A system, method, storage medium, and computer program product for calculating jack cluster positioning commands for jacking of curved bridges.

Abstract

This invention discloses a jack cluster positioning command calculation system, method, storage medium, and computer program product for jacking operations on curved bridges. The method includes: calculating and decentralizing the centroid based on the current and target coordinates of the beam measuring points; performing orthogonal decomposition on the decentralized point set to obtain an initial value of the rotation matrix, and then refining it through gradient descent to obtain the optimal rotation matrix; calculating the global displacement vector of each jack using the centroid and the optimal rotation matrix, and converting it into a three-dimensional positioning amount in the local coordinate system based on the installation deflection angle, thereby generating positioning commands. This invention employs a dual-layer optimization strategy of orthogonal decomposition initial estimation and gradient descent refinement, taking into account both global optimality and local accuracy, achieving fully automatic high-precision calculation from measurement data to equipment commands, eliminating manual conversion errors, and is particularly suitable for multi-point synchronous positioning control of walking-type jacking equipment.

Description

Technical Field

[0001] This invention belongs to the field of bridge engineering technology, specifically relating to a jack cluster positioning command calculation system, method, storage medium, and computer program product for jacking curved bridges. Background Technology

[0002] In the incremental launching method for constructing curved bridges, a core technical challenge lies in precisely adjusting the beam, which is in an arbitrary spatial orientation, to the target orientation specified in the design. This process involves the coordinated control of clusters of jacks at multiple piers.

[0003] Currently, the following methods are commonly used in engineering for position adjustment calculations: (1) Manual geometric drawing method: draw on the drawing according to the measurement data to solve the problem; (2) Single point independent calculation method: calculate the displacement of each jack separately; (3) Simple coordinate transformation method: use the least squares method to solve the overall translation and rotation. The calculation results need to be manually transformed twice before they can be used for on-site equipment control.

[0004] The aforementioned existing technologies generally suffer from the following drawbacks: low efficiency and accuracy greatly affected by human factors, making it difficult to meet millimeter-level construction requirements; neglect of the overall rigid body motion characteristics of the beam, which can easily lead to additional stress or local deformation of the beam after repositioning; and the calculation results are prone to conversion errors after secondary manual conversion. Summary of the Invention

[0005] This invention proposes a jack cluster positioning command calculation system, method, storage medium, and computer program product for jacking curved bridges.

[0006] A jack cluster positioning command calculation system for jacking of curved bridges, which achieves one of the objectives of this invention, includes: The translation and rotation decoupling module is used to calculate the current centroid of all measuring points in the current posture and the target centroid in the target posture based on the measured coordinates of each measuring point in the current posture and the theoretical coordinates in the target posture; subtract the current centroid from the measured coordinates of each measuring point to obtain the current point set; and subtract the target centroid from the theoretical coordinates of each measuring point to obtain the target point set. The rotation matrix solving module is used to perform orthogonal decomposition on the current point set and the target point set to obtain an initial matrix for rotating the beam from the current posture to the target posture. Starting from the initial matrix, iterative optimization is performed to minimize the deviation between the current point set and the target point set after the rotation matrix transformation, thus obtaining the optimal rotation matrix. Orthogonal decomposition refers to decomposing a matrix into the product of two orthogonal matrices and a diagonal matrix (such as singular value decomposition), or into the product of a rotation matrix and a scaling matrix (such as extreme decomposition), or other orthogonal decomposition methods that can extract rotation components from the point set covariance matrix. In this invention, orthogonal decomposition is used to solve for the initial value of the rotation matrix from the current point set and the target point set. The instruction generation module calculates the global displacement vector of each jack from its current position to the target position based on the current centroid, the target centroid, and the optimal rotation matrix. Then, based on the installation deflection angle of each jack, it obtains the three-dimensional adjustment amount of the global displacement vector for each jack in its own coordinate system. This three-dimensional adjustment amount, along with the jack's unique identifier, constitutes the adjustment instruction for each jack. The installation deflection angle δ refers to the angle between the jack's advancing direction and the positive X-axis of the global coordinate system, measured in degrees using a total station, and is used to transform the global displacement vector to the jack's own coordinate system. The centroid refers to the arithmetic mean of the coordinates of all measured points; that is, the current centroid is the average of all current coordinates, and the target centroid is the average of all target coordinates. The centroid reflects the average position of the beam in space and is used to separate the translation component from the overall transformation. The three-dimensional adjustment refers to the three displacement components in the jack's own coordinate system, which correspond to the displacement along the jack's pushing direction (main pushing stroke, positive value indicates pushing, negative value indicates retraction), the horizontal displacement perpendicular to the pushing direction (lateral correction, positive value indicates rightward, negative value indicates leftward), and the vertical displacement (positive value indicates lifting, negative value indicates lowering).

[0007] Furthermore, the rotation matrix solving module obtains the initial matrix of the rotation matrix through the following steps: Based on the measured coordinates of the measuring point in the current attitude and the theoretical coordinates in the target attitude, a covariance matrix is ​​constructed using the current centroid and the target centroid. ;where P c,i and P t,i C represents the measured coordinates of the i-th measurement point in the current attitude and the theoretical coordinates in the target attitude, respectively; c and C t These represent the current centroid and the target centroid, respectively; M represents the number of measurement points; Singular value decomposition of H , where U and V are the left singular vector matrix and the right singular vector matrix, respectively; both U and V are orthogonal matrices; Calculate R0=VU T ; When the determinant of R0 det If (R0) = -1, then invert the third column of the orthogonal matrix V to obtain the corrected right singular vector matrix V', and then calculate R0 = V'U. T ; The matrix R0 is used as the initial matrix of the rotation matrix.

[0008] Furthermore, methods for obtaining the optimal rotation matrix include: The rotation matrix is ​​represented as three rotations around the Z-axis, Y-axis, and X-axis in sequence ( ). The function of R( )= ; Define loss function ; The Euclidean norm of a vector; The Euler angles corresponding to the initial matrix R0 of the rotation matrix ( Starting from ), the following momentum gradient descent method is used for iterative updates: Where: g (k) Let be the gradient direction at step k. Indicates element-wise multiplication; v (k) Let v be the momentum term at the k-th iteration, with an initial value of v. (0) =0; , β The momentum coefficient is used to accelerate gradient descent convergence; The adaptive learning rate at the k-th iteration; The iteration terminates when the loss function is less than a set value or the number of iterations reaches a set number. Substitute the Euler angle at the end of the iteration into R( The function performs matrix transformations to obtain the optimal rotation matrix.

[0009] Furthermore, it also includes an error control module for: For the current coordinates of each measuring point, first subtract the current centroid, then multiply by the optimal rotation matrix, and finally add the target centroid to obtain the transformed position; Calculate multiple error indices between the transformed position and the target position; the multiple error indices include: global root mean square error (RMSE), maximum single-point error (MaxErr), and direction error (ΔDir); When any of the multiple error metrics exceeds the corresponding preset threshold, the learning rate is reduced starting from the current optimal rotation matrix. And / or increase the number of iterations, re-execute the iterative optimization described in the rotation matrix solution module until the error indicators do not exceed the corresponding preset thresholds or reach the upper limit of the number of re-optimizations. The threshold for global root mean square error is 5mm; the threshold for maximum single-point error is 8mm; the threshold for direction error is 0.5°; the above thresholds are only examples and can be adjusted according to factors such as bridge curvature, span, and construction accuracy requirements in actual applications.

[0010] Furthermore, the methods for calculating the current centroid include: Methods for calculating the centroid of a target include: C C This represents the current centroid of all measurement points in the current attitude. C t The target centroid is the centroid of all measurement points under the target attitude; M is the number of measurement points; P c,i and P t,i These represent the measured coordinates of the i-th measurement point in the current attitude and the theoretical coordinates in the target attitude, respectively.

[0011] Furthermore, the method for calculating the global displacement vector of each jack from its current position to the target position includes: The coordinates of the target position of the jack are calculated using the following formula: J tar,i =R(J cur,i -C c )+C t .

[0012] In the formula, R is the optimal rotation matrix; J cur,i and J tar,i Let C be the current position and the target position of the i-th jack, respectively; c and C t These represent the current centroid and the target centroid, respectively. J cur,i and J tar,i The difference Δ global,i This is the global displacement vector that each jack needs to move.

[0013] Furthermore, the method for obtaining the three-dimensional adjustment amount includes: Each jack has its own local coordinate system as follows: Local X-axis direction: along the jack's pushing direction, with the positive direction being the jacking forward direction; Local Y-axis direction: perpendicular to the local X-axis in the horizontal plane, pointing to the right; Local Z-axis direction: Consistent with the global Z-axis direction, vertically upward; Rotate the global displacement vector Δglobal around the global Z-axis by -δ i By calculating the angle, we can obtain the three displacement components in the local coordinate system, where δ i The installation offset angle of the i-th jack: In the formula: X local,i : Indicates the displacement along the direction of the jack's push; Y local,i : Indicates the horizontal displacement perpendicular to the jacking direction; Z local,i : Indicates vertical displacement; ( X local,i ,Y local,i ,Z local,i This refers to the three-way adjustment amount.

[0014] Furthermore, it also includes a data acquisition module, used to obtain the three-dimensional coordinates and installation deflection angle of each jack in the global coordinate system, as well as the current coordinates and target coordinates of each measuring point on the beam; wherein, the measuring points are arranged along the beam length on multiple characteristic sections, and multiple measuring points (such as 3 measuring points) are arranged sequentially along the transverse direction of the bridge on each section.

[0015] A method for calculating the positioning command of a cluster of jacks for jacking curved bridges, which achieves the second objective of this invention, includes: Based on the measured coordinates of each measuring point on the beam in the current posture and the theoretical coordinates in the target posture, calculate the current centroid of all measuring points in the current posture and the target centroid in the target posture; subtract the current centroid from the measured coordinates of each measuring point to obtain the current point set; subtract the target centroid from the theoretical coordinates of each measuring point to obtain the target point set; The current point set and the target point set are orthogonally decomposed to obtain an initial matrix for rotating the beam from the current posture to the target posture. Starting from the initial matrix, the deviation between the current point set and the target point set after the rotation matrix transformation is minimized through iterative optimization, thereby obtaining the optimal rotation matrix. Based on the current centroid, the target centroid, and the optimal rotation matrix, calculate the global displacement vector of each jack from its current position to the target position; then, based on the installation deflection angle of each jack, obtain the three-dimensional adjustment amount of the global displacement vector corresponding to each jack in its own coordinate system. The three-dimensional adjustment amount and the unique identification of the jack constitute the adjustment command of each jack.

[0016] A non-transitory computer-readable storage medium for achieving the third objective of the present invention stores a computer program thereon, wherein when the computer program is executed by a processor, it implements the steps of the method for calculating the jack cluster positioning instructions for jacking a curved bridge.

[0017] A computer program product for achieving the fourth objective of the present invention includes a computer program / instruction that, when executed by a processor, implements the steps of the method for calculating the jack cluster positioning instructions for jacking a curved bridge.

[0018] The beneficial effects of this invention include: An optimization strategy combining SVD initial estimation and gradient descent fine-tuning is adopted. This strategy utilizes the global analytical capability of SVD to avoid local optima and eliminates the influence of measurement noise through gradient descent fine-tuning, thereby meeting the requirements of engineering accuracy control. The entire process from data input to command output requires no manual intervention, significantly reducing computation time and adapting to the needs of rapid on-site decision-making.

[0019] It supports any number of piers, jacks, and measuring point sections, and is compatible with various curved bridge alignments; through local coordinate system transformation, the calculation results can be directly used for equipment control, eliminating secondary errors. It can intuitively display the beam transformation process, making it easier to judge the rationality of the results and improve construction safety. Attached Figure Description

[0020] Figure 1 This is a flowchart illustrating an embodiment of the method described in this invention; Figure 2 This is a schematic diagram of the data acquisition process in the embodiment of the method described in this invention; Figure 3 This is a flowchart illustrating the decoupling of translation and rotation in an embodiment of the method described in this invention; Figure 4 This is a flowchart illustrating the process of solving the optimal rotation matrix in an embodiment of the method described in this invention; Figure 5 This is a schematic diagram of the spatial transformation and error closed loop in the method embodiment of the present invention; Figure 6 This is a schematic diagram of the process for generating jack adjustment instructions in the method embodiment of the present invention; Figure 7 This is a schematic diagram of the result output in the embodiment of the method described in this invention. Detailed Implementation

[0021] The following detailed embodiments are provided to explain the technical solutions of the present invention, so that those skilled in the art can understand the present invention. The scope of protection of the present invention is not limited to the following specific embodiments. Any modifications or improvements made by those skilled in the art that incorporate the technical solutions of the present invention but differ from the following detailed embodiments are also within the scope of protection of the present invention.

[0022] A method for calculating the positioning command of a cluster of jacks used in the jacking of curved bridges includes the following steps: Step 1: Spatial Configuration Modeling This step collects two independent types of spatial data: actuator-level data (jack positions and deflection angles) and controlled object-level data (coordinates of beam measuring points). The jacks are located at each pier, their number and distribution determined by the support system; the beam measuring points are selected along the beam length at several characteristic sections. The two types of data are mapped using subsequent rigid body space transformation formulas, without requiring geometric overlap or correspondence between them.

[0023] The purpose of this step is to establish spatial characteristic parameters that include the actuator (jack) and the controlled object (beam), such as... Figure 2 As shown, it includes: (1) Data collection at the execution level As a typical implementation, two jacks, one on the left and one on the right, are usually arranged at each pier. The three-dimensional coordinates J of the left and right jacks at each pier in the global coordinate system are obtained. cur =(X j ,Y j Z j The angle δ between the jack's pushing direction and the positive X-axis of the global coordinate system (i.e., the jack's installation deflection angle, in degrees, with the global X-axis as the reference, counterclockwise being positive and clockwise being negative, obtained through total station measurement) is also considered. The global coordinate system is defined as follows: X-axis is the longitudinal direction of the bridge design (jacking direction), Y-axis is the horizontal direction, and Z-axis is the vertical direction. This deflection angle defines the orientation of the jack's local coordinate system and is a key parameter for converting the global displacement into a recognizable command. It should be noted that the number of jacks on the pier is not limited to two; it can be configured as one, two, or more depending on the actual support scheme. The calculation method of this invention can automatically adapt to any number of jacks; simply provide the coordinates and deflection angle of each jack in the above format.

[0024] (2) Data acquisition at the controlled object level N characteristic sections are selected along the beam length (i.e., the longitudinal axis of the beam). These characteristic sections should represent the spatial linear and torsional deformation characteristics of the beam and are typically selected at key sections such as jack support locations, joints between adjacent beam segments, mid-span, or quarter-span points. To accurately solve for the rotational components of the rigid body transformation, at least two characteristic sections should be selected, and each section should not be excessively concentrated in a local area of ​​the beam.

[0025] Three measuring points are set up for each cross section: the left side point (L), the middle point (M), and the right side point (R).

[0026] To establish a unique mapping between measuring points and their physical locations, all M measuring points (M=3N) are numbered uniformly according to the following rules: The mapping relationship between index i and section number k, and measurement point type t∈{L,M,R} is i=3(k-1)+idx(t), where idx(L)=1, idx(M)=2, and idx(R)=3. That is, P c,3(k-1)+1 P t,3(k-1)+1 P corresponds to the left side point of the k-th cross section. c,3(k-1)+2 P t,3(k-1)+2 P corresponds to the midpoint of the k-th cross-section c,3(k-1)+3 P t,3(k-1)+3 The right-side point corresponding to the k-th cross-section.

[0027] Record the measured coordinates P of all 3N measurement points in the current attitude. c,i =(x c,i ,y c,i ,z c,i ), and the theoretical coordinates P under the design target attitude. t,i =(x t,i ,y t,i ,z t,i ), where i represents the measurement point number, i∈[1,3N].

[0028] (3) Automatic data verification Check the integrity of the input data, ensuring it is not empty and the values ​​are valid, such as coordinates not being NaN or Inf, and the deflection angle δ being within the range of -180° to 180°; units should be uniformly set to meters or millimeters. Also check the matching of the number of measurement points (i.e., the number of current points and target points must be equal, both being 3N, and N≥2 to support subsequent cross-section normal calculations) to ensure the data quality for subsequent calculations. Output the verified data to step two.

[0029] Step 2: Translation-Rotation Decoupling After step one, we obtained the set of measured points {P} of the beam in its current attitude. c,i} and the theoretical point set {P} under the design target attitude. t,iThe goal of this step is to solve a rigid body space transformation that aligns the current point set with the target point set. This transformation contains six independent components in three-dimensional space: three translations along the X, Y, and Z axes, and three rotations about the X, Y, and Z axes (i.e., six-degree-of-freedom rigid body motion). Solving for these six parameters directly would involve a highly nonlinear coupled optimization problem, which is computationally complex and physically ambiguous. Therefore, this invention decouples translation and rotation, first solving for the global translation vector independently, and then solving for the rotation matrix separately. This decomposition strategy compresses the original six-dimensional search problem into a three-dimensional rotation space problem, significantly reducing computational complexity and improving robustness; for example... Figure 3 As shown, it specifically includes: (1) Calculate the geometric centroid Calculate the current centroid: C C The geometric center of all measurement points in the current attitude. Calculate the centroid of the target: C t The geometric center of all measurement points under the target attitude is . The centroid is the geometric center of the set of points, which intuitively reflects the average position of the beam in space.

[0030] (2) Solve for the global translation vector T= C t - C c Global translation vector T This vector represents the total amount of movement (longitudinal, lateral, vertical) required for the beam to move from its current position to the target position. Its physical meaning is clear, and this vector will be used in step five to calculate the global displacement of the jack.

[0031] (3) Decentralization of point sets By translating the two point sets to near their respective centroids, the combined translation and rotation problem is simplified to a pure rotation alignment problem around the origin. This step removes the translation component from the overall transformation, leaving the remaining point set differences consisting only of the rotation component. Thus, subsequent step three focuses solely on solving the pure rotation matrix, eliminating the need to consider translation. Furthermore, subtracting the centroid reduces the numerical coordinates of each point to a relative order of magnitude, avoiding ill-conditioned matrix problems caused by large number calculations.

[0032] Step 3: Solving for the rotation matrix The purpose of this step is to find the optimal rotation matrix R, which makes the current set of points after decentralization... and After rotation, it should coincide with the target point set as much as possible. This invention employs a two-layer optimization strategy combining initial estimation using Singular Value Decomposition (SVD) with fine-tuning using gradient descent, balancing global convergence and local accuracy. Decentralization refers to subtracting the current centroid from the coordinates of each current measurement point to obtain the current point set, and subtracting the target centroid from the coordinates of each target measurement point to obtain the target point set. This operation decouples the translation and rotation components, requiring only the handling of pure rotation alignment issues subsequently; for example... Figure 4 As shown, it includes the following steps: (1) Global optimal initial value solution based on SVD Due to the decentralized current point set and Both are three-dimensional column vectors, and their outer product is... It is a 3×3 matrix. Construct a 3×3 covariance matrix for the decentralized point set. H : In the least squares sense, such that The minimum rotation matrix R can be obtained by maximizing trace(R). T The analytical solution to this maximization problem is given by the singular value decomposition of H. This is based on the covariance matrix H. H Perform singular value decomposition: Where U and V are both 3×3 orthogonal matrices, i.e., U T U=1, V T V=1. Specifically: the left singular vector matrix of U, whose column vectors are HH. T The eigenvectors of V represent the characteristic directions of the current point set; the right singular vector matrix of V has column vectors H. T The eigenvectors of H represent the characteristic directions of the target point set; It is a 3×3 diagonal matrix where the diagonal elements σ1, σ2, σ3 are singular values ​​of H, and σ1 ≥ σ2 ≥ σ3 ≥ 0. The physical meaning of this equation is: by multiplying V and U, the characteristic directions of the current point set are rotated to align with the target point set. Therefore, the initial analytical value of the rotation matrix is: R0 = VU T R0 is a 3×3 real matrix representing the initial estimate of the rotation matrix from the current point set to the target point set. Under ideal, noise-free conditions, this estimate is already the globally optimal rotation in the least squares sense.

[0033] In rigid body kinematics, for a real physical beam to transform from its current orientation to a target orientation, its rotation matrix must satisfy the mathematical property of orientation preservation, i.e., a determinant of +1 (indicating no mirror flip). However, the R0 directly calculated by the SVD method only guarantees an orthogonal matrix, and its determinant may be +1 or -1. If the determinant is -1, the transformation corresponds to a physically unrealizable mirror transformation, such as flipping the beam into its mirror shape, which cannot be accomplished by any jacking action. Therefore, the SVD calculation results must be judged and corrected. Since SVD decomposition itself does not guarantee... The determinant of R0 is +1, therefore the determinant of R0 needs to be... det (R0) is used to determine whether the transformation involves reflection: if det (R0) = +1 indicates that R0 is a pure rotation matrix, conforming to the laws of rigid body motion, and can be directly used as the initial value for rotation; if det (R0) = -1 indicates that R0 contains a reflection component, corresponding to a physically impossible mirror transformation. This is corrected by inverting the third column of V, i.e., R0 = V U T The function of the correction matrix diag(1,1,-1) is to force the determinant of R0 to be flipped from -1 to +1, thereby ensuring that the subsequently generated jack adjustment commands conform to the actual construction conditions.

[0034] The SVD method provides a global analytical solution in the least squares sense, avoiding the dependence on initial values ​​in iterative algorithms and ensuring the robustness of the algorithm. This initial value is close to the actual rotation, providing a good starting point for subsequent refinement.

[0035] (2) Local refinement based on gradient descent Since R0 given by the SVD method is the global optimal solution under the ideal mathematical model, but the measurement data in actual engineering contains noise, and the beam may also have non-ideal factors such as local deformation, in order to further improve the accuracy, it is necessary to start from R0 and perform local refinement through iterative optimization.

[0036] To quantitatively evaluate the alignment effect of the rotation matrix, a loss function L is introduced. This loss function measures the overall deviation between the current point set and the target point set after rotation by the rotation matrix R. The smaller the loss function value, the better the rotation alignment effect. Its expression is as follows: The physical meaning of this loss function is: the average of the squared distances of each measuring point on the beam from its designed target position after rotation. The optimization objective is to find a set of Euler angles. This minimizes the value of the loss function.

[0037] Since the rotation matrix R has 9 elements, but is constrained by the orthogonality constraint (R... T R=1) and orientation-preserving constraints ( det (R) = +1), which actually only has 3 independent degrees of freedom. Directly optimizing the 9 constrained elements is computationally complex. Therefore, this invention uses... ZYX Euler angles Parameterization is performed so that the rotation parameters can be adjusted through an iterative optimization algorithm. The rotation matrix is ​​expressed in Euler angles as follows: in, These are the standard rotation matrices for rotations about the Z-axis, Y-axis, and X-axis, respectively, and their specific expressions are: , , This parameterization establishes the parameters from Euler angles. The one-to-one mapping to the rotation matrix R has the physical meaning of: first rotate around the Z-axis. Angle (horizontal deflection), then rotate around the Y-axis Angle (pitch), and finally rotation around the X-axis. Angle (twist).

[0038] The optimization goal of this step is to find a set of Euler angles. This makes R The difference between the current point set and the target point set after rotation is minimized.

[0039] The initial values ​​for optimization are derived from the initial SVD value R0. First, the corresponding Euler angles are calculated from R0 using inverse SVD formulas. Then, set the initial point of the iteration to An iterative optimization method using adaptive learning rate momentum gradient descent is employed. The core iterative formula of this method is as follows, where k represents the number of iterations: In the above formula, g (k) Let be the gradient direction at the k-th step; This represents element-wise multiplication, that is, multiplying corresponding elements of two vectors; specifically, for vector a = (a1, a2, a3). T And b = (b1, b2, b3) T , =(a1b1,a2b2,a3b3) T ;v (k) The momentum term has an initial value of v. (0) =0; , β The momentum coefficient is used to accelerate gradient descent convergence and suppress oscillations; the preferred range is 0.09 to 0.99. For adaptive learning rate (dynamically adjusted based on gradient history), the adjustment strategy is as follows: if the loss function value in the current step decreases compared to the previous step, the learning rate is multiplied by 1.05; if the loss function value increases, the learning rate is multiplied by 0.7 and the parameter update is rolled back to the previous step. Simultaneously, the learning rate is restricted to

[10] . -6 Within the range of [0.1]. Through the above iterations, the Euler angle Θ is continuously updated until the termination condition is met.

[0040] gradient It can be calculated analytically using the chain rule, for example: in, It can be obtained analytically using the derivative formula of the Euler angle rotation matrix. and The calculation method is similar.

[0041] The iteration terminates when one of the following conditions is met: 1) The loss function value is less than a preset threshold, such as 10. -8 ; 2) Reach the maximum number of iterations, for example, 500 times; 3) The gradient norm is less than the threshold multiple times consecutively (e.g., 5 times), such as 10. -6 The gradient norm refers to the gradient vector. The modulus length, i.e. .

[0042] Finally, the optimal rotation matrix is ​​obtained. R and the corresponding Euler angles .

[0043] Step 4: Spatial Transformation and Error Closure The purpose of this step is to apply the overall beam translation vector T calculated in step two and the optimal rotation matrix R obtained in step three to all beam measuring points, calculate the theoretical target position, and evaluate the adjustment accuracy through multi-dimensional error indices, forming a closed loop combining forward transformation and reverse verification. Figure 5 As shown, it specifically includes: Perform a complete rigid body transformation on all beam measuring points: P trans,i =R ( P c,i -C c ) +C t Calculate the following three core error metrics: 1) Global Root Mean Square Error (RMSE): It is used to reflect the overall positioning accuracy.

[0044] 2) Maximum single-point error (MaxErr): It is used to identify local out-of-tolerance risks.

[0045] 3) Directional error (ΔDir): Calculates the deviation of the normal direction of each section, specifically including: the deviation of the normal direction of three transformed measurement points {P} belonging to the same section k. trans,3(k-1)+1 ,P trans,3(k-1)+2 ,P trans,3(k-1)+3} and three target measurement points {P t,3(k-1)+1 ,P t,3(k-1)+2 ,P t,3(k-1)+3 Extract them separately. For each group of three points, fit the spatial plane by solving a system of linear equations to obtain the transformed plane normal vector n of the cross section. trans,k With the target plane normal vector n t,k Directional error is defined as the angle between two normal vectors: ΔDir k = This index is used to assess whether the beam is torsional. The final directional error is the maximum value among all cross sections, i.e., ΔDir = max. k (ΔDir k ).

[0046] Based on the bridge's curvature and span grade, preset allowable error thresholds are established. For example, when RMSE exceeds 5mm, MaxErr exceeds 8mm, or ΔDir exceeds a preset threshold (e.g., 0.5°), the system automatically prompts the user to check the input data or consider secondary fine-tuning. Specifically, this includes: If the error exceeds the limit by less than 10%, the system will automatically use the current optimal rotation matrix R as the new initial value, reduce the learning rate of gradient descent to 0.5 times the current value, increase the maximum number of iterations to 1.5 times the current value, and re-execute the gradient descent optimization process in step three.

[0047] If the error exceeds 10%, or if the above re-optimization is executed more than twice and still does not meet the requirements, the system will pause the output of the adjustment command, prompt the user to review the original measurement data (coordinates of the measuring point, coordinates of the jack, installation deviation angle), and suggest checking whether there is local deformation or measurement error in the beam.

[0048] If the directional error ΔDir exceeds the threshold, the system will indicate that the beam may be at risk of torsion and suggest adjusting the lifting height of the jacks at each pier or the grouping action strategy.

[0049] When all the core error indicators do not exceed the corresponding preset thresholds, proceed to step five.

[0050] Step 5: Generating jack positioning instructions The purpose of this step is to transfer the overall spatial transformation of the beam to each jack and convert it into local coordinate system commands that can be directly used for equipment control based on its installation direction, such as... Figure 6 As shown, it includes the following steps: (1) Calculation of the target position of the jack J tar,i =R(J cur,i -C c )+C t ; Among them, C t =C c +T, where T is the global translation vector obtained in step two, and J cur J represents the current position of the jack as collected in step one. tar This is the target position for the jack.

[0051] (2) Solving for the global displacement vector The target position J of the jack calculated in step (1) tar Subtract the current position J of the jack collected in step one. cur This yields the displacement vector that the jack needs to move in the global coordinate system: Δ global =J tar -J cur Where, Δ global The three components of (ΔX, ΔY, ΔZ) represent the movement of the jack along the X-axis (longitudinal), Y-axis (lateral), and Z-axis (vertical) of the global coordinate system, respectively, with units consistent with the input coordinates. This vector serves as a bridge connecting the overall transformation of the beam with the local movements of individual jacks. Subsequently, it will be converted into commands in its local coordinate system based on the installation deflection angle of each jack.

[0052] (3) Local coordinate system transformation Each jack has its own local coordinate system, defined as follows: Local X-axis direction: along the jack's advancing direction (i.e., the direction indicated by the installation angle δ), with the positive direction being the jacking forward direction; Local Y-axis direction: perpendicular to the local X-axis in the horizontal plane, pointing to the right (viewed from the tail of the jack towards the head); Local Z-axis direction: consistent with the global Z-axis direction, vertically upward. Because the jack's advancing direction makes an angle δ with the global X-axis, the displacement vector Δ in the global coordinate system... globalIt cannot be directly used as the stroke command for the jack; it must be projected onto the jack's local coordinate system. Specifically, rotating Δglobal around the global Z-axis by -δ angle yields the three displacement components in the local coordinate system: Where δ is the installation deflection angle of the jack.

[0053] The physical meaning of the output parameters includes: X local,i : Indicates the displacement along the jacking direction (main jacking stroke). Y local,i : Indicates the horizontal displacement (lateral correction amount) perpendicular to the jacking direction. Z local,i : Indicates vertical displacement.

[0054] Therefore, the adjustment instruction for each jack is constructed as follows: a quaternion (jack number, ... X local,i ,Y local,i , Z local,i This instruction can be sent to the control system of the walking jacking equipment for execution.

[0055] Step Six: Output Results The purpose of this step is to deliver the final calculation results in a clear and standardized format, making it easy for users at different levels to use and supporting integration with external systems, such as... Figure 7 As shown, the steps include the following:

[0056] A three-level output system is adopted: 1) Core command layer: List the number of each jack and its local three-dimensional adjustment amount in tabular form. X local,i , Y local,i ,Z local,i This is the standard format of the aforementioned position adjustment command, with the unit uniformly set to meters, which can be directly used for construction briefings and equipment input.

[0057] 2) Auxiliary parameter layer: provides the global translation vector T and rotation Euler angles. The rotation matrix R is provided for technical supervisors to review and archive.

[0058] 3) Metadata layer: Includes information such as RMSE, maximum single-point error MaxErr, data acquisition time, number of piers, and number of cross sections, for quality traceability and process recording.

[0059] Export in multiple formats: 1) CSV: Can be directly imported into the control system of walking jacking equipment to achieve seamless integration of calculation and application.

[0060] 2) TXT: Convenient for document archiving and printing.

[0061] 3) JSON: Supports integration with other information systems (such as BIM and construction management platforms).

[0062] The calculation results can be highlighted in the accompanying web-based software interface, supporting one-click selection and copying, and screenshot saving, making it easy to integrate into construction handover documents. It can also be combined with a 3D visualization module to visualize abstract data.

[0063] This invention also provides an engineering application example of the method described in this invention, specifically including: In the current stage of the jacking project for a curved bridge, a large steel beam segment is being repositioned, supported by four piers. One jack is positioned on the left and right sides of each pier. Two cross-sections (a total of six measuring points) are taken along the beam length. The following data (unit: m) were obtained: The parameters of the jack are shown in Table 1 below: Table 1 The current coordinates of the measuring points on the beam are shown in Table 2 below: Table 2 The coordinates of the target measuring points on the beam are shown in Table 3 below: Table 3 The calculation process is as follows: Step 2: Solving by translation and rotation Current centroid C c =(870.3293,1.2387,32.8925) Target centroid C t =(870.3295,1.2455,32.8985) Translation vector T =(0.0001667,0.006833,0.006) Step 3: Solving the translation-rotation matrix The initial SVD estimate yields a rotation matrix R0, corresponding to Euler angles of approximately (0.002°, 0.008°, 0.005°).

[0064] After gradient descent refinement, η =0.0001, β=After 152 iterations with a value of 0.09, the optimal rotation matrix is ​​obtained: Corresponding Euler angles =(0.1646°, 0.0009351°, 0.004652°).

[0065] Step 4: Spatial Transformation and Error Closure The calculated RMSE after transformation of all measuring points is 0.0017m < 5mm, which meets the engineering accuracy requirements.

[0066] Step 5: Generating jack positioning instructions The output instructions are shown in Table 4 below: Table 4 The above instructions were input into the walking-type jacking equipment, and the beam coordinates were remeasured after one adjustment. The actual maximum single-point error was 1mm, which verified the accuracy and reliability of the method.

[0067] This invention also provides a jack cluster positioning command calculation system for jacking of curved bridges, including: a translation and rotation decoupling module, a rotation matrix solving module, and a command generation module. Optionally, it may also include a data acquisition module, a data verification module, an error control module, etc. The functions of each module are described in detail below with reference to specific steps.

[0068] The data acquisition module is used to obtain the three-dimensional coordinates and installation deflection angle of each jack in the global coordinate system, as well as the current and target coordinates of each measuring point on the beam. Measuring points are arranged along the beam length on N characteristic sections. For each section, three measuring points are sequentially arranged along the transverse direction of the bridge: a left point, a middle point, and a right point, for a total of 3N measuring points. All measuring points are numbered uniformly according to the following rules: for the k-th section (k=1,…,N), the left point corresponds to index i=3(k-1)+1, the middle point to i=3(k-1)+2, and the right point to i=3(k-1)+3. This module also includes a data verification function: checking that the coordinate values ​​are not empty and are valid, the installation deflection angle is within the range of [-180°, 180°], the total number of measuring points is not less than 6, and the number of current coordinates equals the number of target coordinates; if any condition is not met, the calculation is stopped and the user is prompted.

[0069] The translation and rotation decoupling module is used to calculate the current centroid of all measuring points in the current posture and the target centroid in the target posture based on the measured coordinates of each measuring point in the current posture and the theoretical coordinates in the target posture; subtract the current centroid from the measured coordinates of each measuring point to obtain the current point set; and subtract the target centroid from the theoretical coordinates of each measuring point to obtain the target point set. The rotation matrix solving module is used to perform orthogonal decomposition on the current point set and the target point set to obtain an initial matrix for rotating the beam from the current posture to the target posture; starting from the initial matrix, iterative optimization is performed to minimize the deviation between the current point set and the target point set after the rotation matrix transformation, thereby obtaining the optimal rotation matrix; The instruction generation module is used to calculate the global displacement vector of each jack from its current position to the target position based on the current centroid, the target centroid, and the optimal rotation matrix; and then, based on the installation deflection angle of each jack, to obtain the three-dimensional adjustment amount of the global displacement vector of each jack in its own coordinate system. The three-dimensional adjustment amount and the unique identification of the jack constitute the adjustment instruction of each jack.

[0070] In one embodiment, the rotation matrix solving module obtains the initial matrix of the rotation matrix through the following steps: Based on the measured coordinates of the measuring point in the current attitude and the theoretical coordinates in the target attitude, a covariance matrix is ​​constructed using the current centroid and the target centroid. ;where P c,i and P t,i C represents the measured coordinates of the i-th measurement point in the current attitude and the theoretical coordinates in the target attitude, respectively; c and C t These represent the current centroid and the target centroid, respectively; M represents the number of measurement points; Singular value decomposition of H , where U and V are the left singular vector matrix and the right singular vector matrix, respectively; both U and V are orthogonal matrices; Calculate R0=VU T ; When the determinant of R0 det If (R0) = -1, then invert the third column of the orthogonal matrix V to obtain the corrected right singular vector matrix V', and then calculate R0 = V'U. T ; The matrix R0 is used as the initial matrix of the rotation matrix.

[0071] In one embodiment, the method for obtaining the optimal rotation matrix includes: The rotation matrix is ​​represented as three rotations around the Z-axis, Y-axis, and X-axis in sequence ( ). The function of R( )= ; Define loss function ; The Euler angles corresponding to the initial matrix R0 of the rotation matrix ( Starting from ), the following momentum gradient descent method is used for iterative updates: Where: g (k) Let be the gradient direction at step k. Indicates element-wise multiplication, v (k) Let v be the momentum term at the k-th iteration, with an initial value of v. (0) =0; , β The momentum coefficient is used to accelerate gradient descent convergence; The adaptive learning rate at the k-th iteration; The iteration terminates when the loss function is less than a set value or the number of iterations reaches a set number. Substitute the Euler angle at the end of the iteration into R( The function performs matrix transformations to obtain the optimal rotation matrix.

[0072] In one embodiment, an error control module is further included, for: For the current coordinates of each measuring point, first subtract the current centroid, then multiply by the optimal rotation matrix, and finally add the target centroid to obtain the transformed position. P trans,i ; P trans,i =R ( P c,i -C c ) +C t Calculate multiple error indices between the transformed position and the target position; the multiple error indices include: global root mean square error (RMSE), maximum single-point error (MaxErr), and direction error (ΔDir); specifically, it includes: calculating the global root mean square error RMSE and the maximum single-point error MaxErr.

[0073] In one embodiment, the threshold corresponding to the global root mean square error is 5 mm; the threshold corresponding to the maximum single-point error is 8 mm; and the threshold corresponding to the directional error is 0.5°. The above thresholds are only examples and can be adjusted according to factors such as bridge curvature, span, and construction accuracy requirements in actual applications.

[0074] When any of the multiple error metrics exceeds the corresponding preset threshold, the learning rate is reduced starting from the current optimal rotation matrix. And / or increase the number of iterations, re-execute the iterative optimization described in the rotation matrix solution module, until the error indicators do not exceed the corresponding preset threshold or reach the upper limit of the number of re-optimizations.

[0075] In one embodiment, the method for calculating the current centroid includes: Methods for calculating the centroid of a target include: C C This represents the current centroid of all measurement points in the current attitude. C t The target centroid is the centroid of all measurement points under the target attitude; M is the number of measurement points; P c,i and P t,i These represent the measured coordinates of the i-th measurement point in the current attitude and the theoretical coordinates in the target attitude, respectively.

[0076] In one embodiment, the method for calculating the global displacement vector of each jack from its current position to the target position includes: The coordinates of the target position of the jack are calculated using the following formula: J tar,i =R(J cur,i -C c )+C t .

[0077] In the formula, R is the optimal rotation matrix; J cur,i and J tar,i Let C be the current position and the target position of the i-th jack, respectively; c and C t These represent the current centroid and the target centroid, respectively. J cur,i and J tar,i The difference Δ global,i This is the global displacement vector that each jack needs to move.

[0078] In one embodiment, the method for obtaining the three-dimensional adjustment amount includes: Each jack has its own local coordinate system as follows: Local X-axis direction: along the jack's pushing direction, with the positive direction being the jacking forward direction; Local Y-axis direction: perpendicular to the local X-axis in the horizontal plane, pointing to the right; Local Z-axis direction: Consistent with the global Z-axis direction, vertically upward; Rotate the global displacement vector Δglobal around the global Z-axis by -δ i By calculating the angle, we can obtain the three displacement components in the local coordinate system, where δ i The installation offset angle of the i-th jack: In the formula: X local,i : Indicates the displacement along the direction of the jack's push; Ylocal,i : Indicates the horizontal displacement perpendicular to the jacking direction; Z local,i : Indicates vertical displacement; ( X local,i ,Y local,i ,Z local,i This refers to the three-way adjustment amount.

[0079] In one embodiment, a result output module is also included, used to output the number of each jack and its three-way adjustment amount in tabular form, with the unit uniformly in millimeters. It also outputs auxiliary parameters such as the overall translation vector T, rotation Euler angles (φ,θ,ψ), and rotation matrix R, as well as metadata such as RMSE, MaxErr, data acquisition time, number of jacks, and number of cross-sections. Exporting to CSV, TXT, and JSON formats is supported, with CSV files directly importable into the walking-type jacking equipment control system. The calculation results are highlighted in the web-based software interface and displayed in conjunction with a 3D visualization module.

[0080] This invention also provides a method for calculating the positioning command of a cluster of jacks for jacking curved bridges, including: Based on the measured coordinates of each measuring point on the beam in the current posture and the theoretical coordinates in the target posture, calculate the current centroid of all measuring points in the current posture and the target centroid in the target posture; subtract the current centroid from the measured coordinates of each measuring point to obtain the current point set; subtract the target centroid from the theoretical coordinates of each measuring point to obtain the target point set; The current point set and the target point set are orthogonally decomposed to obtain an initial matrix for rotating the beam from the current posture to the target posture. Starting from the initial matrix, the deviation between the current point set and the target point set after the rotation matrix transformation is minimized through iterative optimization, thereby obtaining the optimal rotation matrix. Based on the current centroid, the target centroid, and the optimal rotation matrix, calculate the global displacement vector of each jack from its current position to the target position; then, based on the installation deflection angle of each jack, obtain the three-dimensional adjustment amount of the global displacement vector corresponding to each jack in its own coordinate system. The three-dimensional adjustment amount and the unique identification of the jack constitute the adjustment command of each jack.

[0081] It should be understood that the sequence number of each step in the above embodiments does not imply the order of execution. The execution order of each process should be determined by its function and internal logic, and should not constitute any limitation on the implementation process of the embodiments of the present invention.

[0082] This invention also provides a computer program product, including a computer program / instructions that, when executed by a processor, implement the various steps of the method described in this invention.

[0083] This invention also provides a non-transitory computer-readable storage medium storing a computer program. The computer program includes program instructions that, when executed by a processor, implement the various steps of the method described in this invention, which will not be elaborated further here.

[0084] The computer-readable storage medium can be the data transmission apparatus or the internal storage unit of a computer device provided in any of the foregoing embodiments, such as the hard disk or memory of the computer device. The computer-readable storage medium can also be the external storage device of the computer device, such as the plug-in hard disk, smart media card (SMC), secure digital (SD) card, flash card, etc. equipped on the computer device.

[0085] Furthermore, the computer-readable storage medium may include both internal storage units and external storage devices of the computer device. The computer-readable storage medium is used to store the computer program and other programs and data required by the computer device. The computer-readable storage medium may also be used to temporarily store data that is to be output or has already been output.

[0086] Those skilled in the art will understand that embodiments of the present invention can be provided as methods, systems, or computer program products. Therefore, the present invention can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present invention can take the form of a computer program product embodied on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0087] This invention is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of the invention. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart illustrations and / or block diagrams. Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0088] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0089] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0090] The contents not described in detail in this specification are existing technologies known to those skilled in the art.

Claims

1. A jack cluster positioning command calculation system for jacking of curved bridges, characterized in that, include: The translation and rotation decoupling module is used to calculate the current centroid of all measuring points in the current posture and the target centroid in the target posture based on the measured coordinates of each measuring point in the current posture and the theoretical coordinates in the target posture; subtract the current centroid from the measured coordinates of each measuring point to obtain the current point set; and subtract the target centroid from the theoretical coordinates of each measuring point to obtain the target point set. The rotation matrix solving module is used to perform orthogonal decomposition on the current point set and the target point set to obtain the initial matrix of the rotation matrix used to rotate the beam from the current posture to the target posture; Starting with the initial matrix, the optimal rotation matrix is ​​obtained by iterative optimization to minimize the deviation between the current point set and the target point set after the rotation matrix transformation. The instruction generation module is used to calculate the global displacement vector of each jack from its current position to the target position based on the current centroid, the target centroid, and the optimal rotation matrix; and then, based on the installation deflection angle of each jack, to obtain the three-dimensional adjustment amount of the global displacement vector of each jack in its own coordinate system. The three-dimensional adjustment amount and the unique identification of the jack constitute the adjustment instruction of each jack.

2. The jack cluster positioning command calculation system for jacking curved bridges as described in claim 1, characterized in that, The rotation matrix solving module obtains the initial matrix of the rotation matrix through the following steps: Based on the measured coordinates of the measuring point in the current attitude and the theoretical coordinates in the target attitude, a covariance matrix is ​​constructed using the current centroid and the target centroid. ;where P c,i and P t,i C represents the measured coordinates of the i-th measurement point in the current attitude and the theoretical coordinates in the target attitude, respectively; c and C t These represent the current centroid and the target centroid, respectively; M represents the total number of measurement points; For covariance matrix H Singular value decomposition yields , where U and V are the left singular vector matrix and the right singular vector matrix, respectively; Calculate R0=VU T ; When the determinant of R0 det When (R0) = -1, the third column of the right singular vector matrix V is inverted to obtain the corrected right singular vector matrix V', and then R0 = V'U is calculated. T ; The matrix R0 is used as the initial matrix of the rotation matrix.

3. The jack cluster positioning command calculation system for jacking curved bridges as described in claim 2, characterized in that, Methods for obtaining the optimal rotation matrix include: The rotation matrix is ​​represented as three rotations around the Z-axis, Y-axis, and X-axis in sequence ( ). The function of R( )= ; Define loss function ;in and Represent the current point set and the target point set respectively. i One point; The Euler angles corresponding to the initial matrix R0 of the rotation matrix ( Starting from ), the following momentum gradient descent method is used for iterative updates: Where: g (k) Let be the gradient direction at step k. Indicates element-wise multiplication, v (k) Let v be the momentum term at the k-th iteration, with an initial value of v. (0) =0; , β The momentum coefficient is used to accelerate gradient descent convergence; The adaptive learning rate at the k-th iteration; The iteration terminates when the loss function is less than a set value or the number of iterations reaches a set number. Substitute the Euler angle at the end of the iteration into R( The function performs matrix transformations to obtain the optimal rotation matrix.

4. The jack cluster positioning command calculation system for jacking curved bridges as described in claim 3, characterized in that, It also includes an error control module, used for: For the current coordinates of each measuring point, first subtract the current centroid, then multiply by the optimal rotation matrix, and finally add the target centroid to obtain the transformed position; Calculate multiple error indices between the transformed position and the target position; When any of the multiple error metrics exceeds the corresponding preset threshold, the learning rate is reduced starting from the current optimal rotation matrix. And / or increase the number of iterations, re-execute the iterative optimization described in the rotation matrix solution module, until the error indicators do not exceed the corresponding preset threshold or reach the upper limit of the number of re-optimizations.

5. The jack cluster positioning command calculation system for jacking curved bridges as described in claim 1, characterized in that, Methods for calculating the global displacement vector of each jack from its current position to the target position include: The coordinates of the target position of the jack are calculated using the following formula: J tar,i =R(J cur,i -C c )+C t ; In the formula, R is the optimal rotation matrix; J cur,i and J tar,i Let C be the current position and the target position of the i-th jack, respectively; c and C t These represent the current centroid and the target centroid, respectively. J cur,i and J tar,i The difference Δ global,i This is the global displacement vector that each jack needs to move.

6. The jack cluster positioning command calculation system for jacking curved bridges as described in claim 5, characterized in that, The method for obtaining the three-dimensional adjustment amount includes: Each jack has its own local coordinate system as follows: Local X-axis direction: along the jack's pushing direction, with the positive direction being the jacking forward direction; Local Y-axis direction: perpendicular to the local X-axis in the horizontal plane, pointing to the right; Local Z-axis direction: Consistent with the global Z-axis direction, vertically upward; Rotate the global displacement vector Δglobal around the global Z-axis by -δ i By calculating the angle, we can obtain the three displacement components in the local coordinate system, where δ i The installation offset angle of the i-th jack: In the formula: X local,i : Indicates the displacement along the direction of the jack's push; Y local,i : Indicates the horizontal displacement perpendicular to the jacking direction; Z local,i : Indicates vertical displacement; ( X local,i ,Y local,i ,Z local,i This refers to the three-way adjustment amount.

7. The jack cluster positioning command calculation system for jacking curved bridges as described in claim 1, characterized in that, It also includes a data acquisition module, used to obtain the three-dimensional coordinates and installation deflection angle of each jack in the global coordinate system, as well as the current coordinates and target coordinates of each measuring point on the beam; wherein, the measuring points are arranged along the beam length on multiple characteristic sections, and multiple measuring points are arranged sequentially along the transverse direction of the bridge on each section.

8. A method for calculating the positioning command of a cluster of jacks used in the jacking of curved bridges, applied to the system described in claim 1, characterized in that, include: Based on the measured coordinates of each measuring point on the beam in the current posture and the theoretical coordinates in the target posture, calculate the current centroid of all measuring points in the current posture and the target centroid in the target posture; subtract the current centroid from the measured coordinates of each measuring point to obtain the current point set; subtract the target centroid from the theoretical coordinates of each measuring point to obtain the target point set; Perform orthogonal decomposition on the current point set and the target point set to obtain an initial matrix for the rotation matrix used to rotate the beam from the current posture to the target posture; Starting with the initial matrix, the optimal rotation matrix is ​​obtained by iterative optimization to minimize the deviation between the current point set and the target point set after the rotation matrix transformation. Based on the current centroid, the target centroid, and the optimal rotation matrix, calculate the global displacement vector of each jack from its current position to the target position; then, based on the installation deflection angle of each jack, obtain the three-dimensional adjustment amount of the global displacement vector corresponding to each jack in its own coordinate system. The three-dimensional adjustment amount and the unique identification of the jack constitute the adjustment command of each jack.

9. A non-transitory computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the jack cluster positioning instruction calculation method as described in claim 8 for jacking curved bridges.

10. A computer program product comprising a computer program / instructions, characterized in that, When the computer program / instruction is executed by the processor, it implements the steps of the jack cluster positioning instruction calculation method for jacking curved bridges as described in claim 8.

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