A method for measuring the root opening of a power transmission tower foundation

Abstract

The application relates to a power transmission tower foundation root opening measurement method, belonging to the technical field of engineering installation detection, foundation pre-embedded part positioning detection and geometric position measurement. The application respectively measures the pre-embedded bolt circle center, the pre-embedded bolt group geometric center on multiple cylindrical concrete foundations, and measures the geometric centers of two position-fixed cylindrical marker rods in the local coordinate system of each concrete foundation. The local coordinate system of the first concrete foundation is taken as the overall coordinate system, a rotation matrix and a translation vector are established according to the coordinate corresponding relationship of the same pair of cylindrical marker rods in the local coordinate system and the overall coordinate system, the pre-embedded bolt group geometric centers of the concrete foundations are uniformly converted into the overall coordinate system, and the actual center distance, the relative orientation and the foundation root opening between different pre-embedded bolt group geometric centers are calculated. The application can improve the stability and repeatability of the measurement results, does not need to additionally set an overall measurement site, and is favorable for improving the device portability and the adaptability to different foundation arrangements.

Description

Technical Field

[0001] This invention belongs to the field of engineering installation inspection, foundation embedded part positioning inspection and geometric position measurement technology, and relates to a method for measuring the root opening of a power transmission tower foundation. Background Technology

[0002] The concrete foundation of a transmission tower is a crucial load-bearing structure for overhead transmission lines, and its positional accuracy directly affects the tower's installation, stress state, and operational safety. For a tower supported by multiple separate concrete foundations, the geometric centers of the pre-embedded bolt groups in each foundation have a designed horizontal center distance and relative positional relationship, where the horizontal center distance is the foundation root opening described in this application. If the actual root opening deviates significantly from the design value, even if the position of the pre-embedded bolt groups within a single foundation meets the requirements, problems such as the tower foot mounting holes not aligning simultaneously with the pre-embedded bolts in each foundation, installation difficulties, or uneven stress distribution may still occur.

[0003] Existing pre-embedded bolt group detection devices are mainly designed for detecting the position of pre-embedded bolt groups within a single foundation. For example, Chinese invention patent 202420696576.5 discloses a multi-functional measuring ruler for power tower foundation acceptance, which uses a main ruler and a secondary ruler for measurement; Chinese invention patent 202011305753.5 discloses a tower foundation eccentricity measuring tool, which uses a sleeve, a telescopic rod, and a laser ranging component to form a measuring support. When these devices are used on-site, they require assembly, adjustment, and positioning. Some operations still rely on manual reading and calculation. Furthermore, as the span of the components increases, structural deformation and installation errors may be introduced, affecting detection efficiency and the repeatability of measurement results.

[0004] When performing root opening detection between multiple separate concrete foundations, if a separate station method is used to measure each foundation individually, the resulting geometric center coordinates of the embedded bolt groups will belong to different local coordinate systems due to the different installation positions and initial orientations of the measuring devices. Therefore, these coordinates cannot be directly used to calculate the actual root opening and relative position between the foundations. If a large-span measuring component is used to establish a measurement benchmark across multiple foundations, it is easily limited by foundation spacing, site topography, and working space, increasing the difficulty of on-site layout, positioning, and error control.

[0005] Therefore, it is necessary to propose a method for detecting the root opening of multiple foundations of transmission towers. Based on the local measurement of each foundation's pre-embedded bolt group, the corresponding relationship between different local coordinate systems is established, and the geometric center of each pre-embedded bolt group is unified to the same coordinate system. This allows for the acquisition of the actual root opening and relative positional relationship between different foundations, while reducing reliance on large-span measurement supports, manual readings, and manual calculations, thereby improving the efficiency, accuracy, and repeatability of on-site testing. Summary of the Invention

[0006] To address the problems of existing technologies, this invention provides a method for measuring the foundation root opening of transmission towers. This invention uses a laser displacement sensor to measure radial distance and a rotary encoder to measure the corresponding azimuth angle. The polar coordinates of the measuring points are converted to Cartesian coordinates. Specifically, the laser displacement sensor and rotary encoder are used to measure the centers of pre-embedded bolts and the geometric centers of pre-embedded bolt groups on multiple cylindrical concrete foundations. Simultaneously, the geometric centers of two fixed-position cylindrical marker poles are measured in the local measurement coordinate system of each concrete foundation. For each cylindrical concrete foundation, the centers of each pre-embedded bolt are obtained through circle fitting at multiple measuring points on the cylindrical surface of the pre-embedded bolts, and the geometric center of the pre-embedded bolt group is calculated. At the same time, the geometric centers of the two fixed-position cylindrical marker poles are measured. Using the local coordinate system of the first concrete foundation as the global coordinate system, a rotation matrix and translation vector are established based on the coordinate correspondence between the same pair of cylindrical marker poles in the local and global coordinate systems. This transforms the geometric centers of the pre-embedded bolt groups of each concrete foundation into the global coordinate system, allowing for the calculation of the actual center distance, relative azimuth, and foundation root opening between the geometric centers of different pre-embedded bolt groups.

[0007] To achieve the above objectives, the present invention adopts the following technical solution.

[0008] A method for measuring the foundation root opening of a power transmission tower includes the following steps: The first step is local measurement within each concrete foundation: A measuring device is set up on each concrete foundation to establish a local coordinate system and obtain the local coordinates of the geometric center of the embedded bolt group and the geometric center of the same pair of fixed cylindrical marker poles within that concrete foundation; specifically: Step 1.1: Assemble the foundation root opening measurement device for the power transmission tower and set up cylindrical marker poles; The foundation root opening measurement device for transmission towers includes a measuring device, a data processing and display device, and two cylindrical marker poles. The measuring device acquires distance and angular displacement data of measuring points on the surfaces of the embedded bolts and cylindrical marker poles, and sends the data to the data processing and display device. The data processing and display device converts the polar coordinate data to planar coordinates, calculates the center of the embedded bolts, the geometric center of the embedded bolt group, and the geometric center of the two cylindrical marker poles, establishes the rotation matrix, translation vector, and homogeneous transformation matrix from each local coordinate system to the global coordinate system, and further calculates the actual center distance, relative orientation, and foundation root opening between the geometric centers of different concrete foundation embedded bolt groups.

[0009] The measuring device includes a laser displacement sensor, a laser displacement sensor support, a set screw, a rotary encoder support, a rotary encoder, a cover plate, a foam pad, a battery, a housing, a data transmission device, and two cylindrical marker rods. These two cylindrical marker rods are designated as a first marker rod and a second marker rod, both positioned in stable locations that will not move during measurement. Each marker rod is marked with an identifiable mark to ensure consistent correspondence between the first and second marker rods across different local measurement stages. A detailed structural layout description is as follows: The rotary encoder support is a hollow cylindrical structure with a flange on its lower outer periphery. It serves as a support component for mounting and securing the rotary encoder, and its interior contains a space adapted to the encoder's shape. The rotary encoder body is cylindrical, with an output shaft in the center and a base housing on the outside. The output shaft can rotate freely around the base housing, and its top circumferential surface has threaded holes for fixed connection with the rotary encoder support. The rotary encoder is installed inside the support, and the two are coaxial. A cylindrical positioning boss is located on the upper part of the encoder, and the support has corresponding positioning holes. The cylindrical positioning boss is inserted into the positioning holes, and a clearance fit ensures coaxial positioning between the rotary encoder and the support, guaranteeing that the output shaft axis of the rotary encoder coincides with or remains coaxial with the predetermined rotation axis of the support. The outer housing of the rotary encoder is fixed to the inner wall of the support with screws, thus restricting axial movement and circumferential rotation of the encoder housing relative to the support. The flange has multiple connecting holes spaced circumferentially for screws to pass through and securely connect to the cover plate, ensuring the rotary encoder support is stably mounted on the cover plate. The cover plate supports and secures the rotary encoder support and provides a mounting base for the rotary encoder and its related rotating components.

[0010] The laser displacement sensor support is a block structure with an open bottom. Its upper surface serves as the mounting surface for the laser displacement sensor, and its hollow bottom opening allows for insertion into the upper part of the rotary encoder support. The laser displacement sensor support can rotate relative to the rotary encoder support around the output shaft axis of the rotary encoder. The laser displacement sensor support has a cylindrical hole inside that corresponds to the output shaft of the rotary encoder. The output shaft of the rotary encoder is inserted into the cylindrical hole, with a clearance fit. This clearance fit enables axial assembly and coaxial positioning between the rotary encoder output shaft and the laser displacement sensor support.

[0011] The output shaft of the rotary encoder has a pre-machined flat surface on its outer periphery. The laser displacement sensor support has a threaded hole communicating with a cylindrical hole. A set screw is screwed into the threaded hole, and the end of the set screw presses against the flat surface of the rotary encoder's output shaft. The engagement of the set screw and the flat surface restricts the relative circumferential rotation between the rotary encoder's output shaft and the laser displacement sensor support, forming a fixed circumferential connection. This ensures that the rotation of the laser displacement sensor support synchronously drives the rotary encoder's output shaft. Simultaneously, the flat surface on the output shaft increases the clamping contact area of ​​the set screw, reducing slippage and improving the reliability and measurement accuracy of angle transmission.

[0012] Furthermore, the laser displacement sensor is disposed on the upper surface of the laser displacement sensor support and is fixedly connected to the laser displacement sensor support by screws. The laser displacement sensor support is provided with a mounting plane, connecting holes, lateral positioning baffles, and end positioning baffles for mounting the laser displacement sensor, to ensure the positioning and fixation of the laser displacement sensor on the laser displacement sensor support. The laser emission direction of the laser displacement sensor is preferably set along the radial direction of the laser displacement sensor support, so that the emitted measuring laser can be directed towards the target object to be measured.

[0013] The rotary encoder detects the rotation angle of its output shaft relative to the encoder housing and outputs angular displacement data corresponding to the current measurement direction of the laser displacement sensor. The laser displacement sensor emits a laser along the current measurement direction and measures the straight-line distance between its measurement reference position and the measured point, outputting corresponding distance data. The angular displacement data output by the rotary encoder characterizes the azimuth angle of the measured point relative to the reference direction of the measuring device. The distance data output by the laser displacement sensor, after calibration based on installation geometry, characterizes the radial distance of the measured point relative to the rotation center of the measuring device. By correlating the angular displacement data and distance data obtained at the same measurement moment, the polar coordinate parameters of the measured point in the measurement plane can be obtained. When the laser displacement sensor support rotates continuously or in stages around the output shaft axis of the rotary encoder, the laser displacement sensor can measure the distance to multiple measuring points in different orientations, while the rotary encoder simultaneously records the azimuth angle corresponding to each measuring point. By collecting the azimuth and radial distance of multiple measuring points, the polar coordinates of each measuring point can be further converted into Cartesian coordinates. Based on this, the position of the pre-embedded bolt to be measured in the measurement plane, the geometric center position of the pre-embedded bolt group, and the geometric center position of the two cylindrical marker poles can be calculated. When measuring the cylindrical marker pole, at least three measuring points on its cylindrical surface are obtained using the same distance and azimuth synchronous acquisition method. The coordinates of the intersection point of the cylindrical marker pole axis and the measurement plane are obtained through circle fitting, which is used as the geometric center coordinates of the cylindrical marker pole in the current local coordinate system.

[0014] The cover plate is detachably fixed to the housing, providing a stable support structure and horizontal reference for the entire device.

[0015] The battery, foam pad, and data transmission device are all housed inside the housing. An installation cavity for accommodating the battery and data transmission device is formed inside the housing. An opening is provided at the top of the housing, and a cover plate covers the opening and is detachably fixed to the housing with screws, thus forming a relatively enclosed internal installation space. A notch is provided on the front surface of the housing to allow relevant cables to be led out from inside the housing and connected to the external rotary encoder and laser displacement sensor, respectively.

[0016] During the measurement process, the rotary encoder support and the rotary encoder housing remain fixed relative to the cover plate. The operator rotates the laser displacement sensor support around the output shaft axis of the rotary encoder, and the laser displacement sensor, fixedly mounted on the support, rotates synchronously. Since the laser displacement sensor support is circumferentially fixed to the output shaft of the rotary encoder via set screws, its rotation synchronously drives the output shaft of the rotary encoder. During the measurement, the battery supplies power to the laser displacement sensor, rotary encoder, and data transmission device; the laser displacement sensor collects distance data from the measured point, and the rotary encoder synchronously collects the corresponding angular displacement data; the data transmission device sends the distance and angular displacement data to the data processing and display device. The data processing and display device calculates the center of the embedded bolts, the geometric center of the embedded bolt group, and the geometric center of the two cylindrical marker poles based on the received data, and establishes a coordinate transformation from the local coordinate system to the global coordinate system based on the coordinates of the common marker pole, outputting the foundation root spacing between the geometric centers of different embedded bolt groups.

[0017] Two cylindrical marker poles of identical dimensions are used. The cylindrical marker pole marked with identification mark A is defined as the first marker pole, and the cylindrical marker pole marked with identification mark B is defined as the second marker pole. These two cylindrical marker poles are named the first marker pole and the second marker pole, serving as the first and second common reference points. Both cylindrical marker poles must be placed in stable positions observable from all stations and must not be moved during the entire measurement period. Furthermore, the projection points of the axes of the two cylindrical marker poles onto the horizontal plane must not coincide. The axes of the two cylindrical marker poles should remain vertical so that the centers of the cross-sections obtained at different station heights have the same horizontal projection.

[0018] Step 1.2: Set up the measuring device on the current concrete foundation and establish a local coordinate system.

[0019] The total number of concrete foundations to be tested is denoted as . M , M The number is an integer not less than 2; the current concrete foundation number is recorded as... i , i Take 1 toM An integer. Place the measuring device at the... i The upper surface of the concrete foundation does not obstruct the position of the measuring optical path for the first pre-embedded bolt and the two cylindrical marker poles. During a complete measurement of the concrete foundation, the position, zero angle, and leveling state of the measuring device remain unchanged. Each station uses a horizontal measuring plane, and the center of the pre-embedded bolt is measured according to the agreed installation reference section. This invention calculates the plane position and horizontal root opening, but does not calculate the elevation difference or spatial slope distance.

[0020] A complete setup at a fixed position and a fixed angle zero point is called a measuring station. j Indicates the station number, in S Indicates the total number of stations. j Take 1 to S An integer. Record the first... j The station and the measured number i The correspondence between the concrete foundations; each concrete foundation requires one effective erection, therefore S = M The first measuring station was set up on the first concrete foundation; the local origin O was the intersection of the rotation axis of the rotary encoder and the horizontal measuring plane. j With the initial measurement direction fixed as X j In the positive direction of the axis, within the same horizontal plane, from X j The direction in which the axis rotates 90° counterclockwise is Y. j Establish a local coordinate system O along the positive axis. j -X j Y j Rotary encoder with X j The positive direction of the axis is zero, and counterclockwise is positive. The origin and initial orientation of each station are allowed to be different, but the positive direction of the angle must be consistent.

[0021] Step 1.3: Convert the distance and azimuth into local coordinates.

[0022] The first i The total number of pre-embedded bolts on the concrete foundation is denoted as . , k This indicates the number of the embedded bolts in the concrete foundation. k Take 1 to ;by q This indicates the serial number of the valid measurement point on a single measured cylindrical surface. k The first pre-embedded bolt q The coordinates of the surface measuring points are as follows: The superscript j in parentheses indicates the coordinate system of the station. The total number of valid measuring points for the pre-embedded bolts at this station is denoted as U. ik (j) , q Take 1 to U ik(j) , and U ik (j) Not less than 3. Its polar coordinate transformation formula is: (1) In the formula, , The measuring points are along X j Axis, Y j The coordinate components of the axes; For O j Radial distance to the measuring point; For X j The positive axis is rotated counterclockwise to the directional azimuth angle of the measuring point's radial direction.

[0023] The radial distance is based on the local origin. If the distance measurement reference position of the laser displacement sensor does not coincide with the local origin, the original distance measurement value should first be converted into the distance from the local origin to the measuring point according to the calibrated installation geometry, and then substituted into the coordinate calculation formula.

[0024] Step 1.4: Determine the center of the first pre-embedded bolt.

[0025] In the j The station kept the measuring device stationary and monitored the first... i A concrete foundation ( i = j For the first embedded bolt (indicating measurement completed within a concrete foundation), at least three non-overlapping and non-collinear surface measuring points are selected within the same measuring section. , and The local coordinates obtained in step 1.3 are abbreviated as: (2) In the formula, a, b, c The three selected measuring points are designated as measuring point 1, measuring point 2, and measuring point 3. , , , , , The first, second, and third measuring points are respectively located at the 1st, 2nd, and 3rd measuring points. j Local coordinate components of the station.

[0026] Let the coordinates of the center of the first pre-embedded bolt be... =( , ) T In the formula, For the first j The first station iLocal coordinates of the center of the section of the first embedded bolt in a concrete foundation; , The center of the circle is located along the local coordinate system O. j -X j Y j X j axis and Y j The coordinate components of the axis. The radius of the cross-section circle is... r i1 Then any point on the circumference ( , )satisfy: (3) Substitute the coordinates of the three measuring points into the equation of the circle. Subtract the equation corresponding to the first measuring point from the equations corresponding to the second and third measuring points respectively, eliminating the radius term and the square term of the center coordinates, to obtain a system of linear equations about the center coordinates: (4) The coefficient matrix, written in matrix form, is: (5) When the three measurement points are not collinear, the coefficient matrix is ​​invertible. Solving for the coefficient matrix using a system of two linear equations yields the solution. If the three measuring points are nearly collinear, then select new measuring points with a more adequate distribution.

[0027] Furthermore, in actual measurements, more than three valid measuring points can be collected, and the center of the circle can be determined using least-squares circle fitting to reduce the influence of random errors by utilizing redundant measuring points. The position, zero angle, and measuring cross-section of the measuring device should remain unchanged.

[0028] Step 1.5: Calculate the center of the remaining pre-embedded bolts in sequence.

[0029] (6) In the formula, For the first k Local coordinates of the center of each pre-embedded bolt. , Its coordinate components, Indicates the number of the embedded bolts. Indicates the first i The total number of pre-embedded bolts in a concrete foundation.

[0030] For the remaining embedded bolts in the concrete foundation, convert the coordinates of the surface measuring points according to step 1.3, and then determine the center of the circle according to step 1.4.

[0031] Step 1.6: Calculate the geometric center of the pre-embedded bolt group in the concrete foundation, thus obtaining the centroid of the pre-embedded bolt group in this concrete foundation. .

[0032] (7) In the formula, , Centroid of the pre-embedded bolt group in this concrete foundation The local coordinate components. The centroid of the pre-embedded bolt group in this concrete foundation is taken as the arithmetic mean of the coordinates of the centers of all pre-embedded bolts, and is not replaced by the center of the outer contour of the concrete foundation or the origin of the instrument.

[0033] Step 1.7: Measure the two common marker poles and calculate the direction of the connecting line.

[0034] Keep the first j The measuring device at the station remains stationary. At least three non-coincident and non-collinear cross-sectional measuring points are collected from the cylindrical surfaces of the first and second marker poles, respectively. The coordinates of each measuring point are marked as follows: , , For the first j The first marker pole at the station q The effective surface measuring points are in the local coordinate system O. j -X j Y j The coordinate vector in; For the first j The second marker pole at the station q The coordinate vectors of each effective surface measuring point in the local coordinate system. For the first marker pole, q =1,2,…,U A (j) For the second marker pole, q = 1, 2, ..., U B (j) The total number of effective surface measuring points for the first and second marker poles are U respectively. A (j) U B (j) . q Values ​​are taken within the valid measuring point range of the corresponding marker pole.

[0035] (8) In the formula, For the first marker pole q Each surface measuring point is relative to the local origin O. j The radial distance; For the second marker pole q Each surface measuring point is relative to the local origin O. j The radial distance; For local X j The directional azimuth angle of the radial direction of the measuring point on the qth surface of the first marker rod, rotated counterclockwise in the positive direction of the axis; For local X j The azimuth angle O of the radial direction of the measuring point on the qth surface of the second marker rod is obtained by rotating counterclockwise in the positive direction of the axis.

[0036] (9) In the formula, , The coordinates of the center of the cross-section of the first and second marker poles obtained in step 1.4 are: , and , Its local coordinate components. The center of the circle is obtained by fitting the measurement points on the surface of each rod, and is not replaced by a single surface measurement point.

[0037] The coordinates of the center of the circle can also be expressed using the radius vector and azimuth angle as follows: (10) In the formula, , For O j The radius vector length to the center of the two cylindrical marker poles; , This is the directional azimuth of the corresponding circle's center radius vector. The radius vector and azimuth of the circle's center should be calculated from the fitted circle's center coordinates, not directly using the distance and angle of a single surface measuring point.

[0038] (11) In the formula, Let be the vector of the common line connecting the center of the first marker pole circle to the center of the second marker pole circle. , These are the local coordinate components of the common connection vector. Each station follows the sequence of the first marker pole pointing to the second marker pole.

[0039] (12) In the formula, The common line connecting the center of the first marker pole to the center of the second marker pole is relative to the first... j Local X of the measuring station j The azimuth angle along the positive axis. The distance between the centers of the first and second marker poles is defined in step 1.8. This involves sequentially completing the local measurements of all concrete foundations.

[0040] Set up the measuring device sequentially on the remaining concrete foundations, repeating steps 1.2 to 1.7 until all M concrete foundations have been measured. Record the corresponding concrete foundation number and the centroid P of the pre-embedded bolt group for each foundation at each station. i (j) The coordinates A of the center of the first and second marker poles (j) With B(j) The common line connecting the center of the first marker pole to the center of the second marker pole is relative to the first... j Local X of the measuring station j directional azimuth angle in the positive direction of the axis Distance between the centers of the first and second marker poles d AB (j) The origin and initial orientation of each erection may be different, but the positions, corresponding identities, distance measurement scales, and positive angles of the two cylindrical marker poles must remain consistent.

[0041] The actual distance between the first and second fixed marker poles of the same pair should not change with the measuring station. The center distance measured at each station should be consistent within the allowable error range of the project, which is used to detect errors or abnormal measurement data in the target correspondence. The allowable error range of the project should be determined in advance based on the instrument accuracy, station layout conditions and testing requirements, and unverified uniform values ​​should not be used.

[0042] The second step is to establish the overall coordinate relationship and calculate the foundation root opening between each pre-embedded bolt group: The local coordinate system of the first station is directly defined as the overall coordinate system. The rotation and translation relationships between the remaining local coordinate systems and the overall coordinate system are established using the first and second marker poles. The geometric centers of each pre-embedded bolt group are transformed into the overall coordinate system. The horizontal distance between the geometric centers of any two pre-embedded bolt groups is calculated, i.e., the foundation root opening. Specifically: Step 2.1: Use the local coordinate system of the first station as the global coordinate system.

[0043] The local coordinate system O1-X1Y1 of the first station is directly defined as the global coordinate system O. G -X G Y G . G Mark the global coordinate system. The origins and axes of the two coordinate systems coincide, and the coordinates measured at the first station do not require transformation: (13) Among them, A (G) B (G) These are the global coordinates of the center of the first marker pole and the center of the second marker pole, respectively. (1) B (1) These are their local coordinates at the first station; P1 (G) P1 (1) These are the global coordinates of the centroid of the first pre-embedded bolt group and the local coordinates at the first measuring station, respectively.

[0044] The overall reference datum is fixed using the center coordinates of the first and second marker poles measured at the first survey station. The centroid coordinates of the pre-embedded bolt group of the first concrete foundation are directly used for subsequent root opening calculations. The overall direction of the common line connecting the centers of the two cylindrical marker poles is determined from the overall coordinates of the two cylindrical marker poles. (14) In the formula, and , These are the vectors and components of the common connection line in the global coordinate system. For the common connection relative to X G A directional angle along the positive axis.

[0045] Step 2.2: Calculate the rotation matrix from the angles between the common connecting lines and each X-axis.

[0046] The actual direction of the common connecting line remains unchanged. By using the difference between its directed angles relative to the global horizontal axis and the local horizontal axis, the attitude angles of the local coordinate axes can be obtained: (15) In the formula, For the first j Local X of the station j The axis relative to the total X G The directional attitude angle of the axis, according to "by X G Rotate counterclockwise from the positive axis to X j The "positive direction of the axis" is positive. The common line connecting the center of the first marker pole to the center of the second marker pole is relative to the totality X. G The azimuth angle along the positive axis. The common line connecting the center of the first marker pole to the center of the second marker pole is relative to the first... j Local X of the measuring station j The azimuth angle along the positive axis.

[0047] (16) In the formula, For the first j The rotation matrix from the local coordinate system to the global coordinate system of the survey station. It is a second-order identity matrix. R1 is a second-order identity matrix, representing the rotation matrix from the first station to the global coordinate system. Since the first station is directly used as the global coordinate system, there is no rotation of the coordinate axes from the first station to the global coordinate system, i.e., the attitude angle θ1=0. Therefore, R1=E2 is a second-order identity matrix.

[0048] After the rotation matrix is ​​applied to the connecting vector, its direction should be aligned with the direction of the same connecting vector in the global coordinate system. Here, "rotation" refers to the transformation of the data coordinate components; it does not require rotating the field instrument again. Differences in the position of the coordinate origin will be handled using translation vectors in the next step.

[0049] Step 2.3: Calculate the translation vector using a common reference point and verify it.

[0050] After determining the rotation relationship, the center of the first marker pole is selected as the translation calculation point. Its local coordinates are first rotated according to step 2.2, and then subtracted from the global coordinates of the same point to obtain the position of the local origin in the global coordinate system. (17) In the formula, For the first j The translation vector from the local coordinate system to the global coordinate system of the survey station is also O. j The overall coordinates; , Let t1 be the coordinate components along the two axes of the whole. The origin of the first station coincides with the origin of the whole, so t1=0.

[0051] The above single-point formula is the basic translation solution method of this invention. It can also be solved using the second marker rod; under ideal error-free conditions, the two results are consistent. To suppress random measurement errors, after the measurement quality of the two cylindrical marker rods is similar and the consistency of the center distance and translation vector has been checked, the translation results obtained from the two cylindrical marker rods can be averaged as an optional accuracy improvement method, as shown in formula (19). Where the first... j The difference between the center distance of the two cylindrical marker poles measured at the station and the reference center distance of the first station does not exceed the preset threshold ε. d Furthermore, the difference between the translation vectors obtained using the first and second markers does not exceed a preset threshold ε. t At that time, the data from the measuring station is considered to have passed the verification. Based on the measurement accuracy of the laser displacement sensor and rotary encoder, the center-fitting error, the on-site station layout conditions, and the project's testing requirements, the permissible error threshold ε for the center distance of the common marker poles is pre-set. d Translation vector consistency allowable error threshold ε t .

[0052] (18) In the formula, , To obtain the translation vectors using the centers of the first and second marker poles respectively, the basic scheme is as follows: .

[0053] (19) In the formula, This is the average vector of the two translation results. When selecting the basic scheme, the subsequent transformations... Unified On average, it can reduce the impact of random errors under appropriate conditions, but it cannot guarantee the elimination of systematic biases, nor can it replace the stability check of the marker pole.

[0054] Step 2.4: Transform the geometric center of each pre-embedded bolt group to the global coordinate system.

[0055] (20) In the formula, For the first i The centroid of the pre-embedded bolt group in the concrete foundation is in the global coordinate system O. G -X G Y G Two-dimensional coordinate vectors in; The centroid of the pre-embedded bolt group is located in its respective number. j Local coordinate system O of the station j -X j Y j Two-dimensional coordinate vectors in; For the first j The rotation matrix from the local coordinate system to the global coordinate system of the station; This corresponds to the translation vector. Based on the recorded correspondence between the concrete foundation and the measuring station, select the appropriate... , When performing conversions, parameters from other stations must not be mixed. The basic scheme uses the coordinates of the center of the first marker pole to calculate the translation vector, while the optional averaging scheme uses the average of the centers of the first and second marker poles to calculate the translation vector. Subsequent processing for the same station should maintain consistency in the selection.

[0056] (twenty one) In the formula, , They are respectively Along the overall X G axis and Y G The coordinate components of the axes; , They are respectively Along local X j axis and Y j The coordinate components of the axes; , They are translation vectors Along the overall X G axis and Y G The components of the axes. The above component formula is equivalent to the matrix formula. First, the coordinate components are transformed according to the attitude of the local coordinate axes, and then the translation of the local origin is superimposed. The resulting coordinates are all located in the global coordinate system determined by the first station.

[0057] To facilitate completing rotation and translation in one step, homogeneous coordinates can also be used, with a fixed component added to the end of the planar coordinate column vector: (twenty two) In the formula, For the first j Homogeneous transformation matrix from the station to the global coordinate system. It is a third-order identity matrix. This is the homogeneous transformation matrix from the first station to the global coordinate system.

[0058] (twenty three) In the formula, , Concrete foundation i Local and global homogeneous coordinate column vectors of the centroid of the pre-embedded bolt group; , , , For concrete foundation i Planar coordinate components of the centroid of the pre-embedded bolt group in the local and global coordinate systems.

[0059] (twenty four) In the formula, From the origin O1 of the first station to the... j Origin of the measuring station j Horizontal distance; For the first j Origin of the measuring station j With the origin O1 of the first station at x The square of the difference in coordinates of the directions; For the first j Station origin O j With the origin O1 of the first station at y The square of the coordinate difference in direction. The distance describes the relationship between the instrument's installation origin and is usually not equal to the root gap between two pre-embedded bolt groups; it cannot replace the centroid spacing.

[0060] Step 2.5: Calculate the root opening of any two pre-embedded bolt groups and store the results.

[0061] Select any two different concrete foundations, and i ′ indicates concrete foundation i The other matching concrete foundation number, i Take 1 to M and i '≠ i The global coordinates of the two centroids are obtained through transformations at their respective corresponding stations, and then their coordinate differences are calculated: (25) In the formula, For concrete foundation i The centroid of the pre-embedded bolt group points towards the concrete foundation. i The coordinate difference vector of the centroid of the pre-embedded bolt group. , For each of the following, along the total X G Axis, Y G The coordinate difference of the axes; , The overall coordinates of the centroid of the corresponding pre-embedded bolt group in the concrete foundation; , , , These are the global coordinate components of the two centroids.

[0062] (26) In the formula, This is the horizontal center distance between the centroids of the two sets of pre-embedded bolts, i.e., the measured root opening. This calculation does not require the overall X-axis to coincide with the design axis beforehand.

[0063] (27) In the formula, For the total X G Rotate the axis counterclockwise to the first i The centroid of the group points to the first i The azimuth angle of the centroid direction. If the two centroids coincide, the root is 0, and the azimuth angle is undefined.

[0064] (28) In the formula, For the same pair of pre-embedded bolt groups, the design root opening, The measured root deviation is represented by a positive value indicating a large deviation and a negative value indicating a small deviation. Before comparing coordinate components or azimuth angles, the design coordinates must be transformed to the same global coordinate system.

[0065] The data processing and display device saves the original distance and angle data of each station, the center of each pre-embedded bolt, the centroid of the pre-embedded bolt group, the center of the two cylindrical marker poles, rotation and translation parameters, conversion quality inspection results, and the root opening results of any two groups, and forms a unified planar positional relationship between multiple concrete foundation pre-embedded bolt groups based on this.

[0066] Furthermore, in step 1.1: the battery is positioned at a predetermined installation location inside the housing to provide power to the laser displacement sensor, rotary encoder, and data transmission device. A foam pad is positioned between the cover plate and the battery, with one side of the foam pad contacting the inner surface of the cover plate and the other side contacting the upper surface of the battery. When the cover plate is fixed to the housing with screws, the cover plate presses the foam pad into the housing, causing the foam pad to deform elastically and applying a clamping force to the battery toward its installation position inside the housing. This restricts axial movement, lateral movement, or shaking of the battery within the housing, achieving battery clamping and fixation. The foam pad also buffers and dampens the battery, reducing the impact of vibrations and impacts generated during the movement, transportation, or rotation of the measuring device on the battery and its electrical connections. The data transmission device is located inside the housing and is fixedly mounted to the inner bottom plate of the housing with screws. The inner bottom plate of the housing has mounting holes or mounting bases corresponding to the data transmission device to restrict movement of the data transmission device relative to the housing, ensuring the stability of its installation position and electrical connections. The data transmitting device is electrically connected to both the laser displacement sensor and the rotary encoder, receiving distance data from the laser displacement sensor and angular displacement data from the rotary encoder. The data transmitting device also establishes a wired or wireless communication connection with the data processing and display device, transmitting the distance and angular displacement data collected at the same measurement moment to the data processing and display device. Specifically, the data processing and display device receives the measurement data transmitted by the data transmitting device, performs correspondence, storage, and calculation processing on the distance and angular displacement data, and displays the azimuth angle, radial distance, position coordinates, and corresponding geometric deviation detection results of the measured point. In the power transmission tower foundation root opening measurement device, the cover plate and shell form a fixed reference, the laser displacement sensor support supports the laser displacement sensor and enables circumferential rotation, and the set screw transmits the rotational motion of the laser displacement sensor support to the output shaft of the rotary encoder. The rotary encoder acquires the azimuth angle of the measuring point, and the laser displacement sensor acquires the radial distance of the measuring point. All components cooperate to achieve synchronous acquisition of angle and distance information. By coordinating the battery, foam pad, housing, cover, data transmission device, and data processing and display device, the measuring device achieves independent internal power supply, automatic transmission of measurement data, automatic data processing, and display of test results. This reduces errors caused by manual recording, reading, and calculation, and improves the device's portability, operational stability, and on-site testing efficiency.

[0067] Compared with the prior art, the present invention has the following beneficial effects. First, this invention combines a laser displacement sensor with a rotary encoder, using simultaneous distance and azimuth measurements and circle fitting to obtain the center of each pre-embedded bolt, and then calculates the centroid of the pre-embedded bolt group, eliminating the need for manual searching of the center. Calculations are performed using multiple surface measurement points, reducing the impact of contact readings, manual recording, and single-point surface errors on the results, thus improving the stability and repeatability of the measurement results.

[0068] Second, this invention uses two fixed-position, identically corresponding cylindrical marker poles as common references for all stations. The rotational relationship is first determined by the directed angle between the line connecting the two cylindrical marker poles and each X-axis, and then the translational relationship is determined by a common point, thus completely establishing the two-dimensional rigid body transformation from each local coordinate system to the global coordinate system. The first local coordinate system directly serves as the global coordinate system, eliminating the need for a separate global measurement station.

[0069] Third, this invention allows the measuring device to be installed at locations on each concrete foundation that meet the requirements of line of sight and measurement range, without requiring pre-alignment with the centroid of the pre-embedded bolt group, nor requiring the initial directions of different measuring stations to be the same. Local measurement combined with common reference conversion eliminates the need to construct a large-span measuring frame spanning the entire pre-embedded bolt group or multiple concrete foundations, thus improving the device's portability and adaptability to different foundation layouts.

[0070] Fourth, this invention uses the center of one marker pole to obtain the translation vector, with a clear calculation process. The other marker pole can be used for coordinate transformation residual verification, and the consistency of the center distance between the two cylindrical marker poles can be combined to detect abnormal data. When the measurement quality of the two cylindrical marker poles is similar and the data is valid, the average of the two translation results can be used to reduce the influence of random errors, balancing the simplicity of the basic algorithm with measurement quality control.

[0071] Fifth, this invention transforms the centroids of each pre-embedded bolt group in the concrete foundation to the same overall coordinate system, directly obtaining the actual horizontal center distance, coordinate difference, azimuth angle, and root opening deviation between any two groups. Calculation, display, and storage are achieved through a data processing and display device, avoiding the misuse of local coordinates or the misinterpretation of the instrument origin spacing as the foundation root opening, thus providing a unified basis for detecting the overall installation position of multiple independent foundations. Attached Figure Description

[0072] Figure 1 This is a schematic diagram of the overall structure of the measuring device.

[0073] Figure 2 This is a schematic diagram of the exploded structure of the measuring device.

[0074] Figure 3 This is a cross-sectional view of the inside of the measuring device.

[0075] Figure 4 This is a schematic diagram showing the measuring device in use on the surface of a cylindrical concrete foundation.

[0076] Figure 5 This is a schematic diagram illustrating the principle of measuring the center of a pre-embedded bolt.

[0077] Figure 6 This is a schematic diagram illustrating the measurement principle of two fixed cylindrical marker rods in a local coordinate system.

[0078] Figure 7 This is a front structural view of the laser displacement sensor support.

[0079] Figure 8 This is a reverse structural view of the laser displacement sensor support.

[0080] Figure 9 This is a structural view of the rotary encoder support.

[0081] Figure 10 This is a flowchart of the method of the present invention.

[0082] In the diagram: 1. Laser displacement sensor, 2. Laser displacement sensor support, 3. Set screw, 4. Rotary encoder support, 5. Rotary encoder, 6. Cover plate, 7. Foam pad, 8. Battery, 9. Housing, 10. Data transmission device, 11. Data processing and display device, 12. Concrete foundation, 13. First pre-embedded bolt, 14. Measuring device, 15. Cylindrical marker pole. Detailed Implementation

[0083] The invention will now be described in conjunction with the structure of the measuring device and the on-site measurement process. The specific implementation still consists of two main steps: local measurements within each concrete foundation, and overall coordinate transformation and root opening calculation.

[0084] Example 1 A method for measuring the foundation root opening of a power transmission tower, such as Figure 10 As shown, it includes the following steps: The first step is to complete local measurements within each concrete foundation; Measuring devices are set up on each concrete foundation 12 to establish a local coordinate system and obtain the local coordinates of the geometric center of the pre-embedded bolt group of the concrete foundation 12 and the geometric center of the same pair of fixed cylindrical marker poles 15, wherein the concrete foundation 12 is cylindrical.

[0085] Step 1.1: Assemble the device and set up two fixed cylindrical marker poles 15.

[0086] The overall, disassembled, and cross-sectional structures of the measuring device correspond to respectively Figure 1 , Figure 2 and Figure 3This embodiment consists of a measuring device 14, a data processing and display device 11, and two cylindrical marker rods 15 forming a measuring system. The laser displacement sensor 1 and the rotary encoder 5 in the measuring device 14 synchronously acquire distance and angle data, and the data transmitting device 10 transmits the two types of data to the data processing and display device 11 to complete the calculation of the center, centroid, and root radius.

[0087] The foundation root opening measurement device for transmission towers includes a measuring device 14, a data processing and display device 11, and two cylindrical marker poles 15. The measuring device 14 acquires distance and angular displacement data of the measuring points on the surfaces of the embedded bolts and cylindrical marker poles 15, and sends the data to the data processing and display device 11. The data processing and display device 11 converts the polar coordinate data to planar coordinates, calculates the center of the embedded bolts, the geometric center of the embedded bolt group, and the geometric center of the two cylindrical marker poles 15, establishes the rotation matrix, translation vector, and homogeneous transformation matrix from each local coordinate system to the global coordinate system, and further calculates the actual center distance, relative orientation, and foundation root opening between the geometric centers of the embedded bolt groups of different concrete foundations 12.

[0088] The measuring device 14 includes a laser displacement sensor 1, a laser displacement sensor support 2, a set screw 3, a rotary encoder support 4, a rotary encoder 5, a cover plate 6, a foam pad 7, a battery 8, a housing 9, and a data transmission device 10. The power transmission tower foundation root opening measurement system also includes two cylindrical marker poles 15; the two cylindrical marker poles 15 are set in stable positions that do not move during the measurement, and each is marked with an identifiable mark to ensure that the correspondence between the first and second marker poles remains consistent in each local measurement stage. Detailed structural layout is described below: Combination Figures 1 to 3 The measuring device 14 adopts a compact structure with upper and lower layers. Figure 1 This is a schematic diagram of the overall structure of the measuring device 14 after assembly. The laser displacement sensor 1 is located on the upper part of the device and can rotate around the output shaft axis of the rotary encoder 5 along with the laser displacement sensor support 2. Figure 2 The exploded structural diagram of the measuring device 14 shows the assembly relationship between the laser displacement sensor 1, the laser displacement sensor support 2, the set screw 3, the rotary encoder support 4, the rotary encoder 5, the cover plate 6, the foam pad 7, the battery 8, the housing 9, and the data transmitting device 10. Figure 3 This is an internal sectional view of the measuring device 14, used to illustrate the positioning of the rotary encoder 5 within the rotary encoder support 4, the connection between the cover plate 6 and the housing 9, and the internal arrangement of the battery 8, the foam pad 7, and the data transmission device 10.

[0089] In this embodiment, to balance structural rigidity, quality, on-site durability, and ease of processing, the laser displacement sensor support 2, rotary encoder support 4, cover plate 6, and housing 9 can be made of 6061-T6 aluminum alloy; the set screws 3 and main connecting screws are made of 304 stainless steel; and the foam pad 7 is made of EVA closed-cell foam. The two cylindrical marker rods 15 are identical in size. The cylindrical marker rod 15 with the A identification mark is defined as the first marker rod, and the cylindrical marker rod 15 with the B identification mark is defined as the second marker rod. Key dimensions and component parameters can be implemented using the set of parameters shown in Table 1; this set of dimensions is used to illustrate the feasible implementation methods of this embodiment and does not constitute a limitation on the scope of protection.

[0090] Table 1: Key dimensions, materials, and parameters of the measuring device in this embodiment In this embodiment, the overall outline of the measuring device 14 can be controlled within the range of approximately 180 mm × 140 mm × 140 mm, and the overall weight can be controlled within approximately 2 kg. The device size is mainly determined by the installation and rotation mechanism of the internal components, and does not increase proportionally with the root opening size between different concrete foundations 12; two cylindrical marker poles 15 are set in stable positions on site as independent common reference points.

[0091] The rotary encoder support 4 is a hollow cylindrical structure with a flange on its lower outer periphery. The rotary encoder support 4 is a supporting component for mounting and fixing the rotary encoder 5, and its interior has a receiving space adapted to the shape of the rotary encoder 5. The rotary encoder 5 has a cylindrical main body with an output shaft in the middle and a base housing on the outside. The output shaft can rotate freely around the outer base housing. A mounting threaded hole is provided along the circumference of its top circumference for fixed connection with the rotary encoder support 4. The rotary encoder 5 is installed inside the rotary encoder support 4, and the two are coaxial. A cylindrical positioning boss is provided on its upper part, and a positioning hole corresponding to the cylindrical positioning boss is provided on the rotary encoder support 4. The cylindrical positioning boss is inserted into the positioning hole, and the coaxial positioning between the rotary encoder 5 and the rotary encoder support 4 is achieved through clearance fit, ensuring that the output shaft axis of the rotary encoder 5 coincides with or remains coaxial with the predetermined rotation axis of the rotary encoder support 4. The outer housing of the rotary encoder 5 is fixedly connected to the inner wall of the rotary encoder support 4 by screws, thereby restricting the axial movement and circumferential rotation of the housing of the rotary encoder 5 relative to the rotary encoder support 4. Multiple connecting holes are spaced circumferentially on the flange for screws to pass through and fix it to the cover plate 6, ensuring the rotary encoder support 4 is stably mounted on the cover plate 6. The cover plate 6 serves to support and fix the rotary encoder support 4 and provides a mounting base for the rotary encoder 5 and its related rotating components.

[0092] During assembly, the rotary encoder 5 is installed inside the hollow cylindrical rotary encoder support 4, with the cylindrical positioning boss on the upper part of the encoder inserted into the positioning hole of the support 4. The boss and the hole are positioned using a clearance fit, and then the encoder housing is fixed with screws to restrict its axial movement and circumferential rotation relative to the support 4. The support 4 is then fixed to the cover plate 6 via the connecting holes on the lower flange, forming a fixed support for the encoder housing; the structure of the support 4 corresponds to... Figure 9 .

[0093] like Figure 9 As shown, the main body of the rotary encoder support 4 is a hollow cylindrical structure, and the lower flange is used for fixed connection with the cover plate 6. In this embodiment, four connecting holes are evenly distributed along the circumference. The cylindrical positioning boss on the upper part of the rotary encoder 5 is clearance-fitted with the positioning circular hole on the support 4, so that the output shaft axis of the rotary encoder 5 and the geometric axis of the support 4 remain coaxial. This structure is not only easy to assemble, but also helps to reduce the influence of rotational eccentricity on angle measurement.

[0094] The laser displacement sensor support 2 is a block structure with an opening at the bottom. Its upper surface is the mounting surface of the laser displacement sensor 1, and its hollow bottom opening is used to insert the upper part of the rotary encoder support 4. The laser displacement sensor support 2 can rotate relative to the rotary encoder support 4 around the output shaft axis of the rotary encoder 5. The laser displacement sensor support 2 has a cylindrical hole inside that corresponds to the output shaft of the rotary encoder 5. The output shaft of the rotary encoder 5 is inserted into the cylindrical hole and has a clearance fit with the cylindrical hole. This clearance fit is used to achieve axial assembly and coaxial positioning between the output shaft of the rotary encoder 5 and the laser displacement sensor support 2.

[0095] The output shaft of the rotary encoder 5 has a pre-machined flat surface on its outer periphery. The laser displacement sensor support 2 has a threaded hole communicating with the cylindrical hole. A set screw 3 is screwed into the threaded hole, and its end is pressed against the flat surface of the rotary encoder 5's output shaft. Through the cooperation of the set screw 3 and the flat surface, the relative circumferential rotation between the output shaft of the rotary encoder 5 and the laser displacement sensor support 2 is restricted, forming a circumferentially fixed connection. This ensures that the rotation of the laser displacement sensor support 2 synchronously drives the output shaft of the rotary encoder 5. Simultaneously, the flat surface on the output shaft increases the pressing contact area of ​​the set screw 3, reducing slippage and improving the reliability and measurement accuracy of angle transmission.

[0096] The laser displacement sensor support 2 is a block structure with a hollow interior and an opening at the bottom. The forward and reverse structures correspond to... Figure 7 , Figure 8Mount the encoder onto the upper part of the support 4, inserting the encoder output shaft into the cylindrical hole in the support 2 with a clearance fit. Tighten the set screw 3, which communicates with the hole, so that the end of the screw presses against the flat surface of the output shaft, restricting the relative circumferential rotation between the output shaft and the support 2. After assembly, check that the support 2 can rotate around the axis of the encoder output shaft without interfering with the fixed support.

[0097] like Figure 7 and Figure 8 As shown, Figure 7 The front structure of the laser displacement sensor support 2 is shown, mainly displaying the mounting plane, connecting holes, and lateral and end positioning structures of the laser displacement sensor 1; Figure 8 The reverse structure of support 2 is shown, mainly illustrating the hollow area on the upper part of the support 4 for mounting the rotary encoder, the cylindrical hole that mates with the output shaft of the rotary encoder 5, and the mounting position of the set screw 3. In this embodiment, the cylindrical hole and the Φ8 mm output shaft are fitted with a small clearance to balance assembly convenience and coaxial positioning accuracy.

[0098] Furthermore, the laser displacement sensor 1 is disposed on the upper surface of the laser displacement sensor support 2 and is fixedly connected to the laser displacement sensor support 2 by screws. The laser displacement sensor support 2 is provided with a mounting plane, connecting holes, lateral positioning baffles, and end positioning baffles for mounting the laser displacement sensor 1, so as to ensure the positioning and fixation of the laser displacement sensor 1 on the laser displacement sensor support 2. The laser emission direction of the laser displacement sensor 1 is preferably set along the radial direction of the laser displacement sensor support 2, so that the emitted measuring laser can be directed towards the target object to be measured.

[0099] The laser displacement sensor 1 is placed on the mounting plane of the upper surface of the support 2. The installation position is determined by the lateral and end positioning baffles, and then fixed with screws. The measuring laser is preferably emitted radially along the support. After assembly, the geometric relationship between the optical path and the rotation center is checked, and the installation offset of the distance measuring reference is calibrated. During measurement, the support 4 and the encoder housing remain stationary relative to the cover plate 6. The operator rotates the support 2, causing the sensor 1 and the encoder output shaft to rotate synchronously, so that the acquired distance and rotation angle correspond to the same measurement direction.

[0100] The rotary encoder 5 is used to detect the rotation angle of its output shaft relative to the housing of the rotary encoder 5, and outputs angular displacement data corresponding to the current measurement direction of the laser displacement sensor 1. The laser displacement sensor 1 is used to emit a laser along the current measurement direction and measure the straight-line distance between the measurement reference position of the laser displacement sensor 1 and the measurement point to be measured, and outputs the corresponding distance data. The angular displacement data output by the rotary encoder 5 is used to characterize the azimuth angle of the measurement point to be measured relative to the reference direction of the measuring device. The distance data output by the laser displacement sensor 1, after being calibrated by the installation geometry, is used to characterize the radial distance of the measurement point to be measured relative to the rotation center of the measuring device. By correlating the angular displacement data and distance data obtained at the same measurement moment, the polar coordinate parameters of the measurement point to be measured in the measurement plane can be obtained. When the laser displacement sensor support 2 rotates continuously or stepwise around the output shaft axis of the rotary encoder 5, the laser displacement sensor 1 can measure the distance to multiple measurement points in different orientations, and the rotary encoder 5 simultaneously records the azimuth angle corresponding to each measurement point. By collecting the azimuth and radial distance of multiple measuring points, the polar coordinates of each measuring point can be further converted into Cartesian coordinates. Based on this, the position of the pre-embedded bolt to be measured in the measurement plane, the geometric center position of the pre-embedded bolt group, and the geometric center position of the two cylindrical marker poles 15 can be calculated. When measuring the cylindrical marker pole 15, at least three measuring points on its cylindrical surface are obtained using the same synchronous acquisition method of distance and azimuth. The coordinates of the intersection point of the axis of the cylindrical marker pole 15 and the measurement plane are obtained through circle fitting, which are used as the geometric center coordinates of the cylindrical marker pole 15 in the current local coordinate system.

[0101] The cover plate 6 is detachably fixed to the housing 9 by screws, providing a stable support structure and horizontal reference for the entire device.

[0102] The battery 8, foam pad 7, and data transmission device 10 are all housed inside the housing 9. The housing 9 has an internal mounting cavity for accommodating the battery 8 and data transmission device 10. An opening is provided at the top of the housing 9, and a cover plate 6 covers this opening and is detachably fixed to the housing 9 with screws, thus forming a relatively enclosed internal mounting space. A notch is provided on the front surface of the housing 9 for leading cables from inside the housing 9 and connecting them to the external rotary encoder 5 and laser displacement sensor 1.

[0103] The battery 8 is positioned at a predetermined location inside the housing 9 to provide power to the laser displacement sensor 1, rotary encoder 5, and data transmission device 10. A foam pad 7 is positioned between the cover plate 6 and the battery 8, with one side of the foam pad 7 contacting the inner surface of the cover plate 6 and the other side contacting the upper surface of the battery 8. When the cover plate 6 is fixed to the housing 9 with screws, the cover plate 6 presses the foam pad 7 into the housing 9, causing the foam pad 7 to elastically deform and applying a clamping force to the battery 8 towards its mounting position inside the housing 9. This restricts axial movement, lateral movement, or shaking of the battery 8 within the housing 9, achieving the clamping and fixing of the battery 8. The foam pad 7 also buffers and dampens vibrations of the battery 8, reducing the impact of vibrations and impacts generated during the movement, transportation, or rotation of the measuring device on the battery 8 and its electrical connections.

[0104] The battery 8 is placed in its predetermined mounting position inside the housing 9, and the data transmitting device 10 is fixed to the mounting holes or mounting base on the bottom plate inside the housing with screws. A foam pad 7 is positioned between the cover plate 6 and the battery 8, with its sides contacting the inner surface of the cover plate and the upper surface of the battery, respectively. After the cover plate 6 is fixed to the housing 9 with screws, it compresses the foam pad, using its elastic deformation to press the battery and provide cushioning. The cover plate covers the opening at the top of the housing, and related cables are led out through a notch on the front surface of the housing.

[0105] The data transmitting device 10 is disposed inside the housing 9 and fixedly mounted to the inner bottom plate of the housing 9 with screws. The inner bottom plate of the housing 9 is provided with mounting holes or mounting bases corresponding to the data transmitting device 10 to restrict movement of the data transmitting device 10 relative to the housing 9, ensuring the stability of its installation position and electrical connection. The data transmitting device 10 is electrically connected to the laser displacement sensor 1 and the rotary encoder 5, respectively, for receiving distance data collected by the laser displacement sensor 1 and angular displacement data collected by the rotary encoder 5. The data transmitting device 10 also establishes a wired or wireless communication connection with the data processing and display device 11, and transmits the distance data and angular displacement data collected at the same measurement time to the data processing and display device 11.

[0106] Specifically, the data processing and display device 11 is used to receive the measurement data sent by the data sending device 10, perform corresponding, storage and calculation processing on the distance data and angular displacement data, and display the azimuth angle, radial distance, position coordinates and corresponding geometric deviation detection results of the measured point.

[0107] Battery 8 powers sensor 1, encoder 5, and data transmission device 10. Data transmission device 10 connects to sensor 1 and encoder 5 respectively, and establishes a wired or wireless communication connection with data processing and display device 11. During data acquisition, distance and angle are transmitted in pairs under the same measurement conditions. Data processing and display device 11 saves the pairing records and displays the coordinates of the measurement points and subsequent calculation results. Before formal measurement, all fixed connections, power supply, communication, distance readings, and angle zero point are checked to confirm that the rotation mechanism and data reception are functioning normally.

[0108] During the measurement process, the housings of the rotary encoder support 4 and the rotary encoder 5 remain fixed relative to the cover plate 6. The operator rotates the laser displacement sensor support 2 around the output shaft axis of the rotary encoder 5, and the laser displacement sensor 1, which is fixedly mounted on the laser displacement sensor support 2, rotates synchronously. Since the laser displacement sensor support 2 is circumferentially fixed to the output shaft of the rotary encoder 5 through the set screw 3, the rotation of the laser displacement sensor support 2 synchronously drives the output shaft of the rotary encoder 5 to rotate. During the measurement process, the battery 8 supplies power to the laser displacement sensor 1, the rotary encoder 5, and the data transmission device 10; the laser displacement sensor 1 collects the distance data of the measurement point, and the rotary encoder 5 synchronously collects the corresponding angular displacement data; the data transmission device 10 sends the distance data and angular displacement data to the data processing and display device 11. The data processing and display device 11 calculates the center of the pre-embedded bolt, the geometric center of the pre-embedded bolt group, and the geometric center of the two cylindrical marker poles 15 based on the received data, and establishes a coordinate transformation from the local coordinate system to the global coordinate system based on the coordinates of the common marker pole, and outputs the foundation root opening between the geometric centers of different pre-embedded bolt groups.

[0109] In the aforementioned power transmission tower foundation root opening measurement device, the cover plate 6 and the housing 9 form a fixed reference. The laser displacement sensor support 2 supports the laser displacement sensor 1 and enables circumferential rotation. The set screw 3 transmits the rotational motion of the laser displacement sensor support 2 to the output shaft of the rotary encoder 5. The rotary encoder 5 acquires the azimuth angle of the measuring point, and the laser displacement sensor 1 acquires the radial distance of the measuring point. All components cooperate to achieve synchronous acquisition of angle and distance information. Through the cooperation of the battery 8, foam pad 7, housing 9, cover plate 6, data transmission device 10, and data processing and display device 11, the device achieves independent internal power supply, automatic data transmission, automatic data processing, and display of detection results. This reduces errors caused by manual recording, reading, and calculation, and improves the device's portability, operational stability, and on-site testing efficiency.

[0110] Two cylindrical marker poles 15 are designated A and B, serving as the first and second common reference points. The two cylindrical marker poles 15 must be positioned in stable locations observable from all stations and must not be moved during the entire measurement period. Furthermore, the projection points of the axes of the two cylindrical marker poles 15 onto the horizontal plane must not coincide. The axes of the two cylindrical marker poles 15 should remain vertical, ensuring that the centers of the cross-sections obtained at different station heights have the same horizontal projection.

[0111] Two cylindrical marker poles 15 are positioned where they can be observed from all stations, ensuring their axes are vertical and their horizontal projections do not overlap, and clearly marked with identification markers. The positions of the two cylindrical marker poles 15 are not changed during the measurement. The horizontal position of the pole axis is determined at each station using measuring points on the cylindrical surface, ensuring that the same pair of common reference points are used at different erection heights.

[0112] Step 1.2: Set up the measuring device on the current concrete foundation 12 and establish a local coordinate system.

[0113] The total number of the 12 concrete foundations to be tested is denoted as . M , M The integer is not less than 2; the current concrete foundation number 12 is recorded as i , i Take 1 to M The integer. Place the measuring device 14 at the... i The upper surface of the concrete foundation 12 does not obstruct the position of the pre-embedded bolts 13 and the two cylindrical marker poles 15 for measuring the optical path. During a complete measurement of the concrete foundation 12, the position, zero angle, and leveling state of the measuring device 14 remain unchanged. Each station uses a horizontal measuring plane, and the center of the pre-embedded bolts is measured according to the agreed installation reference section. This invention calculates the plane position and horizontal root opening, but does not calculate the elevation difference or spatial slope distance.

[0114] A complete setup at a fixed position and a fixed angle zero point is called a measuring station. j Indicates the station number, in S Indicates the total number of stations. j Take 1 to S An integer. Record the first... j The station and the measured number i The correspondence of each concrete foundation 12; each concrete foundation 12 needs to be effectively erected once, therefore S = M The first measuring station is located on the first concrete foundation 12; the local origin O is the intersection of the rotation axis of the rotary encoder 5 and the horizontal measuring plane. j With the initial measurement direction fixed as X j In the positive direction of the axis, within the same horizontal plane, from X j The direction in which the axis rotates 90° counterclockwise is Y.j Establish a local coordinate system O along the positive axis. j -X j Y j Rotary encoder with X j The positive direction of the axis is zero, and counterclockwise is positive. The origin and initial orientation of each station are allowed to be different, but the positive direction of the angle must be consistent.

[0115] First, a measuring device 14 is installed on the first concrete foundation 12, and its usage status is corresponding to... Figure 4 Select a location that allows observation of all the pre-embedded bolts 13 and the two cylindrical marker poles 15 of the concrete foundation 12, and stabilize and level the device. The instrument does not need to be pre-aligned with the centroid of the pre-embedded bolt group, and each concrete foundation 12 does not need to have the same initial orientation. After each successful setup, record the correspondence between the concrete foundation 12 and the measuring station.

[0116] Figure 4 The actual usage state of the measuring device 14 on the upper surface of a single cylindrical concrete foundation 12 is shown. The measuring device 14 can be placed in any stable position that meets the laser measurement line of sight and range conditions, and its rotation center is not required to coincide with the centroid of the pre-embedded bolt group; the two cylindrical marker rods 15 are set in stable positions that can be observed between different concrete foundations 12. During the measurement process, from the start of the measurement of the pre-embedded bolts to the end of the measurement of the two cylindrical marker rods 15 within the same measuring station, the device position, zero angle, and leveling state remain unchanged.

[0117] To illustrate the complete calculation process of this invention, this embodiment uses M=2, meaning two separate cylindrical concrete foundations 12 are set up. Each foundation has four M24 pre-embedded bolts, arranged with a distribution radius of approximately 500 mm. The nominal radius of a single M24 pre-embedded bolt within the measurement section is approximately 12 mm. Five measuring points are collected on the cylindrical surface of each pre-embedded bolt, and five measuring points are collected on the first marker pole and B of each of the two cylinders. Using the local coordinate system of the first measuring station as the overall coordinate system, the root opening is designed to be 4000.00 mm, used to illustrate the subsequent root opening calculation and result comparison process.

[0118] Establish O by the intersection of the rotation axis and the horizontal measurement plane. j Select the initial measurement direction and zero the encoder, then determine the coordinate axis and positive angle direction in a counterclockwise direction to form O. j -X j Y j The pre-embedded bolts at the agreed-upon installation reference section are used to ensure that the surface points collected in this study can be used to solve for the same cross-sectional circle.

[0119] From the start of measuring the pre-embedded bolts of this concrete foundation 12 to the completion of the measurement of the two common marker poles, the position, leveling status, and zero angle of the device should remain unchanged. If the device is moved or the zero point is reset midway, the effective measurement of this concrete foundation 12 and the two cylindrical marker poles 15 should be completed again, and the corresponding records of the measuring station should be updated. Data before and after the changes should not be mixed into the same local coordinate system.

[0120] Step 1.3: Convert the distance and azimuth into local coordinates.

[0121] The first i The total number of pre-embedded bolts on the 12 concrete foundations is denoted as follows: , k This indicates the number of the embedded bolts within the concrete foundation 12. k Take 1 to ;by q This indicates the serial number of the valid measurement point on a single measured cylindrical surface. k The first pre-embedded bolt q The coordinates of the surface measuring points are as follows: The superscript j in parentheses indicates the coordinate system of the station. The total number of valid measuring points for the pre-embedded bolts at this station is denoted as U. ik (j) , q Take 1 to U ik (j) , and U ik (j) Not less than 3.

[0122] The measurement sequence of each of the 12 pre-embedded bolts in this concrete foundation is determined sequentially. At least three surface measuring points at different orientations are selected on the agreed-upon cross-section of each pre-embedded bolt. The laser displacement sensor support 2 is rotated, aligned with the measuring points, and distance and angle data are simultaneously acquired and saved. , And their corresponding records, ensuring that each set of distances and angles belongs to the same measuring point. For example... Figure 5 As shown, for ease of illustration, the first... i The first concrete foundation k The three surface measuring points selected for the pre-embedded bolts are numbered q=1, 2, and 3 respectively, and their local coordinates are denoted as: , , .

[0123] calculate: (1) In the formula, , The measuring points are along X j Axis, Y j The coordinate components of the axes; For O jRadial distance to the measuring point; For X j The positive axis is rotated counterclockwise to the directional azimuth angle of the measuring point's radial direction.

[0124] The radial distance is based on the local origin. If the ranging reference position of laser displacement sensor 1 does not coincide with the local origin, the original ranging value should first be converted into the distance from the local origin to the measuring point according to the calibrated installation geometry, and then substituted into the coordinate calculation formula.

[0125] Coordinate transformation was performed on all valid measuring points of the pre-embedded bolt. Measuring points should be taken from the same cross-section of the cylindrical surface to avoid mixing end face or edge data with circumferential data; the distribution of measuring points should not approximately lie on the same straight line. The data processing and display device 11 retains the original distance, angle, and converted coordinates for use in center point determination and anomaly verification.

[0126] Step 1.4: Determine the center of the first pre-embedded bolt 13.

[0127] according to Figure 5 The corresponding principle for measuring the center of a circle is in the first... j The station kept measuring device 14 stationary and monitored the first... i 12 concrete foundations i = j The first embedded bolt 13 (indicating measurement within a concrete foundation) selects at least three non-overlapping and non-collinear surface measuring points within the same measuring section. , and Perform distance and azimuth conversion, such as Figure 5 As shown, the laser displacement sensor 1 sequentially points to different positions on the cylindrical surface of the same pre-embedded bolt 13, and the rotary encoder 5 simultaneously provides the X-ray values ​​of each measuring point relative to the current local area. j The azimuth angle of the axis. The center of the cross section can be obtained by using the above circle equation with at least three non-collinear measuring points. In this embodiment, in order to improve the stability of the circle center calculation, the least squares circle fitting is performed on each pre-embedded bolt using 5 measuring points, and the consistency between the fitting radius and the nominal radius of the M24 pre-embedded bolt and the radial residual are used as auxiliary checks for data quality.

[0128] (2) In the formula, a, b, c The three selected measuring points are designated as measuring point 1, measuring point 2, and measuring point 3. , , , , , The first, second, and third measuring points are respectively located at the 1st, 2nd, and 3rd measuring points. j Local coordinate components of the station.

[0129] Let the coordinates of the center of the first pre-embedded bolt 13 be... =( , ) T In the formula, For the first j The first station i Local coordinates of the center of the section of the first embedded bolt 13 of the concrete foundation 12; , The center of the circle is located along the local coordinate system O. j -X j Y j X j axis and Y j The coordinate components of the axis; the radius of the cross-section circle is r i1 Then any point on the circumference ( , )satisfy: (3) Substitute the coordinates of the three measuring points into the equation of the circle. Subtract the equation corresponding to the first measuring point from the equations corresponding to the second and third measuring points respectively, eliminating the radius term and the square term of the center coordinates, to obtain a system of linear equations about the center coordinates: (4) The coefficient matrix, written in matrix form, is: (5) When the three measurement points are not collinear, the coefficient matrix is ​​invertible. Solving for the coefficient matrix using a system of two linear equations yields the solution. If the three measuring points are nearly collinear, then select new measuring points with a more adequate distribution.

[0130] The data processing and display device 11 uses the known coordinates of three measuring points to form a coefficient matrix and a right-hand column vector. After solving, it saves the result to C. i1 (j) When the three measuring points are not collinear, the center of the circle can be uniquely determined; if the measuring points are nearly collinear, more adequately distributed measuring points should be selected to avoid significant fluctuations in the center result caused by small coordinate errors.

[0131] In actual measurements, more than three valid measuring points can be collected, and the center of the circle can be determined by least-squares circle fitting to reduce the influence of random errors by utilizing redundant measuring points. The position, zero angle, and measuring cross-section of the measuring device 14 should remain unchanged.

[0132] Step 1.5: Calculate the center of the remaining pre-embedded bolts in sequence.

[0133] After measuring the center of the first embedded bolt 13, the centers of the remaining embedded bolts in the concrete foundation 12 are measured sequentially. For each embedded bolt, surface measuring points are collected, local coordinates are transformed, and the center is determined using the three-point method or multi-point circle fitting. The measuring point data for each embedded bolt are saved separately, without mixing in surface points from other embedded bolts. The centers of all embedded bolts are represented as follows: (6) In the formula, For the first k Local coordinates of the center of each pre-embedded bolt. , Its coordinate components, Indicates the number of the embedded bolts. Indicates the first i The total number of pre-embedded bolts for each concrete foundation is 12.

[0134] For the remaining embedded bolts in the concrete foundation 12, convert the coordinates of the surface measuring points according to step 1.3, and then calculate the center of the circle according to step 1.4. Check whether the number of valid center points is consistent with the total number of embedded bolts in the concrete foundation 12. If there are any missed or abnormal center points, first supplement the measurement and check while maintaining the benchmark of this measuring station, and then calculate the centroid of the embedded bolt group.

[0135] Step 1.6: Calculate the geometric center of the 12 pre-embedded bolt groups in the concrete foundation, thus obtaining the centroid of the 12 pre-embedded bolt groups in this concrete foundation. .

[0136] The coordinates of the centers of all 12 pre-embedded bolts in this concrete foundation are summarized. The sum of the x-coordinates of each center is then divided by 1 / 2. n i The ordinate is processed in the same way, resulting in: (7) In the formula, , The centroid of the 12 pre-embedded bolt groups in this concrete foundation The local coordinate components. The centroid of the 12 pre-embedded bolt group in this concrete foundation is taken as the arithmetic mean of the coordinates of the center of all pre-embedded bolts, and is not replaced by the center of the outer contour of the concrete foundation 12 or the origin of the instrument.

[0137] P i (j) The data is associated with and saved in relation to the concrete foundation 12, the current measuring station, and the center records of each embedded bolt. This calculation uses the weighted average of the centers of all embedded bolts, and does not use the center of the outer contour of the concrete foundation 12, a point on the surface of a certain embedded bolt, or the origin of the instrument as the centroid of the embedded bolt group.

[0138] After processing the surface measuring points of the pre-embedded bolts at the two measuring stations according to steps 1.3 to 1.6, a set of exemplary circle fitting results as shown in Table 2 can be obtained. The center data of the four pre-embedded bolts at the first measuring station correspond to the measurement data of the M24 pre-embedded bolts used in this embodiment; the second measuring station provides exemplary local center coordinates under the same arrangement conditions.

[0139] Table 2: Example results of circle fitting and centroid of pre-embedded bolt group at two monitoring stations From Table 2, we can see that the centroid of the pre-embedded bolt group corresponding to the first concrete foundation 12 at the first measuring station is... =(141.26, -30.05) mm; the centroid of the pre-embedded bolt group corresponding to the second concrete foundation 12 at the second measuring station is =(62.30, 54.10) mm. The fitted radii of the eight pre-embedded bolts are all approximately 12 mm, and the radial residuals are all less than 0.10 mm, indicating that the example measuring point can stably determine the center of each pre-embedded bolt and can proceed to the steps of measuring the common marker pole and transforming the overall coordinates.

[0140] Step 1.7: Measure the two common marker poles and calculate the direction of the connecting line.

[0141] Keep the first j The measuring device 14 at the station remains stationary, and at least three non-coincident and non-collinear cross-sectional measuring points are collected from the cylindrical surfaces of the first and second marker poles, respectively. The coordinates of each measuring point are marked as follows: , , For the first j The first marker pole at the station q The effective surface measuring points are in the local coordinate system O. j -X j Y j The coordinate vector in; For the first j The second marker pole at the station q The coordinate vectors of each effective surface measuring point in the local coordinate system. For the first marker pole, q =1,2,…,U A (j) For the second marker pole, q = 1, 2, ..., U B (j) The total number of effective surface measuring points for the first and second marker poles are U respectively. A (j) U B (j) . q Values ​​are taken within the valid measuring point range of the corresponding marker pole.

[0142] Keep the equipment at this station station stationary and press Figure 6 The measurement process for the corresponding public marker poles involves collecting at least three non-overlapping and non-collinear cross-sectional surface points from both the first and second marker poles. The corresponding distances and azimuths are recorded and converted into: (8) In the formula, For the first marker pole q Each surface measuring point is relative to the local origin O. j The radial distance; For the second marker pole q Each surface measuring point is relative to the local origin O. j The radial distance; For local X j The directional azimuth angle of the radial direction of the measuring point on the qth surface of the first marker rod, rotated counterclockwise in the positive direction of the axis; For local X j The directional azimuth angle of the radial direction of the measuring point on the qth surface of the second marker rod, rotated counterclockwise in the positive direction of the axis; By establishing the equation of the circle using the surface measuring points of each rod and solving for the center of the circle, we obtain: (9) In the formula, , The coordinates of the center of the cross-section of the first and second marker poles obtained in step 1.4 are: , and , Its local coordinate components. The center of the circle is obtained by fitting the measurement points on the surface of each rod, and is not replaced by a single surface measurement point.

[0143] Measurements and calculations always distinguish between the two sets of data based on the identification marks on the poles. Surface points from the two cylindrical marker poles 15 are not mixed and fitted together, nor is a surface point directly measured by laser taken as the pole's center. When the two cylindrical marker poles 15 are vertical and in fixed positions, the center of the cross-section obtained from different measuring stations corresponds to the same horizontal reference position.

[0144] The coordinates of the center of the circle can also be expressed using the radius vector and azimuth angle as follows: (10) In the formula, , For O j The radius vector length to the center of the two cylindrical marker poles at point 15; , It is the directional azimuth angle of the corresponding center radius vector.

[0145] The radius and azimuth of the center should be calculated from the fitted center coordinates, not directly using the distance and angle of a single surface measuring point.

[0146] (11) In the formula, Let be the vector of the common line connecting the center of the first marker pole circle to the center of the second marker pole circle. , These are the local coordinate components of the common connection vector. Each station follows the sequence of the first marker pole pointing to the second marker pole.

[0147] Calculate the direction angle of the common connection line and the distance between the centers of the first and second marker poles: (12) In the formula, The common line connecting the center of the first marker pole to the center of the second marker pole is relative to the first... j Local X of the measuring station j The azimuth angle along the positive axis. The distance between the centers of the first and second marker poles is denoted as .

[0148] The calculation results are saved along with the coordinates of the centers of the two cylindrical marker poles (15). All stations are arranged in the order of the first marker pole pointing to the second marker pole to prevent the direction of the connecting line from changing due to the reversal of the target order, which would affect the subsequent solution of the rotation relationship.

[0149] Figure 6 The diagram illustrates the common reference relationship between two fixed cylindrical marker poles 15 in different local coordinate systems. In the diagram, A and B are the centers of the cross-sections of the two cylindrical marker poles 15, and O1-X1Y1 and O2-X2Y2 represent the local coordinate systems of the measuring stations on different concrete foundations 12. Each measuring station constructs a common connecting vector according to a fixed order from A to B. Therefore, the angular difference of the same entity connecting line in different local coordinate systems can be used to determine the rotation relationship of the coordinate axes; after the rotation relationship is determined, the translation relationship is determined using the corresponding coordinates of points A or B.

[0150] In this embodiment, the first station fitted the coordinates of the first marker pole and the center of circle B as follows: =(1800.000, 1200.000) mm、 =(2400.000, -500.000) mm; obtained by fitting at the second station. =(-1877.892, 1724.390) mm、 =(-1801.141, -76.751) mm. The corresponding common connection parameters are shown in Table 3.

[0151] Table 3: Center point and connection parameters of the common marker poles for the two stations As shown in Table 3, the center-to-center distance between the first and second marker poles obtained from the two measuring stations is 1802.776 mm, indicating a consistent center distance. The azimuth angles of the common connecting line at the first and second measuring stations are 289.440° and 272.440°, respectively. This result indicates that the two measuring stations identify the same pair of A and B marker poles, and this can be used to solve for the overall coordinate relationship. In actual engineering, allowable differences should be set according to the instrument accuracy, station layout conditions, and project testing requirements. If the allowable difference is exceeded, the stability of the marker poles, the quality of the measuring points, and the correspondence between A and B should be rechecked.

[0152] Step 1.8: Complete the partial measurements of all concrete foundations 12 in sequence.

[0153] The measuring device 14 is then sequentially set up on the remaining concrete foundations 12, and steps 1.2 to 1.7 are repeated until all M concrete foundations 12 are measured. Each measuring station saves the corresponding concrete foundation 12 number and the centroid P of the pre-embedded bolt group for that concrete foundation 12. i (j) The coordinates A of the center of the first and second marker poles (j) With B (j) The common line connecting the center of the first marker pole to the center of the second marker pole is relative to the first... j Local X of the measuring station j directional azimuth angle in the positive direction of the axis Distance between the centers of the first and second marker poles d AB (j) The origin and initial orientation of each erection may be different, but the positions, corresponding identities, distance measurement scales, and positive angles of the two cylindrical marker poles must remain consistent.

[0154] The actual distance between the first and second fixed marker poles of the same pair should not change with the measuring station. The center distance measured at each station should be consistent within the allowable error range of the project, which is used to detect errors or abnormal measurement data in the target correspondence. The allowable error range of the project should be determined in advance based on the instrument accuracy, station layout conditions and testing requirements, and unverified uniform values ​​should not be used.

[0155] The second step is to establish the overall coordinate relationship and calculate the foundation root opening between each pre-embedded bolt group: The local coordinate system of the first station is directly defined as the overall coordinate system. The rotation and translation relationships between the remaining local coordinate systems and the overall coordinate system are established using the first and second marker poles. The geometric centers of each pre-embedded bolt group are transformed into the overall coordinate system. The horizontal distance between the geometric centers of any two pre-embedded bolt groups is calculated, i.e., the foundation root opening. Specifically: Step 2.1: Use the local coordinate system of the first station as the global coordinate system.

[0156] The local coordinate system O1-X1Y1 of the first station is directly defined as the global coordinate system O. G -X G Y G . G Mark the global coordinate system. The origins and axes of the two coordinate systems coincide, and the coordinates measured at the first station do not need to be transformed.

[0157] according to Figure 6 The corresponding coordinate transformation relationship uses the first measuring station O1-X1Y1 as the overall coordinate system, with its origin and axis remaining unchanged. No additional overall measuring stations are set up, and the overall X-axis is not rotated beforehand for root opening calculation. The coordinates of the common pole center of the first measuring station and the centroid of the first concrete foundation 12 are directly used as the overall datum. (13) Among them, A (G) B (G) These are the global coordinates of the centers of the two fixed marker poles, A. (1) B (1) These are their local coordinates at the first station; P1 (G) P1 (1) These are the global coordinates of the centroid of the first pre-embedded bolt group and the local coordinates at the first measuring station, respectively.

[0158] The overall reference datum is fixed using the center coordinates of the first and second marker poles measured at the first measuring station. The centroid coordinates of the pre-embedded bolt group of the first concrete foundation 12 are directly used for subsequent root opening calculations. The overall direction of the common connecting line is obtained from the overall coordinates of the two cylindrical marker poles 15. (14) In the formula, and , These are the vectors and components of the common connection line in the global coordinate system. For the common connection relative to X G A directional angle along the positive axis.

[0159] Each subsequent station uses the overall reference data of this group to calculate its own transformation, ensuring that the centroid of all pre-embedded bolt groups is ultimately expressed in the same coordinate system.

[0160] Step 2.2: Calculate the rotation matrix from the angles between the common connecting lines and each X-axis.

[0161] The actual direction of the common connecting line remains unchanged. By using the difference between its directed angles relative to the global horizontal axis and the local horizontal axis, the attitude angles of the local coordinate axes can be obtained: Read the first j The station's stored β jThe first station determined β G Subtract the values ​​to obtain the attitude angles of the local coordinate axes relative to the global coordinate axes: (15) In the formula, For the first j Local X of the station j The axis relative to the total X G The directional attitude angle of the axis, according to "by X G Rotate counterclockwise from the positive axis to X j The "positive direction of the axis" is positive. The common line connecting the center of the first marker pole to the center of the second marker pole is relative to the totality X. G The azimuth angle along the positive axis. The common line connecting the center of the first marker pole to the center of the second marker pole is relative to the first... j Local X of the measuring station j The azimuth angle along the positive axis.

[0162] (16) In the formula, For the first j The rotation matrix from the local coordinate system to the global coordinate system of the survey station. It is a second-order identity matrix. R1 is a second-order identity matrix, representing the rotation matrix from the first station to the global coordinate system. Since the first station is directly used as the global coordinate system, there is no rotation of the coordinate axes from the first station to the global coordinate system, i.e., the attitude angle θ1=0. Therefore, R1=E2 is a second-order identity matrix.

[0163] After the rotation matrix is ​​applied to the connecting vector, its direction should be aligned with the direction of the same connecting vector in the global coordinate system. Here, "rotation" refers to the transformation of the data coordinate components; it does not require rotating the field instrument again. Differences in the position of the coordinate origin will be handled using translation vectors in the next step.

[0164] In this embodiment, the first station is directly used as the global coordinate system, therefore β G =β1=289.440°. The azimuth angle of the common connection line of the second station is β2=272.440°. From the difference in azimuth angles, the attitude angle θ2 of the local coordinate axis of the second station relative to the global coordinate axis is obtained as 17.000°. Based on this, the numerical form of R2 is [[0.956305, -0.292372], [0.292372, 0.956305]]. This numerical matrix is ​​only used for data description in this embodiment. The general expression of the rotation matrix is ​​still based on the aforementioned formula.

[0165] Step 2.3: Calculate the translation vector using a common reference point and verify it.

[0166] After determining the rotation relationship, the center of the first marker pole is selected as the translation calculation point. Its local coordinates are first rotated according to step 2.2, and then subtracted from the global coordinates of the same point to obtain the position of the local origin in the global coordinate system. (17) In the formula, For the first j The translation vector from the local coordinate system to the global coordinate system of the survey station is also O. j The overall coordinates; , Let t1 be the coordinate components along the two axes of the whole. The origin of the first station coincides with the origin of the whole, so t1=0.

[0167] The above single-point formula is the basic translation solution method of this invention. It can also be solved using the second marker rod; under ideal error-free conditions, the two results are consistent. To suppress random measurement errors, after the measurement quality of the two cylindrical marker rods 15 is similar and the consistency of the common marker rod center distance and translation vector has been checked, the translation results obtained from the two cylindrical marker rods 15 can be averaged as an optional accuracy improvement method, as shown in Equation 19. Where the first... j The difference between the center distance of the two cylindrical marker poles 15 measured at the station and the reference center distance of the first station does not exceed the preset threshold ε. d Furthermore, the difference between the translation vectors obtained using the first and second markers does not exceed a preset threshold ε. t At that time, the data from the measuring station is considered to have passed the verification. Based on the measurement accuracy of the laser displacement sensor and rotary encoder, the center-fitting error, the on-site station layout conditions, and the project's testing requirements, the permissible error threshold ε for the center distance of the common marker poles is pre-set. d Translation vector consistency allowable error threshold ε t .

[0168] (18) In the formula, , To obtain the translation vectors using the centers of the first and second marker poles respectively, the basic scheme is as follows: .

[0169] (19) In the formula, This is the average vector of the two translation results. When selecting the basic scheme, the subsequent transformations... Unified On average, it can reduce the impact of random errors under appropriate conditions, but it cannot guarantee the elimination of systematic biases, nor can it replace the stability check of the marker pole.

[0170] When using the average scheme, the subsequent centroid transformation is unified. The basic solution continues to take t. j =t Aj Different translation results should not be used alternately at the same station.

[0171] The center A of the first marker pole at the second station (2) First, change the direction using R2, then align with the global coordinate system A. (G) =A (1) By subtracting the values, we can obtain the translation vector t of the second station. 2 =(4100.000, 100.000) mm. Using the same... and t 2 By transforming the center of the second marker pole at the second station, the overall coordinates of point B are obtained as (2400.000, -500.000) mm. These coordinates are then compared with those measured at the first station. The results are consistent, therefore the coordinate transformation residual of point B in this example data set is approximately 0.000 mm. In actual measurements, this residual is generally not zero and can be used as an auxiliary check for the quality of coordinate transformation.

[0172] Step 2.4: Transform the geometric center of each pre-embedded bolt group to the global coordinate system.

[0173] Based on the recorded correspondence between concrete foundation 12 and the measuring station, read the centroid of the pre-embedded bolt group of concrete foundation 12 and the transformation parameters of the corresponding measuring station, and then perform the following: (20) In the formula, For the first i The centroid of the pre-embedded bolt group of 12 concrete foundations is in the global coordinate system O. G -X G Y G Two-dimensional coordinate vectors in; For the centroid of the pre-embedded bolt group in its respective number j Local coordinate system O of the station j -X j Y j Two-dimensional coordinate vectors in; For the first j The rotation matrix from the local coordinate system to the global coordinate system of the station; This corresponds to the translation vector. Based on the recorded correspondence between concrete foundation 12 and the measuring station, the appropriate vector is selected. , When performing conversions, parameters from other stations must not be mixed. The basic scheme uses the coordinates of the center of the first marker pole to calculate the translation vector, while the optional averaging scheme uses the average of the centers of the first and second marker poles to calculate the translation vector. Subsequent processing for the same station should maintain consistency in the selection.

[0174] (twenty one) In the formula, , They are respectively Along the overall X G axis and Y G The coordinate components of the axes; , They are respectively Along local X j axis and Y j The coordinate components of the axes; , They are translation vectors Along the overall X G axis and Y G The components of the axes. The above component formula is equivalent to the matrix formula. First, the coordinate components are transformed according to the attitude of the local coordinate axes, and then the translation of the local origin is superimposed. The resulting coordinates are all located in the global coordinate system determined by the first station.

[0175] Save the transformed centroid global coordinates together with the original local coordinates, the corresponding station, and the transformation parameters. Do not arbitrarily combine the rotation matrices or translation vectors of other stations with the current centroid.

[0176] Add a fixed component to the end of the planar coordinate column vector: (twenty two) In the formula, For the first j Homogeneous transformation matrix from the station to the global coordinate system. It is a third-order identity matrix. This is the homogeneous transformation matrix from the first station to the global coordinate system.

[0177] (twenty three) In the formula, , Concrete foundation 12 i Local and global homogeneous coordinate column vectors of the centroid of the pre-embedded bolt group; , , , 12 concrete foundations i Planar coordinate components of the centroid of the pre-embedded bolt group in the local and global coordinate systems.

[0178] The centroid of the pre-embedded bolt group of the second concrete foundation 12. =(62.30, 54.10) mm Substitute into the corresponding and To obtain its global coordinates =(4143.76, 169.95) mm. The first station serves as the overall datum, therefore... = =(141.26, -30.05) mm. Meanwhile, the global coordinates of the origin O2 of the second station are... =(4100.00, 100.00)mm, so the horizontal distance between the instrument origins of the first and second stations is about 4101.22 mm; this value is different from the root opening calculated from the centroids of the two pre-embedded bolt groups, indicating that the distance between the instrument installation origins cannot be used to replace the foundation root opening.

[0179] (twenty four) In the formula, From the origin O1 of the first station to the... j Station origin O j Horizontal distance; For the first j Station origin O j With the origin O1 of the first station at x The square of the difference in coordinates of the directions; For the first j Station origin O j With the origin O1 of the first station at y The square of the coordinate difference in direction. The distance describes the relationship between the instrument's installation origin and is usually not equal to the root gap between two pre-embedded bolt groups; it cannot replace the centroid spacing.

[0180] Step 2.5: Calculate the root opening of any two pre-embedded bolt groups and store the results.

[0181] Select any two different concrete foundations 12, and... i ′ indicates concrete foundation 12 i The other matching concrete foundation is numbered 12. i Take 1 to M and i '≠ i The global coordinates of the two centroids are obtained through transformations at their respective corresponding stations, and then their coordinate differences are calculated: (25) In the formula, 12 concrete foundations i The centroid of the pre-embedded bolt group points to the concrete foundation 12. i The coordinate difference vector of the centroid of the pre-embedded bolt group. , For each of the following, along the total X G Axis, Y G The coordinate difference of the axes; , The overall coordinates of the centroid of the corresponding 12 pre-embedded bolt group in the concrete foundation; , , , These are the global coordinate components of the two centroids.

[0182] (26) In the formula, This is the horizontal center distance between the centroids of the two sets of pre-embedded bolts, i.e., the measured root opening. This calculation does not require the overall X-axis to coincide with the design axis beforehand.

[0183] (27) In the formula, For the total X G Rotate the axis counterclockwise to the first i The centroid of the group points to the first i The azimuth angle of the centroid direction. If the two centroids coincide, the root is 0, and the azimuth angle is undefined.

[0184] (28) In the formula, For the same pair of pre-embedded bolt groups, the design root opening, The measured root deviation is represented by a positive value indicating a large deviation and a negative value indicating a small deviation. Before comparing coordinate components or azimuth angles, the design coordinates must be transformed to the same global coordinate system.

[0185] When the root deviation is positive, the measured center distance is greater than the design value; when it is negative, it is less than the design value. If it is necessary to compare coordinate components or connecting directions, the design coordinates should be converted to the same overall datum first. When the two centroids coincide, only the zero distance is output, and the undefined azimuth angle is not output.

[0186] The data processing and display device 11 saves the original distance and angle data of each station, the center of each pre-embedded bolt, the centroid of the pre-embedded bolt group, the center of the two cylindrical marker poles 15, the rotation and translation parameters, the conversion quality inspection results, and the root opening results of any two groups, and forms a unified planar positional relationship between multiple concrete foundation 12 pre-embedded bolt groups based on this.

[0187] The main calculation results of this embodiment are summarized in Table 4.

[0188] Table 4: Overall coordinate transformation and root radius calculation results in this embodiment Results: As shown in Table 2, the fitting radius of each M24 pre-embedded bolt is 11.96–12.05 mm, and the radial residuals are all less than 0.10 mm, indicating that the center of the pre-embedded bolt circle and the centroid of the pre-embedded bolt group at both stations can be stably obtained by multi-point circle fitting. As shown in Table 3, the center distances obtained by the two stations for the same pair of fixed cylindrical marker poles 15 are consistent, and the direction angles of the common connecting line differ by 17.000°, which allows the establishment of the rotation relationship from the second station to the overall coordinate system. By using the same first marker pole to determine the translation vector and using the second marker pole for transformation verification, the obtained rigid body transformation relationship can be verified.

[0189] As shown in Table 4, after coordinate unification, the overall centroid coordinates of the pre-embedded bolt groups of the first and second concrete foundations 12 are (141.26, -30.05) mm and (4143.76, 169.95) mm, respectively, with a difference of (4002.50, 200.00) mm. The calculated measured root opening is 4007.49 mm, and the azimuth angle is 2.861°. Compared with the design root opening of 4000.00 mm set in this embodiment, the root opening deviation is +7.49 mm. The data processing and display device 11 can display and store this root opening result together with the original distance of each measuring point, angular displacement, circle fitting result, coordinates of the common marker pole, rotation matrix, and translation vector.

[0190] The results also show that the horizontal distance between the instrument origins of the second and first stations is approximately 4101.22 mm, while the measured root spacing between the centroids of the two foundation pre-embedded bolt groups is 4007.49 mm, indicating a significant difference. This aligns with the present invention's allowance for the measuring device to be installed at any position on each concrete foundation 12 that meets the measurement conditions. It further clarifies that the foundation root spacing must be calculated from the overall coordinates of the centroids of the pre-embedded bolt groups after completing the common reference coordinate transformation, and cannot be directly calculated using the instrument origin spacing. The aforementioned 4007.49 mm and +7.49 mm are merely example output values ​​used to illustrate the calculation process in this embodiment. Whether they meet the allowable deviations for engineering installation should be determined separately based on the specific transmission tower foundation design documents, construction acceptance requirements, or applicable standards.

[0191] In other embodiments, the number of concrete foundations 12 can be greater than 2, and the number of pre-embedded bolts in each foundation can also be greater than 4; the number of effective measuring points for each cylindrical target can be increased according to the measurement accuracy requirements. As long as the two common cylindrical marker poles 15 remain in fixed positions and correspond consistently throughout the entire measurement period, and the distance and angle data in each measuring station are collected under the same local coordinate reference, the centroid of each foundation pre-embedded bolt group can be obtained according to the above steps. After being unified to the global coordinate system through a common reference rigid body transformation, the root opening and its relative positional relationship between any two foundations can be calculated.

[0192] The embodiments described above are only for illustrating specific implementations of the present invention and do not constitute a limitation on the scope of protection of the present invention. Those skilled in the art can make equivalent modifications or improvements to the number of measuring points, device specifications, marker rod dimensions, data communication methods, and coordinate calculation programs without departing from the concept of the present invention, and these modifications or improvements can all be implemented according to the technical solutions described in the present invention.

Claims

1. A method for measuring the root opening of a power transmission tower foundation, characterized in that, Includes the following steps: The first step is local measurement within each concrete foundation (12): A measuring device (14) is set up on each concrete foundation (12) to establish a local coordinate system and obtain the local coordinates of the geometric center of the pre-embedded bolt group of this concrete foundation (12) and the geometric center of the same pair of fixed cylindrical marker poles (15); specifically: Step 1.1: Assemble the foundation root opening measurement device for the power transmission tower and arrange the cylindrical marker poles (15); Step 1.2: Set up the measuring device on the current concrete foundation (12) and establish a local coordinate system; Step 1.3: Convert the distance and azimuth to local coordinates; Step 1.4: Determine the center of the first pre-embedded bolt (13); Step 1.5: Calculate the center of the remaining pre-embedded bolts in sequence; Step 1.6: Calculate the geometric center of the pre-embedded bolt group in the concrete foundation (12) to obtain the centroid of the pre-embedded bolt group in the concrete foundation (12). ; Step 1.7: Measure the two common marker poles and calculate the direction of the connecting line; Step 1.8: Complete the local measurements of all concrete foundations (12) in sequence; The measuring device (14) is set up on the remaining concrete foundations (12) in sequence, and steps 1.2 to 1.7 are repeated until all concrete foundations (12) are measured. The second step is to establish the overall coordinate relationship and calculate the foundation root opening between each pre-embedded bolt group: the local coordinate system of the first station is directly defined as the overall coordinate system. The rotation and translation relationship between the remaining local coordinate systems and the overall coordinate system is established through two cylindrical marker poles (15). The geometric center of each pre-embedded bolt group is transformed into the overall coordinate system. The horizontal distance between the geometric centers of any two pre-embedded bolt groups is calculated, which is the foundation root opening. Specifically: Step 2.1: Use the local coordinate system of the first station as the global coordinate system; Step 2.2: Calculate the rotation matrix from the angles between the common connecting lines and each X-axis; Step 2.3: Calculate the translation vector using a common reference point and verify it; Step 2.4: Transform the geometric center of each pre-embedded bolt group to the global coordinate system; Step 2.5: Calculate the root opening of any two pre-embedded bolt groups and store the results; The data processing and display device (11) of the power transmission tower foundation root opening measurement device saves the original distance and angle data of each station, the center of each pre-embedded bolt, the centroid of the pre-embedded bolt group, the center of the two cylindrical marker poles (15), the rotation and translation parameters, the conversion quality inspection results and any two groups of root opening results, and forms a unified planar position relationship between multiple concrete foundation (12) pre-embedded bolt groups based on this.

2. The method for measuring the root opening of a transmission tower foundation according to claim 1, characterized in that, The first step is specifically: Step 1.1 specifically involves: The foundation root opening measurement device for power transmission towers includes a measuring device (14), a data processing and display device (11), and two cylindrical marker poles (15). The measuring device (14) is used to acquire distance data and angular displacement data of the measuring points on the surface of the pre-embedded bolts and cylindrical marker poles (15), and send the data to the data processing and display device (11). The data processing and display device (11) is used to convert polar coordinate data into planar coordinates, calculate the center of the pre-embedded bolts, the geometric center of the pre-embedded bolt group, the geometric center of the two cylindrical marker poles (15), establish the rotation matrix, translation vector, and homogeneous transformation matrix from each local coordinate system to the global coordinate system, and calculate the actual center distance, relative orientation, and foundation root opening between the geometric centers of the pre-embedded bolt groups of different concrete foundations (12). The measuring device (14) includes a laser displacement sensor (1), a laser displacement sensor support (2), a set screw (3), a rotary encoder support (4), a rotary encoder (5), a cover plate (6), a foam pad (7), a battery (8), a housing (9), a data transmission device (10), and two cylindrical marker rods (15). The two cylindrical marker rods (15) are cylindrical rods of the same size. The cylindrical marker rod (15) with an A identification mark is defined as the first marker rod, and the cylindrical marker rod (15) with a B identification mark is defined as the second marker rod. During the measurement process, the housings of the rotary encoder support (4) and the rotary encoder (5) remain fixed relative to the cover plate (6); the laser displacement sensor support (2) rotates around the output shaft axis of the rotary encoder (5), and the laser displacement sensor (1) rotates synchronously, thereby driving the output shaft of the rotary encoder (5) to rotate; the laser displacement sensor (1) collects the distance data of the measurement point to be measured, and the rotary encoder (5) collects the corresponding angular displacement data synchronously; the data transmission device (10) sends the distance data and angular displacement data to the data processing and display device (11); the data processing and display device (11) calculates the center of the pre-embedded bolt, the geometric center of the pre-embedded bolt group and the geometric center of the two cylindrical marker poles (15) according to the received data, and establishes the coordinate transformation from the local coordinate system to the global coordinate system based on the coordinates of the common marker pole, and outputs the foundation root opening between the geometric centers of different pre-embedded bolt groups; Step 1.2 specifically involves: The total number of concrete foundations (12) to be tested is recorded as follows: M , M The integer is not less than 2; the current concrete foundation (12) is numbered as i , i Take 1 to M Integer; place the measuring device (14) at the first i The upper surface of the concrete foundation (12) does not obstruct the position of the first pre-embedded bolt (13) and the two cylindrical marker poles (15) measuring the optical path; during a complete measurement of the concrete foundation (12), the position, zero angle and leveling state of the measuring device (14) remain unchanged; each station adopts a horizontal measuring plane, and the center of the pre-embedded bolt is measured according to the agreed installation reference section; A complete setup at a fixed position and a fixed angle zero point is called a measuring station. j Indicates the station number, in S Indicates the total number of stations. j Take 1 to S Integer; record the first j The station and the measured number i The correspondence between the concrete foundations (12); each concrete foundation (12) needs to be erected once, therefore S = M The first measuring station is located on the first concrete foundation (12); the local origin O is the intersection of the rotation axis of the rotary encoder (5) and the horizontal measuring plane. j With the initial measurement direction fixed as X j In the positive direction of the axis, within the same horizontal plane, from X j The direction in which the axis rotates 90° counterclockwise is Y. j Establish a local coordinate system O along the positive axis. j -X j Y j Rotary encoder with X j The positive direction of the axis is zero, and counterclockwise is positive; the origin and initial orientation of each station are allowed to be different, but the positive direction of the angle must be consistent; Step 1.3 specifically includes: The first i The total number of pre-embedded bolts on the concrete foundation (12) is denoted as , k This indicates the number of the embedded bolts within the concrete foundation (12). k Take 1 to ;by q Indicates the valid measurement point number of a single measured cylindrical surface; the first k The first pre-embedded bolt q The coordinates of the surface measuring points are as follows: The superscript j in parentheses indicates the coordinate system of the station; the total number of valid measuring points for the pre-embedded bolts at this station is denoted as U. ik (j) , q Take 1 to U ik (j) , and U ik (j) Not less than 3; its polar coordinate transformation formula is: （1） In the formula, , The measuring points are along X j Axis, Y j The coordinate components of the axes; For O j Radial distance to the measuring point; For X j The azimuth angle of the measuring point is rotated counterclockwise from the positive axis direction to the radial direction. Step 1.4 specifically includes: In the j The station kept the measuring device (14) stationary and monitored the first... i For the first embedded bolt (13) of the concrete foundation (12), at least three non-overlapping and non-collinear surface measuring points are selected within the same measuring section. , and The local coordinates obtained in step 1.3 are abbreviated as: （2） In the formula, a, b, c The three selected measuring points are designated as measuring point 1, measuring point 2, and measuring point 3. , , , , , The first, second, and third measuring points are respectively located at the 1st, 2nd, and 3rd measuring points. j Local coordinate components of the station; Let the coordinates of the center of the first pre-embedded bolt (13) be... =( , ) T In the formula, For the first j The first station i Local coordinates of the center of the cross section of the first embedded bolt (13) of the concrete foundation (12); , The center of the circle is along the local coordinate system O. j -X j Y j X j axis and Y j The coordinate components of the axis; the radius of the cross-section circle is r i1 Then any point on the circumference ( , )satisfy: （3） Substitute the coordinates of the three measuring points into the equation of the circle; subtract the equation corresponding to the first measuring point from the equations corresponding to the second and third measuring points respectively, eliminating the radius term and the square term of the center coordinates, to obtain a system of linear equations about the center coordinates: （4） The coefficient matrix, written in matrix form, is: （5） When the three measurement points are not collinear, the coefficient matrix is ​​invertible. Solving for the coefficient matrix using a system of two linear equations yields the solution. If the three measuring points are nearly collinear, then select new measuring points with a more sufficient distribution. Step 1.5 specifically involves: （6） In the formula, For the first k Local coordinates of the center of each pre-embedded bolt. , Its coordinate components, Indicates the number of the embedded bolts. Indicates the first i The total number of pre-embedded bolts in each concrete foundation (12); For the remaining embedded bolts of the concrete foundation (12), calculate the coordinates of the surface measuring points in step 1.3, and then obtain the center of the circle in step 1.

4. Step 1.6 specifically includes: Centroid of pre-embedded bolt group in concrete foundation (12): （7） In the formula, , The centroid of the pre-embedded bolt group for this concrete foundation (12) The local coordinate components; the centroid of the pre-embedded bolt group of this concrete foundation (12) is taken as the arithmetic mean of the coordinates of the center of all pre-embedded bolts, and is not replaced by the center of the outer contour of the concrete foundation (12) or the origin of the instrument. Step 1.7 specifically includes: Keep the first j The measuring device (14) at the station remains stationary, and at least three non-coincident and non-collinear cross-sectional measuring points are collected on the cylindrical surfaces of the first and second marker poles, respectively; the coordinates of each measuring point are marked as follows: , , For the first j The first marker pole at the station q The effective surface measuring points are in the local coordinate system O. j -X j Y j The coordinate vector in; For the first j The second marker pole at the station q The coordinate vectors of each effective surface measuring point in the local coordinate system; for the first marker pole... q =1,2,…,U A (j) For the second marker pole, q = 1, 2, ..., U B (j) The total number of effective surface measuring points for the first and second marker poles are U respectively. A (j) U B (j) ; q Take values ​​within the valid measuring point range of the corresponding marker pole; （8） In the formula, For the first marker pole q Each surface measuring point is relative to the local origin O. j The radial distance; For the second marker pole q Each surface measuring point is relative to the local origin O. j The radial distance; For local X j The directional azimuth angle of the radial direction of the measuring point on the qth surface of the first marker rod, rotated counterclockwise in the positive direction of the axis; For local X j The directional azimuth angle of the radial direction of the measuring point on the qth surface of the second marker rod, rotated counterclockwise in the positive direction of the axis; （9） In the formula, , The coordinates of the center of the cross-section of the first and second marker poles obtained in step 1.4 are: , and , Its local coordinate components; The coordinates of the center of the circle are expressed using the radius vector and azimuth angle as follows: （10） In the formula, , O j The radius vector length from the center of the first marker pole to the center of the second marker pole; , The azimuth angle of the corresponding circle's center radius vector; the circle's center radius vector and azimuth angle should be calculated from the fitted circle center coordinates, not directly using the distance and angle of a single surface measuring point; （11） In the formula, Let be the vector of the common line connecting the center of the first marker pole circle to the center of the second marker pole circle. , The local coordinate components are the common connection vectors; each station adopts the sequence of the first marker pole pointing to the second marker pole; （12） In the formula, The common line connecting the center of the first marker pole to the center of the second marker pole is relative to the first... j Local X of the measuring station j The azimuth angle along the positive axis. The distance between the centers of the first and second marker poles is denoted as .

3. The method for measuring the root opening of a power transmission tower foundation according to claim 2, characterized in that, The measuring device (14) in step 1.1 specifically includes: The rotary encoder support (4) is a hollow cylindrical structure with a flange on its lower outer periphery. The rotary encoder support (4) is a supporting component for installing and fixing the rotary encoder (5). It has an internal accommodating space that matches the shape of the rotary encoder (5). The rotary encoder (5) has a cylindrical body with an output shaft in the middle and a base housing on the outside. The output shaft can rotate freely around the outer base housing. It has a threaded hole on its top circumference for fixing to the rotary encoder support (4). The rotary encoder (5) is installed inside the rotary encoder support (4) and the two are coaxial. It has a cylindrical positioning boss on its upper part and a positioning hole on the rotary encoder support (4) corresponding to the cylindrical positioning boss. The cylindrical positioning boss is inserted into the positioning hole. The rotary encoder (5) and the rotary encoder support (4) are coaxially positioned within the circular hole through clearance fit, ensuring that the output shaft axis of the rotary encoder (5) coincides with or remains coaxial with the predetermined rotation axis of the rotary encoder support (4). The outer housing of the rotary encoder (5) is fixedly connected to the inner wall of the rotary encoder support (4) by screws, thereby restricting the axial movement and circumferential rotation of the housing of the rotary encoder (5) relative to the rotary encoder support (4). Multiple connection holes are spaced along the circumferential direction on the flange for screws to pass through and be fixedly connected to the cover plate (6), so that the rotary encoder support (4) is stably installed on the cover plate (6). The cover plate (6) is used to support and fix the rotary encoder support (4) and provide an installation base for the rotary encoder (5) and its related rotating parts. The laser displacement sensor support (2) is a block structure with an opening at the bottom. Its upper surface is the mounting surface of the laser displacement sensor (1), and its hollow bottom surface is open for inserting into the upper part of the rotary encoder support (4). The laser displacement sensor support (2) can rotate relative to the rotary encoder support (4) around the output shaft axis of the rotary encoder (5). The laser displacement sensor support (2) has a cylindrical hole inside that corresponds to the output shaft of the rotary encoder (5). The output shaft of the rotary encoder (5) is inserted into the cylindrical hole and is clearance-fitted with the cylindrical hole. This clearance fit is used to realize the axial assembly and coaxial positioning between the output shaft of the rotary encoder (5) and the laser displacement sensor support (2). The output shaft of the rotary encoder (5) has a flat surface pre-machined on its outer periphery. The laser displacement sensor support (2) has a threaded hole that communicates with the cylindrical hole. The set screw (3) is screwed into the threaded hole and the end of the set screw (3) is pressed against the flat surface of the output shaft of the rotary encoder (5). Through the cooperation between the set screw (3) and the flat surface, the relative circumferential rotation between the output shaft of the rotary encoder (5) and the laser displacement sensor support (2) can be restricted, so that the two form a circumferential fixed connection, thereby ensuring that the output shaft of the rotary encoder (5) can be driven to rotate synchronously when the laser displacement sensor support (2) rotates. At the same time, the flat surface on the output shaft can increase the pressing contact area of ​​the set screw (3), reduce slippage, and improve the reliability and measurement accuracy of angle transmission. The cover plate (6) is detachably fixed to the housing (9); The battery (8), foam pad (7) and data transmission device (10) are all located inside the housing (9).

4. The method for measuring the root opening of a power transmission tower foundation according to claim 3, characterized in that, Specifically, as stated in 2.1: The local coordinate system O1-X1Y1 of the first station is directly defined as the global coordinate system O. G -X G Y G ; G Mark the global coordinate system; the origins and axes of the two coordinate systems coincide, and the coordinates measured at the first station do not need to be transformed: （13） Among them, A (G) B (G) These are the global coordinates of the center of the first marker pole and the center of the second marker pole, respectively. (1) B (1) These are their local coordinates at the first station; P1 (G) P1 (1) These are the global coordinates of the centroid of the first pre-embedded bolt group and the local coordinates at the first measuring station, respectively. The overall reference datum is fixed by the center coordinates of the first and second marker poles measured at the first station. The centroid coordinates of the pre-embedded bolt group of the first concrete foundation (12) are directly used for subsequent root opening calculations. The overall direction of the common line is obtained from the overall coordinates. （14） In the formula, and , These are the vectors and components of the common connection line in the global coordinate system. For the common connection relative to X G A directional angle along the positive axis.

5. The method for measuring the root opening of a transmission tower foundation according to claim 4, characterized in that, Specifically, as stated in 2.2: The actual direction of the common connecting line remains unchanged. By using the difference between its directed angles relative to the global horizontal axis and the local horizontal axis, the attitude angles of the local coordinate axes can be obtained: （15） In the formula, For the first j Local X of the station j The axis relative to the total X G The directional attitude angle of the axis, according to "by X G Rotate counterclockwise from the positive axis to X j "Positive direction of the axis" is considered positive. The common line connecting the center of the first marker pole to the center of the second marker pole is relative to the totality X. G The azimuth angle along the positive axis. The common line connecting the center of the first marker pole to the center of the second marker pole is relative to the first... j Local X of the measuring station j The azimuth angle along the positive axis; （16） In the formula, For the first j The rotation matrix from the local coordinate system to the global coordinate system of the survey station. It is a second-order identity matrix. It is a second-order identity matrix.

6. The method for measuring the root opening of a transmission tower foundation according to claim 5, characterized in that, Specifically, as stated in 2.3: After determining the rotation relationship, the center of the first marker pole is selected as the translation calculation point; then its position in the global coordinate system is: （17） In the formula, For the first j The translation vector from the local coordinate system of the station to the global coordinate system is also O. j The overall coordinates; , Let these be the coordinate components along the two axes of the whole; The origin of the first station coincides with the origin of the whole, so t1=0; The average of the translation results obtained from the first and second marker poles is used as the accuracy improvement method: （18） In the formula, , To obtain the translation vectors using the centers of the first and second marker poles respectively, the basic scheme is as follows: ; （19） In the formula, This is the average vector of the two translation results; when selecting the basic scheme, the subsequent transformation... Unified .

7. The method for measuring the root opening of a transmission tower foundation according to claim 6, characterized in that, Specifically, as stated in section 2.4: （20） In the formula, For the first i The centroid of the pre-embedded bolt group of the concrete foundation (12) is in the global coordinate system O. G -X G Y G Two-dimensional coordinate vectors in; For the centroid of the pre-embedded bolt group in its respective number j Local coordinate system O of the station j -X j Y j Two-dimensional coordinate vectors in; For the first j The rotation matrix from the local coordinate system to the global coordinate system of the station; The corresponding translation vector; according to the recorded correspondence between the concrete foundation (12) and the measuring station, select the appropriate... , When performing conversions, parameters from other stations must not be mixed; the basic scheme uses the coordinates of the center of the first marker pole to calculate the translation vector, or the average scheme uses the average value of the translation vector obtained from the centers of the first and second marker poles; subsequent processing for the same station should be consistent. （21） In the formula, , They are respectively Along the overall X G axis and Y G The coordinate components of the axes; , They are respectively Along local X j axis and Y j The coordinate components of the axes; , They are translation vectors Along the overall X G axis and Y G The components of the axes; the obtained coordinates are all located in the global coordinate system determined by the first station; Add a fixed component to the end of the planar coordinate column vector: （22） In the formula, For the first j Homogeneous transformation matrix from the station to the global coordinate system. It is a third-order identity matrix. This is the homogeneous transformation matrix from the first station to the global coordinate system; （23） In the formula, , These are concrete foundations (12). i Local and global homogeneous coordinate column vectors of the centroid of the pre-embedded bolt group; , , , For concrete foundation (12) i Planar coordinate components of the centroid of the pre-embedded bolt group in the local and global coordinate systems; （24） In the formula, From the origin O1 of the first station to the... j Station origin O j Horizontal distance; For the first j Origin of the measuring station j With the origin O1 of the first station at x The square of the difference in coordinates of the directions; For the first j Origin of the measuring station j With the origin O1 of the first station at y The square of the difference in coordinates in the direction.

8. The method for measuring the root opening of a power transmission tower foundation according to claim 7, characterized in that, Specifically, as stated in 2.5: Select any two different concrete foundations (12), and... i ′ indicates the concrete foundation (12) i The other concrete foundation (12) of the pair is numbered. i Take 1 to M and i '≠ i The global coordinates of the two centroids are obtained through transformations at their respective corresponding stations, and then their coordinate differences are calculated. （25） In the formula, For concrete foundation (12) i The centroid of the pre-embedded bolt group points towards the concrete foundation (12). i The coordinate difference vector of the centroid of the pre-embedded bolt group. , For each of the following along the total X G Axis, Y G The coordinate difference of the axes; , The overall coordinates of the centroid of the pre-embedded bolt group in the corresponding concrete foundation (12); , , , These are the global coordinate components of the two centroids; （26） In the formula, The horizontal center distance between the centroids of the two sets of pre-embedded bolts is the measured root opening; this calculation does not require the overall X-axis to coincide with the design axis in advance; （27） In the formula, For the total X G Rotate the axis counterclockwise to the first i The centroid of the group points to the first i The azimuth of the centroid direction; if the two centroids coincide, the root is 0 and the azimuth is undefined. （28） In the formula, For the same pair of pre-embedded bolt groups, the design root opening, The value represents the measured root opening deviation; a positive value indicates a large deviation, and a negative value indicates a small deviation.

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