node is known, a first screening is performed on multiple spherical coordinates based on the sphere radius to obtain multiple first optimized spherical coordinates, and the indirect adjustment error equation set is established based on the multiple first optimized spherical coordinates.

[0017] According to some embodiments of the present invention, the first filtering of a plurality of spherical coordinates based on the radius of the sphere to obtain a plurality of first optimized spherical coordinates includes the following steps:

[0018] For multiple spherical coordinates, calculate the distance between any two different spherical coordinates to obtain multiple distance data;

[0019] The distance data is compared with the radius of the sphere to determine the coordinates of the abnormal spherical surface.

[0020] The abnormal spherical coordinates are removed to obtain multiple first optimized spherical coordinates.

[0021] According to some embodiments of the present invention, the optimization process based on the fitting accuracy to output at least the optimized center coordinates of the spatial sphere nodes includes the following steps:

[0022] If the fitting accuracy does not meet the preset fitting accuracy requirements, a second screening is performed on the multiple spherical coordinates based on the fitting accuracy to obtain multiple second optimized spherical coordinates;

[0023] Based on multiple second optimized spherical coordinates, the indirect adjustment error equation system is re-established and adjustment calculations are performed to update the center coordinates and radius of the spatial sphere nodes, thereby updating the fitting accuracy.

[0024] If the updated fitting accuracy meets the preset fitting accuracy requirements, the optimized center coordinates and optimized radius of the spatial sphere node will be output in the end.

[0025] According to some embodiments of the present invention, establishing a system of indirect adjustment error equations based on a plurality of spherical coordinates includes the following steps:

[0026] Based on the sphere center coordinate parameter, the sphere radius parameter, and multiple spherical coordinates, multiple corresponding spherical equations are established. The sphere center coordinate parameter represents the sphere center coordinates to be solved, and the sphere radius parameter represents the sphere radius to be solved.

[0027] Based on the indirect adjustment mathematical model, and according to the preset approximate values ​​of the sphere center coordinates, the preset approximate values ​​of the sphere radius, the sphere center coordinate correction parameter, the sphere radius correction parameter, and multiple spherical equations, multiple adjustment equations are established with the fitted radius difference as the observed value. The sphere center coordinate correction parameter represents the adjustment correction value of the sphere center coordinate parameter, and the sphere radius correction parameter represents the adjustment correction value of the sphere radius parameter.

[0028] Based on the Taylor series expansion principle, and according to the multiple adjustment equations, multiple error equations are obtained, and the multiple error equations are used to form the indirect adjustment error equation set.

[0029] According to some embodiments of the present invention, the adjustment calculation of the indirect adjustment error equation system based on the least squares principle to obtain at least the center coordinates of the spatial sphere nodes includes the following steps:

[0030] Based on the least squares criterion and the principle of indirect adjustment, the indirect adjustment error equations are solved to obtain the correction values ​​for the center coordinates and the radius of the sphere.

[0031] Based on the sphere center coordinate correction value, the sphere radius correction value, the sphere center coordinate approximation value, and the sphere radius approximation value, an iterative formula is constructed to update the sphere center coordinate approximation value and the new sphere radius approximation value;

[0032] Based on the updated approximate values ​​of the sphere's center coordinates, the updated approximate values ​​of the sphere's radius, the sphere's center coordinate correction parameter, the sphere's radius correction parameter, and multiple spherical equations, multiple new adjustment equations are established to form a new set of indirect adjustment error equations. The new set of indirect adjustment error equations is then solved to obtain new sphere's center coordinate correction values ​​and new sphere's radius correction values.

[0033] When the correction values ​​for the center coordinates and the radius of the sphere are both less than preset thresholds, the center coordinates and radius of the spatial sphere node are output.

[0034] According to some embodiments of the present invention, the step of calculating the corresponding fitting accuracy based at least on the center coordinates of the spatial sphere nodes includes the following steps:

[0035] Based on the coordinates of the center of the sphere, the radius of the sphere, and the coordinates of each sphere, the roundness value of each sphere is calculated.

[0036] Based on the roundness values ​​of multiple spherical coordinates, the radius mean square error of the sphere radius is calculated, and the radius mean square error represents the fitting accuracy of the sphere radius;

[0037] Based on the principle of indirect adjustment, the positional error of the sphere's center coordinates is calculated, and the positional error represents the fitting accuracy of the sphere's center coordinates.

[0038] According to a second aspect of the present invention, a method system for determining the nodes of a spatial sphere is provided, the system comprising:

[0039] The spherical coordinate acquisition unit is used to acquire multiple spherical coordinates of a spatial spherical node. The multiple spherical coordinates are obtained by measuring and locating the spatial spherical node using a pre-established spatial measurement and control network.

[0040] An error equation establishment unit is used to establish an indirect adjustment error equation system based on multiple spherical coordinates, wherein the parameters to be solved in the indirect adjustment error equation system include at least the center coordinates of the spatial sphere nodes.

[0041] The error equation solving unit is used to perform adjustment calculations on the indirect adjustment error equation system based on the least squares principle, so as to obtain at least the center coordinates of the spatial sphere nodes.

[0042] The fitting accuracy calculation and optimization unit is used to calculate the corresponding fitting accuracy based at least on the center coordinates of the spatial sphere nodes, and to perform optimization processing based on the fitting accuracy, so as to output at least the optimized center coordinates of the spatial sphere nodes.

[0043] The coordinate transformation unit is used to transform the optimized sphere center coordinates based on the Euler coordinate transformation principle to obtain the target sphere center coordinates in the target coordinate system.

[0044] The spatial sphere node determination method system according to embodiments of the present invention has at least the following beneficial effects:

[0045] By utilizing a spherical coordinate acquisition unit, the spatial spherical nodes of the established spatial measurement control network are measured and located to obtain multiple spherical coordinates. An error equation establishment unit is then used to establish an indirect adjustment error equation system based on these multiple spherical coordinates. The error equation solution unit solves for the center coordinates and radius of the spatial spherical nodes. A fitting accuracy calculation and optimization unit calculates the fitting accuracy of the center coordinates and radius and iteratively optimizes them to obtain optimized center coordinates and radius, thus achieving high-precision positioning of the spatial spherical nodes. Simultaneously, a coordinate transformation unit converts the optimized center coordinates to coordinates in the target coordinate system of the construction design, facilitating subsequent structural deformation assessment of the spatial spherical nodes. The established spatial measurement control network utilizes a simple and easy-to-operate total station, reducing the requirements for surveyors and equipment. Furthermore, the spatial spherical node determination method of this invention improves measurement efficiency and achieves non-contact measurement and positioning.

[0046] A method for evaluating the stress on a spatial spherical node structure according to a third aspect of the present invention includes the following steps:

[0047] Perform the spatial sphere node determination method as described in any of the embodiments of the first aspect of the present invention to obtain the target sphere center coordinates in the target coordinate system;

[0048] The coordinates of the target sphere center are compared with the initial construction design coordinates to obtain the deformation of the spatial sphere node;

[0049] The stress on the spatial sphere node structure is evaluated based on the deformation of the multiple spatial sphere nodes, and the spatial sphere node structure is composed of multiple spatial sphere nodes.

[0050] The stress assessment method for a spatial spherical node structure according to embodiments of the present invention has at least the following beneficial effects:

[0051] After high-precision positioning of the spatial spherical nodes, deformation assessment and stress performance analysis of large-span spatial structures formed by multiple spatial spherical nodes can be further realized. Therefore, the stress assessment method for spatial spherical node structures in this invention can further improve engineering practicality, solve the problems of damage and serious displacement of the original measurement control network in large-span old renovation structures, realize non-destructive testing of key nodes such as non-contact measurement of spatial structure deformation, and can be widely applied to the positioning measurement of welded spheres and bolted spheres in large-span spatial structures, which is conducive to accelerating the assembly construction, deformation assessment, reinforcement and renovation of actual projects.

[0052] According to a fourth aspect of the present invention, a computer-readable storage medium stores computer-executable instructions for performing a spatial sphere node determination method as described in the first aspect of the present invention or a spatial sphere node structure stress assessment method as described in the third aspect of the present invention.

[0053] It is understood that the beneficial effects of the fourth aspect compared with the related technologies are the same as the beneficial effects of the first aspect compared with the related technologies. Please refer to the relevant description in the first aspect above, which will not be repeated here.

[0054] Other features and advantages of the invention will be set forth in the description which follows, and will be apparent in part from the description, or may be learned by practicing the invention. Attached Figure Description

[0055] The above and / or additional aspects and advantages of the present invention will become apparent and readily understood from the description of the embodiments taken in conjunction with the following drawings, in which:

[0056] Figure 1 This is a flowchart of a method for determining the nodes of a spatial sphere according to an embodiment of the present invention;

[0057] Figure 2 This is a structural diagram of a space measurement and control network according to an embodiment of the present invention;

[0058] Figure 3 This is a structural diagram of a spatial sphere node according to an embodiment of the present invention;

[0059] Figure 4 This is a schematic diagram illustrating the implementation of spatial sphere node measurement and positioning according to an embodiment of the present invention;

[0060] Figure 5 This is a structural diagram of a spatial sphere node determination method system according to an embodiment of the present invention;

[0061] Figure 6 This is a flowchart of a method for evaluating the stress on a spatial sphere node structure according to an embodiment of the present invention;

[0062] Figure 7a This is a structural diagram of a gymnasium according to an embodiment of the present invention;

[0063] Figure 7b This is a structural diagram of a key node of a gymnasium according to an embodiment of the present invention;

[0064] Figure 8a This is a structural diagram of a thermal power plant roof grid structure according to an embodiment of the present invention;

[0065] Figure 8b This is a structural diagram of a key node of the roof grid structure of a thermal power plant according to an embodiment of the present invention.

[0066] Figure label:

[0067] Spherical coordinate acquisition unit 100;

[0068] Error equation establishment unit 200;

[0069] Error equation solution unit 300;

[0070] Fitting accuracy calculation optimization unit 400;

[0071] Coordinate transformation unit 500. Detailed Implementation

[0072] Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings, wherein the same or similar reference numerals characterize the same or similar elements or elements having the same or similar functions throughout. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, and should not be construed as limiting the present invention.

[0073] In the description of this invention, the use of terms such as "first," "second," etc., is for the purpose of distinguishing technical features only and should not be construed as indicating or implying relative importance, or implicitly indicating the number of technical features indicated, or implicitly indicating the order of the technical features indicated.

[0074] In the description of this invention, it should be understood that the orientation descriptions, such as up, down, etc., are based on the orientation or positional relationship shown in the drawings and are only for the convenience of describing this invention and simplifying the description, and are not intended to indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation, and therefore should not be construed as a limitation of this invention.

[0075] In the description of this invention, it should be noted that, unless otherwise explicitly defined, terms such as "setting," "installation," and "connection" should be interpreted broadly, and those skilled in the art can reasonably determine the specific meaning of the above terms in this invention in conjunction with the specific content of the technical solution.

[0076] The technical solution of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the embodiments described below are some embodiments of the present invention, not all embodiments.

[0077] It should be noted that, due to the small construction area, severe obstruction, or difficulty in finding the original control network in some urban renewal projects, it is necessary to establish a new control network for the current measurement work. The control network layout mainly considers the local requirements for the measurement and positioning of spherical nodes in large-span spatial structures, namely, relative accuracy. According to the overall plan, it should be set in the internal space of the structure, and the location should be selected with a wide field of view, firm points, and moderate height.

[0078] New control points are determined by affixing reflective sheets, burying small prisms, or making specific measurement markers. Based on the known measurement reference points, the distances and angles between each control point are determined using traverse surveying. The horizontal angle, zenith angle, and side length observation techniques should meet the accuracy requirements of the first-level network. Then, the coordinates of each control point in space are calculated using adjustment software. After verification using polar coordinates, the system can be put into use.

[0079] To avoid damaging the newly established control network, control points can be placed in relatively stable locations on the building, such as high structural columns or near steel structure supports. This not only protects the points but also prevents them from being obstructed, facilitating non-contact measurement and positioning of subsequent large-span spatial structural node displacements. By meeting the above requirements and standards, the necessary spatial measurement control network can be established in advance.

[0080] See Figure 1 The diagram shown is a flowchart of a method for determining the nodes of a spatial sphere according to an embodiment of the present invention. This method includes, but is not limited to, the following steps:

[0081] The coordinates of multiple spherical surfaces of the spatial spherical node are obtained by measuring and locating the spatial spherical node using a pre-established spatial measurement and control network.

[0082] It should be noted that after the spatial measurement control network is established, a free-station method is used to perform non-contact measurement and positioning of the spherical nodes of the large-span structure. For details on using a total station for free-station setup, please refer to [link / reference needed]. Figure 2 After successively measuring the distance and angle from the observation station P to the known control points A, B, and C, the instrument will automatically calculate the coordinates of station P. The accuracy of the calculation can be improved by increasing the number of measurements and shortening the measurement distance. Furthermore, the accuracy of measuring detailed points using the free station method can meet the requirements.

[0083] Continue to refer to Figure 3 and Figure 4 The three-dimensional coordinates of a certain number of points on the surface of a welded sphere or bolted sphere in a large-span structure are collected using a prism-free measurement method with a total station or laser tracker. If the radius of the sphere is known, at least 3 three-dimensional coordinate values ​​of 3 points on the sphere surface should be collected; if the radius of the sphere is unknown, at least 4 three-dimensional coordinate values ​​of 4 points on the sphere surface should be collected. When the diameter of the sphere is less than 15cm and the measurement conditions are good, collecting 5 to 8 points is a suitable number; when the diameter is larger and the line of sight is poor, the number of points should be increased appropriately. Generally, the more points collected, the closer the result of the sphere center coordinates will be to the actual value.

[0084] The higher the measurement accuracy of the laser total station, the smaller the error between the obtained coordinates of the sphere's center and the sphere's radius. Its side measurement accuracy should be less than 2mm + 2ppm, and its angle measurement accuracy should be less than 2″. When the sphere's surface is relatively smooth and the weather conditions are average, the maximum distance measurement range should be controlled at around 60m, and should not exceed 200m.

[0085] When the large-span spatial node sphere is smooth, stable, and light-colored, the accuracy of laser prism-free ranging is basically equivalent to that of prism-based ranging. The data acquisition points should be distributed as evenly and completely as possible across the sphere's surface, avoiding locations such as weld seams, paint peeling, or corrosion on the spatial node sphere's edges. The measurement data from each spatial node sphere's coordinate acquisition point should be uniformly named to avoid confusion with coordinate data from other spheres, which could affect subsequent calculations.

[0086] The measurement work also needs to include the three-dimensional coordinates of more than three support spheres or relatively stable spatial node spheres, as common points for the transformation between the original design coordinate system and the existing coordinate system of the large-span spatial structure.

[0087] An indirect adjustment error equation system is established based on multiple spherical coordinates. The parameters to be solved in the indirect adjustment error equation system include at least the coordinates of the center of the spatial sphere nodes.

[0088] Understandably, given multiple spherical coordinates and with the center coordinates and radius of the sphere as unknown parameters, multiple corresponding equations for the spherical surface can be established. Based on the relevant theory of indirect adjustment, a least squares optimization problem is established to minimize the sum of squares of the radius error, i.e., min(∑e 2), and with the fitted radius difference e i Multiple error equations are established for the observations to obtain the indirect adjustment error equation system.

[0089] Based on the least squares principle, the indirect adjustment error equation system is adjusted to obtain at least the coordinates of the center of the spatial sphere node.

[0090] Understandably, adjusting the indirect adjustment error equation system involves iteratively solving the problem using the least squares criterion and the corrections for the sphere's center coordinates and radius as parameters. The iterative solution process involves using the adjusted results of the sphere's center coordinates and radius as approximations to reconstruct multiple error equations, repeating the adjustment calculations iteratively.

[0091] The fitting accuracy is calculated based on the center coordinates of the spatial sphere nodes, and optimization is performed based on the fitting accuracy to output the optimized center coordinates of the spatial sphere nodes.

[0092] Understandably, the fitting accuracy evaluation metrics mainly use roundness value, the positional error of the sphere's center coordinates, and the radius error. When the fitting accuracy is insufficient, the quality of the observation data is checked based on the roundness value of each acquisition point. Acquisition points with large roundness values ​​are discarded, and then the calculation is iterated again until the accuracy requirements are met before the result is output.

[0093] Based on the Euler coordinate transformation principle, the coordinates of the optimized sphere center are transformed to obtain the coordinates of the target sphere center in the target coordinate system.

[0094] It should be noted that since the initial or design coordinate system of most urban renewal projects is inconsistent with the coordinate system of the existing control network, the calculated sphere center coordinates need to be transformed. Then, by comparing these coordinates with the initial construction or design coordinates, the deflection and planar displacement of the existing structure can be obtained. The coordinate system transformation uses the Euler method. Generally, the transformation common point is set as a relatively stable support sphere node. After iteratively calculating the three-dimensional sphere center coordinates of the specified support sphere node, the transformation is performed based on at least three common points in the two coordinate systems. The three angles α, β, and φ of the transformation parameters along the x-axis, y-axis, and z-axis can be calculated. And three offsets ΔX, ΔY, and ΔZ. Other structural nodes in the large-span space undergo coordinate system transformation based on the deflection angles and offsets obtained from the common points. Assuming the 3D data in coordinate system B is transformed to coordinate system A, M is the rotation matrix, and the rotation order is z-axis, y-axis, x-axis. The transformation formula is as follows:

[0095]

[0096] Finally, the positioning coordinates of the spherical nodes of the large-span spatial structure in the target coordinate system are obtained. By measuring the existing node coordinates and comparing them with the original design node spatial three-dimensional coordinates, the deformation of multiple spatial spherical nodes can be obtained, and the next step is to conduct a stress performance analysis of the entire spatial structure.

[0097] In this embodiment, a spatial measurement control network is established to measure and locate spatial spherical nodes, obtaining multiple spherical coordinates. An indirect adjustment error equation system is then established based on these coordinates, and the coordinates of the sphere's center and radius are solved to obtain the sphere's center coordinates and radius. The fitting accuracy of the sphere's center coordinates and radius is calculated and iteratively optimized to ultimately obtain optimized sphere's center coordinates and radius, thus achieving high-precision positioning of the spatial spherical nodes. Simultaneously, the optimized sphere's center coordinates are converted to coordinates in the target coordinate system of the construction design, facilitating subsequent structural deformation assessment of the spatial spherical nodes. The established spatial measurement control network utilizes a simple and easy-to-operate total station, reducing the requirements for surveyors and equipment. Furthermore, the spatial spherical node determination method of this embodiment improves measurement efficiency and achieves non-contact measurement and positioning.

[0098] In some embodiments, before establishing the indirect adjustment error equation system based on multiple spherical coordinates, the spatial sphere node determination method further includes the following steps:

[0099] When the radius of the sphere at the spatial sphere node is known, multiple spherical coordinates are first filtered based on the sphere radius to obtain multiple first optimized spherical coordinates. The indirect adjustment error equation system is established based on the multiple first optimized spherical coordinates.

[0100] Understandably, before establishing the indirect adjustment error equation set, multiple spherical coordinates collected by the laser total station are screened to reduce the error between the sphere center coordinates and the sphere radius obtained by solving the indirect adjustment error equation set.

[0101] In some embodiments, a first filtering of multiple spherical coordinates based on the sphere radius is performed to obtain multiple first optimized spherical coordinates, including the following steps:

[0102] For multiple spherical coordinates, calculate the distance between any two different spherical coordinates to obtain multiple distance data;

[0103] Multiple distance data points are compared with the radius of the sphere to determine the coordinates of the abnormal spherical surface;

[0104] Abnormal spherical coordinates are removed to obtain multiple first-optimized spherical coordinates.

[0105] It should be noted that when the radius of the sphere is known, i.e., the diameter D is known, the spatial distance between two points collected on the same sphere is calculated. If the distance between the two points is greater than the diameter D, but the calculated distance of one point to other measured points is normal, then the other point is considered not to be on the surface of the sphere. That is, if the distance between point i and point k is greater than D and the distance to all other points is less than D, then point k is considered to have a large coordinate deviation and is discarded. The specific selection principle is based on the following mathematical model:

[0106]

[0107]

[0108] (i,j,k∈n and i≠j≠k)

[0109] If the radius of the sphere is unknown, i.e., the diameter D is unknown, then the steps of this embodiment are skipped. That is, the radius of the sphere is taken as the parameter to be solved and obtained by solving the indirect adjustment error equation system.

[0110] In some embodiments, optimization is performed based on the fitting accuracy to output at least the optimized center coordinates of the spatial sphere nodes, including the following steps:

[0111] If the fitting accuracy does not meet the preset fitting accuracy requirements, a second screening is performed on multiple spherical coordinates based on the fitting accuracy to obtain multiple second optimized spherical coordinates;

[0112] Based on multiple second-optimized spherical coordinates, the indirect adjustment error equation system is re-established and adjustment calculations are performed to update the center coordinates and radius of the spatial sphere nodes, thereby updating the fitting accuracy.

[0113] If the updated fitting accuracy meets the preset fitting accuracy requirements, the final output will be the optimized center coordinates and optimized radius of the spatial sphere nodes.

[0114] Specifically, when the fitting accuracy is insufficient, the quality of the observation data is checked based on the roundness value of each acquisition point. Acquisition points with larger roundness values ​​are removed a second time, and then the calculation is iterated again until the accuracy requirements are met before outputting the result. Generally, under conditions of minimal observation interference and good target object quality, the roundness value, the mean square error of the sphere center point, and the mean square error of the radius are comparable in magnitude to the instrument's nominal accuracy, and the fitting accuracy limit can be set according to actual needs. The mean square error of the fitted sphere center point is calculated from the cofactor matrix of the post-adjustment unit weight mean square error σ0 and the unknown parameter x. The calculated mean square error of the sphere fitting radius is the average of the sum of the squares of the roundness values ​​of all collected points, which avoids the influence of the number of collected sample points n.

[0115] In some embodiments, establishing a system of indirect adjustment error equations based on multiple spherical coordinates includes the following steps:

[0116] Based on the sphere center coordinate parameter, the sphere radius parameter, and multiple spherical coordinates, establish multiple corresponding spherical equations. The sphere center coordinate parameter represents the coordinates of the sphere center to be solved, and the sphere radius parameter represents the radius of the sphere to be solved.

[0117] Based on the indirect adjustment mathematical model, and according to the preset approximate values ​​of the sphere center coordinates, the preset approximate values ​​of the sphere radius, the sphere center coordinate correction parameter, the sphere radius correction parameter, and multiple spherical equations, multiple adjustment equations are established with the fitted radius difference as the observed value. The sphere center coordinate correction parameter represents the adjustment correction value of the sphere center coordinate parameter, and the sphere radius correction parameter represents the adjustment correction value of the sphere radius parameter.

[0118] Based on the Taylor series expansion principle, and based on multiple adjustment equations, multiple error equations are obtained, which are then used to form an indirect adjustment error equation system.

[0119] Specifically, assuming the number of normal sampling points on the surface of the spherical node of the large-span spatial structure is n, and the three-dimensional coordinates of the i-th measuring point are (x, y, y) i ,y i ,z i Given the undetermined coordinates of the sphere's center (x0, y0, z0), the equation of the sphere is established as follows:

[0120]

[0121] Since there is always a difference between the fitted radius estimate and the actual value, a difference e is added to the spherical equation. i The equality holds true on both sides. Based on the indirect adjustment mathematical model, using approximate values ​​of the sphere's center coordinates... Approximate value R of the radius of a sphere 0 and multiple spherical coordinates (x) i ,y i ,z i Given the known quantities, the adjustment corrections Δx, Δy, Δz for the center coordinates and ΔR for the radius are unknown parameters to be solved. A least squares optimization problem is established to minimize the sum of squared errors (∑e...). 2 The minimum value is obtained by fitting the radius difference e. i For the observed values, establish the adjustment equation:

[0122]

[0123] Then, based on Taylor expansion and rearrangement, the error equation is obtained:

[0124]

[0125] In the error equation above, l i =R0 -ΔR, based on the three-dimensional coordinate data of the collection points, yields n error equations, which can be represented in matrix form as V=AX+L. Here, A is the coefficient matrix; when the radius R of the spherical node in a large-span structure is known, A is an n×3 matrix; when the radius A is unknown, A is an n×4 matrix.

[0126] Therefore, the multiple error equations expressed in matrix form constitute the indirect adjustment error equation system.

[0127] In some embodiments, based on the least squares principle, adjustment calculations are performed on the indirect adjustment error equation system to obtain at least the coordinates of the center of the spatial sphere nodes, including the following steps:

[0128] Based on the least squares criterion and the principle of indirect adjustment, the error equations of indirect adjustment are solved to obtain the correction values ​​of the sphere center coordinates and the sphere radius.

[0129] Based on the correction values ​​of the sphere's center coordinates, the correction values ​​of the sphere's radius, the approximate values ​​of the sphere's center coordinates and the approximate values ​​of the sphere's radius, an iterative formula is constructed to update the approximate values ​​of the sphere's center coordinates and the new approximate values ​​of the sphere's radius;

[0130] Based on the updated approximate values ​​of the sphere's center coordinates, the updated approximate values ​​of the sphere's radius, the sphere's center coordinate correction parameter, the sphere's radius correction parameter, and multiple spherical equations, establish multiple new adjustment equations to form a new set of indirect adjustment error equations. Solve the new set of indirect adjustment error equations to obtain new sphere's center coordinate correction values ​​and new sphere's radius correction values.

[0131] When the correction values ​​for the center coordinates and the radius of the sphere are both less than the preset thresholds, the center coordinates and radius of the spatial sphere node are output.

[0132] It should be noted that for indirect adjustment error equation systems with the corrections to the sphere center coordinates and the radius corrections as the parameters to be solved, a single adjustment calculation is often insufficient to meet the positioning accuracy requirements of spherical nodes in large-span spatial structures. Therefore, multiple adjustment calculations are required, and an iterative method is used to solve the problem. The specific process is as follows:

[0133] According to the least squares criterion V T PV = min, which can be obtained using the principle of indirect adjustment. Since the data from each collection point were obtained using the same instrument, they can be considered independent observations of the same precision. Therefore, the weight matrix P can be regarded as the identity matrix, and thus X = (A T A) -1 A T L. The iterative formula is constructed using the obtained corrections for the sphere's center coordinates and radius, as follows:

[0134]

[0135] Then, the adjusted results of the sphere center coordinates are used as approximations to reconstruct the error equations and solve them, forming an iterative calculation process. The initial values ​​for the approximate sphere center coordinates calculated in the first iteration are... It uses the average coordinates of each collection point, i.e. When the radius R of a sphere is unknown, the approximate value of the radius R is... 0 The average geometric distance from each acquisition point to the initial sphere center is taken. The termination condition for the iterative calculation is that each correction value is less than 10. -6 mm.

[0136] In some embodiments, the corresponding fitting accuracy is calculated at least based on the coordinates of the center of the spatial sphere nodes, including the following steps:

[0137] Based on the coordinates of the center of the sphere, the radius of the sphere, and the coordinates of each sphere, the roundness value of each sphere is calculated.

[0138] Based on the roundness values ​​of multiple spherical coordinates, the radius mean error of the sphere is calculated, which represents the fitting accuracy of the sphere's radius.

[0139] Based on the principle of indirect adjustment, the positional error of the sphere's center coordinates is calculated, and the positional error represents the fitting accuracy of the sphere's center coordinates.

[0140] Specifically, the formula for calculating the roundness value is:

[0141]

[0142] Among them, s i Let represent the roundness of the i-th acquisition point, x0, y0, z0 represent the coordinates of the center of the sphere after iterative calculation and fitting, and R represent the fitting radius or a known radius.

[0143] The formula for calculating the mean square error of the center point of a spherical node in a large-span structure is as follows:

[0144]

[0145]

[0146]

[0147] Where σ0 is the posterior unit weight standard error after adjustment, and nt is the degrees of freedom for measuring the maximum and minimum values. M is the cofactor matrix of the unknown parameter x. P M X M Y M Z These are the positional error and the coordinate component error, respectively.

[0148] The mean square error of the sphere fitting radius is the average of the sum of the squares of the roundness values ​​of all collected points, which avoids the influence of the number of collected sample points n. Its calculation formula is:

[0149]

[0150] Therefore, by calculating the fitting accuracy, we can ensure that the final values ​​of the sphere's center coordinates and radius are more accurate.

[0151] In addition, such as Figure 5 As shown, an embodiment of the present invention also provides a spatial sphere node measurement system, including: a spherical coordinate acquisition unit 100, an error equation establishment unit 200, an error equation solution unit 300, a fitting accuracy calculation and optimization unit 400, and a coordinate transformation unit 500. The spherical coordinate acquisition unit 100 is used to acquire multiple spherical coordinates of the spatial spherical node. These multiple spherical coordinates are obtained by measuring and locating the spatial spherical node using a pre-established spatial measurement control network. The error equation establishment unit 200 is used to establish an indirect adjustment error equation system based on the multiple spherical coordinates. The parameters to be solved in the indirect adjustment error equation system include at least the center coordinates of the spatial spherical node. The error equation solution unit 300 is used to perform adjustment calculations on the indirect adjustment error equation system based on the least squares principle to obtain at least the center coordinates of the spatial spherical node. The fitting accuracy calculation and optimization unit 400 is used to calculate the corresponding fitting accuracy based at least on the center coordinates of the spatial spherical node and perform optimization processing based on the fitting accuracy to output at least the optimized center coordinates of the spatial spherical node. The coordinate transformation unit 500 is used to transform the optimized center coordinates based on the Euler coordinate transformation principle to obtain the target center coordinates in the target coordinate system.

[0152] Understandably, by utilizing the spherical coordinate acquisition unit 100, the established spatial measurement and control network is used to measure and locate the spatial spherical nodes, obtaining multiple spherical coordinates. The error equation establishment unit 200 establishes an indirect adjustment error equation system based on these multiple spherical coordinates, and the error equation solution unit 300 solves for the center coordinates and radius of the spatial spherical nodes. The fitting accuracy calculation and optimization unit 400 calculates the fitting accuracy of the center coordinates and radius and performs iterative optimization to ultimately obtain optimized center coordinates and optimized radius, thus achieving high-precision positioning of the spatial spherical nodes. Simultaneously, the coordinate transformation unit 500 converts the optimized center coordinates into coordinates under the target coordinate system of the construction design, facilitating subsequent structural deformation assessment of the spatial spherical nodes. For the established spatial measurement and control network, the total station equipment used is simple and easy to operate. While reducing the requirements for surveyors and equipment, the spatial spherical node determination method of this invention also improves measurement efficiency and achieves non-contact measurement and positioning.

[0153] Additionally, refer to Figure 6 As shown, one embodiment of the present invention also provides a method for evaluating the stress on a spatial spherical node structure, comprising the following steps:

[0154] Perform any of the spatial sphere node determination methods as described in the first aspect of the present invention to obtain the target sphere center coordinates in the target coordinate system;

[0155] The coordinates of the target sphere's center are compared with the initial construction design coordinates to obtain the deformation of the spatial sphere nodes;

[0156] Based on the deformation of multiple spatial spherical nodes, the stress of the spatial spherical node structure is evaluated. The spatial spherical node structure is composed of multiple spatial spherical nodes.

[0157] It is understandable that after high-precision positioning of the spatial spherical nodes, deformation assessment and stress performance analysis of large-span spatial structures formed by multiple spatial spherical nodes can be further realized. Therefore, the stress assessment method for spatial spherical node structures in this invention can further improve engineering practicality, solve the problems of damage and serious displacement of the original measurement control network in large-span old renovation structures, realize non-destructive testing of key nodes such as non-contact measurement of spatial structure deformation, and can be widely used in the positioning measurement of welded spheres and bolted spheres in large-span spatial structures, which is conducive to accelerating the assembly construction, deformation assessment, reinforcement and renovation of actual projects.

[0158] To better illustrate the method for determining a spatial sphere node and the method for evaluating the stress on a spatial sphere node structure according to embodiments of the present invention, two practical engineering examples will be described in detail below.

[0159] Example 1: Combining references Figure 7a and Figure 7b As shown, a gymnasium, shaped like a polygonal lotus flower, boasts a novel structure and aesthetically pleasing appearance. Completed and put into use in 1996, it occupies a floor area of ​​6,000 square meters, with a building area of ​​11,000 square meters and a maximum clear height of 19 meters. It houses 4,177 spectator seats. The roof utilizes a large-span prestressed composite twisted grid shell steel structure, featuring a three-way grid-frame hexagonal central skylight. Prestressed cables are installed at the support nodes of the grid shell. The substructure is a three-layer frame concrete structure, with solid concrete spheres at the supports, each 850mm in diameter. Four prestressed cables are installed between each support. Due to its age, many members and supports show signs of corrosion, and some cables exhibit loosening. Therefore, it is necessary to first measure the coordinates of key structural nodes and compare them with the coordinates from the design and initial construction to determine the deformation of the node spheres, thereby enabling a stress assessment of the entire large-span spatial structure.

[0160] The measurements were conducted using a Leica TS30 total station, achieving an angle measurement accuracy of 0.5 seconds and a distance measurement accuracy of 0.6 mm + 1 ppm. The prism-free measurement range was 1000 m with an accuracy of 2 mm + 2 ppm, ensuring accurate data registration. In this reinforcement and renovation project, a new local control network was established from two conventional control points outside the site, with control points set up at six support columns. Four measuring stations were set up inside the venue. Since two supports were not observable from the ground, one station was set up on the south and north spectator stands, and one station was set up on the east and west third-floor platforms. The measuring points were mainly selected from the lower chord spheres within the six triangular main supports, the six support spheres, and a portion of the lower chord sphere in the central small hexagonal light-transmitting area. The lower chord sphere and support node numbers are detailed below. Figure 7b Using a total station without a prism, spatial coordinate measurements were performed on the lower chord spheres of the space frame, collecting at least five different points on each sphere surface. The collected data were used to calculate the center coordinates of the key node spheres using the proposed non-contact measurement method. By comparing these coordinates with the design coordinates, the relative position offset of the selected lower chord spheres was determined. It was assumed that the center of the sphere at support No. 4 (100, 35, 4.5) was taken as the origin of the relative three-dimensional coordinate system, with transformation angles α = 0, β = 0, ... With offsets of ΔX = 100m, ΔY = 35, and ΔZ = 4.5, a three-dimensional relative coordinate system was established to calculate the diameter and relative spatial position coordinates of the lower chord spheres in other parts. By comparing these coordinates with the design coordinates, the deformation of the nodes was obtained. Furthermore, the load effects caused by the displacement of some nodes with large sphere displacements were simulated, thus revealing the overall stress condition of the space frame at this stage and providing a strong basis for the next stage of reinforcement and maintenance work.

[0161] Example 2: Combining references Figure 8a and Figure 8b As shown, the roof space frame project of a thermal power plant is located 46.7m directly above the generator units. The structural type is a square pyramidal bolted ball joint space frame supported by lattice columns. The planar dimensions (length × width) of the 1-10~1-13×1-A~1-N space frame are 71.8m × 44.9m. The completed 1-10~1-13×1-A~1-G1 section has planar dimensions (length × width) of 33.6m × 44.9m, with an area of ​​1508.64 square meters. To understand the quality status of the completed 1-10~1-13×1-A~1-G1 space frame, it is necessary to measure the height difference of the space frame supports, the relative spatial positions of the bolted ball joints, and the deflection. See [details omitted]. Figure 8a and Figure 8bThis project utilizes a Trimble S8 total station for measurement, with an angle measurement range of 0.5″ and a distance measurement range of 1mm + 1ppm. First, two benchmark observation points, BM1 and BM2, are established on the main steel beam of the erected testing platform. Since the coordinates of the bolt sphere's center cannot be directly measured, the polar coordinate method using a total station is employed. Coordinates of 4-6 spatial measurement points are collected from the surface of the bolt sphere (the number of points is determined by the actual site conditions). Using the coordinates obtained from the bolt sphere surface measurements, the actual coordinates of the bolt sphere's center are analyzed using the spatial sphere center coordinate fitting method proposed in this paper. Further comparison of the current bolt sphere position with the initial design coordinates reveals the actual displacement of the entire space frame.

[0162] Furthermore, one embodiment of the present invention provides a computer-readable storage medium storing computer-executable instructions that are executed by a processor or controller. For example, the processor or controller may execute the spatial sphere node determination method or the spatial sphere node structure stress assessment method described above, for example, performing the above-described... Figure 1 or Figure 6 The method in the middle.

[0163] It will be understood by those skilled in the art that all or some of the steps and systems in the methods disclosed above can be implemented as software, firmware, hardware, and suitable combinations thereof. Some or all of the physical components can be implemented as software executed by a processor, such as a central processing unit, digital signal processor, or microprocessor, or as hardware, or as an integrated circuit, such as an application-specific integrated circuit. Such software can be distributed on a computer-readable medium, which can include computer storage media (or non-transitory media) and communication media (or transient media). As is known to those skilled in the art, the term computer storage media includes volatile and non-volatile, removable and non-removable media implemented in any method or technology for storing information (such as computer-readable instructions, data structures, program modules, or other data). Computer storage media includes, but is not limited to, RAM, ROM, EEPROM, flash memory or other memory technologies, CD-ROM, digital versatile disc (DVD) or other optical disc storage, magnetic cartridges, magnetic tape, disk storage or other magnetic storage devices, or any other medium that can be used to store desired information and is accessible to a computer. Furthermore, as is known to those skilled in the art, communication media typically contain computer-readable instructions, data structures, program modules, or other data in modulated data signals such as carrier waves or other transmission mechanisms, and may include any information delivery medium.

[0164] The embodiments of the present invention have been described in detail above with reference to the accompanying drawings. However, the present invention is not limited to the above embodiments. Within the scope of knowledge possessed by those skilled in the art, various changes can be made without departing from the spirit of the present invention.

Claims

1. A method for determining the nodes of a spatial sphere, characterized in that, The method includes the following steps: Multiple spherical coordinates of a spatial spherical node are obtained, and the multiple spherical coordinates are obtained by measuring and locating the spatial spherical node using a pre-established spatial measurement and control network; An indirect adjustment error equation system is established based on multiple spherical coordinates, wherein the parameters to be solved in the indirect adjustment error equation system include at least the center coordinates of the spatial sphere nodes. Based on the least squares principle, the indirect adjustment error equations are adjusted to obtain at least the center coordinates of the spatial sphere nodes. The fitting accuracy is calculated based on the center coordinates of the spatial sphere nodes, and optimization is performed based on the fitting accuracy to output the optimized center coordinates of the spatial sphere nodes. Based on the Euler coordinate transformation principle, the optimized sphere center coordinates are transformed to obtain the target sphere center coordinates in the target coordinate system; The step of establishing a system of indirect adjustment error equations based on multiple spherical coordinates includes the following steps: Based on the sphere center coordinate parameter, the sphere radius parameter, and multiple spherical coordinates, multiple corresponding spherical equations are established. The sphere center coordinate parameter represents the sphere center coordinates to be solved, and the sphere radius parameter represents the sphere radius to be solved. Based on the indirect adjustment mathematical model, and according to the preset approximate values ​​of the sphere center coordinates, the preset approximate values ​​of the sphere radius, the sphere center coordinate correction parameter, the sphere radius correction parameter, and multiple spherical equations, multiple adjustment equations are established with the fitted radius difference as the observed value. The sphere center coordinate correction parameter represents the adjustment correction value of the sphere center coordinate parameter, and the sphere radius correction parameter represents the adjustment correction value of the sphere radius parameter. Based on the Taylor series expansion principle, and according to the multiple adjustment equations, multiple error equations are obtained, and the multiple error equations are used to form the indirect adjustment error equation set. The calculation of the corresponding fitting accuracy based at least on the center coordinates of the spatial sphere nodes includes the following steps: Based on the coordinates of the center of the sphere, the radius of the sphere, and the coordinates of each sphere, the roundness value of each sphere is calculated. Based on the roundness values ​​of multiple spherical coordinates, the radius mean square error of the sphere radius is calculated, and the radius mean square error represents the fitting accuracy of the sphere radius; Based on the principle of indirect adjustment, the positional error of the sphere's center coordinates is calculated, and the positional error represents the fitting accuracy of the sphere's center coordinates.

2. The method for determining the nodes of a spatial sphere according to claim 1, characterized in that, Before establishing the indirect adjustment error equation system based on the multiple spherical coordinates, the spatial sphere node determination method further includes the following steps: When the radius of the sphere of the spatial sphere node is known, a first screening is performed on multiple spherical coordinates based on the sphere radius to obtain multiple first optimized spherical coordinates, and the indirect adjustment error equation set is established based on the multiple first optimized spherical coordinates.

3. The method for determining the nodes of a spatial sphere according to claim 2, characterized in that, The first filtering of multiple spherical coordinates based on the sphere radius to obtain multiple first optimized spherical coordinates includes the following steps: For multiple spherical coordinates, calculate the distance between any two different spherical coordinates to obtain multiple distance data; The distance data is compared with the radius of the sphere to determine the coordinates of the abnormal spherical surface. The abnormal spherical coordinates are removed to obtain multiple first optimized spherical coordinates.

4. The method for determining the nodes of a spatial sphere according to claim 1, characterized in that, The optimization process based on the fitting accuracy, to output at least the optimized center coordinates of the spatial sphere nodes, includes the following steps: If the fitting accuracy does not meet the preset fitting accuracy requirements, a second screening is performed on the multiple spherical coordinates based on the fitting accuracy to obtain multiple second optimized spherical coordinates; Based on multiple second optimized spherical coordinates, the indirect adjustment error equation system is re-established and adjustment calculations are performed to update the center coordinates and radius of the spatial sphere nodes, thereby updating the fitting accuracy. If the updated fitting accuracy meets the preset fitting accuracy requirements, the optimized center coordinates and optimized radius of the spatial sphere node will be output in the end.

5. The method for determining the nodes of a spatial sphere according to claim 1, characterized in that, The adjustment calculation based on the least squares principle, which adjusts the indirect adjustment error equation system to obtain at least the coordinates of the center of the spatial sphere node, includes the following steps: Based on the least squares criterion and the principle of indirect adjustment, the indirect adjustment error equations are solved to obtain the correction values ​​for the center coordinates and the radius of the sphere. Based on the sphere center coordinate correction value, the sphere radius correction value, the sphere center coordinate approximation value, and the sphere radius approximation value, an iterative formula is constructed to update the sphere center coordinate approximation value and the new sphere radius approximation value; Based on the updated approximate values ​​of the sphere's center coordinates, the updated approximate values ​​of the sphere's radius, the sphere's center coordinate correction parameter, the sphere's radius correction parameter, and multiple spherical equations, multiple new adjustment equations are established to form a new set of indirect adjustment error equations. The new set of indirect adjustment error equations is then solved to obtain new sphere's center coordinate correction values ​​and new sphere's radius correction values. When the correction values ​​for the center coordinates and the radius of the sphere are both less than preset thresholds, the center coordinates and radius of the spatial sphere node are output.

6. A system for measuring the nodes of a spatial sphere, characterized in that, The system includes: The spherical coordinate acquisition unit is used to acquire multiple spherical coordinates of a spatial spherical node. The multiple spherical coordinates are obtained by measuring and locating the spatial spherical node using a pre-established spatial measurement and control network. An error equation establishment unit is used to establish an indirect adjustment error equation system based on multiple spherical coordinates, wherein the parameters to be solved in the indirect adjustment error equation system include at least the center coordinates of the spatial sphere nodes. The error equation solving unit is used to perform adjustment calculations on the indirect adjustment error equation system based on the least squares principle, so as to obtain at least the center coordinates of the spatial sphere nodes. The fitting accuracy calculation and optimization unit is used to calculate the corresponding fitting accuracy based at least on the center coordinates of the spatial sphere nodes, and to perform optimization processing based on the fitting accuracy, so as to output at least the optimized center coordinates of the spatial sphere nodes. The coordinate transformation unit is used to transform the optimized sphere center coordinates based on the Euler coordinate transformation principle to obtain the target sphere center coordinates in the target coordinate system. The step of establishing a system of indirect adjustment error equations based on multiple spherical coordinates includes the following steps: Based on the sphere center coordinate parameter, the sphere radius parameter, and multiple spherical coordinates, multiple corresponding spherical equations are established. The sphere center coordinate parameter represents the sphere center coordinates to be solved, and the sphere radius parameter represents the sphere radius to be solved. Based on the indirect adjustment mathematical model, and according to the preset approximate values ​​of the sphere center coordinates, the preset approximate values ​​of the sphere radius, the sphere center coordinate correction parameter, the sphere radius correction parameter, and multiple spherical equations, multiple adjustment equations are established with the fitted radius difference as the observed value. The sphere center coordinate correction parameter represents the adjustment correction value of the sphere center coordinate parameter, and the sphere radius correction parameter represents the adjustment correction value of the sphere radius parameter. Based on the Taylor series expansion principle, and according to the multiple adjustment equations, multiple error equations are obtained, and the multiple error equations are used to form the indirect adjustment error equation set. The calculation of the corresponding fitting accuracy based at least on the center coordinates of the spatial sphere nodes includes the following steps: Based on the coordinates of the center of the sphere, the radius of the sphere, and the coordinates of each sphere, the roundness value of each sphere is calculated. Based on the roundness values ​​of multiple spherical coordinates, the radius mean square error of the sphere radius is calculated, and the radius mean square error represents the fitting accuracy of the sphere radius; Based on the principle of indirect adjustment, the positional error of the sphere's center coordinates is calculated, and the positional error represents the fitting accuracy of the sphere's center coordinates.

7. A method for evaluating the stress on a spatial spherical node structure, characterized in that, Includes the following steps: Perform the spatial sphere node determination method as described in any one of claims 1 to 5 to obtain the target sphere center coordinates in the target coordinate system; The coordinates of the target sphere center are compared with the initial construction design coordinates to obtain the deformation of the spatial sphere node; The stress on the spatial sphere node structure is evaluated based on the deformation of the multiple spatial sphere nodes, and the spatial sphere node structure is composed of multiple spatial sphere nodes.

8. A computer-readable storage medium, characterized in that, The computer-readable storage medium stores computer-executable instructions for causing a computer to perform the space sphere node determination method as described in any one of claims 1 to 5 or the space sphere node structure stress assessment method as described in claim 7.

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