Cable-stayed bridge cable tensioning control method and device

Abstract

The embodiment of the application provides a cable-stayed bridge cable tension control method and device. The method comprises the following steps: based on the anchor head pull-out amount, each cable is tensioned to the unstressed cable length; based on the cable force deviation of each cable, the non-adjusted cable and the adjusted cable are determined; based on the overall influence matrix of the cable and the quadratic programming method, the non-adjusted cable is locked, and the amplitude of the adjusted cable is determined; and based on the conversion relationship between the amplitude of the adjusted cable and the anchor head pull-out correction value, the unstressed cable length of the adjusted cable is adjusted. The embodiment of the application adjusts the cable by using the unstressed cable length and the anchor head pull-out amount, locks the non-adjusted cable based on the overall influence matrix of the cable and the quadratic programming method, is beneficial to obtaining the more accurate amplitude of the adjusted cable, and further obtains the more accurate adjustment amount, so that the number of cable adjustment times is reduced, and the cable adjustment efficiency is improved.

Description

TECHNICAL FIELD

[0001] The application relates to the technical field of civil engineering, and in particular relates to a cable-stayed bridge cable tensioning control method and device. BACKGROUND

[0002] The cable-stayed bridge is also called a cable-stayed bridge, is a bridge in which a main beam is directly pulled on a tower by a plurality of cables, and is a structural system composed of a pressure-bearing tower, a tension cable and a bending beam body. The cable-stayed bridge is mainly composed of a tower, a main beam and a cable.

[0003] With the development of the economy and society, cable-stayed bridges with spatial modeling aesthetic appeal are emerging in endlessly. Such bridges generally adopt an asymmetric structure and are mostly constructed by using the support method. The three-dimensional deformation characteristics are prominent in the construction process, the stiffness of the main beam midspan and side span is obviously different, the structure is highly asymmetric in stress, and the mutual confirmation of the tension behaviors of different cables is poor. In the cable tensioning process, the contact state of the tower beam of the cable-stayed bridge and the support and the evolution process thereof are difficult to accurately simulate, and the traditional cable-stayed bridge cable force control method needs to be improved. SUMMARY

[0004] The application provides a cable-stayed bridge cable tensioning control method and device.

[0005] According to an embodiment of the application, a cable-stayed bridge cable tensioning control method is provided, which comprises the following steps:

[0006] tensioning each cable to the unstressed cable length based on the anchor head pullout amount;

[0007] determining non-adjusted cables and adjusted cables based on the cable force deviation of each cable;

[0008] locking the non-adjusted cables and determining the amplitude of adjustment of the adjusted cables based on the overall influence matrix of the cables and the quadratic programming method;

[0009] adjusting the unstressed cable length of the adjusted cables based on the conversion relationship between the amplitude of adjustment of the adjusted cables and the anchor head pullout correction value.

[0010] According to another embodiment of the application, a cable-stayed bridge cable tensioning control device is provided, which comprises the following units:

[0011] a control unit configured to tension each cable to the unstressed cable length based on the anchor head pullout amount;

[0012] a first determination unit configured to determine non-adjusted cables and adjusted cables based on the cable force deviation of each cable;

[0013] a second determination unit configured to lock the non-adjusted cables and determine the amplitude of adjustment of the adjusted cables based on the overall influence matrix of the cables and the quadratic programming method;

[0014] The third determining unit is configured to adjust the unstressed cable length of the adjusting cable based on a conversion relationship between the amplitude of the adjusting cable and the anchor head pull-out amount correction value.

[0015] The embodiments of the present application utilize the unstressed cable length and the anchor head pull-out amount to adjust the cable, and lock the non-adjusting cable based on the overall influence matrix of the cable and the quadratic programming method, which is beneficial to obtain more accurate amplitude of the adjusting cable, and further obtain more accurate adjustment amount, so as to reduce the number of cable adjustment and improve the cable adjustment efficiency.

[0016] It should be understood that the content described in this part is not intended to identify key or important features of the embodiments of the present application, nor to limit the scope of the present application. Other features of the present application will become apparent from the following description. BRIEF DESCRIPTION OF DRAWINGS

[0017] The accompanying drawings are used to better understand the present application, and do not constitute a limitation on the present application. Among them:

[0018] Figure 1 is a schematic diagram of the cable tensioning control method of a cable-stayed bridge according to the embodiments of the present application.

[0019] Figure 2 is a schematic diagram of the planar and vertical plane arrangement of a cable-stayed bridge.

[0020] Figure 3 is a schematic diagram of the cable tensioning control process.

[0021] Figure 4 is a schematic diagram of the bridge finite element model.

[0022] Figure 5 is a schematic diagram of the unstressed cable length calculation symbol.

[0023] Figure 6 is a schematic diagram of the calibration coefficient distribution.

[0024] Figure 7 is a schematic diagram of the linear calibration linear correlation coefficient R 2 .

[0025] Figure 8 is a schematic diagram of the relative deviation distribution of the frequency method estimated cable force and the measured cable force.

[0026] Figure 9 is a schematic diagram of the cable force distribution after the initial tensioning is completed.

[0027] Figure 10 is a schematic diagram of the cable force amplitude adjustment and the pull-out amount correction value calculation result.

[0028] Figure 11 is a schematic diagram of the measured cable force distribution of the completed bridge.

[0029] Figure 12 This is a schematic diagram showing the distribution of the anchor head pull-out deviation.

[0030] Figure 13 This is a schematic diagram of a cable tensioning control device for a cable-stayed bridge according to an embodiment of this application. Detailed Implementation

[0031] The following description, in conjunction with the accompanying drawings, illustrates exemplary embodiments of this application, including various details to aid understanding. These should be considered merely exemplary. Therefore, those skilled in the art will recognize that various changes and modifications can be made to the embodiments described herein without departing from the scope and spirit of this application. Similarly, for clarity and brevity, descriptions of well-known functions and structures are omitted in the following description.

[0032] Figure 1 This is a schematic diagram of a cable tensioning control method for a cable-stayed bridge according to an embodiment of this application. The method may include the following steps:

[0033] S1. Based on the anchor head pull-out amount, tension each cable to the stress-free cable length.

[0034] In this embodiment, the cable can be a cable of a cable-stayed bridge, or simply a stay cable. During the initial tensioning of the cable-stayed bridge, each cable can be tensioned in multiple stages according to the anchor head pull-out amount. After tensioning is completed, the hydraulic pressure of the jacks can be recorded to calculate the cable force, and the fundamental frequency of cable vibration can be collected for subsequent cable force identification.

[0035] S2. Based on the cable tension deviation of each cable, determine the non-adjustment cable and the adjustment cable.

[0036] For example, after the initial tensioning is completed, the cable tension can be measured to obtain the tension deviation of each cable. Based on the tension deviation, some cables whose tension deviation does not yet meet the requirements, along with their adjacent cables, can be selected as adjustment cables. Cables whose tension deviation does not yet meet the requirements can also be called adjustment cables. Cables other than the adjustment cables can be called non-adjustment cables.

[0037] S3. Based on the overall influence matrix of the cable and the quadratic programming method, the non-adjustment cable is locked to determine the adjustment amplitude of the adjustment cable.

[0038] For example, based on the overall influence matrix of the cable and the quadratic programming method, the adjustment space of non-adjusting cables in the decision variables can be restricted, the adjustment space of the adjusting cables in the decision variables can be released, and the adjustment amplitude of the adjusting cables can be calculated.

[0039] S4. Based on the conversion relationship between the amplitude adjustment of the adjustment cable and the correction value of the anchor head pull-out, adjust the stress-free cable length of the adjustment cable.

[0040] For example, in the second tensioning process, the selected inhaul cable stress-free cable length can be modified based on the anchor head pull-out amount correction value.

[0041] In a possible implementation, after performing S4 to perform the second tensioning of the inhaul cable, S2 of analyzing the cable force deviation can be continued to determine whether there is an inhaul cable that needs to be adjusted. If yes, S3 to S4 are continued; if no, it can be considered that the cable tensioning control of the cable-stayed bridge is completed.

[0042] In a possible implementation, the stress-free cable length is determined based on the tower offset and the pre-camber. The pre-camber can also be referred to as a lane load pre-camber, etc. Considering the tower offset and the pre-camber, it is beneficial to obtain a more accurate stress-free cable length.

[0043] In a possible implementation, the formula of the stress-free cable length obtained based on the finite element model of the cable-stayed bridge is as follows:

[0044]

[0045] wherein, S0 is the stress-free cable length between the anchoring points, T is the tensioning cable force, A is the cable area, E is the cable elastic modulus, q is the cable self-weight intensity, l0 is the anchoring point distance after the structure deformation, and l is the horizontal projection distance of the cable after the structure deformation, wherein the l0 is determined based on the tower offset and the pre-camber.

[0046] In a possible implementation, the formula of the l0 is as follows:

[0047] l0 = norm([X c , Y c , Z c ] b + [X HE , Y HE , Z HE ] b + [X D0 , Y D0 , Z D0 ] b - [X c , Y c , Z c ] e - [X HE , Y HE , Z HE ] e - [X D0 , Y D0 , Z D0 ] e )

[0048] wherein, X, Y, and Z represent the cable anchoring point coordinates or coordinate correction values.

[0049] b identifies the position of the first node of the cable;

[0050] e identifies the position of the tail node;

[0051] c identifies the reference state;

[0052] HE identifies the erection geometry correction amount, which can be used to identify the pre-camber;

[0053] D0 identifies the deformation amount of the first and tail nodes of the cable under the dead load in the bridge completion state.

[0054] In a possible implementation, in S2, based on the overall influence matrix of the cable and the quadratic programming method, the non-adjustable cable is locked, and the amplitude of the adjustable cable is determined, including:

[0055] Based on the overall influence matrix of the cable, the relationship between the amplitude and the cable force change is established, the target function is constructed according to the percentage of the deviation of the adjusted cable force of each cable relative to the target cable force and the minimum, and the constructed target function is converted into a quadratic formula target function;

[0056] The adjustment space of the non-adjustable cable in the decision variable of the quadratic formula target function is limited, and the adjustment space of the adjustable cable in the decision variable is released;

[0057] The quadratic formula target function is solved to obtain the amplitude of the adjustable cable.

[0058] In a possible implementation, the quadratic formula is:

[0059]

[0060] Where x is the decision variable, H is the symmetric matrix, f T is a row vector, P is a matrix, B is a column vector, Lb is the lower limit of the decision variable, and Ub is the upper limit of the decision variable.

[0061] In a possible implementation, the formula of the quadratic formula target function f(Δ) is:

[0062]

[0063] Where n is the total number of cables;

[0064] F t , F0 are the target cable force and the current cable force of all cables respectively;

[0065] D = F0-F t , is the difference between the current cable force and the target cable force;

[0066] Δ is the amplitude of each cable;

[0067] C is a whole influence matrix of the cable, the i-th row of the whole influence matrix of the cable is an influence value of a unit tension of each cable on the i-th cable, and the j-th column is an influence value of a unit tension of the j-th cable on each cable.

[0068] In a possible implementation, the quadratic formula target function is related to parameters of the quadratic formula as follows:

[0069]

[0070] After the amplitude modulation Δ, P and B in the quadratic formula are as follows:

[0071] P = [C; -C], and B = [(1 + α)F t -F0; -(1 - α)F t +F0]

[0072] C is a whole influence matrix of the cable, α is a percentage limit of a deviation of each cable force after the cable adjustment relative to a design cable force, F t , and F0 are a target cable force and a current cable force of all cables respectively.

[0073] In a possible implementation, the adjustment space of a decision variable of a non-adjusted cable in the quadratic formula target function is limited, and the adjustment space of a decision variable of an adjusted cable is released, including the following steps.

[0074] Supposing that the i-th cable is the non-adjusted cable and the j-th cable is the adjusted cable;

[0075] the upper limit Ub i of the decision variable corresponding to the i-th cable is set to zero, the upper limit Ub j of the decision variable corresponding to the j-th cable is set to β, β is a reasonable large value set in combination with a unit force size, and the upper limit of the decision variable is as follows: Ub = [..., Ub i = 0,..., Ub j ,...] T ;

[0076] The lower limit of the decision variable is set to Lb = -Ub.

[0077] In a possible implementation, based on a conversion relationship between the amplitude modulation of the adjusted cable and the anchor head pull-out amount correction value, the unstressed cable length of the adjusted cable is adjusted, including the following steps.

[0078] Based on the amplitude modulation of the adjusted cable, the cable force increment of the adjusted cable is determined.

[0079] Based on the cable force increment of the adjusted cable, the unstressed cable length change amount of the adjusted cable and the anchor head pull-out amount correction value of the adjusted cable are determined.

[0080] In a possible implementation, the formula of the unstressed cable length change amount ΔS0 is as follows:

[0081]

[0082] wherein S 01 is the unstressed cable length between anchor points before adjustment, S 02 is the unstressed cable length between anchor points after adjustment;

[0083] E is the elastic modulus of the cable, A is the area of the cable, and q is the self-weight gravity of the cable;

[0084] ΔT is the cable force increment calculated based on the adjustment amplitude of the adjustment cable;

[0085] 01 is the distance between anchor points after structural deformation before adjustment, l 02 is the distance between anchor points after structural deformation after adjustment;

[0086] l1 is the horizontal projection distance of the cable after structural deformation before adjustment, and l2 is the horizontal projection distance of the cable after structural deformation after adjustment. 01 02

[0087] T1 is the cable force of the adjustment cable in the finite element model of the cable-stayed bridge before the action of the cable force increment ΔT of each adjustment cable.

[0088] In a possible implementation, after the unstressed cable length change amount is calculated, the corresponding anchor head pull-out amount correction value can be obtained. The unstressed cable length of the adjustment cable can be adjusted by using the anchor head pull-out amount correction value.

[0089] In a possible implementation, the calculation steps of the parameters in the formula of the unstressed cable length change amount ΔS0 include:

[0090] Before simulating the stage of gradually adjusting the cable, a construction stage is inserted, the measured cable force after one-time tensioning is taken as the initial cable force to assign to the corresponding cable element, and the coordinates of the upper and lower anchor points of each adjustment cable in the finite model of the overall influence matrix of the cable are obtained.

[0091] The unit force set in the stage of simulating the gradually adjusting of the cable is multiplied by the corresponding adjustment amplitude, the cable force increment of the non-adjustment cable is zero, the cable force increment of the adjustment cable corresponds to the respective adjustment amplitude ΔT, and the calculation is re-executed.

[0092] The three-direction deformation amounts of the anchor points of the adjustment cable before and after the action of the respective adjustment amplitude ΔT are obtained, the coordinates of the upper and lower anchor points are substituted, and l 01 , l1, l 02 , and l2 are solved.

[0093] Then, the values of the parameters are substituted into the formula of the unstressed cable length change amount ΔS0 one by one, and ΔS0 can be solved.

[0094] ​​​Application examples:

[0095] Through the scheme of the embodiment of the application, the cable tensioning control of a large space special-shaped steel tower cable-stayed bridge can be performed.

[0096] 1Overall process: refer to Figure 2 , a special-shaped steel tower cable-stayed bridge, the tower beam of which is erected based on the support auxiliary installation method. In order to ensure that the cable force of the completed bridge meets the expected state, the unstressed state control method is used to control the cable tensioning, the finite element method is used to establish a full-process simulation calculation model of the bridge, the unstressed cable length is calculated considering the tower deviation and the pre-camber. In the initial tensioning process, the control is performed based on the anchor head pull-out amount, and the linear calibration formula of the frequency and the cable force is obtained. Combined with the initial tensioning cable force deviation analysis, the non-adjusted cable adjustment amplitude is locked, the cable overall influence matrix (which can also be referred to as a cable force tensioning influence matrix, a cable force influence matrix, etc.) and the quadratic programming optimization method are used to calculate the adjusted cable adjustment amplitude. Moreover, the conversion relationship between the adjustment amplitude and the anchor head pull-out amount correction value is established, and the unstressed cable length is modified to realize the secondary cable adjustment.

[0097] 2Cable tensioning control process

[0098] The main construction steps of the bridge can include: assembling the steel tower on the support in sections (erecting the main beam to both sides from the tower root synchronously) → high and low tower closure → erecting the remaining main beam sections (synchronously removing the tower support) → high and low tower closure of the side span main beam → closure of the mid-span main beam → initial cable tensioning → removal of the main beam support → secondary cable adjustment → construction of the bridge deck pavement and auxiliary facilities. Before the closure of the mid-span, the low tower root is temporarily fixed, and the fixing measure is removed after the closure. Combined with the bridge construction scheme, the cable tensioning control mainly reflects the following aspects: ①During the cable manufacturing stage, the unstressed cable length is calculated, and the adjustment range of the cable length is reviewed in combination with the anchoring structure. ②After the conversion of the tower beam closure structure system is completed, the initial tensioning (or primary tensioning) control of the structure located on the support is performed, and all the cable-stayed cables are tensioned to the unstressed cable length. In this process, the frequency and cable force calibration relationship can be established. ③After the removal of the main beam support, the cable force identification and deviation analysis are performed to determine the cable force optimization adjustment control scheme, and the secondary cable adjustment is realized. The cable tensioning control process is shown in Figure 3 .

[0099] 3Cable manufacturing and initial tensioning control

[0100] 3.1Calculation of unstressed cable length

[0101] The unstressed cable length is an important index in construction control. If the length is too short, the effective anchorage length will be insufficient or unable to anchor, and if the length is too long, the tensioning force will be difficult to reach or additional pads will be needed. For medium-span cable-stayed bridges, research and practice show that the unstressed cable length determined based on the Ernst simplified theory using formula (6) can fully meet the accuracy requirements. However, there are problems in the calculation of the unstressed cable length for traditional regular cable-stayed bridges: ① For regular cable-stayed bridges in which the ideal target state is determined in the tower-straight-beam-flat mode, the influence of the tower deflection is not considered. ② When calculating the unstressed cable length according to the designed bridge alignment, the influence of the main girder lane load camber is not considered. Not considering the above two factors will cause deviations in the finished cable length, which will bring great difficulties to the cable tensioning control based on the unstressed state method.

[0102]

[0103] In the above formula, S0 is the unstressed cable length between anchor points, T is the tensioning cable force, A is the cable area, E is the cable elastic modulus, q is the cable self-weight intensity, l0 is the anchor point distance after structural deformation, and lo is the horizontal projection distance of the cable after structural deformation.

[0104] For example, based on Midas / civil2018, a finite element model of the bridge is established, the tower, beam, and support are simulated by beam elements, the cable is simulated by cable elements, the high tower and support root are fixed, the low tower root is connected with the support, sand box, and anchor rod by rigid arms, the vertical displacement between the tower beam and support is constrained, and the model is as shown in the figure. First, the whole process construction simulation is carried out according to the construction step sequence, the tower beam manufacturing and erection geometric shape control data are obtained based on the tangent displacement method, the vehicle live load analysis is carried out based on the ideal finished bridge state, the lane load main girder camber value is calculated, the anchor point distance l0 after deformation is calculated according to formula (2), and the unstressed cable length is calculated by substituting formula (1). For example, the lane load camber of a certain bridge is calculated to be 150 mm, the high tower forming deflection is 78 mm, and if the influence of this factor is ignored, it will bring a large deviation to the unstressed cable length.

[0105] l0=norm([X c ,Y c ,Z c ] b +[X HE ,Y HE ,Z HE ] b +[X D0 ,Y D0 ,Z D0 ] b -[X c ,Y c ,Z c ] e -[X HE ,Y HE, Z HE ] e -[X D0 , Y D0 , Z D0 ] e ) (2)

[0106] In the above formula, X, Y, Z represent the coordinates of the cable anchorage point or the correction amount of the coordinates, b represents the position of the cable head node, e represents the tail node position, C represents the reference state, HE represents the erection geometry correction amount (corresponding to the erection geometry correction value), and D0 represents the cable head and tail node deformation amount under the constant load of the bridge completion state. Some symbols are shown in the figure Figure 5 . Among them, the thick solid line is the reference state, the thin curve is the tower beam erection geometry, and the thick dashed line is the cable tensioning state. HE can include H EG and H EP , H EG is the main beam erection correction amount, and H EP is the pylon erection correction amount.

[0107] After S0 is calculated, the length of the cable is calculated according to the cable anchoring structure, and the adjustable amount of the unstressed cable length (adjustment range of the tensioning end nut) is calculated. For example, the adjustment amount of the unstressed cable length of the bridge 139 type cable is (-115~+170) mm, and the adjustment amount of the 151 type is (-124~+181) mm. If it is positive, the amount of pulling out needs to be reduced, which corresponds to the tension release; if it is negative, the amount of pulling out is increased, which corresponds to the continuous tensioning.

[0108] 3.2 Cable initial tensioning and cable force calibration

[0109] After the tower beam is closed on the support to complete the structural system conversion, the cable is tensioned for the first time, and the cable tensioning is accompanied by the gradual separation of the tower beam from the support, and the boundary conditions of the structure change dynamically. In view of the difficulty in accurately simulating the contact state of the tower beam with the support and its evolution process, the traditional tensioning method mainly controlled by force has many inconveniences. The initial tensioning of the bridge cable is based on the unstressed state method. For example, 8 sets of tensioning equipment are provided on the bridge, and the tensioning is carried out from near to far along the bridge and from low to high vertically around the root of the split tower, which takes advantage of the unstressed state method in different procedures. The cable of the middle span and the low tower side span is tensioned to the position in three stages according to the non-deviation anchor head pulling out amount of 80%, 90% and 100%. Due to the dense temporary load of the high tower side span, the anchor force is greater than the design bridge cable force when tensioned to the position according to the non-deviation pulling out amount. In order to ensure the safety of the structure, the cable can also be tensioned to the position in three stages according to the design cable force of 70%, 85% and 100%. After each stage of tensioning is completed, the oil pressure of the jack is recorded to convert the cable force, and the vibration fundamental frequency of the cable is collected, which provides a basis for subsequent cable force identification.

[0110] Due to the influence of end boundary conditions, bending stiffness, sag and other factors, there is a complex nonlinear relationship between the frequency and the cable force, part of the equation is a transcendental equation, which needs to be iteratively calculated to solve, and there is great inconvenience in engineering application. Through practice and simulation analysis, it is found that the method of establishing the frequency cable force relationship by calibrating the known cable force through measured frequency can meet the demand of cable tension control accuracy. The embodiment of the application adopts a linear formula to obtain the relationship between the frequency square and the cable force, such as formula (3). The coefficient a in the first half of the formula reflects the cable length, wire mass and other factors; the coefficient b is introduced in the second half to reflect the influence of bending stiffness, boundary conditions and other factors. Where T is the cable force, f n is the n-order frequency of the cable, and the coefficients a and b can be obtained based on linear regression of not less than 3 times of measured frequency and cable force.

[0111]

[0112] For example, the aspect ratio of the 139 type cable is between 291 and 1847, and the aspect ratio of the 151 type cable is between 358 and 2767, both of which are greater than 100, and belong to long cables, and the linear calibration coefficients a and b of the frequency and the cable force of each cable can be obtained based on three-stage tensioning data, as shown in Figure 6 . The correlation coefficient R 2 is shown in Figure 7 . The minimum value of R 2 is 0.9822, and the R 2 of 94% of the cables is between 0.9900 and 1.0000. It can be seen that the frequency square and the cable force show a strong linear correlation. At the same time, it is worth noting that the coefficient b is between -590kN and 373kN, and has a large discreteness between cables of different lengths. For example, the contribution of the coefficient b to the cable force is up to 29% in the first tensioning, and therefore, considering the influence of the coefficient b, the cable force can be obtained more accurately and the error can be reduced.

[0113] To verify the reliability of the calibration formula obtained based on the first tensioning, the deviation distribution between the frequency estimated cable force before tensioning and the anchor nut loosening oil pressure calculated cable force during the second cable adjustment of, for example, 49 cables that need to be adjusted can be compared, as shown in Figure 8 . The maximum deviation is 6%, and the deviation of 90% of the cables is within 5%. It can be seen that the method of linearly calibrating the known cable force through measured frequency can meet the demand of cable force control accuracy.

[0114] 4. Second cable adjustment control

[0115] 4.1 Quadratic programming optimization method

[0116] After the initial tensioning is completed, the cable force is measured, and the deviation distribution of the target cable force before the second constant action is shown in Figure 9For example, 21 out of 78 cables that were tensioned to the position according to the unstressed cable length have a deviation greater than 10%, and the tension control effect is good. 21 out of 34 cables in the high tower side span that were not tensioned according to the unstressed cable length have a deviation greater than 10%, and the deviation rate is higher. The main reasons for the deviation of the cable force controlled according to the unstressed cable length are the manufacturing geometry of the component (such as the positioning accuracy of the anchor box) and the erection deviation of the segment, so after the initial tensioning is completed and the cable force and linear deviation are determined, the cable force needs to be adjusted again. The essence of cable force adjustment is to find a set of cable forces that make the target reflecting the performance of the bridge optimal. The quadratic programming method can be used for the secondary cable force adjustment optimization of the bridge.

[0117] For example, if the objective function of the optimization problem can be converted into a quadratic real function, and the boundary can be converted into a linear constraint, the quadratic programming method can be used to solve it. This method is an important way to solve nonlinear programming problems. The mathematical representation of a general quadratic programming problem is shown in equation (4).

[0118]

[0119] where x is the decision variable, H is the symmetric matrix, f T is a row vector, P is a matrix, B is a column vector, Lb is the lower limit of the decision variable, and Ub is the upper limit of the decision variable.

[0120] Let the total number of cables be n. As shown in equation (6), F t and F0 are the target and current cable force values of all cables, respectively, D = F0-F t is the difference between the current cable force and the target cable force, and Δ is the adjustment amplitude of each cable. As shown in equation (6), C is the overall influence matrix of the cable, the i-th row is the influence value of the tension unit force of each cable on the i-th cable, and the j-th column is the influence value of the tension unit force of the j-th cable on the cable force of each cable. The relationship between the adjustment amplitude and the change of the cable force is established through the influence matrix, as shown in equation (7), and the percentage of the deviation of the adjusted cable force of all cables from the target cable force and the minimum construction target optimization function are calculated.

[0121] F t = [F t1 , …, F ti , …, F tn ] T , F0 = [F 01 , …, F 0i , …, F 0n ] T , Δ = [Δ1, …, Δ i , …, Δ j , …, Δ n ] T (5)

[0122]

[0123]

[0124] Expanding formula (7) as formula (8), since D i is a constant, it can be converted into a standard quadratic formula objective function. The parameter values are shown in formula (9).

[0125]

[0126]

[0127] The loop program is compiled, and [H] and f T can be obtained. The application of Ax≤B in the standard type in the cable adjustment is to set the upper and lower limits of the cable force after the amplitude adjustment Δ. The specific settings of P and B in the quadratic programming algorithm formula can be seen in formula (10). Wherein α is the percentage limit of the deviation of each cable force after the cable adjustment relative to the design cable force, which can be flexibly set according to the needs. For example, α = 10%.

[0128] P = [C; -C], B = [(1 + α)F t -F0; -(1-α)F t +F0] (10)

[0129] Since the influence matrix C is a full rank n order matrix, if all the cables can be adjusted, f(Δ) exists as a unique solution of zero, that is, Δ = C -1 D, there is no need to solve Δ by quadratic programming. In fact, since most of the cable forces have reached the target state after the initial tensioning, only a part of the cable force deviation that does not meet the requirements (the cable to be adjusted, and the cable to be adjusted) and its adjacent cable (the cable to be adjusted) need to be adjusted to realize the secondary cable adjustment. That is, there may be a situation that the number of cables to be adjusted is not consistent with the number of cables to be adjusted, and at this time, the cable adjustment can be completed according to the quadratic programming method. The method of adjusting only the cable to be adjusted based on the overall influence matrix of the cable is to limit the adjustment space of the non-cable to be adjusted in the decision variable. Set the i cable (the i cable) as the non-cable to be adjusted, and set its upper limit to zero in formula (11). Set the j cable (the j cable) as the cable to be adjusted, and release its decision variable adjustment space, as shown in formula 11, Ub j = β, β is a reasonable large value set in combination with the size of the unit force. The lower limit of the decision variable can be set as Lb = -Ub. Although the adjustment space of the non-cable to be adjusted is locked, the objective function can still reflect the influence of the cable adjustment on the cable force of all the cables.

[0130] Ub = [..., Ub i = 0,..., Ub j ,...] T (11)

[0131] The quadratic programming method can be programmed based on, for example, the Lemke method, or can be solved by using mathematical software such as the Matlab optimization toolbox Quadprog() function. The examples of the embodiments of the present application are solved based on the Matlab mathematical software.

[0132] 4.2 Calculation of the adjustment of the cable force

[0133] Based on the quadratic programming method of the embodiments of the present application, a total of, for example, 49 cables, including the cable with a relative deviation of the pre-target cable force greater than, for example, 10% and the individual adjacent cables, are selected for the adjustment of the cable force. In one example, the influence matrix is based on the unit force of 500 kN, and the relative deviation of the upper limit of the cable force of each cable after the initial tensioning is obtained as 4079 kN for the 139-type cable and 3209 kN for the 151-type cable, and the adjustment limit β of the cable force is safely taken as 6.41. The calculation results are shown in Table 1. Figure 10 The adjustment of the cable force is calculated to be between -0.9 and 1.7. The overall deviation of the cable force of the cable after the adjustment is less than 10% relative to the target state, as shown in Table 2. Figure 9

[0134] 4.3 Correction value of the anchor head pull-out amount

[0135] When the adjustment of the cable force is obtained, there are the incremental cable adjustment method, the absolute cable force adjustment method, and the stress-free cable length adjustment method. The absolute cable force adjustment method needs to be strictly performed according to the adjustment sequence corresponding to the adjustment, and it is difficult to meet the parallel operation of multiple tensioning devices, and the efficiency is low. In the medium-span, non-linear cable-stayed bridge, the incremental cable adjustment method can ignore the adjustment sequence, but when the adjustment of the cable is dense, the tensioning force of the adjacent cable influences each other, and multiple tensioning devices should not be tensioned at the same time. The stress-free cable length adjustment method can avoid the shortcomings of the above two methods, meet the requirements of multi-step sequence parallel operation, and only need to control the pull-out amount of the tensioning end on site, and the efficiency of the cable adjustment is obviously improved.

[0136] The stress-free cable length adjustment method is used in the embodiments of the present application, based on formula (1), the change amount ΔS0 of the stress-free cable length caused by the calculation of the adjustment of the cable force can be derived, as shown in formula (12), where "1" represents the pre-adjustment state, "2" represents the post-adjustment state, E, A, and q are known quantities (see formula (1)), and ΔT is the increment of the cable force calculated by the adjustment of the cable force.

[0137]

[0138] ​l0, l, T1 can be obtained by a finite model calculating the overall influence matrix of the cable. The specific steps are as follows: ① Before simulating the stage of tensioning the cable by root, a construction stage is inserted, the measured cable force after the first tensioning is taken as the initial cable force to assign to the corresponding cable element, and the coordinates of the upper and lower anchor points of each cable element are obtained. ② The unit force of the cable element set in the stage of simulating the tensioning of the cable by root is multiplied by the corresponding amplitude, then the cable force increment of the non-adjusted cable is zero, the cable force increment of the adjusted cable corresponds to ΔT, and the calculation is re-executed. ③ The three-dimensional deformation of the adjusted cable before and after the action of ΔT is obtained, which is substituted into the coordinates of the upper and lower anchor points to solve l 01 , l1, l 02 , l2, it should be noted that T1 is not the cable force after the first tensioning, but the cable force calculated in the previous stage before the action of ΔT of the adjusted cable in the model. ④ Substitute the above elements into formula (12) to calculate ΔS0. ⑤ Combined with the cable anchoring structure, check whether the cable is still within the effective anchoring range after the displacement is changed. The distribution of the calculated anchor head displacement and the corresponding relationship with the amplitude are shown in Figure 10 .

[0139] 4.4 Bridge control effect

[0140] After the secondary cable adjustment, the bridge deck paving is carried out, and after the cable force is measured, a plurality of cables with relative deviation not meeting the requirements can still be selected for adjustment according to the same method. The final bridge cable force distribution is shown in Figure 11 . An exemplary result shows that the relative design cable force deviation is all within 10%, the maximum deviation is 9%, the cable force deviation of 30 cables is between 5% and 9%, and the cable force relative deviation of 82 cables is within 5%. The tensioning end displacement distribution of each cable is shown in Figure 12 . It can be seen that the displacement of 70 cables is in the unbiased state, and the displacement of 42 cables deviates, but is within the effective adjustment range of the tensioning end anchoring structure. After the bridge is completed, the structure stress and the main beam elevation meet the design requirements.

[0141] 5 Main advantages

[0142] The embodiments of the present application are aimed at the Chang'an Street West Extension Cross-Yongding River Special-shaped Steel Tower Cable-Stayed Bridge, the tensioning of the cable is controlled by the stress-free state control method, and the stress-free cable length calculation, cable force calibration and secondary cable adjustment method are improved, which at least has the following advantages:

[0143] (1) The calculation of the stress-free cable length of the cable considers the influence of the tower deviation and the lane load pre-camber, which can obtain more accurate stress-free cable length.

[0144] (2) The method of linear calibration of the measured frequency to identify the known cable force can meet the tensioning control requirements of the cable, and the identification accuracy of the cable force is about 5%, and the influence of the linear calibration constant term is fully considered.

[0145] (3) The optimization adjustment model is based on the overall influence matrix of the cable and the quadratic programming method for locking the adjustment space of the non-adjustable cable, which can avoid the cumbersome construction of the influence matrix for the adjustable cable and take into account the influence of the adjustable cable on the force of other cables, and has the advantages of simple implementation and comprehensive analysis.

[0146] (4) The bridge is secondarily adjusted based on the change of the unstressed cable length of the cable, the bridge cable force deviation is about 5%, 65% of the cable anchor head pull-out amount is in the non-deviation state, and the remaining cable anchor head pull-out amount is within the effective adjustment range, and the bridge in the completed state meets the requirements.

[0147] Figure 13 is a schematic diagram of a cable tension control device for a cable-stayed bridge according to an embodiment of the present application. The device can include:

[0148] The control unit 11 is configured to tension each cable to the unstressed cable length based on the anchor head pull-out amount.

[0149] The first determination unit 12 is configured to determine the non-adjustable cable and the adjustable cable based on the cable force deviation of each cable.

[0150] The second determination unit 13 is configured to lock the non-adjustable cable and determine the adjustment amplitude of the adjustable cable based on the overall influence matrix of the cable and the quadratic programming method.

[0151] The third determination unit 14 is configured to adjust the unstressed cable length of the adjustable cable based on the conversion relationship between the adjustment amplitude of the adjustable cable and the anchor head pull-out correction value.

[0152] In a possible implementation, the unstressed cable length is determined based on the tower deviation and the pre-camber.

[0153] In a possible implementation, the formula for the unstressed cable length based on the finite element model of the cable-stayed bridge is:

[0154]

[0155] where S0 is the unstressed cable length between the anchor points, T is the tension cable force, A is the cable area, E is the cable elastic modulus, q is the cable self-weight concentration, l0 is the anchor point distance after structural deformation, and l is the horizontal projection distance of the cable after structural deformation, where l0 is determined based on the tower deviation and the pre-camber.

[0156] 14. The device of claim 13, wherein the formula for l0 is:

[0157] l0 = norm([X c , Y c , Z c ] b + [XHE , Y HE , Z HE ] b + [X D0 , Y D0 , Z D0 ] b - [X c , Y c , Z c ] e - [X HE , Y HE , Z HE ] e - [X D0 , Y D0 , Z D0 ] e

[0158] wherein X, Y, Z identify cable anchorage point coordinates or coordinate correction amounts;

[0159] b identifies the cable head node position;

[0160] e identifies the tail node position;

[0161] c identifies the reference state;

[0162] HE identifies the erection geometry correction amount;

[0163] D0 identifies the cable head and tail node deformation amount under the dead load in the bridge completion state.

[0164] In a possible implementation, the second determining unit is specifically configured to:

[0165] establish the relationship between the amplitude adjustment and the cable force change based on the overall influence matrix of the cable, construct a target function according to the minimum and the percentage of the deviation of the adjusted cable force of each cable relative to the target cable force, and convert the constructed target function into a quadratic formula target function;

[0166] limit the adjustment space of the non-adjusted cable in the decision variable of the quadratic formula target function, and release the adjustment space of the adjusted cable in the decision variable;

[0167] solve the quadratic formula target function to obtain the amplitude adjustment of the adjusted cable.

[0168] In a possible implementation, the quadratic formula is:

[0169]

[0170] wherein x is the decision variable, H is a symmetric matrix, f T is a row vector, P is a matrix, B is a column vector, Lb is the lower limit of the decision variable, and Ub is the upper limit of the decision variable.​

[0171] In a possible implementation, the formula of the quadratic formula objective function f(Δ) is:

[0172]

[0173] Wherein, n is the total number of cables;

[0174] F t , F0 are the target cable force and the current cable force of all cables respectively;

[0175] D = F0-F t , is the difference between the current cable force and the target cable force;

[0176] Δ is the amplitude of each cable;

[0177] C is the cable overall influence matrix, the i-th row of the cable overall influence matrix is the influence value of the unit force of each cable on the i-th cable, and the j-th column is the influence value of the unit force of the j-th cable on each cable.

[0178] In a possible implementation, the parameter relationship of the quadratic formula objective function and the quadratic formula is:

[0179]

[0180] After the action of the amplitude Δ, P and B in the quadratic formula are specifically:

[0181] P = [C; -C], B = [(1+α)F t -F0; -(1-α)F t +F0]

[0182] Wherein, C is the cable overall influence matrix, α is the percentage limit of the deviation of each cable force after the cable adjustment relative to the design cable force; F t , F0 are the target cable force and the current cable force of all cables respectively.

[0183] In a possible implementation, the second determination unit is configured to limit the adjustment space of the non-adjusted cable in the decision variable of the quadratic formula objective function, and release the adjustment space of the adjusted cable in the decision variable, and specifically includes:

[0184] Suppose that the i-th cable is a non-adjusted cable and the j-th cable is an adjusted cable;

[0185] Set the upper limit Ub i of the decision variable corresponding to the i-th cable to zero, and set the upper limit Ub j of the decision variable corresponding to the j-th cable to β, and β is a reasonable large value set in combination with the unit force, and the upper limit of the decision variable is: Ub = [..., Ub i= 0,..., Ub j ,...] T ;

[0186] The lower limit of the decision variable is set as Lb = -Ub.

[0187] In a possible implementation, the third determining unit is specifically configured to:

[0188] determine the cable force increment of the adjusting cable based on the amplitude modulation of the adjusting cable;

[0189] determine the stress-free cable length change amount of the adjusting cable and the anchor head pull-out amount correction value of the adjusting cable based on the cable force increment of the adjusting cable.

[0190] In a possible implementation, the formula of the stress-free cable length change amount ΔS0 is as follows:

[0191]

[0192] wherein S 01 is the stress-free cable length between the anchor points before adjustment, S 02 is the stress-free cable length between the anchor points after adjustment;

[0193] E is the elastic modulus of the cable, A is the cable area, and q is the cable self-weight intensity;

[0194] ΔT is the cable force increment calculated based on the amplitude modulation of the adjusting cable;

[0195] l 01 is the anchor point spacing after structural deformation before adjustment, l 02 is the anchor point spacing after structural deformation after adjustment;

[0196] l1 is the horizontal projection distance of the cable after structural deformation before adjustment, and l2 is the horizontal projection distance of the cable after structural deformation after adjustment; 01 02

[0197] T1 is the cable force of the adjusting cable in the finite element model of the cable-stayed bridge before the action of the respective cable force increment ΔT.

[0198] Each unit or module in the device of each embodiment of the present application can implement the related functions of the above method embodiments, and specific implementation can be referred to the related description of the above method embodiments, which will not be repeated here.

[0199] In a possible implementation, the third determining unit is further configured to calculate the parameters in the formula of the stress-free cable length change amount ΔS0 by adopting the following steps:

[0200] ​​Before simulating the stage of tensioning the cable by root, a construction stage is inserted, the cable force measured after one-time tensioning is taken as the initial cable force of the corresponding cable element, the coordinates of the upper and lower anchor points of each cable element in the finite model of the overall influence matrix of the cable are obtained;

[0201] The unit force set in the stage of simulating the tensioning of the cable by root is multiplied by the corresponding amplitude, then the cable force increment of the non-adjusted cable is zero, the cable force increment of the adjusted cable corresponds to the respective amplitude ΔT, and the calculation is re-executed;

[0202] The three-direction deformation amounts of the anchor points of the adjusted cable before and after the action of the respective amplitude ΔT are obtained, which are substituted into the coordinates of the upper and lower anchor points to solve l 01 , l 02 , l2;

[0203] The above element-by-element is substituted into the formula of ΔS0 to calculate ΔS0.

[0204] The above specific embodiments of the present application are only used to illustrate the technical solutions of the present application, and do not constitute a limitation on the protection scope of the present application. Those skilled in the art should understand that any modifications, combinations, equivalent replacements and improvements made within the spirit and principles of the present application shall be included in the protection scope of the present application.

Claims

1. A method for controlling the tensioning of cables in a cable-stayed bridge, characterized in that, include: Each cable is tensioned to stress-free cable length based on the anchor head pull-out amount; Based on the cable tension deviation of each cable, the non-adjustment cables and the adjustment cables are determined; Based on the overall influence matrix of the cables and the quadratic programming method, the non-adjustment cables are locked, and the adjustment amplitude of the adjustment cables is determined, including: Based on the overall influence matrix of the cables, the relationship between amplitude adjustment and cable force change is established. According to the minimum percentage of the deviation between the adjusted cable force and the target cable force of each cable, an objective function is constructed and then converted into a quadratic formula objective function. The formula for a quadratic form is: ； ； in, As decision variables, It is a symmetric matrix. For row vectors, For a matrix, It is a column vector. As the lower bound of the decision variable, This represents the upper limit of the decision variables; Quadratic formula objective function The formula is: ； in, This refers to the total number of cables; , These represent the target cable force and the current cable force for all cables, respectively. , which is the difference between the current cable force and the target cable force; For the amplitude adjustment of each cable; Let's consider the overall influence matrix of the cable system. The first part of the overall influence matrix of the cable system... The behavior of each cable tension unit force on the first The influence value of the cable force on the root cable, the first Listed as the number The effect of a unit tension force on the cable force of each cable; Limit the adjustment space of non-adjusting factors in the decision variables of the quadratic formula objective function, and release the adjustment space of adjusting factors in the decision variables; Solve the objective function of the quadratic formula to obtain the amplitude adjustment of the adjustment cable; Based on the conversion relationship between the amplitude adjustment of the adjustment cable and the correction value of the anchor head pull-out, the stress-free cable length of the adjustment cable is adjusted.

2. The method according to claim 1, characterized in that, The stress-free cable length is determined based on the tower offset and pre-camber.

3. The method according to claim 2, characterized in that, The formula for the stress-free cable length obtained from the finite element model of a cable-stayed bridge is: ； in, For the length of the stress-free cable between anchor points, For tension cable force, For the cable area, For the elastic modulus of the cable, For the self-weight set degree of the cable, The anchor point spacing after structural deformation. For the cables after structural deformation Horizontal projection distance, where, It is determined based on the tower offset and pre-camber.

4. The method according to claim 3, characterized in that, The The formula is: ； Among them, X, Y, and Z indicate the coordinates of the cable anchorage point or the coordinate correction amount; Identify the position of the first node of the cable; Identify the position of the tail node; Identify the baseline status; Geometric shape correction for signage installation; This indicates the deformation of the cable joints at both ends under dead load in the completed state of the bridge.

5. The method according to claim 1, characterized in that, The relationship between the objective function and the parameters of the quadratic form formula is as follows: ； After amplitude adjustment After the action, the upper and lower limits of the cable force in the quadratic formula are as follows: ; in, The overall influence matrix of the cable system. This represents the percentage limit of the deviation of each cable force from the design cable force after adjustment; , These represent the target cable force and the current cable force for all cables, respectively.

6. The method according to any one of claims 1 to 5, characterized in that, Restricting the adjustment space of non-adjusting factors in the decision variables of the quadratic formula objective function, and releasing the adjustment space of adjusting factors in the decision variables, includes: Let the first The root cable is a non-adjustment cable and the first The root cable is the adjustment cable; The first Upper bound of decision variables corresponding to root Lasso Set it to zero, and set the first... Upper bound of decision variables corresponding to root Lasso , To incorporate the magnitude of unit force, a reasonable maximum value is set, and the upper limit of the decision variable is: ; Set the lower limit of the decision variable to .

7. The method according to claim 1, characterized in that, Based on the conversion relationship between the adjustment amplitude of the adjustment cable and the anchor head pull-out correction value, the stress-free cable length of the adjustment cable is adjusted, including: Based on the amplitude adjustment of the adjusting cable, determine the cable force increment of the adjusting cable; Based on the increase in cable force of the adjustment cable, determine the change in stress-free cable length of the adjustment cable and the correction value for the anchor head pull-out of the adjustment cable.

8. The method according to claim 7, characterized in that, Change in stress-free cable length The formula is: ； in The length of the stress-free cable between the anchor points before adjustment. The length of the stress-free cable between the anchor points after adjustment; For the elastic modulus of the cable, For the cable area, The self-weight of the cable; The cable force increment is calculated based on the amplitude adjustment of the control cable. The anchor point spacing is the distance between the anchor points after structural deformation before adjustment. The spacing between anchor points after structural deformation following adjustment; The cables after structural deformation before adjustment Horizontal projection distance, For the cables after structural deformation following adjustment Horizontal projection distance; In the finite element model of a cable-stayed bridge, the adjustment cables are at their respective cable force increments. The cable force calculated in the previous stage.

9. The method according to claim 8, characterized in that, Change in stress-free cable length The calculation steps for the parameters in the formula include: Before simulating the tensioning of each cable, a construction stage is inserted. The cable force measured after one tensioning is used as the initial cable force and assigned to the corresponding cable unit. The coordinates of the upper and lower anchor points of each cable in the finite model of the overall influence matrix of the cable are obtained. Multiplying the unit force set in the simulated cable tensioning stage by the corresponding amplitude results in zero cable force increment for non-tensioned cables and the cable force increment for tensioned cables corresponding to their respective amplitudes. Recalculate; Obtain the amplitude of the adjustment of the adjustment line in their respective positions. Substitute the three-dimensional deformation of the anchor points before and after the action into the coordinates of the upper and lower anchor points, and solve. , , , .

10. A cable tensioning control device for a cable-stayed bridge, characterized in that, include: Control unit, used to tension each cable to stress-free cable length based on the anchor head pull-out amount; The first determining unit is used to determine the non-adjusting cable and the adjusting cable based on the cable force deviation of each cable; The second determining unit is used to lock the non-adjustment cable based on the overall influence matrix of the cable and the quadratic programming method, and to determine the adjustment amplitude of the adjustment cable; The second determining unit is specifically used for: Based on the overall influence matrix of the cables, the relationship between amplitude adjustment and cable force change is established. According to the minimum percentage of the deviation between the adjusted cable force and the target cable force of each cable, an objective function is constructed and then converted into a quadratic formula objective function. Limit the adjustment space of non-adjusting factors in the decision variables of the quadratic formula objective function, and release the adjustment space of adjusting factors in the decision variables; Solving the quadratic form objective function yields the amplitude adjustment of the adjustment cable; The formula for a quadratic form is: ； ； in As decision variables, It is a symmetric matrix. For row vectors, For a matrix, It is a column vector. As the lower bound of the decision variable, This represents the upper limit of the decision variables; Quadratic formula objective function The formula is: ； in, This refers to the total number of cables; , These represent the target cable force and the current cable force for all cables, respectively. , which is the difference between the current cable force and the target cable force; For the amplitude adjustment of each cable; Let's consider the overall influence matrix of the cable system. The first part of the overall influence matrix of the cable system... The behavior of each cable tension unit force on the first The influence value of the cable force on the root cable, the first Listed as the number The effect of a unit tension force on the cable force of each cable; The third determining unit is used to adjust the stress-free cable length of the adjusting cable based on the conversion relationship between the amplitude adjustment of the adjusting cable and the correction value of the anchor head pull-out amount.

11. The apparatus according to claim 10, characterized in that, The stress-free cable length is determined based on the tower offset and pre-camber.

12. The apparatus according to claim 11, characterized in that, The formula for the stress-free cable length obtained from the finite element model of a cable-stayed bridge is: ； in, For the length of the stress-free cable between anchor points, For tension cable force, For the cable area, For the elastic modulus of the cable, For the self-weight set degree of the cable, The anchor point spacing after structural deformation. For the cables after structural deformation Horizontal projection distance, where, It is determined based on the tower offset and pre-camber.

13. The apparatus according to claim 12, characterized in that, The The formula is: ； Among them, X, Y, and Z indicate the coordinates of the cable anchorage point or the coordinate correction amount; Identify the position of the first node of the cable; Identify the position of the tail node; Identify the baseline status; Geometric shape correction for signage installation; This indicates the deformation of the cable joints at both ends under dead load in the completed state of the bridge.

14. The apparatus according to claim 10, characterized in that, The relationship between the objective function and the parameters of the quadratic form formula is as follows: ； After amplitude adjustment After the action, the upper and lower limits of the cable force in the quadratic formula are as follows: ； in, The overall influence matrix of the cable system. This represents the percentage limit of the deviation of each cable force from the design cable force after adjustment; , These represent the target cable force and the current cable force for all cables, respectively.

15. The apparatus according to claim 10, characterized in that, The second determining unit is used to restrict the adjustment space of non-adjusting factors in the decision variables of the quadratic formula objective function, and to release the adjustment space of adjusting factors in the decision variables. Specifically, it includes: Let the first The root cable is a non-adjustment cable and the first The root cable is the adjustment cable; The first Upper bound of decision variables corresponding to root Lasso Set it to zero, and set the first... Upper bound of decision variables corresponding to root Lasso , To incorporate the magnitude of unit force, a reasonable maximum value is set, and the upper limit of the decision variable is: ; Set the lower limit of the decision variable to .

16. The apparatus according to any one of claims 10 to 15, characterized in that, The third determining unit is specifically used for: Based on the amplitude adjustment of the adjusting cable, determine the cable force increment of the adjusting cable; Based on the increase in cable force of the adjustment cable, determine the change in stress-free cable length of the adjustment cable and the correction value for the anchor head pull-out of the adjustment cable.

17. The apparatus according to claim 16, characterized in that, Change in stress-free cable length The formula is: ； in The length of the stress-free cable between the anchor points before adjustment. The length of the stress-free cable between the anchor points after adjustment; For the elastic modulus of the cable, For the cable area, The self-weight of the cable; The cable force increment is calculated based on the amplitude adjustment of the control cable. The anchor point spacing is the distance between the anchor points after structural deformation before adjustment. The spacing between anchor points after structural deformation following adjustment; The cables after structural deformation before adjustment Horizontal projection distance, For the cables after structural deformation following adjustment Horizontal projection distance; In the finite element model of a cable-stayed bridge, the adjustment cables are at their respective cable force increments. The cable force calculated in the previous stage.

18. The apparatus according to claim 17, characterized in that, The third determining unit is further configured to employ the following steps Calculate the change in length of the stress-free cable Parameters in the formula: Before simulating the tensioning of each cable, a construction stage is inserted. The cable force measured after one tensioning is used as the initial cable force and assigned to the corresponding cable unit. The coordinates of the upper and lower anchor points of each cable in the finite model of the overall influence matrix of the cable are obtained. Multiplying the unit force set in the simulated cable tensioning stage by the corresponding amplitude results in zero cable force increment for non-tensioned cables and the cable force increment for tensioned cables corresponding to their respective amplitudes. Recalculate; Obtain the amplitude of the adjustment of the adjustment line in their respective positions. Substitute the three-dimensional deformation of the anchor points before and after the action into the coordinates of the upper and lower anchor points, and solve. , , , .

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