Spherical coordinate positioning method for welded ball net rack

Abstract

The invention provides a welding ball net rack ball coordinate positioning method, and belongs to the technical field of net rack construction, and the method comprises the steps: building a site control network, employing a rank depletion free network adjustment method to process observation data, eliminating a multi-stage transmission accumulation error, employing error ellipse analysis to recognize a precision weak region, and carrying out the positioning of the welding ball net rack ball coordinate. Establishing a double-layer game optimization model to solve the optimal number of supplementary observation stations, determining the positions of the supplementary observation stations by adopting a Steiner tree algorithm, adding redundant observation stations in a region with weak precision to realize uniform distribution of the precision of a control network, performing three-dimensional coordinate measurement on welding ball nodes, and performing least square adjustment calculation to obtain corrected ball center coordinates; the outer contour line of the ball is measured and placed according to the corrected ball center coordinates, space positioning of the ball rod assembly is completed through a plumb bob instrument, and the technical problem that ball center positioning errors accumulate and exceed the limit due to non-uniform control net precision distribution is solved.

Description

Technical Field

[0001] This invention belongs to the field of space frame construction technology, and specifically relates to a method for spherical coordinate positioning of a welded spherical space frame. Background Technology

[0002] In the construction of welded sphere space frames for large-span terminal buildings, traditional methods employ multi-level control networks to progressively transfer coordinate systems. This involves acquiring the three-dimensional coordinates of control points through the deployment of GPS-RTK reference stations and total stations, and then using these coordinates to locate the welded sphere nodes. However, in current space frame construction surveying practices, due to the vast construction area and uneven distribution of control points, traditional methods suffer from significant variations in control network accuracy across different regions. In areas with low accuracy, the error ellipse's major semi-axis can reach over 5 mm, leading to accumulated errors in sphere center positioning. While traditional techniques improve local accuracy by adding stations, they lack a systematic optimization method for the number and location of stations, often resulting in redundant station deployment or insufficient accuracy improvement. This makes it impossible to control observation time costs while ensuring uniform accuracy distribution across the entire network. In other words, existing technologies suffer from the technical problem of uneven control network accuracy distribution leading to excessive accumulation of sphere center positioning errors. Summary of the Invention

[0003] In view of this, the present invention provides a method for spherical coordinate positioning of a welded spherical grid structure, which can solve the technical problem in the prior art where the uneven distribution of control network accuracy during the construction of a large-span welded spherical grid structure for a terminal building leads to the cumulative error exceeding the limit for spherical center positioning.

[0004] This invention is implemented as follows: A method for locating the coordinates of a welded ball grid frame is provided. A site control network is established, and the observation data is processed using a rank-deficient free network adjustment method to eliminate multi-level propagation and cumulative errors. Error ellipses are used to identify areas with low precision. A two-layer game optimization model is established to solve for the optimal number of supplementary monitoring stations. The Steiner tree algorithm is used to determine the locations of the supplementary monitoring stations. Redundant observation stations are added in areas with low precision to achieve a uniform distribution of control network precision. Three-dimensional coordinate measurements are performed on the welded ball nodes, and the corrected ball center coordinates are obtained through least-squares adjustment. Based on the corrected ball center coordinates, the outer contour line of the ball is measured and the spatial positioning of the ball rod assembly is completed using a plumb bob.

[0005] The steps for establishing a site control network include setting up GPS-RTK base stations and total stations in the terminal construction area, obtaining the three-dimensional coordinates of the initial control points through redundant observations, and recording the straight-line distance between adjacent stations.

[0006] Redundant observation refers to using two independent measurement methods, GPS-RTK and total station, to conduct multiple observations of the same control point, obtaining multiple sets of three-dimensional coordinate data of the control point, and eliminating gross error observations through data comparison and statistical analysis.

[0007] Among them, the rank-deficient free network adjustment method refers to the method of not fixing the coordinates of any known points in the adjustment calculation of the control network, but treating all control points as undetermined parameters to participate in the adjustment, and solving the normal equations through the least squares criterion.

[0008] The error ellipse refers to the error distribution graph of the plane coordinates of the control points. It is calculated and drawn based on the covariance matrix of the control point position error values. The major semi-axis represents the direction and value of the maximum error of the control point, and the minor semi-axis represents the direction and value of the minimum error.

[0009] Among them, the area with weak precision refers to the area in the control network where the length of the semi-major axis of the error ellipse is greater than 3mm.

[0010] In the two-layer game optimization model, the upper-layer game model establishes an accuracy optimization objective function with the goal of minimizing the overall network accuracy unevenness, while the lower-layer game model establishes a time efficiency objective function with the goal of minimizing the total observation time.

[0011] Specifically, the calculation of the accuracy optimization objective function is as follows: the uniformity of accuracy across the entire network is equal to the standard deviation of the control point position error value divided by the average value of the control point position error value, then divided by the square root of the number of supplementary stations, plus 1.

[0012] Specifically, the calculation of the objective function for time efficiency is as follows: the total observation time is equal to the average straight-line distance between adjacent stations divided by 20 m / min, multiplied by the number of supplementary stations, plus the observation time of a single station multiplied by the number of supplementary stations.

[0013] Among them, the game equilibrium solution refers to the number of supplementary stations corresponding to the minimum value of the weighted sum of the accuracy optimization objective function and the time efficiency objective function. It is obtained by iteratively calculating the network-wide accuracy non-uniformity and total observation time under different numbers of supplementary stations.

[0014] The Steiner tree algorithm refers to a computational method for finding the shortest network tree connecting all given points in a given set of planar points, allowing the addition of extra nodes beyond the given points to reduce the total connection length.

[0015] Among them, least squares adjustment calculation refers to establishing a set of error equations and solving for undetermined parameters based on the principle of minimizing the sum of squared residuals between observed and theoretical values, and performing least squares adjustment calculation on the measured sphere center coordinates and the design sphere center coordinates.

[0016] When the spatial deviation between the measured sphere center coordinates and the designed sphere center coordinates is ≥2mm, the station position is adjusted and the welded sphere node is remeasured. When the spatial deviation is <2mm, the next welded sphere node measurement is performed.

[0017] The positioning of the outer contour of the ball node is achieved using a ground compass tool, which consists of a central positioning rod and an adjustable radius arm. The central positioning rod is fixed to the coordinate point of the corrected ball center, and the length of the radius arm is adjusted to the radius of the welding ball. The radius arm is rotated around the central positioning rod to mark the outer contour circle of the sphere projection on the ground.

[0018] The bottom chord club assembly is positioned using a one-ball-one-club method. After assembling the bottom chord ball and bottom chord club, it is hoisted onto the jig, and a plumb bob is used to align the center of the bottom chord ball with the center of its outer contour on the ground. The top chord club assembly is positioned using a one-ball-two-club method. After assembling the top chord ball with two web clubs, it is hoisted, and a third web club is used for spatial constraint positioning. A plumb bob is used to align the center of the top chord ball with the center of its outer contour on the ground.

[0019] This invention establishes a two-layer game optimization model, with minimizing the overall network accuracy unevenness as the upper-layer objective and minimizing the total observation time as the lower-layer objective. It utilizes a coupling term involving the number of supplementary stations to solve the game equilibrium solution, determining the optimal number of supplementary stations. Then, the Steiner tree algorithm is used to calculate the optimal supplementary station locations within areas of low accuracy, achieving a uniform distribution of control network accuracy. This invention employs a rank-deficient free network adjustment method to process redundant observation data, eliminating multi-level propagation and cumulative errors. Combined with error ellipse analysis, it identifies areas of low accuracy. By scientifically deploying redundant observation stations in these areas, the dispersion of positional errors at each control point in the control network is significantly reduced, ensuring that the spatial deviation of the sphere's center is controlled within 2 millimeters. In summary, this invention solves the technical problem mentioned in the background art where uneven distribution of control network accuracy leads to excessive cumulative errors in sphere center positioning. Attached Figure Description

[0020] Figure 1 This is a schematic diagram of the positioning of the topspin cue.

[0021] Figure 2 This is a schematic diagram of the positioning of the bottom string club.

[0022] Figure 3 This is a schematic diagram of a hoisting setup consisting of a ball and a rod.

[0023] Figure 4 This is a schematic diagram of the hoisting of a two-pole configuration with a ball. Detailed Implementation

[0024] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0025] This invention provides a method for spherical coordinate positioning of a welded spherical grid frame, comprising the following steps:

[0026] S01. Establish a site control network. Deploy GPS-RTK base stations and total station stations in the terminal construction area. Obtain the three-dimensional coordinates of the initial control points through redundant observations, record the straight-line distance between adjacent stations, and establish a site control network coordinate system.

[0027] S02. Construct a unified high-precision control network, use the rank-deficient free network adjustment method to process the site control network observation data, eliminate multi-level transmission cumulative errors, calculate the position error value of each control point, and establish the construction control network coordinate system.

[0028] S03. Calculate the accuracy distribution of the control network, draw error ellipses based on the positional error values ​​of each control point, count the length of the major semi-axis of the error ellipse, and identify the precision weak areas where the length of the major semi-axis of the error ellipse is greater than 3mm.

[0029] S04. Perform two-level game optimization. The upper-level game model establishes an accuracy optimization objective function with the goal of minimizing the overall network accuracy unevenness, while the lower-level game model establishes a time efficiency objective function with the goal of minimizing the total observation time. The optimal number of supplementary stations is obtained by solving the game equilibrium solution through the coupling term of the number of supplementary stations.

[0030] S05. Optimize the station layout. Use the Steiner tree algorithm to calculate the optimal location of supplementary stations in the area with weak accuracy. Add redundant observation stations in the area with weak accuracy according to the optimal number of supplementary stations. Re-execute redundant observation to obtain the three-dimensional coordinates of the supplementary stations.

[0031] S06. Measure the coordinates of the center of the spheres in the space frame. Use a total station to perform three-dimensional coordinate measurements on each welded sphere node. Perform least-squares adjustment between the measured center of the spheres and the designed center of the spheres to obtain the corrected center of the spheres.

[0032] S07. Determine the positioning accuracy of the ball center, calculate the spatial deviation between the measured ball center coordinates and the designed ball center coordinates. When the spatial deviation is ≥2mm, adjust the station position and remeasure the welded ball node. When the spatial deviation is <2mm, proceed to the next welded ball node measurement.

[0033] S08. Locate the outer contour of the ball node. Based on the corrected ball center coordinates and the diameter of the welded ball, use a ground compass to measure the outer contour lines of the lower chord ball and the upper chord ball.

[0034] S09. Install the bottom chord club assembly. Assemble the bottom chord ball and bottom chord club using a one-ball-one-club method and hoist them onto the jig. Use a plumb bob to align the center of the bottom chord ball with the center of the outer contour line of the bottom chord ball on the ground to complete the positioning of the bottom chord club assembly.

[0035] S10. Install the topspin club assembly. Assemble the topspin ball and two side clubs using a one-ball-two-club method and hoist it in place. Use the third side club for spatial constraint positioning. Align the center of the topspin ball with the center of the outer contour line of the topspin ball on the ground using a plumb bob to complete the positioning of the topspin club assembly.

[0036] Redundant observation refers to using two independent measurement methods, GPS-RTK and total station, to conduct multiple observations of the same control point, obtaining multiple sets of three-dimensional coordinate data of the control point. By comparing and statistically analyzing the data, gross errors are eliminated, thereby improving the reliability of the three-dimensional coordinates of the control point.

[0037] Among them, the straight-line distance between adjacent stations refers to the straight-line distance between two stations that are spatially adjacent in the site control network. It is obtained by direct measurement with a total station or by calculation based on the three-dimensional coordinates of the station, and is used for subsequent accuracy optimization objective function calculation.

[0038] Among them, the rank-deficient free network adjustment method refers to the method of adjusting control networks without fixing the coordinates of any known points, and using all control points as undetermined parameters to participate in the adjustment. The method equations are solved by the least squares criterion. The rank-deficient free network adjustment method eliminates the systematic deviation transmission caused by the error of known points and is suitable for the unified processing of coordinates of multi-level control networks.

[0039] Among them, the control point position error value refers to the mean error of the coordinates after the control point adjustment. It is obtained by extracting the covariance matrix in the calculation process of the rank-deficient free network adjustment method, and represents the reliability of the three-dimensional coordinates of the control point.

[0040] Among them, the error ellipse refers to the error distribution graph of the plane coordinates of the control point. It is drawn based on the covariance matrix of the position error values ​​of the control point. Its major semi-axis represents the direction and value of the maximum error of the control point, and its minor semi-axis represents the direction and value of the minimum error. By analyzing the shape and azimuth of the error ellipse, weak links in the accuracy of the control network can be identified.

[0041] Among them, the low-precision area refers to the area where the length of the major semi-axis of the error ellipse in the control network is greater than 3mm. The positioning accuracy of the low-precision area is lower than the requirements of the grid installation, and it is necessary to improve the observation accuracy by adding redundant observation stations.

[0042] Among them, the overall network accuracy non-uniformity refers to the degree of dispersion of the position error values ​​of each control point in the control network. The smaller the overall network accuracy non-uniformity value, the more uniform the distribution of control network accuracy.

[0043] The accuracy optimization objective function is used to evaluate the uniformity of the control network accuracy distribution. The inputs include the standard deviation of the control point position error value, the average value of the control point position error value, and the number of supplementary stations. The output is the minimum value of the accuracy non-uniformity of the entire network. The accuracy optimization objective function is expressed as follows: The accuracy non-uniformity of the entire network is equal to the standard deviation of the control point position error value divided by the average value of the control point position error value, then divided by the square root of the number of supplementary stations, plus 1.

[0044] The total observation time refers to the cumulative time required to complete redundant observations of all control points, including the time for setting up the station, the observation time, and the time for transferring the station.

[0045] The time efficiency objective function is used to evaluate the time cost required to complete the control network observation. The inputs include the average straight-line distance between adjacent stations, the observation time of a single station, and the number of supplementary stations. The output is the minimum total observation time. The time efficiency objective function is expressed as follows: The total observation time is equal to the average straight-line distance between adjacent stations divided by 20 m / min, multiplied by the number of supplementary stations, plus the observation time of a single station multiplied by the number of supplementary stations.

[0046] Among them, the supplementary station quantity coupling term refers to the supplementary station quantity parameter that appears in both the accuracy optimization objective function and the time efficiency objective function. Increasing the value of the supplementary station quantity coupling term will reduce the overall network accuracy unevenness but will increase the total observation time. By adjusting the supplementary station quantity coupling term, a balance between accuracy improvement and time cost can be achieved.

[0047] In this context, the game equilibrium solution refers to the number of additional monitoring stations required when the weighted sum of the accuracy optimization objective function and the time efficiency objective function reaches its minimum value in the two-layer game model. By iteratively calculating the network-wide accuracy non-uniformity and total observation time under different numbers of additional monitoring stations, the number of additional monitoring stations is the game equilibrium solution when the weighted sum of the normalized value of the network-wide accuracy non-uniformity and the normalized value of the total observation time is minimized.

[0048] The optimal number of supplementary stations refers to the number of redundant observation stations that need to be added in areas with weak accuracy, as determined by the game equilibrium solution. The optimal number of supplementary stations ensures that the accuracy distribution of the control network is uniform and the observation time cost is reasonable.

[0049] The Steiner tree algorithm is a computational method for finding the shortest network tree connecting all given points in a given set of planar points. It allows the addition of extra nodes outside the given points to reduce the total connection length. In the deployment of stations, the Steiner tree algorithm is used to take the existing stations in the low-precision area as the given set of points and calculate the optimal location of the supplementary stations, so that the control network observation path is the shortest and the accuracy transfer is optimal.

[0050] Among them, redundant observation stations refer to additional stations added in areas with weak accuracy in order to improve the accuracy of the control network. The redundant observation stations form a redundant observation network with the existing stations, and the reliability of the three-dimensional coordinates of the control points is improved by increasing the observation paths.

[0051] The least squares adjustment calculation refers to a mathematical method that establishes a set of error equations and solves for undetermined parameters based on the principle of minimizing the sum of squared residuals between observed and theoretical values. In the processing of grid coordinates, the least squares adjustment calculation is used to integrate multiple observation data to obtain the optimal estimated corrected sphere center coordinates and eliminate the influence of random observation errors.

[0052] Among them, the ground compass tool refers to a measuring instrument consisting of a central positioning rod and an adjustable radius arm. The central positioning rod is fixed at the coordinate point of the correction sphere, and the length of the radius arm is adjusted to the radius of the welded sphere. The radius arm is rotated around the central positioning rod to mark the outer contour circle of the sphere's projection on the ground.

[0053] The "one ball with one stick" method refers to the installation method in which a bottom chord ball and a bottom chord stick are connected to each other on the ground by bolts to form a bottom chord ball and stick assembly, and then the bottom chord ball and stick assembly is hoisted as a whole onto the jig. The "one ball with one stick" method reduces the number of high-altitude operations and improves installation accuracy.

[0054] The "one ball with two clubs" method refers to the installation method in which a topspin ball and two side clubs are connected to form a topspin club assembly by bolts on the ground, and then the topspin club assembly is hoisted to the installation position as a whole. The final position of the topspin ball is determined by the spatial constraint of the third side club in the "one ball with two clubs" method.

[0055] Among them, the plumb bob is a measuring instrument that uses the direction of gravity to determine the vertical reference. By aligning the plumb bob with the center of the outer contour line of the ground, the spatial position of the welded ball joint can be checked.

[0056] Among them, the single-station observation time refers to the time required to complete redundant observations of all visible control points at one station location, including instrument leveling time, target aiming time, and data recording time, which is empirically set to 30 minutes.

[0057] The specific implementation methods of the above steps are described in detail below.

[0058] The specific implementation of step S01 is as follows: First, select a location with a wide field of vision and stable terrain in the terminal construction area to set up GPS-RTK reference stations. The number of reference stations should not be less than 3 to ensure good satellite signal reception. Then, set up total station stations around the reference stations at intervals of 50m to 100m. The station layout should follow the form of triangulation network or traverse network to ensure the strength of the observation network. Next, use the GPS-RTK system to conduct at least 3 independent observations on each control point. At the same time, use the total station to perform intersection measurements on the same control point from different stations to obtain multiple sets of three-dimensional coordinate data for each control point. Then, use statistical verification methods to remove gross errors exceeding 3 times the mean square error from the observation data. Finally, use the total station's distance measurement function to directly measure and record the spatial straight-line distance between adjacent stations, thereby establishing a site control network coordinate system containing the three-dimensional coordinates of control points and the distance between stations. The purpose of this step is to provide an initial spatial reference for the subsequent installation of the grid structure.

[0059] The specific implementation of step S02 is as follows: all control point observation data obtained in step S01 are imported into the adjustment calculation software and processed using the rank-deficient free network adjustment method. This method does not fix any control point coordinates as known values, but instead uses all control point coordinates as undetermined parameters to establish observation equations. The least squares problem is solved by constructing a normal equation matrix and introducing rank-deficient constraints. During the adjustment process, singular value decomposition technology is used to process the rank-deficient matrix, and the optimal estimated value of the control point coordinates is determined through the minimum norm solution. At the same time, the position error value of each control point is extracted from the covariance matrix of the adjustment calculation, including eastward error, northward error and elevation error. This step eliminates the systematic cumulative error caused by the transmission of multi-level control networks, so that the coordinate system of the entire construction control network reaches a unified high-precision standard. The reference threshold for the position error value should be controlled within 2mm.

[0060] The specific implementation of step S03 is as follows: Based on the covariance matrix of the position error values ​​of each control point calculated in step S02, the principal components of the plane coordinate error are extracted. The lengths of the major and minor axes and their azimuth angles of the error ellipse are calculated through eigenvalue decomposition. The major axis corresponds to the square root of the largest eigenvalue of the covariance matrix, and the minor axis corresponds to the square root of the smallest eigenvalue. Then, the error ellipse of each control point is drawn on the control network plan. The direction of the major axis of the ellipse represents the direction of the largest position error at that point. Next, the error ellipses of all control points are traversed, the length values ​​of the major axes are counted, and control points and their surrounding areas with a major axis length exceeding the 3mm threshold are identified. These areas are marked as areas with weak accuracy. The purpose of this step is to visually identify the locations in the control network that need to be improved by visualizing the error distribution, providing target areas for subsequent optimization.

[0061] The specific implementation of step S04 is as follows: A two-layer game optimization model is constructed. The upper-layer game establishes an accuracy optimization objective function, which uses the ratio of the standard deviation to the average value of the control point position error as a measure of accuracy non-uniformity. This ratio is divided by the square root of the number of additional stations to reflect the diminishing marginal effect of the number of stations on accuracy improvement. Finally, 1 is added for normalization. The lower-layer game establishes a time efficiency objective function, which divides the average straight-line distance between adjacent stations by the station transfer speed of 20 m / min to obtain the travel time, multiplies it by the number of additional stations, and adds the time for a single measurement. The total observation time is obtained by multiplying the 30-minute observation time of the station by the number of supplementary stations. The two objective functions are coupled through the common variable of the number of supplementary stations. Then, an iterative search algorithm is used to calculate the network-wide accuracy non-uniformity and the total observation time one by one within the range of the number of supplementary stations changing from 1 to 20. After normalizing both to the interval of 0 to 1, they are weighted and summed according to the weight coefficients of 0.6 and 0.4. The number of supplementary stations corresponding to the minimum value of the weighted sum is the game equilibrium solution. This step achieves the optimal balance between accuracy improvement and construction efficiency.

[0062] The specific implementation of step S05 is as follows: In the identified areas with low accuracy, the planar coordinates of existing stations are used as a given set of points and input into the Steiner tree algorithm. This algorithm finds the shortest tree network connecting all given points through enumeration or heuristic search. The algorithm allows adding Steiner points outside the given points as new station locations, minimizing the total length of the connection paths between all stations. During the calculation process, Delaunay triangulation is used to generate candidate Steiner points, and then the connection method is optimized through the minimum spanning tree algorithm. Based on the optimal number of supplementary stations determined in step S04, the first few candidate locations calculated by the Steiner tree algorithm are selected as the actual supplementary station locations. Then, GPS-RTK and total stations are set up at these locations for redundant observation according to the method in step S01, and the three-dimensional coordinates of the supplementary stations are obtained and incorporated into the control network system. This step improves the observation intensity in areas with low accuracy by optimizing the spatial distribution of stations.

[0063] The specific implementation of step S06 is as follows: a total station is set up on the control network stations, and the three-dimensional coordinates of the center of each welded sphere node are measured. During the measurement, the prism reflection method or the prism-free distance measurement method is used. Each sphere center is observed from at least 3 different stations to form a spatial intersection. After obtaining the measured three-dimensional coordinates of the sphere center, the theoretical design coordinates of the corresponding sphere center are extracted from the design drawings. The measured coordinates and the design coordinates are used as the observed values ​​and theoretical values ​​to establish an error equation. The least squares adjustment principle is used to construct the normal equation with the minimum sum of squared residuals as the criterion and solve it. The corrected sphere center coordinates after eliminating random errors are obtained through adjustment calculation. This coordinate integrates the observation information of multiple stations and has a significantly higher reliability than the results of a single measurement. The purpose of this step is to obtain a high-precision spatial position of the sphere center.

[0064] The specific implementation of step S07 is as follows: calculate the coordinate differences between the corrected sphere center coordinates and the designed sphere center coordinates in the three directions of east, north, and elevation. The spatial deviation value is obtained by calculating the three-dimensional spatial distance. When the spatial deviation value is greater than or equal to the 2mm threshold, it indicates that the current station position or observation conditions are causing insufficient measurement accuracy. At this time, it is necessary to adjust the station position and select a position closer to the sphere node or with a better line of sight to re-set up the total station. Then, the measurement and adjustment calculation process of step S06 is executed again. When the spatial deviation value is less than 2mm, it indicates that the sphere center positioning accuracy meets the requirements of the grid installation. Record the corrected coordinates of the sphere node and continue to measure the next welded sphere node. This step ensures that the positioning accuracy of each sphere node meets the standard through closed-loop verification.

[0065] The specific implementation of step S08 is as follows: Based on the corrected ball center coordinates obtained in step S06, a total station or GPS-RTK device is used to mark the plane projection point of the ball center on the ground. The center positioning rod of the ground compass tool is vertically inserted into the projection point. The radius arm length of the compass is adjusted to the actual radius value of the ball to be welded. For the lower chord ball, the radius arm length is set to the lower chord ball radius. The radius arm is rotated 360 degrees around the center positioning rod to draw the projection circle of the lower chord ball's outer contour on the ground. For the upper chord ball, the radius arm is set to the upper chord ball radius in the same way, and the projection circle of the upper chord ball's outer contour is drawn. The drawn circle is marked with lime powder or measuring nails for identification by construction personnel. The purpose of this step is to convert the three-dimensional position of the ball into a two-dimensional visible mark on the ground, providing an intuitive alignment reference for the subsequent installation of the ball club assembly.

[0066] The specific implementation of step S09 is as follows: In the ground assembly area, the lower chord ball is connected to a lower chord rod using high-strength bolts. Before connection, the position deviation of the bolt holes is checked to ensure that the deviation is less than 0.5mm. After connection, the lower chord ball and rod assembly is hoisted to the top of the jig using lifting equipment. During hoisting, the horizontal and vertical positions of the assembly are controlled by the tower crane's fine-tuning function. When the assembly is close to the installation position, the construction personnel use a plumb bob to project a plumb line from the center of the upper chord ball downwards. The hoisting position is adjusted so that the plumb line is accurately aligned with the center of the lower chord ball's outer contour line marked in step S08. Through repeated fine-tuning, the plumb line is made to coincide with the center of the circle on the ground. The coincidence error is controlled within 1mm. Then, the lower chord ball and rod assembly is fixed on the jig. This step uses the direction of gravity as a vertical reference to achieve spatial positioning of the ball's center.

[0067] The specific implementation of step S10 is as follows: In the ground assembly area, the upper chord ball and two web members are connected by bolts to form an upper chord ball-and-club assembly. During connection, ensure that the angle between the two web members and the center of the ball meets the design requirements, and the angle deviation is controlled within 0.3 degrees. Use lifting equipment to hoist the upper chord ball-and-club assembly to the vicinity of the installation position. At this time, spatial constraint is achieved through a third web member. One end of the third web member is connected to the already installed lower chord ball node, and the other end is connected to the reserved bolt hole of the upper chord ball. By adjusting the hoisting height and horizontal position, the bolt hole of the third web member is aligned with the bolt hole of the upper chord ball. During the alignment process, a plumb bob is used to project a vertical line downward from the center of the upper chord ball to ensure that the vertical line is aligned with the center of the outer contour line of the upper chord ball marked in step S08. When the vertical line alignment error is less than 1mm and the bolt holes of the third web member are completely aligned, the spatial positioning of the upper chord ball-and-club assembly is completed and all connecting bolts are tightened. This step uniquely determines the installation position of the upper chord ball through the spatial triangle constraint formed by the three web members.

[0068] It should be noted that the key technical ideas of this invention are analyzed as follows: The first key technology is to construct a unified high-precision control network using the rank-deficient free network adjustment method. This method does not rely on fixed known points, but uses all control points as undetermined parameters to participate in the adjustment calculation. This fundamentally eliminates the systematic deviation transmission problem caused by the error of known points in the traditional hierarchical control network. Compared with the traditional constrained adjustment method, the rank-deficient free network adjustment processes the rank-deficient matrix through singular value decomposition technology to obtain the minimum norm solution of the coordinates of the entire network. This ensures that the geometric relationship inside the control network maintains optimal consistency, avoids the accumulation and amplification of errors in the multi-level transmission process, and significantly improves the overall control accuracy uniformity of a large-scale construction area. The second key technology is to establish a two-layer game optimization model to achieve a dynamic balance between accuracy improvement and construction efficiency. The upper-layer game aims to minimize the uniformity of accuracy across the entire network, while the lower-layer game aims to minimize the total observation time. The two layers of games are coupled and interact through the common decision variable of increasing the number of monitoring stations. Compared with traditional single-objective optimization methods that only consider accuracy improvement or efficiency improvement, the two-layer game model finds the optimal trade-off between accuracy requirements and time costs by solving the game equilibrium point. This avoids the waste of resources caused by blindly increasing the number of monitoring stations and the insufficient accuracy caused by excessively compressing the observation time, thus achieving the economic rationality of control network optimization. The third key technology is the use of the Steiner tree algorithm to optimize the spatial layout of stations. This algorithm finds the shortest network tree connecting existing stations in areas with low accuracy and allows the addition of extra nodes as new station locations. Compared with the traditional equidistant or empirical layout methods, the Steiner tree algorithm starts from the perspective of graph theory optimization. By minimizing the total length of the connection path between stations, the addition of station locations can effectively cover areas with low accuracy, while ensuring the shortest observation path and optimal accuracy transfer, which significantly improves the observation efficiency and overall geometric strength of the control network. The synergistic effect of these three key technologies lies in the fact that the rank-deficient free network adjustment method provides a high-precision unified coordinate benchmark for the control network, the two-level game optimization model scientifically determines the number of additional stations based on this, and the Steiner tree algorithm further optimizes the spatial location of the additional stations. The three form a complete closed loop from accuracy assessment to quantity decision and then to location optimization. Compared with the local optima caused by independent decision-making in each link of the traditional method, this collaborative technical route achieves the global optimization of control network construction. Under the premise of ensuring the accuracy requirements of the grid installation, it minimizes the measurement workload and construction cycle, and improves the overall quality and efficiency of large-scale spatial grid construction.

[0069] It should be noted that this invention also solves the following technical problem: In the construction of large-span space frames, traditional methods use a single measurement means to obtain the coordinates of control points, lacking an independent verification mechanism. Gross errors are difficult to effectively eliminate, leading to insufficient reliability of the three-dimensional coordinates of control points. This invention uses both GPS-RTK and total station as independent measurement methods to perform redundant observations of the same control point, obtaining multiple sets of three-dimensional coordinate data. Gross errors are eliminated through data comparison and statistical analysis. Redundant observation stations are added in areas with weak accuracy to form a redundant observation network, increasing the observation path and improving the reliability of the three-dimensional coordinates of the control points. This ensures that the benchmark accuracy of subsequent sphere center positioning measurements meets the requirements of space frame installation, effectively solving the technical problem of insufficient reliability of control point coordinates. Furthermore, traditional space frame installation methods involve welding the ball rods one by one at high altitude, resulting in low work efficiency and difficulty in ensuring positioning accuracy. This invention adopts a ground pre-assembly method with one ball rod and one ball rod with two balls. After the ball rod components are bolted together on the ground, they are hoisted as a whole, reducing the number of high-altitude operations. A plumb bob is used to align the center of the ball with the center of the outer contour line on the ground to verify the spatial position. The final position of the upper chord ball is determined by the spatial constraint of the third web member, which improves the efficiency and positioning accuracy of space frame installation.

[0070] Specifically, the principle of this invention is as follows: This invention can solve the technical problem of excessive accumulation of sphere center positioning errors caused by uneven distribution of control network accuracy. Its principle lies in using the rank-deficient free network adjustment method to treat all control points as undetermined parameters in the adjustment, avoiding the systematic deviation transmission introduced by fixed known points, achieving unified coordinate processing of multi-level control networks, and eliminating the error accumulation mechanism from the source. The two-layer game optimization model quantifies the uniformity of accuracy by minimizing the ratio of the standard deviation to the average value of the control point position error in the upper-layer game, and controls time cost by minimizing the sum of the station transfer distance and observation time in the lower-layer game. The two objectives are mutually constrained by the coupling term of the number of supplementary stations. When the weighted sum reaches its minimum value, the game equilibrium solution obtained ensures both accuracy improvement and construction efficiency. The Steiner tree algorithm uses existing stations as a given set of points, and constructs the shortest connection network by adding optimal position nodes, so that the supplementary stations and existing stations form the optimal observation path, improving accuracy transmission efficiency and ensuring that the major semi-axis of the error ellipse in the weak accuracy area is reduced to below 3 mm, ultimately achieving the high-precision requirement of controlling the spatial deviation of sphere center positioning within 2 mm.

[0071] The following provides a specific embodiment 1 of the present invention, and the specific implementation of each step in this embodiment 1 is described in detail below.

[0072] In this embodiment, the specific implementation of step S01 is the same as described above, and will not be repeated in detail here.

[0073] The specific implementation of step S02 is as follows: all control point observation data obtained in step S01 are imported into the adjustment calculation software and processed using the rank-deficient free network adjustment method. This method does not fix any control point coordinates as known values, but instead uses all control point coordinates as undetermined parameters to establish the observation equations. The observation equations are expressed as follows:

[0074] ;

[0075] In the formula, This is a vector of corrections for the observations, in units of... ; It is a coefficient matrix that reflects the geometric relationship between the observed values ​​and the undetermined parameters. Its elements are direction cosines or distance coefficients, which are dimensionless. The parameter vector is to be determined, containing the three-dimensional coordinates of all control points, in units of... ; The observation vector contains Observation data from the total station, in units of .

[0076] The least squares problem is solved by constructing the normal equation matrix and introducing rank deficiency constraints. The normal equations are expressed as follows:

[0077] ;

[0078] In the formula, The optimal estimate of the undetermined parameter is given in units of . ; The weight matrix is ​​determined based on the observation accuracy. The diagonal elements are the weights of the observations, representing the relative reliability of each observation, and are dimensionless. Coefficient matrix The transpose of .

[0079] In the adjustment process, singular value decomposition is used to process the rank-deficient matrix, and the optimal estimated values ​​of the control point coordinates are determined through the minimum norm solution. At the same time, the position error value of each control point is extracted from the covariance matrix calculated in the adjustment. The covariance matrix is ​​expressed as follows:

[0080] ;

[0081] In the formula, Undetermined parameters The covariance matrix, in units of .

[0082] The calculation of the control point position error value is described as follows:

[0083] ;

[0084] In the formula, For the first The position error value of each control point, in units of ; Covariance matrix The diagonal elements, unit: ; The control point number ranges from 1 to the total number of control points. Dimensionless; The total number of control points in the control network is dimensionless.

[0085] The specific implementation of step S03 is as follows: based on the covariance matrix of the position error values ​​of each control point obtained in step S02, the principal components of the plane coordinate error are extracted, and the lengths of the major and minor axes of the error ellipse and their azimuth angles are calculated through eigenvalue decomposition. The calculation of the major axis of the error ellipse is described as follows:

[0086] ;

[0087] In the formula, For the first The length of the semi-major axis of the error ellipse for each control point, in units of... ; For the first The largest eigenvalue of the covariance matrix of the plane coordinates of each control point, in units of .

[0088] The calculation method for the minor semi-axis of the error ellipse is as follows:

[0089] ;

[0090] In the formula, For the first The length of the minor semi-axis of the error ellipse at each control point, in units of... ; For the first The smallest eigenvalue of the covariance matrix of the plane coordinates of control points, in units of .

[0091] Then, draw the error ellipse for each control point on the control network plan. The direction of the major axis of the ellipse indicates the direction of the maximum error at that point. Next, iterate through the error ellipses of all control points, count the length of the semi-major axis, and identify those with a semi-major axis length exceeding 3. The control points of the threshold and their surrounding areas are marked as areas of low precision.

[0092] The specific implementation of step S04 is as follows: a two-layer game optimization model is constructed. The upper-layer game establishes an accuracy optimization objective function. This function uses the ratio of the standard deviation to the average value of the control point position error as a measure of accuracy non-uniformity. It is divided by the square root of the number of additional stations to reflect the diminishing marginal effect of the number of stations on accuracy improvement. Finally, 1 is added for normalization. The accuracy optimization objective function is expressed as follows:

[0093] ;

[0094] In the formula, The overall network accuracy non-uniformity is dimensionless. The standard deviation of the control point location error values, in units of The calculation formula is: ,in The summation index for control points, with values ​​ranging from 1 to... Dimensionless For the first The position error value of each control point, in units of ; This represents the average value of the control point position error, in units of... The calculation formula is: ; To supplement the number of stations, dimensionless; The number of normalized reference stations is 10, which is dimensionless.

[0095] The lower-level game establishes a time efficiency objective function, which divides the average straight-line distance between adjacent stations by 20. The station transfer speed is used to obtain the travel time, which is then multiplied by the number of additional stations and then added to the 30 for a single station. The total observation time is obtained by multiplying the observation duration by the number of additional stations. The objective function for time efficiency is expressed as follows:

[0096] ;

[0097] In the formula, Total observation time, in units of ; The average straight-line distance between adjacent stations, in units of The calculation formula is: ,in The number of adjacent station pairs, dimensionless. The summation index for the station pairs, with values ​​ranging from 1 to... Dimensionless For the first The straight-line distance between adjacent stations is expressed in units of 1. ; The station transfer speed is set to 20. ; This represents the observation duration at a single station, with a value of 30. ; The number of normalized reference stations is 10, which is dimensionless.

[0098] The two objective functions are coupled through the common variable of the number of supplementary stations. Increasing the number of supplementary stations reduces the overall network accuracy unevenness but increases the total observation time. A balance between accuracy improvement and time cost is achieved by adjusting the number of supplementary stations. Then, an iterative search algorithm is used to calculate the overall network accuracy unevenness and total observation time one by one as the number of supplementary stations varies from 1 to 20. After normalizing both to the interval 0 to 1, they are weighted and summed using weight coefficients of 0.6 and 0.4 respectively. The weighted objective function is expressed as follows:

[0099] ;

[0100] In the formula, The weighted overall objective function is dimensionless. To optimize accuracy, the weighting coefficient is set to 0.6, which is dimensionless. This is the time efficiency weighting coefficient, with a value of 0.4, and is dimensionless. The minimum value of the network-wide accuracy non-uniformity in the range of 1 to 20 supplementary stations is dimensionless. The value of the network-wide accuracy non-uniformity is the maximum value within the range of 1 to 20 supplementary stations, and is dimensionless. The total observation time is the minimum value within the range of 1 to 20 supplementary stations, expressed in units of... ; The total observation time is the maximum value within the range of 1 to 20 supplementary stations, in units of... .

[0101] The number of additional monitoring stations required when the weighted sum reaches its minimum value is the game equilibrium solution. The calculation of the game equilibrium solution is expressed as follows:

[0102] ;

[0103] In the formula, The optimal number of additional monitoring stations, i.e., the game equilibrium solution, is dimensionless. This represents the value of the independent variable that minimizes the objective function.

[0104] The specific implementation of step S05 is as follows: In the identified areas with weak accuracy, the planar coordinates of existing stations are used as a given set of points and input into the Steiner tree algorithm. This algorithm finds the shortest tree network connecting all given points through enumeration or heuristic search. The algorithm allows adding Steiner points outside the given points as new station locations, minimizing the total length of the connection paths between all stations. The calculation of the total length of the connection paths is as follows:

[0105] ;

[0106] In the formula, This represents the total length of the connecting path, in units of... ; The number of connecting edges is dimensionless. The summation index for connecting edges, with values ​​ranging from 1 to... Dimensionless; For the first The planar coordinate vectors of the nodes, in units of ; For the first The planar coordinate vectors of the nodes, in units of ; The Euclidean distance norm is calculated using the following formula: ,in and The first The eastward and northward coordinates of each node, in units of , and The first The eastward and northward coordinates of each node, in units of .

[0107] During the calculation process, Delaunay triangulation is used to generate candidate Steiner points. Then, the connection method is optimized using the minimum spanning tree algorithm. Based on the optimal number of supplementary stations determined in step S04, the first few candidate positions calculated by the Steiner tree algorithm are selected as the actual supplementary station positions. Then, the stations are erected at these positions according to the method in step S01. Redundant observations were conducted with the total station to obtain the three-dimensional coordinates of the supplementary stations and incorporate them into the control network system.

[0108] The specific implementation of step S06 is as follows: A total station is set up on the control network stations to measure the three-dimensional coordinates of the center of each welded sphere node. During the measurement, a prism reflection method or a prism-free distance measurement method is used. Each sphere center is observed from at least three different stations to form a spatial intersection. After obtaining the measured three-dimensional coordinates of the sphere center, the theoretical design coordinates of the corresponding sphere center are extracted from the design drawings. The measured coordinates and design coordinates are used as the observed and theoretical values ​​to establish an error equation. The least squares adjustment principle is used, and the normal equation is constructed and solved using the minimum sum of squared residuals as the criterion. The corrected sphere center coordinate calculation is described as follows:

[0109] ;

[0110] In the formula, To correct the coordinate vector of the sphere's center, the unit is... ; The coefficient matrix of the observation equation reflects the geometric relationship of observations from multiple stations. Its elements are direction cosines or distance coefficients, which are dimensionless. The weight matrix for observations at the sphere center is determined based on the observation distance and angular accuracy. The diagonal elements are the weights of the sphere center observations and are dimensionless. The coefficient matrix of the observation equation transpose; This is the sphere center observation coordinate vector, containing the three-dimensional coordinates of the sphere center obtained from observations at multiple stations, in units of 1. .

[0111] The specific implementation of step S07 is to calculate the coordinate differences between the corrected sphere center coordinates and the design sphere center coordinates in the three directions of east, north, and elevation, and obtain the spatial deviation value through three-dimensional spatial distance calculation. The calculation of the spatial deviation value is described as follows:

[0112] ;

[0113] In the formula, This is the spatial deviation value, in units of ; , , These represent the eastward, northward, and elevation components of the corrected sphere center coordinates, respectively, in units of [units missing]. ; , , These represent the eastward, northward, and elevation components of the design sphere's center coordinates, respectively, in units of... .

[0114] When the spatial deviation value is greater than or equal to 2 If the threshold value is reached, it indicates that the current station location or observation conditions are causing insufficient measurement accuracy. In this case, the station location needs to be adjusted. The total station should be re-established at a location closer to the sphere node or with a better line of sight, and the measurement and adjustment calculation process in step S06 should be executed again. When the spatial deviation value is less than 2... When the accuracy of the ball center positioning meets the requirements of the space frame installation, the corrected coordinates of the ball node are recorded and the measurement of the next welded ball node continues.

[0115] The specific implementation methods of steps S08-S10 are the same as those described above, and will not be repeated in detail here.

[0116] Regarding the principle and effect of the accuracy optimization objective function, this function measures the uniformity of the control network accuracy distribution by the dispersion of the control point position error values. Its core calculation term is: This item reflects the relative fluctuation of the error; the larger the value, the more uneven the distribution of accuracy.

[0117] ;

[0118] This item divided by This reflects the diminishing marginal returns principle of increasing accuracy with the addition of monitoring stations; that is, increasing the number of monitoring stations significantly improves accuracy in the initial stage, but the effect gradually weakens in the later stages. This function enables the optimization process to achieve a global equilibrium in accuracy distribution with limited resources, avoiding situations where local areas have excessively high accuracy while other areas have insufficient accuracy, thus ensuring that every node in the entire grid structure meets the 2... Positioning accuracy requirements within [a certain range].

[0119] Regarding the principle and effect of the time efficiency objective function, this function comprehensively considers the station transfer time and observation time, and its core calculation term is: and The former calculates the moving cost by the ratio of the average straight-line distance between adjacent stations to the transfer speed, and multiplies it by the normalized number of supplementary stations to reflect the total transfer time.

[0120] ;

[0121] The latter is the product of the observation time at a single station and the normalized number of supplementary stations, yielding the total observation time. This function allows the optimization process to balance accuracy improvement with construction efficiency, avoiding excessive increases in the number of stations that could lead to longer construction periods and higher costs. Through a coupled game with the accuracy optimization objective function, an optimal balance between the accuracy of the space frame installation and construction efficiency is achieved, ensuring that the following conditions are met: Under the premise of meeting positioning accuracy requirements, the total observation time was controlled within a reasonable range, which improved the construction quality and economic benefits of the large terminal building's grid structure.

[0122] It should be noted that the variables involved in this invention are explained in detail in Tables 1 and 2.

[0123] Table 1. Variable Explanation Table (Part 1)

[0124]

[0125] Table 2. Variable Explanation Table (Part Two)

[0126]

[0127] To better understand and implement this invention, a specific application scenario, Example 2, is provided below: The technical team first established a site control network in the terminal construction area. Twelve GPS-RTK base stations and eighteen total station stations were deployed within the construction area, covering the entire projection range of the grid structure. For each control point, three independent observations were conducted using both GPS-RTK and total station methods to obtain multiple sets of three-dimensional coordinate data. Through data comparison and statistical analysis, gross errors exceeding 1.5mm were eliminated, ultimately obtaining reliable three-dimensional coordinates for 30 initial control points. The technical team used a total station to measure the straight-line distance between adjacent stations, recording that the straight-line distance ranged from 18m to 45m, with an average of 28m. Based on this observation data, the technical team established a site control network coordinate system. This coordinate system adopted a local coordinate system for the construction site, with the origin set at the center of the grid structure.

[0128] After obtaining the initial control network, the technical team used the rank-deficient free network adjustment method to uniformly process the observation data. In the adjustment calculation, the coordinates of any known points were not fixed; all 30 control points were treated as undetermined parameters. By establishing normal equations and solving them using the least squares criterion, the team obtained the adjusted coordinates and covariance matrix of each control point. The adjustment results showed that the positional error of the control points ranged from 1.2 mm to 5.8 mm, with an overall mean square error of 2.4 mm. The rank-deficient free network adjustment method effectively eliminated the systematic deviation propagation caused by errors in known points, achieving coordinate unification across multiple control networks.

[0129] Based on the covariance matrix obtained from the adjustment calculations, the technical team plotted the error ellipse for each control point, as shown in Table 3.

[0130] Table 3. Statistical Table of Error Ellipse Parameters for Some Control Points

[0131]

[0132] The technical team's analysis revealed that 8 out of 30 control points had a semi-major axis length greater than 3mm on their error ellipses. These control points were mainly distributed in the northeast and southwest regions of the grid structure. These two regions were identified as areas with low accuracy, requiring the addition of redundant observation stations to improve positioning accuracy. The formation of these low-accuracy areas was primarily due to the low station density and long observation paths during the initial station deployment, leading to significant error accumulation.

[0133] To determine the optimal number of additional monitoring stations, the technical team performed a two-level game theory optimization calculation. The upper-level game model aimed to minimize the overall network accuracy non-uniformity, while the lower-level game model aimed to minimize the total observation time. The team first calculated the standard deviation of the control point location errors to be 1.35 mm and the average to be 2.4 mm. According to the accuracy optimization objective function, the overall network accuracy non-uniformity equals the standard deviation of the control point location errors divided by the average control point location errors, then divided by the square root of the number of additional monitoring stations, plus 1. The team also calculated the observation time per station to be 30 minutes and the average straight-line distance between adjacent stations to be 28 meters. According to the time efficiency objective function, the total observation time equals the average straight-line distance between adjacent stations divided by... Then multiply by the number of additional stations, and add the observation time of a single station multiplied by the number of additional stations.

[0134] The technical team obtained the optimization results shown in Table 4 by iteratively calculating the network-wide accuracy non-uniformity and total observation time under different numbers of supplementary stations:

[0135] Table 4 Calculation Results of Optimized Number of Supplementary Stations

[0136]

[0137] By comparing the weighted sum and normalized values, the technical team determined that when the number of supplementary stations is 6, the weighted sum of the normalized value of the network-wide accuracy non-uniformity and the normalized value of the total observation time reaches a minimum of 0.516. The number of supplementary stations at this point represents the game equilibrium solution. Therefore, the optimal number of supplementary stations is determined to be 6.

[0138] The technical team used the Steiner tree algorithm to calculate the optimal locations for six additional monitoring stations. The algorithm takes eight existing stations in areas with low accuracy as a given set of points, calculates the shortest network tree connecting all given points, and allows for the addition of six extra nodes to reduce the total connection length. The calculation results showed that three additional stations were needed in the northeast region and three in the southwest region. Based on the calculated location coordinates, the technical team added six redundant observation stations, numbered RS-01 to RS-06, in the areas with low accuracy. These six additional stations were observed using GPS-RTK and a total station to obtain their three-dimensional coordinates. After adding the stations, the technical team re-performed the rank-deficient free network adjustment calculation. The results showed a significant improvement in the overall accuracy of the control network; the number of control points with a semi-major axis length greater than 3mm on the error ellipse decreased from eight to zero, and the overall network accuracy non-uniformity decreased from 1.563 to 1.230.

[0139] After completing the construction of the high-precision control network, the technical team began measuring the coordinates of the sphere centers of the grid structure. The team used a total station to perform three-dimensional coordinate measurements on each welded sphere node, taking five measurements and averaging the results for each sphere center position. For the first lower chord sphere node B-0001, the designed sphere center coordinates were... The measured coordinates of the sphere's center are The technical team performed least-squares adjustment calculations on the measured and designed center coordinates of the sphere, and obtained the corrected center coordinates by combining data from five observations. .

[0140] The technical team calculated the spatial deviation between the measured and designed sphere center coordinates. For node B-0001, the spatial deviation was 1.8mm, less than the 2mm accuracy requirement. Therefore, the positioning accuracy of this node was acceptable, and the measurement of the next welded sphere node could proceed. During the measurement of 2847 welded sphere nodes, the technical team found that 127 nodes had a spatial deviation greater than or equal to 2mm, accounting for 4.5% of the total. For these nodes with unacceptable accuracy, the technical team adjusted the station positions and remeasured. Ultimately, the spatial deviation of all nodes was less than 2mm, meeting the accuracy requirements for the space frame installation.

[0141] The technical team located the outer contour of the ball joint based on the corrected sphere center coordinates and the diameter of the welded sphere. For the lower chord ball joint B-0001, the welded sphere diameter is 420mm and the radius is 210mm. The technical team used a ground compass tool to fix the center positioning rod at the corrected sphere center coordinate point. At the projected position on the ground, the radius arm length was adjusted to 210mm, and the radius arm was rotated around the central positioning rod to mark the outer contour line of the lower chord ball on the ground. For the upper chord ball nodes, the welded ball diameter was 380mm and the radius was 190mm; the outer contour line of the upper chord ball was marked using the same method. The technical team marked the outer contour lines of a total of 2847 ball nodes on the ground, providing a precise positioning reference for the subsequent installation of the club assembly.

[0142] The technical team began installing the bottom-chord club assembly. For example... Figure 2 As shown, using a one-ball-one-club method, the bottom chord ball B-0001 and the bottom chord club L-0001 are connected on the ground with M48 bolts to form the bottom chord club assembly. For example... Figure 3 As shown, the component weighs 385 kg and was hoisted onto the jig using a 25t truck crane. During the hoisting process, the technical team used a plumb bob to check the spatial position, aligning the plumb line with the center of the lower chord ball's outer contour on the ground. When the plumb bob indicated that the deviation between the lower chord ball's center and the center of the ground's outer contour was less than 1 mm, the technical team fixed the lower chord ball assembly, completing its positioning. The technical team completed the installation of all lower chord ball assemblies using this method, with the lower chord layer space frame installation cycle taking 23 days.

[0143] The technical team then installed the topswing club assembly. For example... Figure 1 As shown, a one-ball-two-club configuration is used. On the ground, the topspin ball T-0001 is connected to the two web clubs W-0001 and W-0002 using M42 bolts to form the topspin club assembly. Figure 4 As shown, the component weighs 296 kg and was lifted to its installation position using a truck crane. The technical team used the third web member W-0003 for spatial constraint positioning. One end of this web member is connected to the already installed lower chord ball, and the other end is connected to the upper chord ball. By adjusting the spatial angles of the three web members, the technical team used a plumb bob to align the center of the upper chord ball with the center of its outer contour line on the ground. When the plumb bob indicated that the deviation between the center of the upper chord ball and the center of its outer contour line on the ground was less than 1 mm, and the connecting bolts of the third web member could be easily assembled, the technical team fixed the upper chord ball member assembly, completing the positioning of the upper chord ball member assembly. The technical team completed the installation of all upper chord ball member assemblies using this method. The installation period for the upper chord layer space frame was 27 days, and the overall space frame construction period was 50 days.

[0144] After construction was completed, the technical team conducted a precision test on the entire space frame. (See Table 5 for details.)

[0145] Table 5. Statistics on the Positioning Accuracy of the Center of the Grid

[0146]

[0147] Statistical results show that among the 2847 welded ball joints, 75.7% of the joints have a spatial deviation of less than 1.0 mm, 20.0% have a spatial deviation between 1.0 mm and 1.5 mm, and 4.3% have a spatial deviation between 1.5 mm and 2.0 mm. All joints meet the design requirement of 2 mm accuracy. The overall closure accuracy of the space frame is good, and the bolts connecting the members are assembled smoothly without the need for secondary adjustments.

[0148] This invention represents a significant advancement over traditional grid-based positioning methods. Traditional methods typically employ a single-level control network, where control point errors accumulate and propagate along the observation path, leading to a substantial decrease in positioning accuracy in areas far from the benchmark. This invention utilizes a rank-deficient free network adjustment method, treating all control points as undetermined parameters without fixing any known point coordinates, thus fundamentally eliminating the systematic deviation propagation caused by known point errors. Traditional methods often rely on experience to add monitoring stations after identifying areas with low accuracy, lacking scientific basis and easily resulting in station redundancy or insufficiency. This invention establishes a mathematical relationship between accuracy improvement and time cost through a two-layer game optimization model, determining the optimal number of supplementary monitoring stations by solving the game equilibrium solution, achieving a balance between control network accuracy and construction efficiency. Traditional methods rely on the experience of technicians for selecting supplementary monitoring station locations, making it difficult to guarantee optimal observation paths. This invention uses the Steiner tree algorithm to calculate the optimal supplementary monitoring station locations, minimizing the control network observation path and optimizing accuracy propagation, thus ensuring control network quality from a geometric topology perspective. Traditional methods for locating the ball center typically involve point-by-point measurement and installation, lacking overall error control. This invention corrects the ball center coordinates using least-squares adjustment calculations, obtaining the optimal estimate by integrating multiple observation data, effectively eliminating the influence of random observation errors. Traditional methods often require multiple high-altitude adjustments during club assembly installation, resulting in low construction efficiency and safety hazards. This invention uses a ground compass to pre-mark the outer contour of the ball nodes, combining a one-ball-one-club and one-ball-two-club pre-assembly method on the ground, and uses a plumb bob to achieve precise alignment of the ball center, reducing the number of high-altitude operations and improving installation accuracy. These technological improvements comprehensively enhance the positioning accuracy and construction efficiency of large and complex space frame structures, providing a reliable technical reference for similar projects.

[0149] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for locating a ball of a welded ball net rack in a spherical coordinate, characterized in that, The site control network is established, the rank defect free network adjustment method is used to process the observation data to eliminate the multi-level transmission cumulative error, the error ellipse is used to identify the weak precision area, the double-layer game optimization model is established to solve the optimal number of supplementary stations, the Steiner tree algorithm is used to determine the position of the supplementary stations, the redundant observation stations are added in the weak precision area to realize the uniform distribution of the control network precision, the three-dimensional coordinate measurement is carried out on the welded ball nodes, the least square adjustment is used to calculate the corrected ball center coordinates, and the ball outline is measured according to the corrected ball center coordinates, and the space positioning of the ball rod assembly is completed by using the plumb instrument.

2. The method of claim 1, wherein, The steps of establishing the site control network are as follows: the GPS-RTK reference station and the total station station are arranged in the terminal building construction area, the initial control point three-dimensional coordinates are obtained through redundant observation, and the straight line distance between adjacent stations is recorded.

3. The method of claim 2, wherein, Redundant observation refers to the use of GPS-RTK and total station two independent measurement methods to observe the same control point multiple times to obtain multiple sets of three-dimensional coordinate data of the control point position, and the gross error observation value is eliminated through data comparison and statistical analysis.

4. The method of claim 3, wherein, The rank defect free network adjustment method refers to not fixing any known point coordinates in the control network adjustment calculation, and all control points are used as undetermined parameters to participate in the adjustment, and the normal equation is solved by the least square criterion.

5. The method of claim 4, wherein, The error ellipse refers to the error distribution graph of the control point plane coordinates, which is calculated and drawn according to the covariance matrix of the control point position error value, the long semi-axis represents the maximum error direction and value of the control point position, and the short semi-axis represents the minimum error direction and value.

6. The method of claim 5, wherein, The weak precision area refers to the area where the length of the long semi-axis of the error ellipse in the control network is greater than 3mm.

7. The method of claim 6, wherein, In the double-layer game optimization model, the upper game model establishes the precision optimization objective function with the minimum precision non-uniformity of the whole network as the target, and the lower game model establishes the time efficiency objective function with the minimum total observation time as the target.

8. The method of claim 7, wherein, The calculation of the precision optimization objective function is as follows: the precision non-uniformity of the whole network is equal to the standard deviation of the control point position error value divided by the average value of the control point position error value, and then divided by the square root of the number of supplementary stations, and then added by 1.

9. The method of claim 8, wherein, The calculation of the time efficiency objective function is as follows: the total observation time is equal to the average value of the straight line distance between adjacent stations divided by 20m / min, multiplied by the number of supplementary stations, and then added by the observation time of a single station multiplied by the number of supplementary stations.

10. The method of claim 9, wherein, The game equilibrium solution refers to the number of supplementary stations corresponding to the minimum weighted sum of the precision optimization objective function and the time efficiency objective function, which is obtained by iteratively calculating the precision non-uniformity of the whole network and the total observation time under different numbers of supplementary stations.

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