Method for calculating longitudinal anti-thrust stiffness of multi-tower cable-stayed bridge

Abstract

The invention provides a multi-tower cable-stayed bridge longitudinal anti-thrust stiffness calculation method, and belongs to the technical field of multi-tower cable-stayed bridges, and the method comprises the following steps: disassembling a multi-tower cable-stayed bridge system to obtain multiple groups of cable-tower systems and cable-beam systems; constructing a first series-parallel connection system corresponding to the cable-tower system and a second series-parallel connection system corresponding to the cable-beam system; the method comprises the following steps: acquiring first rigidity of each component corresponding to each tower in a multi-tower cable-stayed bridge system under different longitudinal applied forces, and meanwhile, respectively constructing an equivalent cable surface of the corresponding tower under each longitudinal applied force; and all the first rigidities and the equivalent cable surfaces of the corresponding towers under the same longitudinal applied force are fused with the corresponding first series-parallel system and the second series-parallel system, and the longitudinal rigidities of the corresponding towers are obtained in combination with historical errors. Therefore, the accuracy of rigidity calculation is ensured, and the reasonable optimization of the structure is realized.

Description

Technical Field

[0001] The present invention relates to the technical field of multi-tower cable-stayed bridges, and particularly relates to a calculation method for the longitudinal anti-pushing stiffness of a multi-tower cable-stayed bridge. Background Art

[0002] A cable-stayed bridge, also known as a cable-stretched bridge, is a bridge in which the main girder is directly pulled on the bridge tower by many stay cables, and is a structural system composed of a pressurized tower, a tensioned cable, and a beam body that bears bending. Among them, one of the key design contents of a multi-tower cable-stayed bridge is to provide sufficient bridge stiffness to ensure traffic safety.

[0003] Common bridge stiffness is achieved by using the structural force transmission method. However, in the calculation process, it is necessary to perform a force analysis on each structural component in the system, which undoubtedly increases the calculation amount, and only the current force situation is considered during the calculation process, resulting in a reduction in calculation accuracy.

[0004] Therefore, the present invention proposes a calculation method for the longitudinal anti-pushing stiffness of a multi-tower cable-stayed bridge. Summary of the Invention

[0005] The present invention provides a calculation method for the longitudinal anti-pushing stiffness of a multi-tower cable-stayed bridge, which is used to effectively reduce the calculation amount of force analysis by constructing a series-parallel system for the cable-tower and cable-beam for structural equivalent replacement, and then through the fusion processing of stiffness and the system, and combining the historical stiffness reference error, to ensure the accuracy of stiffness calculation, and further realize the reasonable optimization of the structure.

[0006] The present invention provides a calculation method for the longitudinal anti-pushing stiffness of a multi-tower cable-stayed bridge, including:

[0007] Step 1: Disassemble the multi-tower cable-stayed bridge system to obtain multiple groups of cable-tower systems and cable-beam systems;

[0008] Step 2: Construct a first series-parallel system corresponding to the cable-tower system and a second series-parallel system corresponding to the cable-beam system;

[0009] Step 3: Obtain the first stiffness of each component corresponding to each tower in the multi-tower cable-stayed bridge system under different longitudinal applied forces. At the same time, respectively construct an equivalent cable plane for each tower under each longitudinal applied force;

[0010] Step 4: Perform fusion processing on all the first stiffness and the equivalent cable plane corresponding to the same longitudinal applied force of the corresponding tower with the corresponding first series system and the second series-parallel system, and combine the historical error to obtain the longitudinal stiffness of the corresponding tower, and optimize the structure of the multi-tower cable-stayed bridge system.

[0011] Preferably, before disassembling the multi-tower cable-stayed bridge system, it includes:

[0012] Obtain the structural diagram of the multi-tower cable-stayed bridge system, and determine the number of towers N existing in the structural diagram;

[0013] Disassemble the multi-tower cable-stayed bridge system according to the number of towers N, where N≥3.

[0014] Preferably, construct a first series-parallel system corresponding to the cable-tower system and a second series-parallel system corresponding to the cable-girder system, including:

[0015] Lock the i-th tower, the cable-tower system for the i-th tower, and the cable-girder system for the i-th tower;

[0016] Based on the spring equivalence principle, perform line conversion on the cable-tower system of the i-th tower and the cable-girder system of the i-th tower to obtain the corresponding first series-parallel system and second series-parallel system.

[0017] Preferably, fuse all the first stiffnesses and the equivalent cable planes under the same longitudinal applied force for the corresponding tower with the corresponding first series system and second series-parallel system, and combine the historical errors to obtain the longitudinal stiffness of the corresponding tower, including:

[0018] According to the obtained first stiffness and equivalent cable plane, perform numerical calibration on the first series system and the second series system corresponding to the tower in sequence;

[0019] Respectively obtain the first actual deformation structure diagram of the corresponding cable-tower system under the corresponding longitudinal applied force, and the second actual deformation structure diagram of the corresponding cable-girder system under the corresponding longitudinal applied force;

[0020] Based on the numerical calibration results and the errors obtained from the first actual deformation structure diagram, the second actual deformation structure diagram, and the deformation variable set under different longitudinal applied forces, obtain the longitudinal stiffness of the corresponding tower under the corresponding longitudinal applied force.

[0021] Preferably, obtain the first actual deformation structure diagram of the corresponding cable-tower system under the corresponding longitudinal applied force, including:

[0022] Respectively obtain from the historical database the process diagrams of the built towers that are the same as the corresponding tower under the longitudinal applied force, where the process diagrams are the diagrams at different application time points of the corresponding tower under the longitudinal applied force;

[0023] Perform global processing and local processing on each process diagram to obtain the corresponding first diagram and second diagram;

[0024] Align the key points of each first diagram and second diagram respectively according to the application process of the longitudinal applied force, and draw the first deformation trajectory diagram and the second deformation trajectory diagram of the corresponding tower;

[0025] Overlay the first deformation trajectory map and the second deformation trajectory map, and lock the first variation trajectory based on the first deformation trajectory map and the second variation trajectory based on the second deformation trajectory map;

[0026] Construct a first distribution function based on the first variation trajectory and a second distribution function based on the second variation trajectory, and combine the tower attributes, service life, and maintenance information of the built tower to determine the set of sway amplitudes under the longitudinal applied force of the built tower, and determine the end trajectory of each first abnormal trajectory at the corresponding applied time point;

[0027] Perform a first capture on the number of images in the first figure in a continuously stable state, and at the same time, perform a second capture on the number of images in the second figure in a continuously stable state;

[0028] Based on the first capture result and the second capture result, determine the number screening boundary for the first figure that satisfies the continuously stable state;

[0029] Align the number screening boundary with the applied time point, and lock the third figure in the first figure;

[0030] When the number of the third figure is 1, regard the third figure as the fourth figure;

[0031] When the number of the third figure is not 1, randomly select one from all the third figures as the fourth figure;

[0032] Obtain the end trajectory based on the fourth figure from all the end trajectories and apply it to the fourth figure to obtain the first actual deformation structure diagram of the corresponding tower.

[0033] Preferably, determining the number screening boundary for the first figure that satisfies the continuously stable state includes:

[0034] Based on the first capture result and the second capture result, construct a first number distribution for the first figure and a second number distribution for the second figure, where the number distribution includes the number of images before the applied force reaches the stable state, the number of images in the continuously stable state, and the number of images after the stable state until the applied force ends;

[0035] Align the first number distribution and the second number distribution according to the applied time point, and determine whether there is an intersection area in the continuously stable state. If so, regard the two side boundaries of the intersection area as the number screening boundary;

[0036] Otherwise, obtain the union area of the first number distribution and the second number distribution in the stable state and the interval area depending on the union area, and combine the number of images in the continuously stable state in the first number distribution to calculate the left value and the right value;

[0037]

[0038] Among them, N b represents the number of images in the union area; N Jg represents the number of images in the interval area; max represents the maximum symbol; min represents the minimum symbol; N 01 represents the number of images before the force is applied to the stable state in the first quantity distribution; Z z represents the corresponding left value; Z y represents the corresponding right value; represents the floor symbol;

[0039] According to the left value and the right value, a quantity screening boundary is obtained.

[0040] Preferably, obtaining the longitudinal stiffness of the corresponding tower under the corresponding longitudinal applied force includes:

[0041] Based on the numerical calibration result, obtaining the initial stiffness of the corresponding tower under the corresponding longitudinal applied force;

[0042] Comparing the first deformation values of each first sub-component involved in the first actual deformation structure diagram and the second actual deformation structure diagram with the standard deformation values of the same sub-component under the corresponding longitudinal applied force respectively, and constructing a deformation array;

[0043] Based on the deformation array, determining the first stiffness error ε1;

[0044] ε1 = |r1 j1 - r0 j1 | min + S1

[0045]

[0046] Among them, m1 represents the number of comparison results existing in the deformation array; r1 j1 represents the first deformation value based on the j1-th comparison result; r0 j1 represents the standard deformation value based on the j1-th comparison result; represents all r1 j1 - r0 j1 where r1 j1 - r0 j1 ≥ 0; represents all r1 j1 - r0 j1 where r1 j1 - r0 j1 < 0; represents based on r1 j1 - r0 j1Deformation weight ≥ 0; Indicates based on r1 j1 -r0 j1 Deformation weight < 0; Indicates all |r1 j1 -r0 j1 | variance; S1 represents an additional error function based on the deformation array; |r1 j1 -r0 j1 | min Indicates all |r1 j1 -r0 j1 | minimum value;

[0047] Based on the set of deformation variables under different longitudinal applied forces, determine the second stiffness error ε2;

[0048] ε2 = |W(L j2 ,R j2 ,S j2 ) - B0 j2 | min +S2

[0049]

[0050] Among them, Indicates based on all |W(L j2 ,R j2 ,S j2 ) - B0 j2 | variance; W(L j2 ,R j2 ,S j2 ) represents the variable function of the line change length L j2 in the set of deformation variables based on the i2th longitudinal applied force R j2 , line change area S j2 ; B0 j2 represents the standard variable function based on the i2th longitudinal applied force R j2 ; ln represents the natural logarithm function symbol; S2 represents an additional error function based on the set of deformation variables; W(L j2 ,R j2 ,S j2 ) - B0 j2 | min Indicates all |W(L j2 ,R j2 ,S j2 ) - B0 j2 | minimum value;

[0051] Dependent on the first stiffness error and the second stiffness error, and combining the dependence relationship between the first stiffness error and the second stiffness error, adjust the initial stiffness to obtain the longitudinal stiffness.

[0052] Preferably, adjusting the initial stiffness to obtain the longitudinal stiffness includes:

[0053]

[0054] wherein, Δ represents a sign variable; C0 represents the initial stiffness; and Gd represents the longitudinal stiffness.

[0055] Compared with the prior art, the beneficial effects of the present application are as follows:

[0056] By constructing a series-parallel system for the cable-tower and cable-girder for structural equivalent replacement, the computational amount of force analysis is effectively reduced. Subsequently, through the fusion processing of stiffness and the system, and combined with the historical stiffness reference error, the accuracy of stiffness calculation is ensured, thereby realizing the reasonable optimization of the structure.

[0057] Other features and advantages of the present invention will be described in the subsequent description, and part of them will become obvious from the description, or be understood by implementing the present invention. The objectives and other advantages of the present invention can be achieved and obtained through the structures specifically pointed out in the written description and the accompanying drawings.

[0058] The technical solutions of the present invention will be further described in detail below with reference to the accompanying drawings and embodiments. Description of the Drawings

[0059] The drawings are used to provide a further understanding of the present invention, and constitute a part of the description. They are used together with the embodiments of the present invention to explain the present invention, and do not constitute a limitation to the present invention. In the drawings:

[0060] Figure 1 is a flowchart of a method for calculating the longitudinal anti-pushing stiffness of a multi-tower cable-stayed bridge in an embodiment of the present invention;

[0061] Figure 2 is a schematic diagram of the system of a multi-tower cable-stayed bridge in an embodiment of the present invention;

[0062] Figure 3 is a schematic diagram of the first series-parallel system of the cable-tower system in an embodiment of the present invention;

[0063] Figure 4 is a schematic diagram of the second series-parallel system of the cable-girder system in an embodiment of the present invention;

[0064] Figure 5 is a simplified schematic diagram of the cable plane calculation of the stay cables in an embodiment of the present invention;

[0065] Figure 6 is a structural diagram related to the intersection area in an embodiment of the present invention. Detailed Embodiments

[0066] The preferred embodiments of the present invention will be described below in conjunction with the accompanying drawings. It should be understood that the preferred embodiments described herein are only for the purpose of illustrating and explaining the present invention, and are not intended to limit the present invention.

[0067] The present invention provides a method for calculating the longitudinal anti-pushing stiffness of a multi-tower cable-stayed bridge, as Figure 1 shown, including:

[0068] Step 1: Disassemble the multi-tower cable-stayed bridge system to obtain multiple groups of cable-tower systems and cable-girder systems;

[0069] Step 2: Construct a first series-parallel system corresponding to the cable-tower system and a second series-parallel system corresponding to the cable-girder system;

[0070] Step 3: Obtain the first stiffness of each component corresponding to each tower in the multi-tower cable-stayed bridge system under different longitudinal applied forces. At the same time, construct an equivalent cable plane for each tower under each longitudinal applied force;

[0071] Step 4: Fuse all the first stiffnesses and the equivalent cable planes corresponding to the same longitudinal applied force of the corresponding tower with the corresponding first series system and the second series-parallel system to obtain the longitudinal stiffness of the corresponding tower, and perform structural optimization on the multi-tower cable-stayed bridge system.

[0072] Preferably, the method further includes: before disassembling the multi-tower cable-stayed bridge system, including:

[0073] Obtain the structure diagram of the multi-tower cable-stayed bridge system and determine the number of towers N existing in the structure diagram;

[0074] Disassemble the multi-tower cable-stayed bridge system according to the number of towers N, where N≥3.

[0075] In this embodiment, as Figure 2 shown, K t,i (i = 1, 2, 3) is the longitudinal flexural stiffness of the i-th tower, K b,i(i+1) (i = 0, 1, 2, 3) is the vertical flexural stiffness of the girder of the i-th span, K c,i,l (i = 1, 2, 3) is the longitudinal stiffness of the left cable-stayed cable of the i-th tower, K c,i,r (i = 1, 2, 3) is the longitudinal stiffness of the right cable-stayed cable of the i-th tower. The vertical stiffness of the cable-stayed cable is represented by K c,i,l,v (i = 1, 2, 3) and K c,i,r,v (i = 1, 2, 3).

[0076] As Figure 3As shown in the figure, for the cable-tower system, when a longitudinal force f is applied to the top of the i-th bridge tower, the longitudinal deformations of the i-th tower, the cable on the left side of the i-th tower, and the cable on the right side of the i-th tower are the same, forming a parallel system. At the same time, the cable on the right side of the (i - 1)-th tower pulls the (i - 1)-th tower and the cable on the left side of the (i - 1)-th tower, and the cable on the left side of the (i + 1)-th tower pulls the (i + 1)-th tower and the cable on the right side of the (i + 1)-th tower to deform.

[0077] As Figure 4 shown in the figure, for the cable-beam system, when a longitudinal force f is applied to the top of the i-th bridge tower, under the action of the cable force of the cable on the left side of the i-th tower, the cable force of the cable on the right side of the (i - 1)-th tower decreases, and the i-th span beam resists vertical bending. It can be regarded as the vertical stiffness springs of the cable on the right side of the (i - 1)-th tower and the (i - 1)-th span beam being "connected in parallel", and then being "connected in series" with the vertical stiffness spring of the cable on the left side of the i-th tower. Similarly, under the action of the cable force of the cable on the right side of the i-th tower, the cable on the left side of the (i + 1)-th tower is in tension, and the (i + 1)-th span beam resists vertical bending, also forming a similar vertical stiffness spring "series-parallel" system.

[0078] In this embodiment, the structural systems of the left and right spans of the loading tower (taking the i-th tower as an example) remain unchanged, that is, the cable planes of the right side of the (i - 1)-th tower, the left and right cable planes of the i-th tower, and the left cable plane of the (i + 1)-th tower, and the cable arrangements of these four cable planes remain unchanged.

[0079] For the stay cables of other cable planes, simplify them. Combine two or several stay cables and "merge" them into an equivalent stay cable. The cross-sectional area of the equivalent stay cable is the same as the area of several stay cables before merging. The spatial position relationship of the equivalent stay cable is only approximated preliminarily here, and it is considered that its position on the beam is the midpoint of the positions of several stay cables on the beam before equivalence.

[0080] During the simplification process, the number of stay cables in each cable plane of the cable-stayed bridge is simplified to: 1, 1…1, 1, n, n, n, n, 1, 1…1, 1, as specifically Figure 5 shown in the figure.

[0081] In this embodiment, the fusion process is to establish a connection between the corresponding data and the relevant lines on the system to facilitate the platform for calculation.

[0082] In this embodiment, the structural optimization can refer to adding bridge piers, increasing the number of cable ropes, etc. to the multi-tower cable-stayed bridge system.

[0083] The beneficial effects of the above technical solutions are as follows: By constructing a series-parallel system for the cable-tower and cable-beam for structural equivalent replacement, the computational amount of force analysis is effectively reduced. And subsequently, through the fusion process of stiffness and the system, and combined with the historical stiffness reference error, the accuracy of stiffness calculation is ensured, thereby realizing the reasonable optimization of the structure.

[0084] The present invention provides a method for calculating the longitudinal anti-pushing stiffness of a multi-tower cable-stayed bridge, which constructs a first series-parallel system corresponding to the cable-tower system and a second series-parallel system corresponding to the cable-girder system, including:

[0085] Lock the i-th tower, the cable-tower system for the i-th tower, and the cable-girder system for the i-th tower;

[0086] Based on the spring equivalent principle, perform line conversion on the cable-tower system of the i-th tower and the cable-girder system of the i-th tower to obtain the corresponding first series-parallel system and second series-parallel system.

[0087] In this embodiment, for the specific line conversion, refer to Figure 3 and Figure 4 .

[0088] The beneficial effect of the above technical solution is that by converting the tower into cable-tower and cable-girder, it is convenient for subsequent reasonable calculation of stiffness.

[0089] The present invention provides a method for calculating the longitudinal anti-pushing stiffness of a multi-tower cable-stayed bridge, which fuses all the first stiffnesses under the same longitudinal applied force of the corresponding tower, the equivalent cable plane, the corresponding first series system, and the second series-parallel system, and combines the historical error to obtain the longitudinal stiffness of the corresponding tower, including:

[0090] According to the obtained first stiffness and equivalent cable plane, perform numerical calibration on the first series system and the second series system corresponding to the tower in sequence;

[0091] Respectively obtain the first actual deformation structure diagram of the corresponding cable-tower system under the corresponding longitudinal applied force, and the second actual deformation structure diagram of the corresponding cable-girder system under the corresponding longitudinal applied force;

[0092] Based on the numerical calibration result and the error obtained based on the first actual deformation structure diagram, the second actual deformation structure diagram, and the deformation variable set under different longitudinal applied forces, obtain the longitudinal stiffness of the corresponding tower under the corresponding longitudinal applied force.

[0093] In this embodiment, the obtained first actual deformation structure diagram and the second actual deformation structure diagram are obtained from the historical database as a reference for the deformation conditions of the structure that is exactly the same as the original set structure of the cable-tower system under different longitudinal applied forces. Therefore, the corresponding deformation structure diagram can be obtained and used as a reference error.

[0094] In this embodiment, the deformation variable set is for the overall multi-tower cable-stayed bridge system.

[0095] In this embodiment, the error refers to the error for the deformation structure diagram and the error for the deformation variable set.

[0096] The beneficial effects of the above technical solution are as follows: By performing numerical calibration, it is convenient to achieve the preliminary calculation of stiffness, and subsequently, by combining the errors in the deformation structure diagram and the deformation variable set, the adjustment of stiffness is comprehensively realized to ensure the accuracy of the calculation.

[0097] The present invention provides a method for calculating the longitudinal anti-pushing stiffness of a multi-tower cable-stayed bridge, which obtains the first actual deformation structure diagram of the corresponding cable-tower system under the corresponding longitudinal applied force, including:

[0098] Respectively obtain the process diagrams of the built towers corresponding to the towers taken from the historical database under the longitudinal applied force, where the process diagrams are diagrams of the corresponding towers at different applied time points under the longitudinal applied force;

[0099] Perform global processing and local processing on each process diagram to obtain the corresponding first diagram and second diagram;

[0100] Align the key points of each first diagram and second diagram according to the application process of the longitudinal applied force, and draw the first deformation trajectory diagram and the second deformation trajectory diagram of the corresponding tower;

[0101] Overlap the first deformation trajectory diagram and the second deformation trajectory diagram, and lock the first variant trajectory based on the first deformation trajectory diagram and the second variant trajectory based on the second deformation trajectory diagram;

[0102] Construct a first distribution function based on the first variant trajectory and a second distribution function based on the second variant trajectory, and combine the tower attributes, service life, and maintenance information of the built tower to determine the set of sway amplitudes of the built tower under the longitudinal applied force, and determine the end trajectory of each first variant trajectory at the corresponding applied time point;

[0103] Perform a first capture on the number of images in the first diagram that are in a continuously stable state, and at the same time, perform a second capture on the number of images in the second diagram that are in a continuously stable state;

[0104] Based on the first capture result and the second capture result, determine the number screening boundary for the number of images in the first diagram that satisfy the continuously stable state;

[0105] Align the number screening boundary with the applied time point for alignment processing, and lock the third diagram in the first diagram;

[0106] When the number of the third diagram is 1, regard the third diagram as the fourth diagram;

[0107] When the number of the third diagram is not 1, randomly select one from all the third diagrams as the fourth diagram;

[0108] Obtain the end trajectory based on the fourth figure from all the end trajectories and apply it to the fourth figure to obtain the first actual deformation structure diagram of the corresponding tower.

[0109] In this embodiment, the historical database contains the actual deformation diagrams of towers with different structures under different longitudinal applied forces, that is, it includes the process from applying force to the tower to removing the force from the tower. Therefore, those with the same structure can be selected as references for error calculation.

[0110] In this embodiment, global processing refers to performing overall image processing on the image, and local processing refers to performing image processing on the key points in the image, and the key points can be the points at the joints of each component.

[0111] In this embodiment, alignment processing refers to the alignment of the points at the joints, and then the deformation trajectory situation during the process of applying force can be obtained.

[0112] In this embodiment, overlapping processing refers to overlapping the images through image processing in both global and local aspects, effectively ensuring the abnormalities existing in the captured images, and thus facilitating the obtaining of errors.

[0113] In this embodiment, for example, there are trajectory 1, trajectory 2, and trajectory 3 in the first deformation trajectory diagram, and there are trajectory a, trajectory b, and trajectory c in the second deformation trajectory diagram. At this time, trajectory 1 overlaps with trajectory a, trajectory 3 overlaps with trajectory c, and trajectory 2 does not overlap with trajectory b. At this time, the first variant trajectory based on the first deformation trajectory diagram is trajectory 2, and the second variant trajectory based on the second deformation trajectory diagram is trajectory b.

[0114] In this embodiment, the first distribution function = F1(first variant trajectory), the second distribution function = F2(second variant trajectory), and the tower attributes are obtained by matching based on the tower-attribute comparison table. The attributes are related to the materials used for the tower. This table contains the models of the built towers and the materials matching the models, and the models are unique.

[0115] In this embodiment, by inputting the distribution function, tower attributes, service life, and maintenance information into the sway analysis model, the sway amplitude set of the corresponding built tower is obtained. The sway analysis model is trained for the neural network model with different combinations of distribution functions, tower attributes, service life, and maintenance information and the corresponding sway amplitude sets as samples. The sway amplitude sets in the samples are collected and include the sway amplitudes of different cable surfaces.

[0116] In this embodiment, select the cables in the sway amplitude set whose appearance sequence numbers are the same as those of the first mutant trajectory, and use the corresponding sway amplitude trajectory as the end trajectory of the first mutant trajectory. For example, if the appearance sequence number is 2, then select the second trajectory with sway in the sway amplitude set.

[0117] In this embodiment, since the longitudinal applied force is a process, in this process, in order to analyze reasonably, a continuous stage is generally carried out after the applied force is relatively stable. At this time, this continuous stage is regarded as a continuous stable state, and then the number of images is captured. Among them, the application time points can be achieved at an interval of 1 s.

[0118] In this embodiment, the acquisition principle of the second actual deformation structure diagram is similar to that of the first actual deformation structure diagram, which will not be elaborated here.

[0119] The beneficial effects of the above technical solution are as follows: by obtaining the process diagram of the built tower under the longitudinal applied force and performing global and local processing on the diagram to ensure the rationality of determining the variation trajectory subsequently, and further through the distribution function, and combining the relevant information of the tower to obtain the end trajectory at different time points, which provides convenience for the subsequent adjustment of the fourth diagram, and by capturing the number of images in the continuous stable state, effectively screening out the required diagrams, ensuring the authenticity of obtaining the actual deformation structure of the tower, and providing a basis for ensuring the accuracy of the stiffness calculation.

[0120] The present invention provides a method for calculating the longitudinal anti-pushing stiffness of a multi-tower cable-stayed bridge, which determines the quantity screening boundary satisfying the continuous stable state in the first diagram, including:

[0121] Based on the first capture result and the second capture result, construct the first quantity distribution for the first diagram and the second quantity distribution for the second diagram. Among them, the quantity distribution includes the number of images from the start of the applied force to before the stable state, the number of images in the continuous stable state, and the number of images from after the stable state to the end of the applied force;

[0122] Align the first quantity distribution and the second quantity distribution according to the application time points, and determine whether there is an intersection area in the continuous stable state. If so, regard the two side boundaries of the intersection area as the quantity screening boundary;

[0123] Otherwise, obtain the union area of the first quantity distribution and the second quantity distribution in the stable state and the interval area depending on the union area, and combine the number of images in the continuous stable state in the first quantity distribution to calculate the left value and the right value;

[0124]

[0125] Among them, N b represents the number of images in the union area; N Jg represents the number of images in the interval area; max represents the maximum symbol; min represents the minimum symbol; N 01 represents the number of images from the start of the applied force to before the stable state in the first quantity distribution; Zz Indicates the corresponding left value; Z y Indicates the corresponding right value; Indicates the floor symbol;

[0126] Based on the left value and the right value, obtain the quantity screening boundary.

[0127] As Figure 6 Shown in the figure, for the first figure: the number of images before starting to apply force to the stable state is 3, the number of images in the continuous stable state is 4, and the number of images after the stable state until the end of applying force is 2;

[0128] For the second figure: the number of images before starting to apply force to the stable state is 4, the number of images in the continuous stable state is 2, and the number of images after the stable state until the end of applying force is 3, and the unit size corresponding to each quantity is the same.

[0129] In this embodiment, the interval region refers to the non-connected region between the region in the stable state in the first capture result and the region in the stable state in the second capture result.

[0130] The beneficial effect of the above technical solution is: by arranging the capture structures, the boundary calculation is carried out in different ways, and the acquisition of the fourth figure is effectively realized.

[0131] The present invention provides a method for calculating the longitudinal anti-pushing stiffness of a multi-tower cable-stayed bridge, to obtain the longitudinal stiffness of the corresponding tower under the corresponding longitudinal applied force, including:

[0132] Based on the numerical calibration result, obtain the initial stiffness of the corresponding tower under the corresponding longitudinal applied force;

[0133] Compare the first deformation values of each first sub-component involved in the first actual deformation structure diagram and the second actual deformation structure diagram with the standard deformation values of the same sub-component under the corresponding longitudinal applied force respectively, and construct a deformation array;

[0134] Based on the deformation array, determine the first stiffness error ε1;

[0135] ε1 = |r1 j1 - r0 j1 | min + S1

[0136]

[0137] Wherein, m1 represents the number of comparison results existing in the deformation array; r1 j1 represents the first deformation value based on the j1-th comparison result; r0 j1 represents the standard deformation value based on the j1-th comparison result; Denote all r1 j1 -r0 j1 in r1 j1 -r0 j1 ≥0; Denote all r1 j1 -r0 j1 in r1 j1 -r0 j1 <0; Denote the deformation weight based on r1 j1 -r0 j1 ≥0; Denote the deformation weight based on r1 j1 -r0 j1 <0; Denote the variance of all |r1 j1 -r0 j1 |; S1 denotes the additional error function based on the deformation array; |r1 j1 -r0 j1 | min Denote the minimum value of all |r1 j1 -r0 j1 |;

[0138] Determine the second stiffness error ε2 based on the set of deformation variables under different longitudinal applied forces;

[0139] ε2 = |W(L j2 ,R j2 ,S j2 ) - B0 j2 | min + S2

[0140]

[0141] where, Denote the variance of all |W(L j2 ,R j2 ,S j2 ) - B0 j2 |; W(L j2 ,R j2 ,S j2 ) denotes the variable function of the line change length L j2 in the set of deformation variables based on the i2th longitudinal applied force R j2 and the line change area S j2 ; B0 j2 denotes the standard variable function based on the i2th longitudinal applied force R j2 ; ln denotes the logarithmic function symbol; S2 denotes the additional error function based on the set of deformation variables; W(L j2 ,R j2,S j2 )-B0 j2 | min Represents all |W(L j2 ,R j2 ,S j2 )-B0 j2 The minimum value in |;

[0142] Depending on the first stiffness error and the second stiffness error, and combining the dependency relationship between the first stiffness error and the second stiffness error, the initial stiffness is adjusted to obtain the longitudinal stiffness.

[0143] Preferably, adjusting the initial stiffness to obtain the longitudinal stiffness includes:

[0144]

[0145] Where Δ represents a symbolic variable; C0 represents the initial stiffness; Gd represents the longitudinal stiffness.

[0146] In this embodiment, the calculation of the initial stiffness includes:

[0147] In the solution of the member stiffness, considering the variable cross-section property of the bridge tower, the method for solving the bridge tower stiffness is:

[0148]

[0149] Where E t Is the elastic modulus of the material; l T , b are the height and the transverse width of the tower; h, H are the longitudinal lengths of the top and bottom of the tower respectively, and β = H / h;

[0150] In the solution of the member stiffness, considering the elongation or shortening of the stay cable due to the force, the method for solving the longitudinal stiffness of the stay cable is:

[0151]

[0152] The method for solving the vertical stiffness of the stay cable is:

[0153]

[0154] Where E c Is the elastic modulus of the stay cable, A c Is the cross-sectional area of the stay cable; the inclination angle of the stay cable is α, and the cable length is l c ;

[0155] In the solution of the member stiffness, the deflection equivalent method is used to solve the beam stiffness. The calculation method for the vertical stiffness at a certain point of the continuous beam is:

[0156]

[0157] Among them, E is the elastic modulus, and I b is the moment of inertia of the beam cross-section, l is the single-span length, β is the ratio of the distance from the calculation position point to the adjacent support to l, w is the vertical deflection of the continuous beam under the unit load at the corresponding point, and w 简 is the simply supported beam with a span of l and the deflection under the action of a unit load at the same position.

[0158] In this embodiment, the sub-components refer to cables, beams, etc.

[0159] In this embodiment, the set of deformation variables includes the linear change length, linear change area, and longitudinal applied force corresponding to the already built tower. Among them, the linear change length is the length change obtained by straight-line connecting the two end points of the line to get a new straight line and the straight-line connection of the two end points of the original line. The linear change area refers to the area change of the closed area after straight-line connecting the two end points.

[0160] The beneficial effects of the above technical solution are: obtaining the single deformation of the sub-component from the deformation array and obtaining the overall deformation of the tower from the set of deformation variables, determining the errors from these two aspects respectively, ensuring the reliability and rationality of the stiffness correction, and further ensuring the accuracy of the stiffness calculation.

[0161] Obviously, those skilled in the art can make various changes and modifications to the present invention without departing from the spirit and scope of the present invention. Thus, if these modifications and variations of the present invention fall within the scope of the claims of the present invention and their equivalent technologies, the present invention also intends to include these changes and modifications.

Claims

1. A method for calculating the longitudinal thrust stiffness of a multi-tower cable-stayed bridge, characterized in that: include: Step 1: Disassemble the multi-tower cable-stayed bridge system to obtain multiple sets of cable-tower systems and cable-beam systems; Step 2: construct a first series-parallel system corresponding to the cable-tower system and a second series-parallel system corresponding to the cable-beam system; Step 3: obtaining the first stiffness of each component corresponding to each tower in the multi-tower cable-stayed bridge system under different longitudinal applied forces, and at the same time, constructing the equivalent cable surface of the corresponding tower under each longitudinal applied force; Step 4: All first stiffnesses and equivalent cable surfaces under the same longitudinal applied force of the corresponding tower are integrated with the corresponding first series system and the second series-parallel system, and the longitudinal stiffness of the corresponding tower is obtained in combination with the historical error to perform structural optimization on the multi-tower cable-stayed bridge system.

2. The method for calculating longitudinal thrust stiffness of a multi-tower cable-stayed bridge according to claim 1 is characterized in that: include: Before dismantling the multi-tower cable-stayed bridge system, the following procedures must be performed: Obtaining a structural diagram of the multi-tower cable-stayed bridge system, and determining the number N of towers present in the structural diagram; The multi-tower cable-stayed bridge system is disassembled according to the number of towers N, wherein N≥3.

3. The method for calculating longitudinal thrust stiffness of a multi-tower cable-stayed bridge according to claim 1 is characterized in that: Constructing a first series-parallel system corresponding to the cable-tower system and a second series-parallel system corresponding to the cable-beam system, including: Locking the i-th tower and the cable-tower system and the cable-beam system of the i-th tower; Based on the spring equivalent principle, the cable-tower system of the i-th tower and the cable-beam system of the i-th tower are converted into lines to obtain the corresponding first series-parallel system and the second series-parallel system.

4. The method for calculating longitudinal thrust stiffness of a multi-tower cable-stayed bridge according to claim 1 is characterized in that: All the first stiffness and equivalent cable surface of the corresponding tower under the same longitudinal force are integrated with the corresponding first series system and the second series-parallel system, and the longitudinal stiffness of the corresponding tower is obtained by combining the historical error, including: According to the obtained first stiffness and equivalent cable surface, numerical calibration is performed on the first series system and the second series system of the corresponding tower in turn; Respectively obtain a first actual deformation structure diagram of the corresponding cable-tower system in the corresponding longitudinal direction in which a force is applied, and a second actual deformation structure diagram of the corresponding cable-beam system in the corresponding longitudinal direction in which a force is applied; Based on the numerical calibration results and the errors obtained based on the first actual deformation structure diagram, the second actual deformation structure diagram, and the deformation variable set under different longitudinal applied forces, the longitudinal stiffness of the corresponding tower under the corresponding longitudinal applied force is obtained.

5. The method for calculating longitudinal thrust stiffness of a multi-tower cable-stayed bridge according to claim 4 is characterized in that: Obtaining a first actual deformation structure diagram of the corresponding cable-tower system in the corresponding longitudinal direction of the applied force, including: Respectively obtain from the historical database the process diagrams of the constructed towers that are the same as the corresponding towers under the longitudinal force applied, wherein the process diagrams are diagrams of the corresponding towers at different application time points of the longitudinal force applied; Perform global processing and local processing on each process graph to obtain the corresponding first graph and second graph; Align key points of each first image and second image according to the longitudinal force application process, and draw a first deformation trajectory image and a second deformation trajectory image of the corresponding tower; Overlapping the first deformation trajectory map and the second deformation trajectory map, locking a first variation trajectory based on the first deformation trajectory map and a second variation trajectory based on the second deformation trajectory map; Constructing a first distribution function based on the first variation trajectory and a second distribution function based on the second variation trajectory, and determining a sway amplitude set under the longitudinal force applied to the constructed tower in combination with tower properties, service life, and maintenance information of the constructed tower, and determining a terminal trajectory of each first variation trajectory at a corresponding application time point; Performing a first capture of the number of images in the first image that are in a continuous stable state, and at the same time, performing a second capture of the number of images in the second image that are in a continuous stable state; Determine, based on the first capture result and the second capture result, a quantity screening boundary that satisfies a continuous stable state in the first graph; Performing alignment processing on the selection boundary and the application time point according to the quantity, and locking the third image in the first image; When the number of the third graph is 1, the third graph is regarded as the fourth graph; When the number of the third images is not 1, randomly selecting one from all the third images as the fourth image; A terminal trajectory based on the fourth graph is obtained from all terminal trajectories and applied to the fourth graph to obtain a first actual deformation structure graph of the corresponding tower.

6. The method for calculating longitudinal thrust stiffness of a multi-tower cable-stayed bridge according to claim 5 is characterized in that: Determine the quantity screening boundary that satisfies the continuous stable state in the first figure, including: Based on the first capture result and the second capture result, construct a first quantity distribution for the first image and a second quantity distribution for the second image, wherein the quantity distribution includes the number of images before the force is applied to a stable state, the number of images in a continuous stable state, and the number of images after the stable state to the end of the force application; Align the first quantity distribution and the second quantity distribution according to the application time point to determine whether there is an intersection area in a continuous stable state. If so, consider the boundaries on both sides of the intersection area as quantity screening boundaries; Otherwise, obtaining a union region where the first quantity distribution and the second quantity distribution are in a stable state and an interval region dependent on the union region, and calculating a left value and a right value in combination with the number of images in a continuously stable state in the first quantity distribution; Among them, N b Indicates the number of images under the union area; N Jg Indicates the number of images in the interval area; max indicates the maximum value symbol; min indicates the minimum value symbol; N 01 represents the number of images before the force starts to be applied to the stable state in the first number distribution; Z z Indicates the corresponding left value; Z y Indicates the corresponding right side value; Indicates the floor symbol; A quantity screening boundary is obtained according to the left side value and the right side value.

7. The method for calculating longitudinal thrust stiffness of a multi-tower cable-stayed bridge according to claim 6 is characterized in that: The longitudinal stiffness of the corresponding tower under the corresponding longitudinal force is obtained, including: Based on the numerical calibration results, the initial stiffness of the corresponding tower under the corresponding longitudinal force is obtained; Comparing the first deformation value of each first sub-component involved in the first actual deformation structure diagram and the second actual deformation structure diagram with the standard deformation value of the same sub-component under the corresponding longitudinal applied force, and constructing a deformation array; Based on the deformation array, determining a first stiffness error ε1; ε1=|r1 j1 -r0 j1 | min +S1 Among them, m1 represents the number of comparison results in the deformation array; r1 j1 represents the first deformation value based on the j1th comparison result; r0 j1 represents the standard deformation value based on the j1th comparison result; Represents all r1 j1 -r0 j1 Middle r1 j1 -r0 j1 ≥0 number; Represents all r1 j1 -r0 j1 Middle r1 j1 -r0 j1 <0 quantity; Indicates based on r1 j1 -r0 j1 Deformation weight ≥ 0; Indicates based on r1 j1 -r0 j1 <0 deformation weight; Represents all |r1 j1 -r0 j1 | variance; S1 represents the additional error function based on the deformation array; |r1 j1 -r0 j1 | min Represents all |r1 j1 -r0 j1 The minimum value among | Determine the second stiffness error ε2 based on the deformation variable set under different longitudinal applied forces; ε2=|W(L j2 ,R j2 ,S j2 )-B0 j2 | min +S2 in, Represents based on all |W(L j2 ,R j2 ,S j2 )-B0 j2 Variance of |; W(L j2 ,R j2 ,S j2 ) represents the i2-th longitudinal force R j2 The linear variation length L in the deformation variable set j2 , Line change area S j2 Function of variables; B0 j2 Indicates the i2-th longitudinal force R j2 The standard variable function of; ln represents the logarithmic function symbol; S2 represents the additional error function based on the deformation variable set; W(L j2 ,R j2 ,S j2 )-B0 j2 | min Indicates all |W(L j2 ,R j2 ,S j2 )-B0 j2 The minimum value among | Depending on the first stiffness error and the second stiffness error and in combination with the dependency relationship between the first stiffness error and the second stiffness error, the initial stiffness is adjusted to obtain the longitudinal stiffness.

8. The method for calculating longitudinal thrust stiffness of a multi-tower cable-stayed bridge according to claim 7 is characterized in that: The initial stiffness is adjusted to obtain the longitudinal stiffness, including: Where Δ represents a symbolic variable; C0 represents the initial stiffness; and Gd represents the longitudinal stiffness.

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