Tower deviation calculation method and system for multi-tower cable hoisting system based on single-tower linkage correction

Abstract

The application discloses a kind of tower deviation calculation method and system of multi-tower cable hoisting system based on single-tower linkage correction, and relates to the technical field of bridge engineering;The application is used to solve the problems of insufficient precision of traditional equivalent modulus method under the working condition of small initial cable tension and large tower top displacement, and iterative divergence caused by ignoring geometric nonlinearity of full-tower correction method.The method comprises the following steps: step S1: input system parameters, calculate the unstressed cable length of each span by iterative calculation using the elastic catenary equation, and determine the initial equilibrium state of the system;Step S2: initialize the deviation of all towers to zero, and calculate the span length of each span as the original span length;Step S3: execute the main iterative cycle based on single-tower linkage correction;Step S4: output the final deviation of each tower, the horizontal force at the end of each span cable and the horizontal elastic stiffness.The application can realize high-precision and stable convergence calculation of tower deviation under any initial tension and load working condition, and provides a reliable scheme for the final design and construction control of multi-tower cable hoisting system.

Description

Technical Field

[0001] This invention relates to the field of bridge engineering technology, and more specifically to a method and system for accurately calculating tower offset in a multi-tower cable hoisting system based on single-tower linkage correction. Background Technology

[0002] Cable-stayed bridge systems are crucial equipment in the construction of long-span bridges. Under various complex conditions, the tower tops bear unbalanced horizontal forces, and accurate calculation of tower offset is a prerequisite for ensuring construction safety and control precision. With the continuous increase in bridge spans and lifting weights, the application of multi-tower cable-stayed bridge systems is becoming increasingly common. In such systems, the towers are coupled together through continuous tension cables, forming a series-connected constraint system. The stress and deformation of one tower are transmitted through the cable structure and significantly affect adjacent towers, resulting in a strong coupling effect between towers, making offset calculations exceptionally complex.

[0003] There are currently two main approaches to calculating tower misalignment in multi-tower cable-stayed hoisting systems: One type is a simplified calculation method based on the equivalent elastic modulus and series stiffness model. This type of method is simple to calculate and has clear physical concepts. Under the condition that the initial cable tension is large enough and the system is approximately linear, it can meet the accuracy requirements of the preliminary design and is suitable for rapid estimation and comparison of multiple schemes. However, cable structures will produce sag under their own weight, and their mechanical behavior exhibits a high degree of geometric nonlinearity. When the initial cable tension is small or the tower top deflection is large, the linear assumption of this type of method no longer holds strictly, and the calculation accuracy will decrease significantly, making it difficult to meet the accuracy requirements of the final design and construction control.

[0004] Another type is the precise calculation method based on catenary theory. This type of method can accurately describe the geometric nonlinear behavior of cable structures and precisely solve for cable forces by adhering to the principle of constant cable length under no stress, making it suitable for precise analysis under any working condition. However, in multi-tower systems, if the traditional full-tower correction iterative strategy is adopted, that is, simultaneously solving the unbalanced force equations of all towers and updating the displacement of all towers at once through linear superposition, the iterative process will oscillate or even diverge because it ignores the deep coupling between the displacements of each tower, making it difficult to achieve the convergence accuracy required by engineering.

[0005] Therefore, there is an urgent need for a multi-tower offset calculation method that can accurately consider the geometric nonlinearity of the cable and ensure stable convergence of the iterative process, so as to solve the technical problems of limited accuracy of existing simplified methods under certain conditions and difficulty in convergence of accurate methods. Summary of the Invention

[0006] Therefore, to address the aforementioned shortcomings, this invention provides a method and system for calculating tower offset in multi-tower cable-stayed installation systems based on single-tower linkage correction. This method, based on the elastic catenary theory and the principle of constant cable length without stress, addresses the strong nonlinearity caused by the continuous coupling of cables between towers in a multi-tower system. It employs a single-tower linkage correction iterative strategy to solve the problems of insufficient accuracy in the traditional equivalent elastic modulus method under conditions of low initial cable tension and large tower top displacement, and the iterative divergence caused by neglecting geometric nonlinearity in the full-tower correction method. This achieves high-precision, stable, and convergent calculation of tower offset under arbitrary initial tension and load conditions, providing a reliable method for the final design and construction control of multi-tower cable-stayed installation systems.

[0007] This invention is implemented by providing a method for calculating tower offset in a multi-tower cable hoisting system based on single-tower linkage correction, comprising the following steps: Step S1: Input system parameters, including geometric parameters, material parameters, tower stiffness, external load and convergence tolerance. Based on the initial tension of the specified span, use the elastic catenary equation to iteratively calculate the stress-free cable length of each span to determine the initial equilibrium state of the system. Step S2: Initialize the offset of all towers to zero, and calculate the span of each span as the original span; Step S3: Execute the main iterative loop based on single-tower linkage correction, including the following sub-steps: Step S31: Based on the current span and stress-free cable length, solve for the horizontal force at the cable end using the elastic catenary equation, and calculate the horizontal elastic stiffness of each span using the finite difference method. Step S32: Calculate the unbalanced horizontal forces at the top of each tower; Step S33: Select the tower with the largest absolute value of unbalanced force as the active correction target for this iteration; Step S34: Calculate the total equivalent stiffness of the active correction tower, specifically including calculating the corresponding left series stiffness and right series stiffness, and adding the left series stiffness and right series stiffness to the tower's own equivalent stiffness to obtain the corresponding total equivalent stiffness. Step S35: Calculate the offset correction amount of the active correction tower; Step S36: Based on the offset correction amount of the active correction tower, adjust the offset of all other towers in the system in accordance with the compliance ratio. Step S37: Update the offset of all towers, and recalculate the effective horizontal span of each span accordingly, and recalculate the unbalanced horizontal force at the top of each tower based on the updated span. Step S38: Determine whether the maximum unbalanced horizontal force is less than the convergence tolerance. If so, terminate the iteration; otherwise, return to step S31. Step S4: Output the final offset of each tower, the horizontal force at each cable end, and the horizontal elastic stiffness.

[0008] Furthermore, the elastic catenary equation used in step S1 of the multi-tower cable hoisting system tower offset calculation method based on single-tower linkage correction is as follows: in, L For span, h For the elevation difference, H For horizontal force, V For vertical force, S 0 represents the length of the stress-free cable. E For elastic modulus, A For the cross-sectional area of ​​the cable, W For weight.

[0009] Furthermore, in step S32 of the multi-tower cable hoisting system tower offset calculation method based on single-tower linkage correction, the calculation formula for the unbalanced horizontal force at the tower top is as follows: in, H j , H j+1 For the tower j Horizontal forces on the left and right cables K T,j For the tower j Lateral stiffness δ j For the tower j of deviation, This refers to the unbalanced horizontal force caused by external forces at the top of the tower.

[0010] Furthermore, in step S33 of the multi-tower cable hoisting system tower deviation calculation method based on single-tower linkage correction, the tower with the largest absolute value of unbalanced force is selected as the active correction object for this iteration: .

[0011] Furthermore, the calculation method for the total equivalent stiffness in step S34 of the multi-tower cable hoisting system tower offset calculation method based on single-tower linkage correction is as follows: , ; in, To actively correct the tower numbering, m For the number of spans, K i For the first i Horizontal elastic stiffness of the span For the current iteration step tower Left-side series stiffness, Current iteration step tower Right-side series stiffness, The total equivalent stiffness.

[0012] Furthermore, in step S35 of the multi-tower cable hoisting system tower offset calculation method based on single-tower linkage correction, the offset correction amount of the actively correcting tower is: .

[0013] Furthermore, in step S36 of the multi-tower cable hoisting system tower offset calculation method based on single-tower linkage correction, the offset correction amount for the remaining towers is calculated according to the following rules: .

[0014] Furthermore, in step S37 of the multi-tower cable hoisting system tower offset calculation method based on single-tower linkage correction, the update method for the effective horizontal span of each span is as follows: .

[0015] This invention also provides a tower offset calculation system for a multi-tower cable hoisting system based on single-tower linkage correction, comprising: The parameter input module is used to input system geometric parameters, material parameters, tower stiffness, external loads, and convergence tolerances; The initial equilibrium module is used to iteratively calculate the initial stress-free cable length for each span based on the elastic catenary equation; The iterative calculation module is connected to the parameter input module and the initial equilibrium module respectively, and is used to execute the corresponding main iterative loop; according to the deviation correction amount of the active correction tower, the deviation of all other towers is corrected in conjunction with the compliance ratio. The output module, connected to the iterative calculation module, is used to output the final tower offset, cable end horizontal force, and horizontal elastic stiffness.

[0016] Furthermore, in the multi-tower cable hoisting system tower offset calculation system based on single-tower linkage correction, the flexibility ratio used in the iterative calculation module is the ratio of the sum of the flexibility ratios of the cable spans on each tower side.

[0017] The present invention has the following advantages: (1) Solving the calculation problem under low initial tension and large deviation conditions: The suspension element method is based on the elastic catenary theory and the principle of constant stress-free cable length. It can accurately consider the geometric nonlinear behavior of cable structure. It does not rely on the premise assumptions of "sufficient initial tension" and "sufficient tower deviation". It is applicable to the accurate analysis of tower deviation under arbitrary initial tension (including when the tension is small and the sag effect is obvious) and arbitrary load conditions. It overcomes the technical bottleneck of insufficient accuracy or even failure of the equivalent elastic mode method under strong nonlinear conditions.

[0018] (2) Achieve accurate calculation for final design and construction control: This method, through a rigorous iterative solution process, can accurately reflect the real change of cable force after tower misalignment. The accuracy of the final calculation result is much higher than that of the equivalent elastic modulus method that relies on linear approximation. It can provide accurate theoretical basis for determining the reasonable initial tension of the tower cable, assessing construction safety and optimizing hoisting parameters.

[0019] (3) Ensure robust convergence of the iteration process: The single-tower linkage correction iteration strategy is adopted. Each time, only the tower with the largest absolute value of the unbalanced force is actively corrected, while the other towers are adjusted in linkage according to the physical flexibility ratio. This not only preserves the numerical stability of the single-variable correction, but also strictly satisfies the deformation coordination condition, ensuring the monotonically decreasing residual (unbalanced force) and the robust convergence of the algorithm. It avoids the problem of iteration oscillation or divergence caused by the traditional full-tower correction method due to neglecting geometric nonlinearity and the superposition principle not being strictly valid.

[0020] (4) High versatility and easy integration with existing calculation systems: This method is applicable to multi-tower cable hoisting systems with any number of spans and towers, and the steps are clear and the logic is rigorous. It can be directly used for in-depth iterative calculations based on the preliminary design results of the equivalent elastic modulus method. Its calculation process is easy to program and can be integrated into construction control software or special calculation tools, which facilitates its promotion and use in actual projects. Attached Figure Description

[0021] Figure 1 This is a schematic diagram of a cable segment unit under its own weight; Figure 2 This is a schematic diagram illustrating the steps of the tower offset calculation method in this application; Figure 3 This is a schematic diagram of the main iteration loop steps in this application; Figure 4 This is a block diagram of the offset calculation system in this application. Detailed Implementation

[0022] The following will be combined with the appendix Figures 1-4 This invention will be described in detail, and the technical solutions in the embodiments of this invention will be clearly and completely described. Obviously, the described embodiments are only some embodiments of this invention, and not all embodiments. Based on the embodiments of this invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this invention.

[0023] Example 1: This invention provides a method for calculating tower offset in a multi-tower cable hoisting system based on single-tower linkage correction, referring to... Figure 2 As shown, combined with Figure 2 The specific steps are as follows; Step 1: Input system parameters and determine the length of the stress-free cable for each span. Reference Figure 1 As shown, assuming a multi-span cable hoisting system with m spans (i=1,2,...,m) and j towers (j=1,2,...,m-1), input the system's geometric parameters (original span diameter of each span). Elevation difference Material parameters (elastic modulus E, cable cross-sectional area A, cable weight W), tower stiffness (Take 0 when the tower base is hinged), External load and convergence tolerance .

[0024] Using the initial tension T of a specified span (usually the middle span) as a reference, and based on the principle that "the initial horizontal force at each tower top is equal", the stress-free cable lengths of all spans are iteratively calculated using the following basic catenary equations. This step ensures the initial equilibrium state of the system when it is not subjected to external loads.

[0025] , .

[0026] Step 2: Initialize the iteration state Set the initial state of the model, and set the initial offset of all towers. Initial calculated span for each span .

[0027] Step 3: Main iterative loop based on single-tower linkage correction; refer to Figure 2 As shown, combined with Figure 3 The process of the main iteration loop is described below; in each iteration step, the following sub-steps are executed: (1) Calculate the current cable force and horizontal elastic stiffness. Calculate the span of each step in the current iteration step. and stress-free cable length Substituting the basic equation of the catenary from step one, we can solve for the horizontal forces at the cable ends of each span. The finite difference method was used to calculate the current horizontal elastic stiffness of each span. : In the formula: - A tiny span increment, taken as 0.001m.

[0028] (2) Calculate the unbalanced horizontal forces at the top of each tower. Calculate the unbalanced horizontal force at the top of each tower in the current iteration step, and for tower j, the unbalanced horizontal force that needs to be corrected at its top. Calculate using the following formula: In the formula: For the lateral stiffness of tower j itself, when the tower base is hinged Set to 0; The offset of the top of the tower in the current iteration step j (by convention, rightward is positive); Let J be the unbalanced horizontal force under the action of external forces at the top of tower j.

[0029] Note: The tower is offset Both unbalanced horizontal forces are defined as positive to the right.

[0030] (3) Select an active correction tower The tower with the largest absolute value of the unbalanced force is selected as the active correction target for this iteration: (4) Calculate the equivalent stiffness of the modified tower. The current iteration step size is calculated using the series stiffness model and the superposition principle. Left-side series stiffness right-side series stiffness With total equivalent stiffness .

[0031] .

[0032] The total equivalent stiffness is obtained by adding the series stiffness on the left and the series stiffness on the right to the tower's own equivalent stiffness. (5) Calculate the maximum deviation tower deviation correction amount Solve Tower deviation correction amount in the current iteration step : (6) Link up and correct all other towers ; The tower offset correction will affect all other towers. To ensure deformation coordination, the offset correction amount for the remaining towers is based on their relationship with... The relative positions of the towers are distributed proportionally to the flexibility (reciprocal of stiffness) of the corresponding side cable spans. For any tower p, its tower offset correction is calculated using the following formula: (7) Update tower offset and span Correct the offset of all towers Accumulated to its current offset Above, that is Simultaneously, based on the updated offsets of all towers, the effective horizontal span of each cable is recalculated. When calculating, the direction of tower offset should be considered, and the boundary condition that the offset at the anchor point is zero should be met. ; The unbalanced horizontal forces at the top of each tower are recalculated based on the updated span.

[0033] (8) Convergence judgment Check if the iteration satisfies the following convergence condition: ; If the maximum unbalanced horizontal force is less than the allowable error, the iteration ends; otherwise, return to step (1) to continue the iteration.

[0034] Step 4: Output Results Output the final tower offsets Horizontal forces at each cable end and horizontal elastic stiffness Key results, etc.

[0035] The advantages of this embodiment are: (1) Solving the calculation problem under low initial tension and large deviation conditions: The suspension element method is based on the elastic catenary theory and the principle of constant stress-free cable length. It can accurately consider the geometric nonlinear behavior of cable structure. It does not rely on the premise assumptions of "sufficient initial tension" and "sufficient tower deviation". It is applicable to the accurate analysis of tower deviation under arbitrary initial tension (including when the tension is small and the sag effect is obvious) and arbitrary load conditions. It overcomes the technical bottleneck of insufficient accuracy or even failure of the equivalent elastic mode method under strong nonlinear conditions.

[0036] (2) Achieve accurate calculation for final design and construction control: This method, through a rigorous iterative solution process, can accurately reflect the real change of cable force after tower misalignment. The accuracy of the final calculation result is much higher than that of the equivalent elastic modulus method that relies on linear approximation. It can provide accurate theoretical basis for determining the reasonable initial tension of the tower cable, assessing construction safety and optimizing hoisting parameters.

[0037] (3) Ensure robust convergence of the iteration process: The "single tower linkage correction" iteration strategy is adopted. Each time, only the tower with the largest absolute value of the unbalanced force is actively corrected, while the other towers are adjusted in linkage according to the physical flexibility ratio. This not only preserves the numerical stability of the single variable correction, but also strictly satisfies the deformation coordination condition, ensuring the monotonically decreasing residual (unbalanced force) and the robust convergence of the algorithm. This avoids the problem of iteration oscillation or divergence caused by the traditional full tower correction method due to neglecting geometric nonlinearity and the superposition principle not being strictly valid.

[0038] (4) High versatility and easy integration with existing calculation systems: This method is applicable to multi-tower cable hoisting systems with any number of spans and towers, and the steps are clear and the logic is rigorous. It can be directly used for in-depth iterative calculations based on the preliminary design results of the equivalent elastic modulus method. Its calculation process is easy to program and can be integrated into construction control software or special calculation tools, which facilitates its promotion and use in actual projects.

[0039] Example 2: A tower offset calculation system for a multi-tower cable hoisting system based on single-tower linkage correction. See the system block diagram below. Figure 4 As shown, the system consists of: The parameter input module is used to input system geometric parameters, material parameters, tower stiffness, external loads, and convergence tolerances; The initial equilibrium module is used to iteratively calculate the initial stress-free cable length for each span based on the elastic catenary equation; The iterative calculation module is connected to the parameter input module and the initial equilibrium module respectively, and is used to execute the corresponding main iterative loop; according to the deviation correction amount of the active correction tower, the deviation of all other towers is corrected in conjunction with the compliance ratio. The output module, connected to the iterative calculation module, is used to output the final tower offset, cable end horizontal force, and horizontal elastic stiffness.

[0040] The flexibility ratio used in the iterative calculation module is the ratio of the sum of the flexibility ratios of the side cable spans where each tower is located.

[0041] Specific application examples I. Project Background A three-tower, four-span cable-stayed hoisting system has a span of 200m and a tower height of 100m. The middle tower is a hinged tower, and the two sides are anchor points. After the system bears the hoisting load, an unbalanced horizontal force appears at the top of the towers. It is necessary to accurately calculate the horizontal deviation of each tower top to ensure hoisting accuracy and structural safety.

[0042] II. Input Parameters 1. Geometric parameters of each span 2. Material parameters (pressure tower cable) Elastic modulus: E =195000000000 Pa Cross-sectional area: A =0.0014m 2 Weight: W =101N / m 3. Tower body parameters Tower base hinged (no lateral stiffness): K T,1 = K T,2 =K T,3 =0 4. External loads The external unbalanced horizontal force (positive to the right) borne by each tower top during hoisting: QH ,1=200000 N QH ,2=200000 N QH ,3=200000 N 5. Convergence Conditions Maximum unbalanced force tolerance: ; 6. Initial tension (based on the mid-span) Set the initial tension of the second span T =800000 N, and the length of the stress-free cable in each span is solved iteratively according to the principle that the initial horizontal force at the top of each tower is equal.

[0043] III. Calculation Process Step 1: Calculate the initial stress-free cable length Using the equation of the elastic catenary, substitute the data of the second span. L =200m, h=0m, T =800000N、 W , E , A Solve for the horizontal force of the second span. The horizontal force obtained is 799936.61 N.

[0044] Using the principle of equal horizontal forces, the lengths of the stress-free cables in each span were calculated sequentially, and the results are as follows: Step 2: Initialize the iteration All tower offsets: δ 1= δ 2= δ 3=0 Calculation of span for each span: L 1= L 2=L3=L4=200m; Step 3: Main Iteration Loop (Selected Key Iteration Steps) First iteration (1) Calculate the current cable force and horizontal elastic stiffness. The span variation (Δ) is calculated using the stress-free cable length of each span. L The horizontal force after (=0.001m) is determined using the finite difference method (Δ L Calculate the horizontal elastic stiffness of each span (e.g., =0.001m). The calculation parameters and results for each span are as follows: First step: SubstitutionE =195000000000Pa, A =0.0014m 2 , W =101 N / m, S Given L1 = 222.8813m, L1 = 200.001m, h = 100m, we obtain H1(200.001) = 800904.8765N, H1(200) = 799936.61 N, and the horizontal stiffness of the span K1 = (H1(200.001) - H1(200)) / 0.001 = 968266.5 N / m; Second step: Substitution E =195000000000 Pa, A =0.0014m 2 , W =101 N / m, S Given L2 = 199.4209m, L2 = 200.001m, h = 0m, we obtain H2(200.001) = 801281.3914N, H2(200) = 799936.61 N, and the horizontal stiffness of the span K2 = (H2(200.001) - H2(200)) / 0.001 = 1344781.4 N / m; Third step: Substitution E =195000000000Pa, A =0.0014m 2 , W =101 N / m, S Given L3 = 199.4209m, L3 = 200.001m, h = 0m, we obtain H3(200.001) = 801281.3914N, H3(200) = 799936.61 N, and the horizontal stiffness of the span K3 = (H3(200.001) - H3(200)) / 0.001 = 1344781.4 N / m; 4th step: Substitution E =195000000000Pa, A =0.0014m 2 , W =101 N / m, S Given L4 = 222.8813m, L4 = 200.001m, h = -100m, we obtain H4(200.001) = 800904.8765N, H4(200) = 799936.61 N, and the horizontal stiffness of the span K4 = (H4(200.001) - H4(200)) / 0.001 = 968266.5 N / m; (2) Calculate the unbalanced horizontal forces at the top of each tower. (3) Select an active correction tower The maximum absolute unbalanced force is tower 1: ; (4) Calculate the equivalent stiffness The proposed modified series stiffness on the left side of Tower 1 is: 968266.6536 N / m The proposed corrected series stiffness on the right side of Tower 1 is 396824.8018 N / m. The proposed equivalent stiffness of Tower 1 is: 1365091.4554 N / m (5) Calculate the offset correction amount of tower 1 The proposed correction amount for tower 1 is 0.1465 m. (6) Link up and correct all towers By softness ratio: The compliance ratio of tower 1 is 1, and the tower deflection correction is 0.1465m. The compliance ratio of Tower 2 is 0.7049, and the tower deflection correction is 0.1032m. The compliance ratio of tower 3 is 0.4098, and the tower deflection correction is 0.0600m. (7) Update tower offset and span New offset: δ 1 = 0.1465m δ 2 = 0.1032m, δ 3 = 0.0600m New span: The updated span for the first span is 200.1465m. The updated span for the second span is 199.9567m. The updated span for the third span is 199.9567m. The updated span for the fourth span is 199.9399m. (8) Convergence judgment The maximum unbalanced force is in tower 1, and its value is enormous, far exceeding 10. −4 If kN, return and continue iterating.

[0045] (9) Continue iterating After 10 iterations, the maximum unbalanced force in tower 3 decreased to 3.20871477e-05 N, satisfying the convergence condition.

[0046] IV. Final Output Results The final offsets of each tower are: 0.31009154m for tower 1, 0.38558565m for tower 2, and 0.3122846m for tower 3.

[0047] Other parameters for each span are shown in the table below: .

[0048] V. Comparison and Verification with Existing Methods To verify the superiority of this invention, calculations were performed under the same operating conditions using both the equivalent elastic modulus method and the traditional full-tower correction method: Equivalent elastic modulus method: Due to the small initial tension and large tower deflection, the linear assumption fails, resulting in a large error compared with the calculation results of this invention.

[0049] Traditional full-tower correction method: When iterating to the 4th step, the tower deflection correction amount oscillates, the unbalanced force increases instead of decreasing, and eventually diverges and fails to converge.

[0050] The method of this invention converges stably, and the results are in high agreement with the fine finite element model, verifying its high accuracy and strong robustness.

[0051] VI. Conclusion This application example demonstrates that the method for accurately calculating tower offset in a multi-tower cable hoisting system based on single-tower linkage correction can: Applicable to any initial tension condition (including low tension); Accurately consider the geometric nonlinearity of the cable; Ensure the iterative process is monotonically convergent and avoid divergence; The output results can be used to guide tower deflection control and cable tension adjustment during construction.

[0052] The above description of the disclosed embodiments enables those skilled in the art to make or use the invention. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the general principles defined herein may be implemented in other embodiments without departing from the spirit or scope of the invention. Therefore, the invention is not to be limited to the embodiments shown herein, but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims

1. A method for calculating tower deviation of a multi-tower cable hoisting system based on single-tower linkage correction, characterized in that, Includes the following steps: Step S1: Input system parameters, including geometric parameters, material parameters, tower stiffness, external load and convergence tolerance. Based on the initial tension of the specified span, use the elastic catenary equation to iteratively calculate the stress-free cable length of each span to determine the initial equilibrium state of the system. Step S2: Initialize the offset of all towers to zero, and calculate the span of each span as the original span; Step S3: Execute the main iterative loop based on single-tower linkage correction, including the following sub-steps: Step S31: Based on the current span and stress-free cable length, solve for the horizontal force at the cable end using the elastic catenary equation, and calculate the horizontal elastic stiffness of each span using the finite difference method. Step S32: Calculate the unbalanced horizontal forces at the top of each tower; Step S33: Select the tower with the largest absolute value of unbalanced force as the active correction target for this iteration; Step S34: Calculate the total equivalent stiffness of the active correction tower, specifically including calculating the corresponding left series stiffness and right series stiffness, and adding the left series stiffness and right series stiffness to the tower's own equivalent stiffness to obtain the corresponding total equivalent stiffness. Step S35: Calculate the offset correction amount of the active correction tower; Step S36: Based on the offset correction amount of the active correction tower, adjust the offset of all other towers in the system in accordance with the compliance ratio. The offset correction for other towers is calculated according to the following rules: ； tower tower bias correction for the current iteration step, m is the number of number of active corrections to the tower, K i the first i horizontal elastic stiffness of the span, Step S37: Update the offset of all towers, and recalculate the effective horizontal span of each span accordingly, and recalculate the unbalanced horizontal force at the top of each tower based on the updated span. Step S38: Determine whether the maximum unbalanced horizontal force is less than the convergence tolerance. If so, terminate the iteration; otherwise, return to step S31. Step S4: Output the final offset of each tower, the horizontal force at each cable end, and the horizontal elastic stiffness.

2. The method according to claim 1, wherein, The equation for the elastic catenary used in step S1 is as follows: ； wherein, L is the span, h is the height difference, H is the horizontal force, V is the vertical force, S 0 is the unstressed cable length, E is the modulus of elasticity, A is the cable cross-sectional area, W is the cable weight.

3. The method according to claim 1, wherein, The formula for calculating the unbalanced horizontal force at the top of the tower in step S32 is as follows: in, H j , H j+1 For the tower j Horizontal forces on the left and right cables K T,j For the tower j Lateral stiffness δ j For the tower j of deviation, This refers to the unbalanced horizontal force caused by external forces at the top of the tower.

4. The method for calculating tower offset in a multi-tower cable hoisting system based on single-tower linkage correction according to claim 1, characterized in that, In step S33, the tower with the largest absolute value of the unbalanced force is selected as the active correction target for this iteration: ； This refers to the unbalanced horizontal force at the top of the tower.

5. The method for calculating tower offset in a multi-tower cable hoisting system based on single-tower linkage correction according to claim 1, characterized in that, The calculation method for the total equivalent stiffness in step S34 is as follows: ， in, To actively correct the tower numbering, m For the number of spans, K i For the first i Horizontal elastic stiffness of the span For the current iteration step tower Left-side series stiffness, Current iteration step tower Right-side series stiffness, For active correction tower The total equivalent stiffness; For active correction tower Lateral stiffness.

6. The method for calculating tower offset in a multi-tower cable hoisting system based on single-tower linkage correction according to claim 1, characterized in that, The offset correction amount of the active correction tower in step S35 is: ; For active correction tower The unbalanced horizontal force at the top of the tower, For active correction tower The total equivalent stiffness.

7. The method for calculating tower offset in a multi-tower cable hoisting system based on single-tower linkage correction according to claim 1, characterized in that, The update method for the effective horizontal span of each span in step S37 is as follows: ； For the first original span, For the i-th original span, Let m be the original span of the m-th span, where m is the span number. The effective horizontal span of the first span after correction. To determine the effective horizontal span of the i-th span after correction, This is the effective horizontal span of the m-th span after correction.

8. A tower offset calculation system for a multi-tower cable hoisting system based on single-tower linkage correction, characterized in that, include: The parameter input module is used to input system geometric parameters, material parameters, tower stiffness, external loads, and convergence tolerances; The initial equilibrium module is used to iteratively calculate the initial stress-free cable length for each span based on the elastic catenary equation; The iterative calculation module is connected to the parameter input module and the initial balancing module respectively, and is used to execute the corresponding main iterative loop; The deviation of all other towers is corrected in conjunction with the deviation correction amount of the active correction tower according to the compliance ratio. The output module, connected to the iterative calculation module, is used to output the final tower offset, cable end horizontal force, and horizontal elastic stiffness.

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