Second-order continuous path planning method for shield tunnel axis correction

Abstract

This invention relates to a second-order continuous path planning method for shield tunneling axis correction, comprising the following steps: obtaining the actual shield axis based on the shield guidance system; determining the starting point information of the shield correction curve based on the actual shield axis; searching for the closest point to the CTA starting point coordinates on the tunnel design axis, using this as the initial endpoint of the correction curve, and obtaining the initial endpoint information; determining the CTA constraints based on the minimum turning radius and curve continuity conditions; establishing a second-order continuous Euler spiral equation based on the given CTA starting and endpoint information; searching along the DTA towards the tunneling direction from the initial endpoint of the CTA to obtain the optimal endpoint information of the CTA that satisfies the CTA constraints and has the shortest CTA length, and using the CTA-satisfied curve as the shield correction planning path. This invention can achieve smooth shield machine axis correction, improve correction accuracy and efficiency, and is of great significance for ensuring tunnel construction quality, controlling project progress, and ensuring the safety of construction personnel and equipment.

Description

Technical Field

[0001] This invention relates to the field of tunnel boring machine (TBM) construction, and more specifically, to a second-order continuous path planning method for TBM axis correction. Background Technology

[0002] Shield tunneling is a highly efficient, safe, concealed, environmentally friendly, and reliable method of tunnel excavation. Due to its high degree of automation and good engineering quality, it has become the mainstream tunneling technology in my country and worldwide. However, shield tunneling also has some problems and drawbacks. One major issue is that the complexity of the construction environment, geological variations, and changes in the route can easily cause the shield machine's axis to deviate from the design line. Excessive axis deviation can lead to delays in the construction period, decreased construction quality, and even result in tunnels that do not meet design requirements.

[0003] To avoid the above problems, it is necessary to correct the tunnel boring machine's (TBM) axis of travel in a timely manner during construction. Currently, most correction curves are cubic curves or continuous reverse circular curves, which cannot guarantee curvature continuity (G2 continuity). Traditional G1 correction curves experience abrupt changes in curvature at the junctions, resulting in low smoothness. This can lead to sudden changes in centrifugal force during tunneling, affecting the tunnel's stability and safety. Furthermore, in engineering applications, experts often need to determine the correction scheme and select it based on the TBM parameters, but this often cannot guarantee high-precision and high-efficiency correction. Summary of the Invention

[0004] The technical problem to be solved by this invention is to provide a second-order continuous path planning method for shield machine axis correction, which can realize smooth axis correction of the shield machine, improve the accuracy and efficiency of correction, and is of great significance for ensuring the quality of tunnel construction, controlling the project progress, and ensuring the safety of construction personnel and equipment.

[0005] The technical solution adopted by this invention to solve its technical problem is: to construct a second-order continuous path planning method for shield tunnel axis correction, including the following steps:

[0006] S1. Obtain the actual axis ATA of the shield based on the shield guidance system, and determine the starting point information of the shield correction curve CTA based on the ATA, including coordinates, direction angle and curvature;

[0007] S2. Search for the point closest to the starting point of the CTA on the tunnel design axis DTA, and use this as the initial endpoint of the correction curve CTA to obtain the initial endpoint information of the CTA, including coordinates, direction angle and curvature.

[0008] S3. Determine the CTA constraints based on the minimum turning radius and curve continuity conditions;

[0009] S4. Establish the second-order continuous Euler spiral equation based on the given CTA start and end information;

[0010] S5. Starting from the initial endpoint of CTA, search along DTA in the tunneling direction to obtain the optimal endpoint information of CTA that satisfies the CTA constraints and has the shortest CTA length. Use the CTA curve that satisfies the optimal endpoint information, starting point information and constraints as the shield tunneling correction planning path.

[0011] According to the above scheme, in step S1, the starting point information of the shield tunneling correction curve CTA specifically includes: shield position vector q = [xyz] T Shield angle vector The shield curvature vector u = [κ1κ2]; where (x,y,z) represents the position coordinates of the shield machine cutterhead center at the starting point of the CTA correction curve; This indicates the azimuth of the tunnel boring machine at the CTA starting point, including the horizontal azimuth θ and the pitch azimuth θ. (κ1, κ2) represent the curvatures of the starting curve of the correction curve CTA on the horizontal xoy plane and the vertical xoz plane, respectively.

[0012] According to the above scheme, in step S2, the location point closest to the starting point coordinates of the CTA is searched on the tunnel design axis DTA, and this point is used as the initial endpoint of the correction curve CTA. The initial endpoint information of the CTA is obtained, including coordinates, orientation angle, curvature, and the initial endpoint coordinates (x1, y1, z1) and azimuth angle of the correction curve CTA.

[0013] According to the above scheme, in step S3, the CTA constraints include minimum turning radius, geometric continuity, and turning radius R. min The minimum turning radius R of the tunnel boring machine m Minimum turning radius R of tunnel segments s Minimum turning radius R required by the track r To ensure a smooth transition of the correction curve, the following formula must be satisfied:

[0014]

[0015] Where R is the radius of curvature of the correction curve; y′ and y″ are the first and second derivatives of equation y, respectively;

[0016] The first-order continuity requirement for the correction curve:

[0017]

[0018] Where x0, y0 are the coordinates of the starting point of the correction, x1, y1 are the coordinates of the ending point of the correction, L is the length of the correction spline, κ′ is the curvature of the curve's endpoint, and azimuth of the starting point of the correction is... and the azimuth of the correction endpoint X0, Y0 are combinations of generalized Fresnel integrals about the Euler spiral:

[0019]

[0020] The second-order continuity requirement of the correction curve:

[0021]

[0022] Among them, L i =s i+1 -s i >0, i = 0, 1, ..., N-1, the constraint (4) of the above vector form satisfies when i = 0, 1, ..., N-1

[0023] According to the above scheme, in step S4, the Euler spiral equation is established based on the CTA start and end point information. The second-order continuous interpolation solution of the Euler spiral introduces a nonlinear function to define the first-order continuous interpolation condition:

[0024]

[0025]

[0026] Among them, h(A)X0(2A, δ-A, φ0),

[0027] Here is a nonlinear equation for each node of the simplified second-order continuity:

[0028]

[0029] According to the above scheme, in step S5, starting from the initial endpoint of CTA, a search is performed along DTA towards the tunneling direction to obtain the optimal endpoint information of CTA that satisfies the CTA constraints and has the shortest CTA length. The CTA curve that satisfies the optimal endpoint information, starting point information, and constraints is used as the shield tunneling correction planning path.

[0030] The second-order continuous path planning method for shield tunnel axis correction according to the present invention has the following beneficial effects:

[0031] This invention can generate correction trajectories that adapt to the current situation for different axis deviations, and derive the optimal strategy for shield trajectory correction. It can effectively correct axis deviations in shield construction, smoothly correct the shield machine, improve correction accuracy and efficiency, and provide a theoretical basis for shield axis correction during shield construction. Attached Figure Description

[0032] The present invention will be further described below with reference to the accompanying drawings and embodiments. In the accompanying drawings:

[0033] Figure 1 This is a flowchart of the second-order continuous path planning method for shield tunnel axis correction according to the present invention;

[0034] Figure 2 This is a three-dimensional schematic diagram of the optimized correction path in Embodiment 1 of the present invention;

[0035] Figure 3 This is a schematic diagram of the first optimized axis correction route planning result in Embodiment 2 of the present invention.

[0036] Figure 4 This is a schematic diagram of the second optimized axis correction route planning result in Embodiment 2 of the present invention. Detailed Implementation

[0037] To provide a clearer understanding of the technical features, objectives, and effects of the present invention, specific embodiments of the present invention will now be described in detail with reference to the accompanying drawings.

[0038] like Figure 1-3 As shown, the second-order continuous path planning method for shield tunnel axis correction of the present invention ensures the second-order continuity of the shield axis and that it does not exceed the turning radius by requiring the linearity and continuity of the correction curve. This further ensures that the shield machine can quickly and smoothly correct from the deviation state to the designed axis, thus solving the problems of low correction efficiency and abrupt curvature changes during the correction process of traditional correction curves. The method includes the following steps:

[0039] S1. Obtain the actual axis ATA of the shield based on the shield guidance system, and determine the starting point information of the shield correction curve CTA based on the ATA, including coordinates, direction angle and curvature;

[0040] The CTA starting point information for the shield tunneling correction curve specifically includes: the shield position vector q = [xyz]. T Shield angle vector The shield curvature vector u = [κ1κ2]; where (x,y,z) represents the position coordinates of the shield machine cutterhead center at the starting point of the CTA correction curve; This indicates the azimuth of the tunnel boring machine at the CTA starting point, including the horizontal azimuth θ and the pitch azimuth θ. (κ1, κ2) represent the curvatures of the starting curve of the correction curve CTA on the horizontal xoy plane and the vertical xoz plane, respectively.

[0041] S2. Search for the point closest to the starting point of the CTA on the tunnel design axis DTA, and use this as the initial endpoint of the correction curve CTA to obtain the initial endpoint information of the CTA, including coordinates, direction angle and curvature.

[0042] On the tunnel design axis DTA, search for the point closest to the CTA starting point coordinates. Use this point as the initial endpoint of the CTA correction curve, and obtain the initial endpoint information of the CTA, including coordinates, orientation angle, curvature, and the initial endpoint coordinates (x1, y1, z1) and azimuth angle of the CTA correction curve.

[0043] S3. Determine the CTA constraints based on the minimum turning radius and curve continuity conditions;

[0044] CTA constraints include minimum turning radius, geometric continuity, and turning radius R. min The minimum turning radius R of the tunnel boring machine m Minimum turning radius R of tunnel segments s Minimum turning radius R required by the track r To ensure a smooth transition of the correction curve, the following formula must be satisfied:

[0045]

[0046] Where R is the radius of curvature of the correction curve; y′ and y″ are the first and second derivatives of equation y, respectively;

[0047] The first-order continuity requirement for the correction curve:

[0048]

[0049] Where x0, y0 are the coordinates of the starting point of the correction, x1, y1 are the coordinates of the ending point of the correction, L is the length of the correction spline, κ′ is the curvature of the curve's endpoint, and azimuth of the starting point of the correction is... and the azimuth of the correction endpoint X0, Y0 are combinations of generalized Fresnel integrals about the Euler spiral:

[0050]

[0051] The second-order continuity requirement of the correction curve:

[0052]

[0053] Among them, L i =s i+1 -s i >0, i = 0, 1, ..., N-1, the constraint (11) of the above vector form satisfies when i = 0, 1, ..., N-1

[0054] S4. Establish the second-order continuous Euler spiral equation based on the given CTA start and end information;

[0055] Based on the CTA start and end point information, the Euler spiral equation is established. A second-order continuous interpolation method for the Euler spiral is used, and a nonlinear function is introduced to define the first-order continuous interpolation condition.

[0056]

[0057]

[0058] Among them, h(A)=X0(2A, δ-A, φ0),

[0059] Here is a nonlinear equation for each node of the simplified second-order continuity:

[0060]

[0061] S5. Starting from the initial endpoint of CTA, search along DTA in the tunneling direction to obtain the optimal endpoint information of CTA that satisfies the CTA constraints and has the shortest CTA length. Use the CTA curve that satisfies the optimal endpoint information, starting point information and constraints as the shield tunneling correction planning path.

[0062] Starting from the initial endpoint of the CTA, search along the DTA towards the tunneling direction to obtain the optimal endpoint information of the CTA that satisfies the CTA constraints and has the shortest CTA length. The CTA curve that satisfies the optimal endpoint information, starting point information, and constraints is used as the shield tunneling correction planning path.

[0063] Example 1

[0064] like Figure 1 The flowchart shown below illustrates the path correction planning method, which includes the following steps:

[0065] S1. Obtain the actual axis ATA of the shield based on the shield guidance system, and determine the starting point information of the shield correction curve CTA based on the ATA, including coordinates, direction angle, and curvature.

[0066] S2. Search for the point closest to the starting point of the CTA on the tunnel design axis DTA, and use this as the initial endpoint of the correction curve CTA to obtain the initial endpoint information of the CTA, including coordinates, direction angle, and curvature.

[0067] S3. Determine the CTA constraints based on conditions such as minimum turning radius and curve continuity;

[0068] S4. Establish the second-order continuous Euler spiral equation based on the given CTA start and end information;

[0069] S5. Starting from the initial endpoint of CTA, search along DTA in the tunneling direction to obtain the optimal endpoint information of CTA that satisfies the CTA constraints and has the shortest CTA length. Use the CTA curve that satisfies the optimal endpoint information, starting point information and constraints as the shield tunneling correction planning path.

[0070] In step S1, the shield guidance system acquires the actual ATA (Automatic Anchorage Traverse) of the shield and determines the starting point information of the shield correction curve CTA (Correction Traverse Traverse) based on the ATA; specifically, this includes: the shield position vector q = [xyz]. T Shield angle vector The shield curvature vector u = [κ1κ2]; where (x,y,z) represents the position coordinates of the shield machine cutterhead center at the starting point of the CTA correction curve; This indicates the azimuth of the tunnel boring machine at the CTA starting point, including the horizontal azimuth θ and the pitch azimuth θ. (κ1, κ2) represent the curvatures of the starting curve of the correction curve CTA on the horizontal xoy plane and the vertical xoz plane, respectively.

[0071] In step S2, the point closest to the starting point of the CTA is searched on the tunnel design axis DTA. This point is used as the initial endpoint of the correction curve CTA, and the initial endpoint information of the CTA is obtained, including coordinates, orientation angle, curvature, and the initial endpoint coordinates (x1, y1, z1) and azimuth angle of the correction curve CTA.

[0072] In step S3, the minimum turning radius R min The minimum turning radius R of the tunnel boring machine can be determined based on engineering data. m Minimum turning radius R of tunnel segments s Minimum turning radius R required by the track r Together, it is determined that, in the horizontal direction, to ensure a smooth transition of the correction curve, the following formula must be satisfied:

[0073]

[0074] Where R is the radius of curvature of the correction curve; y′ and y″ are the first and second derivatives of equation y, respectively.

[0075] The first-order continuity requirement for the correction curve:

[0076]

[0077] Where x0, y0 are the coordinates of the starting point of the correction, x1, y1 are the coordinates of the ending point of the correction, L is the length of the correction spline, κ′ is the curvature of the curve endpoint, and the horizontal azimuth angle of the starting point of the correction is... And the horizontal azimuth of the correction endpoint X0, Y0 are combinations of generalized Fresnel integrals about the Euler spiral:

[0078]

[0079]

[0080] The second-order continuity requirement of the spline from the i-th end to the (i+1)-th end of the correction curve:

[0081]

[0082] Where L i =s i+1 -s i >0, i = 0, 1, ..., N-1. The above vector form constraint (19) satisfies when i = 0, 1, ..., N-1

[0083] The vertical constraints are similar to those for the horizontal constraints. By decomposing the three-dimensional coordinates onto the XOY and XOZ planes, we have:

[0084]

[0085] Where x0, z0 are the coordinates of the starting point of the correction, x1, z1 are the coordinates of the ending point of the correction, L is the length of the correction spline, κ′ is the curvature of the curve endpoint, and the horizontal azimuth angle of the starting point of the correction is... And the horizontal azimuth of the correction endpoint X0, Z0 are combinations of generalized Fresnel integrals about the Euler spiral:

[0086]

[0087]

[0088] The second-order continuity requirement of the spline from the i-th end to the (i+1)-th end of the correction curve:

[0089]

[0090] Where L i =s i+1 -s i >0, i = 0, 1, ..., N-1. The above vector form constraint (23) satisfies when i = 0, 1, ..., N-1

[0091] In step S4, G is satisfied. 2 Hermite's Euler spiral interpolation can be achieved by solving G... 1Hermite interpolation further simplifies the second-order continuity condition by adding constraints to ensure that the interpolation curve meets the requirements of the correction curve.

[0092] Introduce the condition for continuous interpolation of the first derivative of a nonlinear function (24):

[0093]

[0094]

[0095] Among them, h(A)=X0(2A, δ-A, φ0), Here It is the result of polar coordinate decomposition.

[0096] We introduce Newton's iteration method to approximate the solution of formula (24), and choose the initial value as:

[0097]

[0098] Here is a nonlinear equation for each node of the simplified G2 continuity:

[0099]

[0100] Adding endpoint angle variable θ to the first derivative continuous interpolation begin θ end Adding angle constraints reduces the degrees of freedom, making the problem solvable.

[0101]

[0102] In step S5, starting from the initial endpoint of the CTA, a search is performed along the DTA towards the tunneling direction to obtain the optimal endpoint information of the CTA that satisfies the CTA constraints and has the shortest CTA length. The CTA curve that satisfies the optimal endpoint information, starting point information, and constraints is used as the shield tunneling correction planning path.

[0103] The above allows the tunnel boring machine to start from the initial coordinates (x0, y0, z0) and azimuth angle under the initial deviation state. The Euler spiral correction curve, following a second-order continuous shortest path, reaches a point on the design axis with the correction endpoint coordinates (x1, y1, z1), and the azimuth angle is... The path planning for shield axis correction under other deviation conditions can be determined using the same method.

[0104] Example 2

[0105] like Figure 3 As shown, a second-order continuous path planning method for shield tunnel axis correction includes the following steps:

[0106] S1. Obtain the actual axis ATA of the shield based on the shield guidance system, and determine the starting point information of the shield correction curve CTA based on the ATA, including coordinates, direction angle, and curvature.

[0107] S2. Search for the point closest to the starting point of the CTA on the tunnel design axis DTA, and use this as the initial endpoint of the correction curve CTA to obtain the initial endpoint information of the CTA, including coordinates, direction angle, and curvature.

[0108] S3. Determine the CTA constraints based on conditions such as minimum turning radius and curve continuity;

[0109] S4. Establish the second-order continuous Euler spiral equation based on the given CTA start and end information;

[0110] S5. Starting from the initial endpoint of CTA, search along DTA in the tunneling direction to obtain the optimal endpoint information of CTA that satisfies the CTA constraints and has the shortest CTA length. Use the CTA curve that satisfies the optimal endpoint information, starting point information and constraints as the shield tunneling correction planning path.

[0111] In step S1, the shield tunneling guidance system acquires historical shield location information, specifically including: shield location vector q = [xyz]. T Shield angle vector The shield tunnel curvature vector u = [κ1κ2]; in this example, q = [0.05-0.05-0.05]. T p = [1° - 1°] T , u = [-0.0033 0.0033].

[0112] In step S2, the point closest to the starting point of the CTA is searched on the tunnel design axis DTA. This point is used as the initial endpoint of the correction curve CTA, and the initial endpoint information of the CTA is obtained, including coordinates, orientation angle, curvature, and the initial endpoint coordinates (x1, y1, z1) and azimuth angle of the correction curve CTA. In this example, the design axis is a straight line on the xoy plane that is collinear with the x-axis, and the expression is as follows:

[0113]

[0114]

[0115] It can be seen that the initial endpoint coordinates of the CTA curve are (0,0,0) and the azimuth angle is (0°,0°);

[0116] In step S3, the minimum turning radius R min The minimum turning radius R of the tunnel boring machine can be determined based on engineering data. m Minimum turning radius R of tunnel segmentss Minimum turning radius R required by the track r The decision is made jointly; in this example, the minimum turning radius R is chosen. min The length is 300m. To ensure a smooth transition of the correction curve, the following formula must be satisfied:

[0117]

[0118] Where R is the radius of curvature of the correction curve; y′ and y″ are the first and second derivatives of equation y, respectively.

[0119] In step S4, Newton's iteration method is introduced to approximate the solution of formula (24), and the initial value is selected as:

[0120]

[0121] in

[0122] Adding endpoint angle variable θ to the first derivative continuous interpolation begin θ end Adding angular constraints reduces the degrees of freedom, making the problem solvable.

[0123]

[0124] By setting the initial conditions and CTA endpoint coordinates, the initial interpolation correction path can be obtained, which satisfies the shortest distance and geometric continuity, but cannot meet the requirement of minimum turning radius.

[0125] In step S5, starting from the initial endpoint of the CTA, a search is performed along the DTA towards the tunneling direction to obtain the optimal endpoint information of the CTA that satisfies the CTA constraints and has the shortest CTA length. The CTA curve that satisfies the optimal endpoint information, starting point information, and constraints is used as the shield tunneling correction planning path.

[0126] As can be seen, the second-order continuous path planning method for shield axis correction of the present invention can accurately and reasonably provide the correction path of the shield machine when the shield machine deviates from the axis, ensuring that the shield machine smoothly corrects its trajectory without curvature abrupt change, so that the shield machine can continue to move along the designed route.

[0127] The embodiments of the present invention have been described above with reference to the accompanying drawings. However, the present invention is not limited to the specific embodiments described above. The specific embodiments described above are merely illustrative and not restrictive. Those skilled in the art can make many other forms under the guidance of the present invention without departing from the spirit and scope of the claims. All of these forms are within the protection scope of the present invention.

Claims

1. A second-order continuous path planning method for shield tunnel axis correction, characterized in that, Includes the following steps: S1. Obtain the actual axis ATA of the shield based on the shield guidance system, and determine the starting point information of the shield correction curve CTA based on the ATA, including coordinates, direction angle and curvature; S2. Search for the point closest to the starting point of the CTA on the tunnel design axis DTA, and use this as the initial endpoint of the correction curve CTA to obtain the initial endpoint information of the CTA, including coordinates, direction angle and curvature. S3. Determine the constraints of CTA based on the minimum turning radius and curve continuity conditions; S4. Establish the second-order continuous Euler spiral equation based on the given CTA start and end information; S5. Starting from the initial endpoint of CTA, search along DTA in the tunneling direction to obtain the optimal endpoint information of CTA that satisfies the CTA constraint conditions and has the shortest CTA length. Use the CTA curve that satisfies the optimal endpoint information, starting point information and constraint conditions as the shield tunneling correction planning path. In step S1, the shield tunneling correction curve CTA starting point information specifically includes: shield position vector q=[xyz] T , shield angle vector p=[ ] T , shield curvature vector u=[ ];in( () indicates the coordinates of the center of the shield machine cutterhead at the starting point of the CTA (Correction Traction Aspect) curve; () indicates the azimuth angle of the tunnel boring machine at the CTA starting point, including the horizontal azimuth angle. and elevation azimuth , ( () represents the curvature of the starting curve of the correction curve CTA on the horizontal xoy plane and the vertical xoz plane, respectively; In step S2, the location point closest to the starting point coordinates of the CTA is searched on the tunnel design axis DTA. This point is used as the initial endpoint of the correction curve CTA, and the initial endpoint information of the CTA is obtained, including coordinates, direction angle, curvature, and the initial endpoint coordinates of the correction curve CTA. ), azimuth ( ); In step S3, the constraints of CTA include minimum turning radius and geometric continuity. Minimum turning radius of the tunnel boring machine Minimum turning radius of tunnel segments Minimum turning radius required by the track To ensure a smooth transition of the correction curve, the following formula must be satisfied: Where R is the radius of curvature of the correction curve; and These are the first and second derivatives of equation y, respectively; The first-order continuity requirement for the correction curve: in, To correct the coordinates of the starting point, The coordinates of the endpoint for correction. To determine the length of the correction spline, The curvature at the endpoint of the curve, and the azimuth angle at the starting point of the correction. and the azimuth of the correction endpoint , For the combination of generalized Fresnel integrals with respect to the Euler spiral: The second-order continuity requirement of the correction curve: in, =0, 1, ..., -1, the constraint (4) in the above vector form satisfies when =0, 1, ..., -1 o'clock .

2. The second-order continuous path planning method for shield tunnel axis correction according to claim 1, characterized in that, In step S4, the Euler spiral equation is established based on the CTA start and end point information. The second-order continuous interpolation solution of the Euler spiral introduces a nonlinear function to define the first-order continuous interpolation condition: in, , Here is a nonlinear equation for each node of the simplified second-order continuity: 。 3. The second-order continuous path planning method for shield tunnel axis correction according to claim 1, characterized in that, In step S5, starting from the initial endpoint of CTA, a search is performed along DTA towards the tunneling direction to obtain the optimal endpoint information of CTA that satisfies the CTA constraints and has the shortest CTA length. The CTA curve that satisfies the optimal endpoint information, starting point information, and constraints is used as the shield tunneling correction planning path.

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