Suspender force identification method and device considering multi-rigidity characteristics of main cable of suspension bridge

Abstract

The present application belongs to the technical fields of suspension bridge cable force identification, and discloses a suspension bridge cable force identification method and equipment considering the multi-rigidity characteristics of the main cable, which comprises the following steps: S1, a string spring system analytical model of the main cable of the suspension bridge is established, the string spring system analytical model is used to simulate the geometric flexibility, material elasticity and tension-related quadratic bending rigidity characteristics of the main cable by using a combined string spring unit, and an equivalent node correction force is used to simulate the local bending effect of the cable clamp area; S2, an incremental balance equation considering the construction history information is established based on the string spring system analytical model, an inverse problem optimization model for solving the cable force under the geometric observation of the main cable is established based on the incremental balance equation, and a variable step iterative algorithm is used to solve the inverse problem optimization model to obtain the cable force. The present application improves the identification accuracy of the cable force.

Description

Technical Field

[0001] This invention belongs to the technical field of suspension bridge cable force identification, and more specifically, relates to a method and device for suspension bridge cable force identification that considers the multi-stiffness characteristics of the main cable. Background Technology

[0002] The "geometric observation method" (hereinafter referred to as the "geometric method"), which indirectly identifies cable forces by utilizing the linear characteristics of the main cable of a suspension bridge, is a simple, economical, and rapid new method for identifying cable forces that has emerged in recent years. It can partially make up for the shortcomings of existing cable force measurement methods and has become a powerful supplement to sensor-based direct measurement methods.

[0003] However, the traditional geometric method based on the segmented catenary form finding principle assumes that the large-diameter main cable is an ideal flexible body, ignoring its "multi-stiffness characteristics" such as cable clamp stiffness, geometric flexibility, and variable secondary bending stiffness related to construction history. As a result, the vertical stiffness of the main cable cannot be accurately included, which increases the error in the physical mechanism of cable force identification. Summary of the Invention

[0004] In view of the above-mentioned defects or improvement needs of the existing technology, the present invention provides a method and device for identifying the cable force of a suspension bridge that takes into account the multi-stiffness characteristics of the main cable, which aims to solve the problem of low identification accuracy of existing cable force.

[0005] To achieve the above objectives, according to one aspect of the present invention, a method for identifying the cable force of a suspension bridge considering the multi-stiffness characteristics of the main cable is provided, comprising the following steps: S1. Establish an analytical model of the chord spring system of the main cable of the suspension bridge. The analytical model of the chord spring system uses combined chord spring units to simulate the geometric flexibility, material elasticity and tension-related secondary bending stiffness characteristics of the main cable, and uses equivalent nodal correction force to simulate the local bending effect in the cable clamping area. S2. Based on the analytical model of the string spring system, an incremental equilibrium equation considering construction history information is established. Based on the incremental equilibrium equation, an inverse problem optimization model for solving the suspending cable force under the geometric observation of the main cable is established. A variable step-size iterative algorithm is used to solve the inverse problem optimization model to obtain the suspending cable force.

[0006] Furthermore, the mechanical behavior of the main cable is decomposed into flexible tension and rigid bending, and a combined string spring element model is introduced to couple the flexible tensile stiffness. Bending stiffness and equivalent chord stiffness

[0007] Furthermore, the flexible tensile stiffness of the coupled flexible portion Rigid bending stiffness of the rigid part Combining them into a composite string spring unit, the equivalent string stiffness is... The formula is:

[0008] in, Let E be the chord tensile stiffness, where E is the elastic modulus, A is the cross-sectional area of ​​the cable, and C is the chord length of the cable.

[0009] Furthermore, the calculations of the bending chord's geometric stiffness and the flexible chord's geometric stiffness are based on idealized cable segment models: a parabolic assumption model with shared parameters and a catenary reference model, respectively; both models share the horizontal projected length L, vertical projected height H, chord length C, and stress-free length. and horizontal force components .

[0010] Furthermore, the parabolic model adopts the simplified assumption that the weight is uniformly distributed along the chord, and the horizontal angle of the chord is... The catenary baseline model strictly considers the distribution of the cable segment's self-weight along the arc length, and the horizontal angle of the catenary segment tangent is... By establishing a stiffness decoupling mechanism, two different stiffnesses were achieved to resist bending chordal forces separately. With flexible chordal force ; The geometric stiffness of the bending chord is ,in:

[0011] in This is a uniformly distributed load representing the cable's self-weight along its length. This represents the increment of the bending chord force; middle , where n represents the nth stage; Geometric stiffness of flexible string:

[0012] In the formula, .

[0013] Furthermore, based on the system equilibrium, a nonlinear analytical equation was established and solved using the hybrid incremental method, ultimately obtaining the coordinates of the suspension points during the final construction stage of the main cable. By calculating the coordinates of the lifting point Coordinates of the actual suspended point The coordinate difference is obtained by comparison, where:

[0014] The cable force is continuously optimized by using a variable step size search method combined with the coordinate difference information of the suspension point, so that the final calculated main cable suspension point coordinates match the observed coordinates within the error range. The final cable force is the cable force of the completed bridge. in, The x-coordinate of node i is calculated; The calculated y-coordinate of node i; Here is the x-coordinate of node i obtained from actual measurement; The y-coordinate of node i is obtained from actual measurement.

[0015] Furthermore, the tangential force Decomposed into chordal force and vertical residual force Their relationship is as follows:

[0016] By ignoring vertical residual force The equilibrium equations are simplified to a pure chordal force form; The chordal unit vector of unit AB Represented by the global coordinate system unit vectors i and j:

[0017] The equilibrium relationship between nodal forces and coordinates is expressed as follows:

[0018] Therefore, the above formula can be written as:

[0019] in, , , , It is the identity matrix; The angle between the tangential and chordal directions of the cable segment; , These are the nodal forces at both ends of element AB; , These represent the displacements of the nodes at both ends of element AB.

[0020] Furthermore, the mathematical expression of the inverse problem optimization model is:

[0021] Where m is the number of slings to be determined. The difference between the calculated alignment and the target alignment is a function of the cable force. , These are the minimum and maximum values ​​of the cable force of the suspension bridge; Let i be the node force of node i.

[0022] The present invention also provides a suspension bridge cable force identification system that considers the multi-stiffness characteristics of the main cable. The fault diagnosis system includes a memory and a processor. The memory stores a computer program. When the processor executes the computer program, it performs the suspension bridge cable force identification method that considers the multi-stiffness characteristics of the main cable as described above.

[0023] The present invention also provides a computer-readable storage medium storing machine-executable instructions, which, when invoked and executed by a processor, cause the processor to implement the suspension bridge cable force identification method considering the multi-stiffness characteristics of the main cable as described above.

[0024] In summary, compared with the prior art, the suspension bridge cable force identification method and equipment considering the multi-stiffness characteristics of the main cable provided by the present invention have the following advantages: 1. This invention relates to a main cable chord spring system and moment correction method in the traditional geometric method, so as to achieve accurate identification of suspension bridge cable force based on the multi-stiffness characteristics of the main cable.

[0025] 2. This invention can achieve higher accuracy by taking into account the multi-stiffness characteristics of the main cable and the influence of construction history. It is more suitable for low-cost and high-efficiency accurate monitoring of the cable force of actual bridges. The effectiveness and accuracy of this invention have been verified through model tests and actual bridge tests.

[0026] 3. The variable step-size iterative algorithm is used to determine the calculated vertical coordinate of the lifting point in this round. Does the ordinate calculated in the previous round fall within the ordinate of the target hoisting point? If the coordinates are distributed on both sides, it indicates that the difference between the calculated vertical coordinate of the suspension point and the vertical coordinate of the target suspension point has already exceeded the range of the previous step size. Under these circumstances, the application formula is as follows. Modify the step size at the lifting point for the next round of calculations to achieve a more accurate solution for the cable force. Attached Figure Description

[0027] Figure 1 This is a schematic diagram of the parallel structure of the combined string-spring unit provided in an embodiment of the present invention; Figure 2 This is a schematic diagram of a cable segment provided in an embodiment of the present invention; Figure 3 This is a force decomposition diagram of a cable element in the overall coordinate system provided in an embodiment of the present invention; Figure 4 This is a schematic diagram of the incremental solution for the construction stage of the main cable multi-stiffness mechanism balance provided by the present invention. Figure 5This is a schematic diagram of the experimental device provided in the embodiment of the present invention, wherein (a) and (b) correspond to a three-dimensional structural schematic diagram and a planar schematic diagram, respectively; Figure 6 This is a comparison chart of the geometric method and the improved geometric method for identifying cable force errors provided in the embodiments of the present invention; Figure 7 This is a comparison chart of the cable force identification results provided by the geometric method and the improved geometric method in the embodiments of the present invention; Figure 8 This is a comparison chart of the geometric method and the improved geometric method for identifying cable force errors provided in the embodiments of the present invention; Figure 9 This is a schematic diagram of a suspension bridge provided in an embodiment of the present invention; Figure 10 yes Figure 9 The diagram shows the node distribution of the suspension bridge. Detailed Implementation

[0028] To make the objectives, technical solutions, and advantages of this invention clearer, the invention will be further described in detail below with reference to the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are merely illustrative and not intended to limit the invention. Furthermore, the technical features involved in the various embodiments of this invention described below can be combined with each other as long as they do not conflict with each other.

[0029] This invention provides a method for identifying the cable force of a suspension bridge that considers the multi-stiffness characteristics of the main cable. The method improves the traditional geometric method by introducing a chord spring system of the main cable and a moment correction mode, so as to achieve accurate identification of the cable force of the suspension bridge based on the multi-stiffness characteristics of the main cable.

[0030] The identification method mainly includes the following steps: S1. Establish an analytical model of the chord spring system of the main cable of the suspension bridge. The analytical model of the chord spring system uses combined chord spring units to simulate the geometric flexibility, material elasticity and tensile-related secondary bending stiffness characteristics of the main cable, and uses equivalent nodal correction forces to simulate the local bending effect in the cable clamping area.

[0031] S2. Based on the analytical model of the string spring system, an incremental equilibrium equation considering construction history information is established. Based on the incremental equilibrium equation, an inverse problem optimization model for solving the suspending cable force under the geometric observation of the main cable is established. A variable step-size iterative algorithm is used to solve the inverse problem optimization model to obtain the suspending cable force.

[0032] A nonlinear solver program was developed using the FORTRAN95 platform to achieve accurate identification and calculation of suspension bridge cable forces under geometric observation. Comparative analysis of measured data from the completed bridge phase of the Huajiang Canyon Bridge in Guizhou Province was conducted to verify the applicability and accuracy of the method provided in this invention. Results show that the maximum error in cable force identification using the method provided in this invention is 4.82%, with over 75% of the cable errors having an absolute value below 2.7%. The accuracy in the mid-span region is even better (error <2%), significantly superior to traditional methods (average error approximately 5%). Therefore, the cable force identification method provided in this invention has higher accuracy and robustness, making it more suitable for high-precision identification of suspension bridge cable forces under geometric observation.

[0033] The present invention will be further described in detail below with reference to specific embodiments.

[0034] Please see Figure 1 , Figure 2 , Figure 3 , Figure 4 , Figure 5 , Figure 6 and Figure 8 The suspension bridge cable force identification method considering the multi-stiffness characteristics of the main cable provided in this embodiment of the invention mainly includes the following steps: S1 decomposes the mechanical behavior of the main cable into flexible tension and rigid bending, and introduces a composite string spring element model to couple the flexible tensile stiffness. Bending stiffness and equivalent chord stiffness It accurately characterizes the rigid-flexible coupling effect.

[0035] Flexible tensile stiffness of the coupled flexible part Rigid bending stiffness of the rigid part Combining them into a composite string spring unit, the equivalent string stiffness is... The formula is:

[0036] in, Let E be the chord tensile stiffness, where E is the elastic modulus, A is the cross-sectional area of ​​the cable, and C is the chord length of the cable.

[0037] In the theoretical analysis model of the main cable structure, the calculation of the bending chord geometric stiffness and the flexible chord geometric stiffness are based on idealized cable segment models: a parabolic assumption model with shared parameters and a catenary reference model, respectively. Both models share the horizontal projected length L, vertical projected height H, chord length C, and stress-free length. and horizontal force components Core parameters, etc. The parabolic model employs a simplified assumption that the weight is uniformly distributed along the chord, with a horizontal angle of chord. The catenary baseline model strictly considers the distribution of the cable segment's self-weight along the arc length, and the horizontal angle of the catenary segment tangent is... Theoretical studies show that when the cable sag is relatively small, the two models exhibit high consistency in geometric shape and sag characteristics, with their differences controlled within engineering limits. By establishing a stiffness decoupling mechanism, two different stiffnesses were achieved to resist bending chordal forces independently. With flexible chordal force .

[0038] The geometric stiffness of the bending chord is ,in:

[0039] in .

[0040] Geometric stiffness of flexible string:

[0041] In summary, by simplifying complex nonlinear problems through chordal coupling, an analytical model for the main cable's alignment and internal forces is established to simulate the multi-stiffness mechanism of the main cable. The specific method is as follows: a. Divide the construction into stages and clarify the stiffness and stress characteristics of each stage; b. Separate the rigid and flexible parts and derive the chord stiffness separately; C-combined string-spring unit achieves coupling; The equivalent bending resistance at the cable clamp is incorporated into the overall equilibrium equation.

[0042] S2, The geometric method for identifying cable forces considering multiple stiffness mechanisms is to first provide a set of coarse initial values ​​for the cable forces. The equations are then incorporated into an equivalent string system considering multiple stiffness mechanisms. Based on the system equilibrium, nonlinear analytical equations are established and solved using the hybrid incremental method. Finally, the coordinates of the suspension points of the main cable during the final construction stage are obtained. By calculating the coordinates of the lifting points Coordinates of the actual suspended point The coordinate difference is obtained by comparison, where:

[0043] The cable force is continuously optimized by using a variable step size search method combined with the coordinate difference information of the suspension point, so that the final calculated main cable suspension point coordinates match the observed coordinates within the error range. The final cable force is the cable force of the completed bridge.

[0044] (1) Mechanical model and equilibrium equation The cable elements between any two adjacent cables exhibit a catenary shape in the global coordinate system. To establish equilibrium, the tangential force needs to be... Decomposed into chordal force and vertical residual force The relationship is as follows:

[0045] By ignoring vertical residual force The equilibrium equations can be simplified to a pure chordal force form.

[0046] The chordal unit vector of unit AB Represented by the global coordinate system unit vectors i and j:

[0047] The equilibrium relationship between nodal forces and coordinates can be expressed as:

[0048] Therefore, the above formula can be written as:

[0049] =

[0050] in, , , , It is an identity matrix.

[0051] The aforementioned mechanical model is based on equilibrium equations constructed using a catenary as a reference, and its analytical scope is limited to the flexible deformation characteristics of materials. To address the multi-stiffness mechanisms present in main cables in practical engineering, the original theoretical framework needs to be expanded. This is achieved by introducing a multi-parameter coupled string-spring combination model, which characterizes the chordal stiffness coefficient under flexible tension. Upgraded to a combined chord stiffness that integrates bending and sag effects. This improved strategy, through stiffness matrix reconstruction, enables the cable segment to simultaneously reflect flexible tension, rigid bending, and their interaction in the chordal equilibrium equation, ultimately achieving the precise embedding of the main cable's multi-stiffness mechanism into mechanical equilibrium.

[0052] For the element equilibrium equations, in the nth loading stage, the mechanical behavior of any cable element can be described by the following equation: =

[0053] In the formula, The geometric stiffness matrix of the composite chord. Let be the nodal displacement vector. This represents the equivalent nodal force vector. This equation establishes the dynamic relationship between nodal displacements and applied forces.

[0054] For the overall equilibrium equations, the equilibrium equations of all elements are integrated, and the equivalent nodal forces resisting bending at the cable clamps are superimposed. The global nonlinear equilibrium equation is obtained as follows:

[0055] in, For sling force Including the weight of the main cable, This represents the bending correction force of the cable clamp. This equation systematically reflects the rigid-flexible coupled mechanical characteristics of the main cable during construction, laying the foundation for subsequent incremental solutions.

[0056] (2) Incremental Iterative Solution Strategy for Construction Process For solving general nonlinear analytical equations, a hybrid phased incremental loading method combining updated Lagrange schemes can be applied to approximate the large deformation problem of the main cable during construction into small deformation problems within each loading stage. In the equivalent chord system model, it is assumed that the cable segment between adjacent suspenders is an independent element. By considering the geometric stiffness of the main cable composite chord and the rigidity correction force at the cable clamp position, an incremental equilibrium solution process is established.

[0057] In the nth construction stage, the endpoint coordinates and nodal forces of any main cable element e must satisfy the following equilibrium relationship:

[0058] In the formula, , , As a key parameter, it can be calculated using the following formula:

[0059] The overall equilibrium equation can then be expressed as:

[0060] In the formula, Represents equivalent nodal force, The sling force to be determined Adding the self-weight of the main cable evenly distributed to the nodes, the final solution yields the given cable force. Main cable node coordinates in the final construction phase .

[0061] (3) Strategy for solving cable force Based on the above process, the final stage main cable alignment coordinates can be determined. It can be expressed as the independent variable, the cable force. The function is to obtain the target linear shape. The sling force needs to be continuously adjusted to make the calculated alignment infinitely close to the target alignment. Finally, the optimized sling force is the sling force value corresponding to the target alignment. This optimization model can be expressed by the following formula:

[0062] Where m is the number of slings to be determined. The difference between the calculated alignment and the target alignment is a function of the cable force. , The minimum and maximum possible values ​​of the cable force of the suspension bridge can often be obtained from the bridge design documents or derived empirically. The larger the range of cable force to be solved, the longer the calculation time will be, but it will not affect the calculation accuracy.

[0063] The specific solution flow consists of the following steps: Step a: Sling force and related initialization parameter input Assume a set of initial values ​​for the cable forces. Substitute the values ​​into the input to perform the calculation, and input the initial parameters. and The flexible equilibrium results are obtained based on the form-finding analysis in stage 0. The initial values ​​for the iteration of the equations in stage 1 are set, including the initial chord geometric stiffness and bending stiffness.

[0064] Step b: Determine the equilibrium of the multi-stiffness mechanism in stage 1 In stage 0, the main cable is in pure flexible equilibrium; in stages n ≥ 1, it transitions to a mixed rigid-flexible equilibrium. When n = 1, the bending chord force needs to be determined iteratively. With bending chord geometric stiffness The specific process is as follows: I. Phase 0 Cable Segment The geometric stiffness of the combined chord is calculated by the following formula:

[0065] And used for synthesis .

[0066] II. Phase 1 passed calculate Update the item on the right. The chordal elongation is determined as follows:

[0067] III. Derivation of bending string force based on the geometric stiffness of bending string It can be obtained from the following formula:

[0068] IV. Derivation based on geometric relationships , , , The geometric stiffness of a flexible string is expressed by the following formula:

[0069] V. Given bending stiffness ,make The combined chord stiffness is then updated as follows:

[0070] 6. Repeat steps 2 through 5 to solve iteratively. , Equal parameters, until the convergence condition is met:

[0071] Step c: Parameter transfer under incremental load Add the weight of the main cable at the lifting point to the sling force, according to get Based on the geometric parameters, internal force parameters, and stiffness parameters of the (n-1)th stage, the combined chord stiffness of the nth stage is calculated. .

[0072] Step d: Update and iteratively correct nodal coordinates and nodal forces Utilization renew Correcting the stiffness of the cable clamp And recalculate the equivalent load. .

[0073] Step e: Node coordinates convergence Iterate until Convergence occurs when the final construction stage is reached, at which point the coordinates of the lifting points, calculated based on the input sling force, are obtained.

[0074] Step f: Obtain the coordinates of the suspension point Compared with the actual observed coordinates of the suspension point By comparison, based on the coordinate difference, a variable step-size iterative method is used to correct the input cable force. Return to step one, re-enter the new cable force, and perform a new round of calculation. Iterate continuously until the difference in the coordinates of the suspension points converges. Finally, output the input cable force of the last round, which is the desired cable force. End the iteration and store the equilibrium data of each stage of the last round of calculation.

[0075] (4) Variable step size iteration method The variable step size iterative method is an iterative calculation approach based on nonlinear analytical methods. It first assumes a set of cable forces, then performs nonlinear loading calculations to obtain the final construction stage alignment. The assumed cable forces are then corrected based on the difference between the calculated alignment and the control points of the observed target shape. This process is repeated until the calculation result reaches the observed target shape.

[0076] In short, the variable step size iteration method is a method that optimizes the input parameters by calculating the difference between the calculated output parameters and the target output parameters, so as to make the calculated output parameters closer to the target output parameters. The iteration stops when the difference between the calculated output parameters and the target output parameters is within the allowable error range, and the input parameters of the last round are output, which is the desired result.

[0077] The specific iterative approach is as follows: Step 1: Input a set of initial values ​​for the sling force The value of i ranges from 1 to the number of slings m. After the above nonlinear loading calculation, the coordinates of the main cable suspension point in the final construction stage are obtained. Simultaneously input a step size to modify the input sling force. Step length here There are no restrictions on the value of , but it is best to choose one-tenth to one-hundredth of the estimated sling force, which will help to converge faster. Step 2: Calculate the longitudinal coordinates of the main cable suspension point Horizontal coordinates of observation points The difference ,in:

[0078] Recalculate Difference between the lifting point coordinates and those in the previous iteration product ,in:

[0079] Step 3: Judgment If the value is less than 0, the step size is halved for subsequent calculations.

[0080] Here The value is 0.5, in fact Any number between 0 and 1 can be used without restriction; if it is not less than 0, the step size remains unchanged during the calculation.

[0081] The significance of this step is to determine the vertical coordinate of the lifting point calculated in this round. Does the ordinate calculated in the previous round fall within the ordinate of the target hoisting point? If the coordinates are distributed on both sides, it indicates that the difference between the calculated vertical coordinate of the suspension point and the vertical coordinate of the target suspension point has already exceeded the range of the previous step size. Under these circumstances, the application formula is as follows. The step size at the lifting point is modified for the next round of calculations to achieve a higher accuracy in solving the cable force. This is the core idea of ​​variable step size cable force calculation.

[0082] Step 4: Determine the calculated coordinates of the main cable suspension point Is it greater than the coordinates of the observation point? If it is greater than the previous value, the cable force at that point will be increased by one step based on the previous value, that is:

[0083] If it is less than, the cable force value will be reduced by one step from the previous round, that is:

[0084] Step 5: Determine if the last sling has been calculated. If not, return to Step 2 to calculate the next sling, and continue until the last sling has been calculated.

[0085] Step Six: Calculate the difference e between the coordinates of all lifting points and the target coordinates:

[0086] like e<Ω , Ω To set the allowable error, a value of 0.01m is used in the program, which then outputs the cable force input value for the last round. This is the desired cable force; otherwise, substitute the modified cable force into step one for the next iteration until the convergence error is satisfied.

[0087] Experimental verification: A scaled-down model of the main cable-sling system was established. Using relevant information such as the main cable profile after a given sling force was applied, the method was approached from the inverse problem. The results of identifying the sling force were compared between the improved geometric method and the geometric method to verify the accuracy of the proposed method.

[0088] The results are as follows Figure 7 As shown, except for the first two loading stages where the cable forces identified by the two methods are relatively close, the error of the improved geometric method is significantly smaller than that of the geometric method in all other loading stages. Especially after loading stage III, the accuracy of the improved geometric method in identifying cable forces is within about 2%, which is significantly better than the accuracy of the geometric method at the same stage (about 3.5% or more). Therefore, it is evident that the improved geometric method for cable forces proposed in this invention has a significant advantage over the geometric method.

[0089] Verification of the Huajiang Canyon Bridge: Please see Figure 9 and Figure 10 A comparison of the cable force identification results and errors using the geometric method and the improved geometric method reveals that the improved geometric method significantly improves the accuracy of cable force identification by incorporating the multi-stiffness characteristics of the main cable and construction process simulation. During the bridge completion stage, the maximum error in cable force identification was -4.82% (node ​​19), and the minimum error was 0.03% (node ​​41), with over 75% of the cables showing an absolute error value below 2.7%. Particularly in the mid-span region (nodes 35-50), the error was generally controlled within 2%, indicating the method's strong adaptability.

[0090] The present invention also provides a suspension bridge cable force identification system that considers the multi-stiffness characteristics of the main cable. The fault diagnosis system includes a memory and a processor. The memory stores a computer program. When the processor executes the computer program, it performs the suspension bridge cable force identification method that considers the multi-stiffness characteristics of the main cable as described above.

[0091] The present invention also provides a computer-readable storage medium storing machine-executable instructions, which, when invoked and executed by a processor, cause the processor to implement the suspension bridge cable force identification method considering the multi-stiffness characteristics of the main cable as described above.

[0092] Those skilled in the art will readily understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for identifying the cable force of a suspension bridge considering the multi-stiffness characteristics of the main cable, characterized in that, The steps are as follows: S1. Establish an analytical model of the chord spring system of the main cable of the suspension bridge. The analytical model of the chord spring system uses combined chord spring units to simulate the geometric flexibility, material elasticity and tension-related secondary bending stiffness characteristics of the main cable, and uses equivalent nodal correction force to simulate the local bending effect in the cable clamping area. S2, Based on the analytical model of the string spring system, an incremental equilibrium equation considering construction history information is established. Based on the incremental equilibrium equation, an inverse problem optimization model for solving the suspender force under the geometric observation of the main cable is established. A variable step-size iterative algorithm is used to solve the inverse problem optimization model to obtain the suspender force. The calculations of the geometric stiffness of the bending chord and the flexible chord are based on idealized cable segment models: a parabolic assumption model with shared parameters and a catenary reference model, respectively. Both models share the horizontal projected length L, vertical projected height H, chord length C, and stress-free length. and horizontal force components ; The parabolic model employs the simplified assumption that the weight is uniformly distributed along the chord, with a horizontal angle of chord. The catenary baseline model strictly considers the distribution of the cable segment's self-weight along the arc length, and the horizontal angle of the catenary segment tangent is... By establishing a stiffness decoupling mechanism, two different stiffnesses were achieved to resist bending chordal forces separately. With flexible chordal force ; The geometric stiffness of the bending chord is ,in: in This is a uniformly distributed load representing the cable's self-weight along its length. This represents the increment of the bending chord force; middle , where n represents the nth stage; Geometric stiffness of flexible string: In the formula, ; Based on the system equilibrium, a nonlinear analytical equation was established and solved using the hybrid incremental method, ultimately yielding the coordinates of the suspension points during the final construction stage of the main cable. By calculating the coordinates of the lifting point Coordinates of the actual suspended point The coordinate difference is obtained by comparison, where: The cable force is continuously optimized by using a variable step size search method combined with the coordinate difference information of the suspension point, so that the final calculated main cable suspension point coordinates match the observed coordinates within the error range. The final cable force is the cable force of the completed bridge. in, The x-coordinate of node i is calculated; The calculated y-coordinate of node i; Here is the x-coordinate of node i obtained from actual measurement; Here is the measured y-coordinate of node i; The mathematical expression for the inverse problem optimization model is: Where m is the number of slings to be determined. The difference between the calculated alignment and the target alignment is a function of the cable force. , These are the minimum and maximum values ​​of the cable force of the suspension bridge; Let i be the node force of node i.

2. The suspension bridge cable force identification method considering the multi-stiffness characteristics of the main cable as described in claim 1, characterized in that: The mechanical behavior of the main cable is decomposed into flexible tension and rigid bending, and a combined string-spring element model is introduced to couple the flexible tensile stiffness. Bending stiffness and equivalent chord stiffness 3. The suspension bridge cable force identification method considering the multi-stiffness characteristics of the main cable as described in claim 2, characterized in that: Flexible tensile stiffness of the coupled flexible part Rigid bending stiffness of the rigid part Combining them into a composite string spring unit, the equivalent string stiffness is... The formula is: in, Let E be the chord tensile stiffness, where E is the elastic modulus, A is the cross-sectional area of ​​the cable, and C is the chord length of the cable.

4. The suspension bridge cable force identification method considering the multi-stiffness characteristics of the main cable as described in claim 1, characterized in that: tangential force Decomposed into chordal force and vertical residual force Their relationship is as follows: By ignoring vertical residual force The equilibrium equations are simplified to a pure chordal force form; The chordal unit vector of unit AB Represented by the global coordinate system unit vectors i and j: The equilibrium relationship between nodal forces and coordinates is expressed as follows: Therefore, the above formula can be written as: in, , , , It is the identity matrix; The angle between the tangential and chordal directions of the cable segment; , These are the nodal forces at both ends of element AB; , These represent the displacements of the nodes at both ends of element AB.

5. A suspension bridge cable force identification system considering the multi-stiffness characteristics of the main cable, characterized in that: The system includes a memory and a processor. The memory stores a computer program, and when the processor executes the computer program, it performs the suspension bridge cable force identification method considering the multi-stiffness characteristics of the main cable as described in any one of claims 1-4.

6. A computer-readable storage medium, characterized in that: The computer-readable storage medium stores machine-executable instructions, which, when invoked and executed by a processor, cause the processor to implement the suspension bridge cable force identification method considering the multi-stiffness characteristics of the main cable as described in any one of claims 1-4.

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