Installation and construction method for arch-shaped cantilever on section of special tunnel

Abstract

The invention discloses an installation and construction method for a special tunnel section arch-shaped cantilever, and belongs to the technical field of tunnel section design. The method comprises the following steps: constructing a tunnel section inner contour geometric model and a pantograph geometric model; based on constraint conditions of the arch cantilever, constructing a geometric model of the arch cantilever, installing the geometric model in the inner contour model in a simulation manner, and outputting the geometric model meeting installation constraint conditions and installation data; an installation scheme is verified in advance through accurate geometric modeling and simulation technologies, it is ensured that components are not in contact with a pantograph dynamic envelope, and the requirement for the minimum insulation distance is met; in order to further improve the safety of the overhead line system, the maximization of the minimum insulation distance and the maximization of the distance between the dynamic envelope line of the pantograph and the arch-shaped cantilever are taken as optimization objectives, and a multi-objective optimization model is utilized to balance different objective relations so as to obtain a more optimized installation scheme. According to the optimized data, the arch-shaped cantilever is selected and installed, and the problems that an existing construction mode is low in construction efficiency and low in construction precision are solved.

Description

Technical Field

[0001] The present invention belongs to the technical field of railway transportation systems, and particularly relates to a construction method for installing bow-shaped cantilevers with a special tunnel section. Background Art

[0002] With the rapid development of the domestic economy, the scale of the railway transportation system has become increasingly perfect, and the transportation scale has been continuously expanding. Under this background, local railways have also been vigorously developed. In local railways mainly for freight transportation, single-track low-clearance tunnels can not only meet the transportation needs of railways but also save investment to the greatest extent. A special tunnel section refers to a tunnel opened in special landforms, including medium and low mountains, hills, mountain valleys, etc. When constructing tunnels in these special landforms, multiple tunnel segments often need to be connected, resulting in many curved sections in the tunnels.

[0003] In the installation of the catenary contact suspension of single-track low-clearance tunnels, using bow-shaped cantilevers has a series of advantages such as simple structure, convenient installation, and reliable operation. However, due to the high requirements for the contact network insulation gap in the construction of tunnel bow-shaped cantilevers, the installation positions of bow-shaped cantilevers in curved sections are different from those in straight sections, and the bending degree of each curved section is different, and its installation position needs to be re-measured to be determined. The existing construction method requires obtaining data inside the tunnel multiple times after the tunnel is completed to determine the installation position of the bow-shaped cantilever and then install it. This method of multiple measurements results in low efficiency in installing bow-shaped cantilevers.

[0004] In summary, the existing construction method has problems of low construction efficiency and low construction accuracy. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to provide a construction method for installing bow-shaped cantilevers with a special tunnel section, which has a short design and construction time, accurate installation positions, and is convenient for popularization and use, aiming at the deficiencies in the above-mentioned prior art.

[0006] To solve the above technical problems, the technical solution adopted by the present invention is:

[0007] A construction method for installing bow-shaped cantilevers with a special tunnel section, the method comprising the following steps:

[0008] Step 1: First, construct the inner contour geometric model and the pantograph geometric model of the current tunnel section, determine the installation position of the pantograph, and assemble it into the model. Then, construct the bow-shaped cantilever geometric model based on the bow-shaped cantilever constraint conditions, simulate and install the bow-shaped cantilever geometric model into the inner contour geometric model, and output the bow-shaped cantilever geometric model that meets the installation constraint conditions and the corresponding installation data;

[0009] The constraint conditions of the bow-shaped cantilever include: the connection relationships of various components of the bow-shaped cantilever, the height of the contact wire, the effective length of the insulator, the diameter of the insulator, the horizontal angle of the insulator, the size of the carrier cable base, the base size, the length of the inclined cantilever, the length of the horizontal cantilever, the angle between the horizontal cantilever and the inclined cantilever, the installation height of the base, the length of the positioner, and the slope of the positioner;

[0010] The installation constraint conditions include: each component of the bow-shaped cantilever does not contact the dynamic envelope of the pantograph, meets the requirement of the minimum insulation distance, and the pull-out value of the contact wire does not exceed the standard numerical range;

[0011] Step 2: Construct a multi-objective optimization model. The output in Step 1 is used as the input of the multi-objective optimization model. With maximizing the minimum insulation distance and maximizing the distance between the dynamic envelope of the pantograph and the bow-shaped cantilever as the optimization objectives, the optimal geometric model of the bow-shaped cantilever and the corresponding installation data are output;

[0012] Step 3: Select the corresponding bow-shaped cantilever according to the output data in Step 2 and install it.

[0013] Furthermore, in Step 1, the length of the inclined cantilever is 550 mm to 700 mm; the length of the horizontal cantilever is 700 mm to 1200 mm; the angle between the horizontal cantilever and the inclined cantilever is 145° to 150°; the installation height of the base is 5320 mm to 5600 mm; the length of the positioner is 550 mm to 950 mm; the slope of the positioner is 8° to 12°.

[0014] Furthermore, the construction process of the inner contour geometric model is: obtain the basic contour data and widening data of the current tunnel section, determine the corresponding lining inner contour data according to the widening data, adjust the basic contour data according to the lining inner contour data to obtain the inner contour data, and thus use a drawing tool to draw the inner contour geometric model of the current tunnel.

[0015] Furthermore, the construction process of the pantograph geometric model is: draw the pantograph geometric model using a drawing tool according to the size data of the pantograph;

[0016] The determination process of the installation position of the pantograph is: obtain the superelevation data of the outer rail and the standard gauge data, and calculate the installation position of the pantograph based on the pantograph being perpendicular to the rail plane.

[0017] Furthermore, the minimum insulation distance refers to: the insulation distance between the energized parts of the bow-shaped cantilever and the tunnel wall. The energized parts of the bow-shaped cantilever include the carrier cable base, the horizontal cantilever, and the inclined cantilever.

[0018] Furthermore, the contact wire stagger value refers to the horizontal distance between the contact wire and the center of the pantograph at the positioning point; in a straight section, the standard value range is -300 mm to 300 mm, and in a curved section, the standard value range is 0 to 400 mm; the process of determining the section type of the current tunnel section is as follows: when the superelevation of the outer rail is equal to 0, it is determined that the tunnel section is in a straight section, and when the superelevation of the outer rail is greater than 0, it is determined that the tunnel section is in a curved section.

[0019] Furthermore, the calculation formula for the contact wire stagger value is:

[0020]

[0021] Where a is the contact wire stagger value, m is the horizontal distance between the contact wire and the center of the line, c is the horizontal distance between the pantograph and the center of the line, h is the superelevation data of the outer rail, H is the height of the contact wire, and L is the standard gauge.

[0022] Furthermore, when drilling holes for installing the bow-shaped cantilever, the tunnel expansion joint needs to be avoided.

[0023] Furthermore, the lining inner contour data is a lining inner contour coordinate table, including the base skirt point, the maximum span point, the arch springing point, the radius transformation point, and the section values at the crown, and the section values include the transverse widening value and the longitudinal widening value.

[0024] Furthermore, the data corresponding to the optimal bow-shaped cantilever geometric model and the corresponding inner contour geometric model, as well as the corresponding installation data, are summarized and plotted into a table to guide the installation work of other subsequent tunnels.

[0025] The present invention has the following advantages compared with the prior art:

[0026] The present invention determines the installation position of a pantograph by constructing a geometric model of the inner contour of a tunnel section and a geometric model of the pantograph, and assembles it into the model; based on the constraint conditions of the bow-shaped cantilever, constructs its geometric model and simulates its installation into the inner contour model, and outputs a geometric model and installation data that meet the installation constraint conditions; through precise geometric modeling and simulation technology, verifies the installation scheme of the bow-shaped cantilever in a virtual environment in advance to ensure that the installed components do not contact the dynamic envelope of the pantograph and meet the requirements of the minimum insulation distance. Further, the present invention takes the output of step one as the input of a multi-objective optimization model, with maximizing the minimum insulation distance and maximizing the distance between the dynamic envelope of the pantograph and the bow-shaped cantilever as the optimization objectives; uses the multi-objective optimization model to balance the relationship between different objectives, and obtains a more optimized installation scheme by optimizing the minimum insulation distance and the distance between the dynamic envelope of the pantograph and the bow-shaped cantilever, improving the safety of the catenary; ensures the accuracy of the installation scheme through precise geometric modeling and multi-objective optimization, reducing potential safety hazards and subsequent maintenance costs caused by insufficient construction accuracy. Finally, selects the corresponding bow-shaped cantilever according to the optimized data and installs it; performs actual installation based on the output data of the optimization model to ensure the accuracy and efficiency of the construction process; the optimized installation scheme reduces material waste and construction time, thereby reducing the construction cost and solving the problem of low efficiency in installing the bow-shaped cantilever in the prior art.

[0027] 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

[0028] Figure 1 It is a schematic structural diagram of a geometric model of a simulated installation when the widening is 0 mm, which is the output of step one of an embodiment of the installation construction method of a bow-shaped cantilever in a special tunnel section of the present invention;

[0029] Figure 2 It is a schematic structural diagram of a geometric model of a simulated installation when the widening is 10 mm, which is the output of step one of an embodiment of the installation construction method of a bow-shaped cantilever in a special tunnel section of the present invention;

[0030] Figure 3 It is a schematic structural diagram of a geometric model of a simulated installation when the widening is 30 mm, which is the output of step one of an embodiment of the installation construction method of a bow-shaped cantilever in a special tunnel section of the present invention;

[0031] Figure 4 It is a schematic structural diagram of a geometric model of a simulated installation when the widening is 50 mm, which is the output of step one of an embodiment of the installation construction method of a bow-shaped cantilever in a special tunnel section of the present invention;

[0032] Figure 5Schematic diagram of the geometric model of the simulated installation when the widening is 60 mm, which is the output of Step 1 of the embodiment of the installation construction method of the bow-shaped cantilever for a special tunnel section of the present invention;

[0033] Figure 6 Schematic diagram of the bow-shaped cantilever structure of the embodiment of the installation construction method of the bow-shaped cantilever for a special tunnel section of the present invention;

[0034] Figure 7 Schematic diagram of the base structure of the embodiment of the installation construction method of the bow-shaped cantilever for a special tunnel section of the present invention;

[0035] Figure 8 Schematic diagram of the cantilever body structure of the embodiment of the installation construction method of the bow-shaped cantilever for a special tunnel section of the present invention;

[0036] Figure 9 Schematic diagram of the positioner structure of the embodiment of the installation construction method of the bow-shaped cantilever for a special tunnel section of the present invention;

[0037] Figure 10 Table chart of the lining inner contour coordinates of the embodiment of the installation construction method of the bow-shaped cantilever for a special tunnel section of the present invention;

[0038] Figure 11 Summary table chart of the installation data of the embodiment of the installation construction method of the bow-shaped cantilever for a special tunnel section of the present invention;

[0039] Figure 12 Schematic diagram of the basic contour structure of the embodiment of the installation construction method of the bow-shaped cantilever for a special tunnel section of the present invention;

[0040] Explanation of reference numerals:

[0041] 1. Pantograph; 2. Pantograph dynamic envelope; 3. Insulator; 4. Contact wire; 5. Catenary base; 6. Base; 7. Inclined cantilever; 8. Horizontal cantilever; 9. Positioner; 10. Inner contour; 11. Basic contour. Detailed implementation manners

[0042] Embodiment of the installation construction method of the bow-shaped cantilever for a special tunnel section:

[0043] This embodiment is described by taking the construction of Railway W as an example. The installation construction method of the bow-shaped cantilever for a special tunnel section includes the following steps:

[0044] As Figures 1-5As shown in the figure, in Step 1, first construct the geometric model of the inner contour 10 of the current tunnel section and the geometric model of the pantograph 1, determine the installation position of the pantograph 1, and assemble it into the model. Then, based on the constraint conditions of the bow-shaped wrist arm, construct the geometric model of the bow-shaped wrist arm, simulate and install the geometric model of the bow-shaped wrist arm into the geometric model of the inner contour 10, and output the geometric model of the bow-shaped wrist arm that meets the installation constraint conditions and the corresponding installation data. That is to say, first simulate the situation of the inner contour 10 of the tunnel section and the pantograph 1, and then, according to the constraint conditions of the bow-shaped wrist arm, establish the geometric model of the bow-shaped wrist arm; according to the installation constraint conditions, simulate and install the bow-shaped wrist arm into the geometric model of the inner contour 10, and output the geometric model of the bow-shaped wrist arm that meets the requirements and the corresponding installation data. The installation position of the pantograph 1 is determined according to industry specifications.

[0045] The construction process of the above-mentioned geometric model of the inner contour 10 is as follows: Obtain the basic contour 11 data and widening data of the current tunnel section, determine the corresponding lining inner contour 10 data according to the widening data, adjust the basic contour 11 data according to the lining inner contour 10 data to obtain the inner contour 10 data, and thus use a drawing tool to draw the geometric model of the inner contour 10 of the current tunnel. That is to say, the inner contour 10 of the tunnel section is based on the widened basic contour 11. The drawing tool uses AUTOCAD or COMSOL Multiphysics.

[0046] As Figure 12 shown, specifically, the lining inner contour 10 data is a lining inner contour 10 coordinate table, including the base skirt points, maximum span points, arch foot points, radius transformation points, and cross-section values at the arch top. The cross-section values include lateral widening values and longitudinal widening values. Figure 12 The numbers 1, 2, 3, 4, and 5 marked above are Figure 10 the point numbers in Figure 10 shown. Among them, the widening data generally includes 7 types such as 0mm, 100mm, 200mm, 300mm, 400mm, 500mm, 600mm, 700mm, and 800mm. The specific corresponding relationship between the widening data and the lining inner contour 10 data, that is, the lining inner contour 10 coordinate table is as

[0047] As Figures 1-5 shown, it is the structural view of the geometric model of the bow-shaped bent arm simulated and installed into the inner contour 10 model output in Step 1. Specifically, Figure 1 it is the geometric model simulation installation view corresponding to the widening of 0 cm, the outer rail superelevation of 0 mm, and the offset data of the line center also being 0 mm. The 6650 marked in the figure refers to the height of the track from the tunnel roof, and 5750 is the height of the contact wire 4, and 5400 is the installation height of the lower row of holes of the base 6, and the unit is all mm. Figure 2The geometric model simulation installation view corresponding to a widening of 10 cm, a superelevation of the outer rail of 0 mm, and an offset data of the line center of 50 mm. In the figure, 6670 marked refers to the height of the track from the tunnel roof, 5750 is the height of the contact wire 4, 5400 is the installation height of the lower row of holes of the base 6, 50 is the offset distance of the line center, and the unit is mm for all. Figure 3 The geometric model simulation installation view corresponding to a widening of 30 cm, a superelevation of the outer rail of 60 mm, and an offset data of the line center of 90 mm. In the figure, 6710 marked refers to the height of the track from the tunnel roof, 5750 is the height of the contact wire 4, 5550 is the installation height of the lower row of holes of the base 6, 60 is the superelevation of the outer rail, 90 is the offset distance of the line center, and the unit is mm for all. Figure 4 The geometric model simulation installation view corresponding to a widening of 50 cm, a superelevation of the outer rail of 60 mm, and an offset data of the line center of 180 mm. In the figure, 6750 marked refers to the height of the track from the tunnel roof, 5750 is the height of the contact wire 4, 5550 is the installation height of the lower row of holes of the base 6, 60 is the superelevation of the outer rail, 180 is the offset distance of the line center, and the unit is mm for all. Figure 5 The geometric model simulation installation view corresponding to a widening of 60 cm, a superelevation of the outer rail of 80 mm, and an offset data of the line center of 190 mm. In the figure, 6770 marked refers to the height of the track from the tunnel roof, 5750 is the height of the contact wire 4, 5550 is the installation height of the lower row of holes of the base 6, 80 is the superelevation of the outer rail 195 is the offset distance of the line center, and the unit is mm for all.

[0048] The above-mentioned bow-shaped cantilever constraint conditions include: the connection relationship of each component of the bow-shaped cantilever, the height of the contact wire 4, the effective length of the insulator 3, the diameter of the insulator 3, the horizontal angle of the insulator 3, the size of the carrier cable base 5, the size of the base 6, the length of the inclined cantilever 7, the length of the horizontal cantilever 8, the angle between the horizontal cantilever 8 and the inclined cantilever 7, the installation height of the base 6, the length of the positioner 9, and the slope of the positioner 9. In step one, the length of the inclined cantilever 7 is 550 mm to 700 mm; the length of the horizontal cantilever 8 is 700 mm to 1200 mm; the angle between the horizontal cantilever 8 and the inclined cantilever 7 is 145° to 150°; the installation height of the base 6 is 5320 mm to 5600 mm; the length of the positioner 9 is 550 mm to 950 mm; the slope of the positioner 9 is 8° to 12°. In this embodiment, the height of the contact wire 4 is 5750 mm; the effective length of the insulator 3 is 850 mm; the diameter of the insulator 3 is 175 mm; the horizontal angle of the insulator 3 is 30°.

[0049] As Figures 6-9As shown in the figure, the connection relationships of each component of the bow-shaped cantilever are as follows: The cantilever body serves as the main support structure, and the insulator 3 is installed on the cantilever body; the contact wire 4 is fixed to the cantilever body through the positioning device, and the positioner 9 is used to adjust the extension value of the contact wire 4. The carrier cable base 5 is installed on the cantilever body, and the base 6 serves as the support foundation of the entire system and is installed on the tunnel wall; the inclined cantilever 7 and the horizontal cantilever 8 are connected through a specific connection method, and the inclined cantilever 7 and the horizontal cantilever 8 form the cantilever body.

[0050] The construction process of the pantograph 1 geometric model is as follows: The pantograph 1 geometric model is drawn using a drawing tool according to the dimensional data of the pantograph 1. In this embodiment, the length of the pantograph 1 is 1950 mm, and the range of the pantograph dynamic envelope 2 is 120 mm for the up-and-down shaking of the pantograph 1 and 250 mm for the left-and-right swing. The determination process of the installation position of the pantograph 1 is as follows: The superelevation data of the outer rail and the standard gauge data are obtained, and the installation position of the pantograph 1 is calculated based on the pantograph 1 being perpendicular to the rail plane. The superelevation of the outer rail changes with the change of the track curve radius in the tunnel, aiming to reduce the influence of centrifugal force on train operation.

[0051] The above installation constraint conditions include: Each component of the bow-shaped cantilever does not contact the pantograph dynamic envelope 2, meeting the requirement of the minimum insulation distance, and the extension value of the contact wire 4 does not exceed the standard numerical range. The minimum insulation distance refers to: The insulation distance between the energized parts of the bow-shaped cantilever and the tunnel wall. The energized parts of the bow-shaped cantilever include the carrier cable base 5, the horizontal cantilever 8, and the inclined cantilever 7. The pantograph dynamic envelope 2 refers to the maximum contour line that the running pantograph 1 may reach during maximum lift and swing.

[0052] Specifically, it is required that each component of the bow-shaped cantilever does not contact the pantograph dynamic envelope 2, and the purpose is to prevent mechanical collision between the pantograph 1 and the catenary components. When the pantograph 1 is running at high speed, if it collides with the cantilever components, it may cause serious accidents such as damage to the pantograph 1 and detachment of the catenary components, endangering the safety of train operation. It is required to meet the requirement of the minimum insulation distance, and the purpose is to ensure electrical insulation safety and prevent electrical short circuits and electric shock accidents. In the catenary system, sufficient insulation distance needs to be maintained between components with different potentials to avoid electrical short circuits. If the insulation distance is insufficient, it may cause current to leak through air or other media, triggering short circuit faults and affecting the normal operation of the power supply system. It is required that the extension value of the contact wire 4 does not exceed the standard numerical range, and the purpose is to ensure reliable contact between the pantograph 1 and the contact wire 4 and improve the power supply quality. The extension value of the contact wire 4 is the horizontal distance of the contact wire 4 relative to the center of the line. A reasonable extension value can ensure that the pantograph 1 always maintains good contact with the contact wire 4 during operation, avoiding problems such as arcs and sparks caused by poor contact, thereby improving the reliability and stability of power supply.

[0053] Among them, the stagger value of the contact wire 4 refers to the horizontal distance between the contact wire 4 and the center of the pantograph 1 at the positioning point; in the straight section, the standard value range is -300 mm to 300 mm, and in the curved section, the standard value range is 0 to 400 mm; the process of judging the section type of the current tunnel section is as follows: when the superelevation of the outer rail is equal to 0, it is determined that the tunnel section is in the straight section, and when the superelevation of the outer rail is greater than 0, it is determined that the tunnel section is in the curved section.

[0054] The calculation formula for the stagger value of the contact wire 4 is:

[0055]

[0056] Among them, a is the stagger value of the contact wire 4, m is the horizontal distance between the contact wire 4 and the center of the line, c is the horizontal distance between the pantograph 1 and the center of the line, h is the superelevation data of the outer rail, H is the height of the contact wire 4, and L is the standard gauge.

[0057] The output in Step 1 is not necessarily unique, and multiple sets of data may meet the requirements of Step 1; to further improve the safety of the catenary, multi-objective optimization is carried out. Step 2: Construct a multi-objective optimization model. The output in Step 1 is used as the input of the multi-objective optimization model. With maximizing the minimum insulation distance and maximizing the distance between the dynamic envelope 2 of the pantograph and the bow-shaped wrist arm as the optimization objectives, the optimal bow-shaped wrist arm geometric model and the corresponding installation data are output. This multi-objective optimization model can be constructed according to the linear weighted method, the approximation target method, the genetic algorithm, etc.

[0058] Step 3: Select the corresponding bow-shaped wrist arm according to the output data in Step 2 and install it.

[0059] As Figure 11 shown, the data corresponding to the optimal bow-shaped wrist arm geometric model and the corresponding inner contour 10 geometric model, as well as the corresponding installation data, are summarized and plotted in a table to guide the installation work of other subsequent tunnels. In Figure 11 the length L1 + L2 of the bow-shaped wrist arm represents the inclined wrist arm 7 and the flat wrist arm 8.

[0060] Specifically, when installing the bow-shaped cantilever according to the actual installation data, the following steps should be followed: First, install the base 6. To facilitate construction, convert the height data of the base 6 into the height data of the lower row of holes of the base 6. According to the height data of the lower row of holes of the base 6, use chemical anchor bolts to drill holes on the tunnel wall. Use a plumb bob to measure the vertical height to ensure the accuracy of the installation height and strictly control the error. Clean and inject glue into the holes to ensure the stability of the installation. When drilling holes for installing the bow-shaped cantilever, avoid the tunnel expansion joint. Then prepare the cantilever body and the locator 9, and prepare the corresponding locator 9 and cantilever body according to the length of the locator 9, the length and angle of the cantilever body. Finally, complete the assembly and installation of the cantilever body, the locator 9 and the base 6. By adjusting the angle of the base 6, make the cantilever body at the angle required by the design. Assemble the cantilever body, the locator 9, the insulator 3, etc., and install them on the tunnel wall through the base 6. The above steps ensure the installation accuracy and reliability of the bow-shaped cantilever, and at the same time avoid conflicts with the tunnel structure. In addition, install the pantograph 1 according to the angle of the pantograph 1.

[0061] In this application, the installation data of the bow-shaped cantilever is obtained through simulation means and installed accordingly. Compared with the prior art, the prior art requires on-site measurement of tunnel data and installation adjustment in the actual tunnel, while the installation in this application has higher accuracy, faster speed and higher efficiency. The bow-shaped cantilever installed according to this application has a lower rework rate, thus improving the overall installation efficiency and greatly saving costs such as labor costs, material costs, fuel and machinery costs.

[0062] The above is only a preferred embodiment of the present invention and does not impose any limitation on the present invention. Any simple modification, change and equivalent structural change made to the above embodiments according to the technical essence of the present invention still fall within the protection scope of the technical solution of the present invention.

Claims

1. A construction method for installing bow-shaped cantilever in a special tunnel section, characterized in that: The method includes the following steps: Step 1: First, construct the geometric model of the inner contour (10) of the current tunnel section and the geometric model of the pantograph (1), determine the installation position of the pantograph (1), and assemble it into the model. Then, construct the geometric model of the bow-shaped wrist arm based on the constraint conditions of the bow-shaped wrist arm, simulate and install the geometric model of the bow-shaped wrist arm into the geometric model of the inner contour (10), and output the geometric model of the bow-shaped wrist arm that meets the installation constraint conditions and the corresponding installation data. The constraint conditions of the bow-shaped wrist arm include: the connection relationship of each component of the bow-shaped wrist arm, the height of the contact wire (4), the effective length of the insulator (3), the diameter of the insulator (3), the horizontal angle of the insulator (3), the size of the carrier cable base (5), the size of the base (6), the length of the inclined wrist arm (7), the length of the horizontal wrist arm (8), the angle between the horizontal wrist arm (8) and the inclined wrist arm (7), the installation height of the base (6), the length of the positioner (9), and the slope of the positioner (9). The installation constraint conditions include: each component of the bow-shaped wrist arm does not contact the dynamic envelope line (2) of the pantograph, meets the requirement of the minimum insulation distance, and the pull-out value of the contact wire (4) does not exceed the standard numerical range. Step 2: Construct a multi-objective optimization model. The output in Step 1 is used as the input of the multi-objective optimization model. With maximizing the minimum insulation distance and maximizing the distance between the dynamic envelope line (2) of the pantograph and the bow-shaped wrist arm as the optimization objectives, output the optimal geometric model of the bow-shaped wrist arm and the corresponding installation data. Step 3: Select the corresponding bow-shaped wrist arm according to the output data in Step 2 and install it.

2. A construction method for installing a special tunnel section bow-shaped cantilever according to claim 1, characterized in that: In Step 1, the length of the inclined wrist arm (7) is 550 mm to 700 mm; the length of the horizontal wrist arm (8) is 700 mm to 1200 mm; the angle between the horizontal wrist arm (8) and the inclined wrist arm (7) is 145° to 150°; the installation height of the base (6) is 5320 mm to 5600 mm; the length of the positioner (9) is 550 mm to 950 mm; the slope of the positioner (9) is 8° to 12°.

3. A construction method for installing an arched cantilever in a special tunnel section according to claim 1, characterized in that: The construction process of the geometric model of the inner contour (10) is as follows: Obtain the basic contour (11) data and widening data of the current tunnel section, determine the corresponding lining inner contour data according to the widening data, adjust the basic contour (11) data according to the lining inner contour data to obtain the inner contour (10) data, and thus use a drawing tool to draw the geometric model of the inner contour (10) of the current tunnel.

4. A construction method for installing an arched catenary mast in a special tunnel section according to claim 1, characterized in that: The construction process of the geometric model of the pantograph (1) is as follows: Use a drawing tool to draw the geometric model of the pantograph (1) according to the size data of the pantograph (1). The determination process of the installation position of the pantograph (1) is as follows: Obtain the superelevation data of the outer rail and the standard gauge data, and calculate the installation position of the pantograph (1) based on the pantograph (1) being perpendicular to the rail plane.

5. A construction method for installing an arched cantilever in a special tunnel section according to claim 1, characterized in that: The so-called minimum insulation distance refers to: the insulation distance between the energized body of the bow-shaped wrist arm and the tunnel wall. The energized body of the bow-shaped wrist arm includes the carrier cable base (5), the horizontal wrist arm (8), and the inclined wrist arm (7).

6. A construction method for installing an arched cantilever in a special tunnel section according to claim 1, characterized in that: The stagger value of the contact wire (4) refers to the horizontal distance between the contact wire (4) and the center of the pantograph (1) at the positioning point; in a straight section, the standard value range is -300 mm to 300 mm, and in a curved section, the standard value range is 0 to 400 mm; the process of determining the section type of the current tunnel section is as follows: when the superelevation of the outer rail is equal to 0, it is determined that the tunnel section is in a straight section, and when the superelevation of the outer rail is greater than 0, it is determined that the tunnel section is in a curved section.

7. A construction method for installing an arched cantilever in a special tunnel section according to claim 6, characterized in that: The calculation formula for the stagger value of the contact wire (4) is: where a is the stagger value of the contact wire (4), m is the horizontal distance between the contact wire (4) and the center of the line, c is the horizontal distance between the pantograph (1) and the center of the line, h is the superelevation data of the outer rail, H is the height of the contact wire (4), and L is the standard gauge.

8. A construction method for installing an arched cantilever in a special tunnel section according to claim 1, characterized in that: When drilling holes for installing the bow-shaped cantilever, the tunnel expansion joint should be avoided.

9. A construction method for installing an arched cantilever in a special tunnel section according to claim 1, characterized in that: The inner contour data of the lining is a table of inner contour coordinates of the lining, including the base skirt points, the maximum span points, the arch foot points, the radius transformation points, and the section values at the crown, and the section values include the lateral widening value and the longitudinal widening value.

10. A construction method for installing an arched cantilever in a special tunnel section according to claim 1, characterized in that: The data corresponding to the optimal geometric model of the bow-shaped cantilever and the geometric model of the corresponding inner contour (10), as well as the corresponding installation data, are summarized and plotted in a table to guide the installation work of other subsequent tunnels.

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