A shield construction path optimization method and device considering shield tail gap constraint and segment arrangement

Abstract

This invention discloses a method and apparatus for optimizing the tunnel boring machine (TBM) construction path, considering the shield tail gap constraint and segment arrangement, belonging to the field of TBM construction. Based on the design axis, the TBM correction axis is obtained through an interpolation algorithm; multiple segment ring models and the tunnel axis of the tunnel model are initialized; the tunnel axis is fitted to the shield correction axis using an optimization algorithm; a three-dimensional motion envelope surface of the TBM tail is established based on the correction axis; the shield tail gap is detected by comparing the tunnel model and the shield tail envelope surface ring by ring; if it is less than a threshold, the tunnel correction path optimization algorithm is called, and the tunnel axis is refitted; the optimized TBM construction path and segment arrangement scheme are output. By combining the TBM movement and segment ring assembly quality in the TBM correction path planning, dynamic adjustment of the correction path is achieved to ensure the stable operation of the TBM, which is of great significance for tunnel construction quality control, project progress tracking, and the safety of construction personnel and equipment.

Description

TECHNICAL FIELD

[0001] The present application belongs to the field of shield machine construction, and more particularly to a shield construction path optimization method and device considering shield tail gap constraint and segment arrangement. BACKGROUND

[0002] In the shield tunnel construction phase, due to the complexity of the construction environment, the forward geological conditions cannot be completely explored, combined with human operation errors and changes in line direction, there is an inevitable deviation between the running route of the shield machine and the design axis of the tunnel, especially when the shield machine turns or adjusts its posture. Therefore, it is necessary to plan the running path of the shield machine in real time. If the space between the outer surface of the segment and the tail brush is not enough during the operation of the shield machine, the shield machine will squeeze the segment when it advances. The squeezing action of the shield machine often causes the segment to dislocate. When the dislocation capacity exceeds a certain value, the segment will crack, which seriously affects the quality of the formed tunnel, the tunnel operation time, and increases the safety risk.

[0003] Currently, the design of the deviation correction path of the shield machine is to fit the tunnel design axis DTA with different deviation correction path linearities under the premise of ensuring the turning radius, such as straight line, quadratic curve, etc. However, the shield tail gap constraint condition is not considered in the deviation correction path planning stage. In addition, the real-time posture process of the shield machine relies on the subjective judgment of the operator based on the current deviation and the shield tail gap, and lacks a certain foresight. The commonly used methods to generate deviation correction curves are reverse circle correction, cubic curve correction, and cubic spline line correction. Among them, the effect of reverse circle correction is stronger than that of cubic curve correction. Reverse circle correction only satisfies the slope continuity at the start and end points and the interpolation points, and cubic spline line correction satisfies the curvature continuity at the two interpolation points, but only satisfies the slope continuity at the start and end points. The Euler spiral satisfies the curvature continuity at the interpolation points, the start and end points.

[0004] When the shield machine deviates from the tunnel axis, a deviation correction axis needs to be generated to guide the shield machine back to the tunnel axis. At the same time, the tunnel is a continuous structure, and the segment arrangement needs to be performed on the deviation correction curve to obtain a complete tunnel.

[0005] The current segment ring layout is usually determined according to the layout of the previous segment ring and the shield tail gap. The mature automatic layout means is now in the hands of companies such as VMT, and is listed as a commercial secret in combination with the guidance system, which is difficult for outsiders to know. In academic research, automatic layout is often optimized according to fitting error, and segment assembly quality factors such as shield tail gap are rarely used as constraints. In the process of deviation correction of the shield machine, the segment assembly quality and the movement process of the shield machine are not comprehensively considered. When the layout fails, the curvature radius of the deviation correction curve needs to be adjusted, which further limits the curvature radius; when the adjustment of the curvature radius has no obvious effect on the layout optimization, the time complexity needs to be sacrificed, and more accurate optimization algorithms need to be called. SUMMARY

[0006] In view of the defects of the related art, the purpose of the present application is to provide a shield construction path optimization method and device considering shield tail gap constraints and segment arrangement, aiming to solve the problems that in the existing shield tunnel construction process, the shield machine deviation correction path planning relies on the subjective experience of the operator, the shield tail gap constraints are not fully considered, and the shield machine posture adjustment process and the segment assembly and layout scheme are not optimized coordinately.

[0007] To achieve the above-mentioned purpose, the present application provides a shield construction path optimization method considering shield tail gap constraints and segment arrangement in a first aspect, comprising:

[0008] S100, obtaining preset posture data of a shield machine at each sampling point on a preset route, calculating a design axis of the shield machine according to the preset posture data; obtaining current posture data of the shield machine, generating an original deviation correction axis of the shield machine at each sampling point according to the current posture data and the preset posture data by using an interpolation algorithm, and converting it to the geodetic coordinate system to obtain a deviation correction axis;

[0009] S200, initializing a plurality of segment lining ring models, splicing to obtain a tunnel model according to the rule that adjacent rings are connected in head-to-tail and the center points of adjacent end faces coincide, and the center points of the head end face and the tail end face of each ring form a tunnel axis of the shield machine together;

[0010] S300, using an optimization algorithm to gradually adjust each segment of the tunnel axis, so that the tunnel axis fits the deviation correction axis to obtain an optimized tunnel axis; based on the deviation correction axis, a shield tail three-dimensional motion envelope surface of the shield machine is established, and the tunnel model is updated based on the optimized tunnel axis;

[0011] S400, discretizing the updated tunnel model and the shield tail three-dimensional motion envelope surface, and comparing the obtained point cloud data, and detecting the shield tail gap ring by ring at the measuring point; if the shield tail gap is less than the warning threshold, calling a tunnel deviation correction path optimization algorithm to obtain the rotation angle of each ring segment when the tail end face is closest to the design axis, obtaining an initial angle sequence, and setting it as the initial solution of the optimization algorithm, and returning to S300; if the shield tail gap is greater than or equal to the warning threshold, S500 is executed;

[0012] S500, outputting the optimized shield machine construction path and the segment arrangement scheme based on the optimized tunnel axis.

[0013] Optionally, S1 specifically comprises:

[0014] S101, obtaining preset posture data of a shield machine at each sampling point on a preset route, calculating the spatial coordinates of the shield machine at each sampling point, and connecting them in turn to obtain a design axis;

[0015] S102. Obtain the current attitude data of the tunnel boring machine and use a second-order continuous interpolation algorithm to generate the original correction axis of the tunnel boring machine at each sampling point based on the current attitude data and the preset attitude data.

[0016] S103. Based on the rotation matrix, rotate the original correction axis to the geodetic coordinate system where the tunnel boring machine is located to obtain the correction axis:

[0017] Global L r =R*L o

[0018] Among them, L o L represents the initial correction axis. r Indicates the correction axis. Global L r L represents r In the world coordinate system, R is the rotation matrix.

[0019] Optionally, the expression for the segment lining ring model is as follows:

[0020]

[0021] Where: l1 is the standard ring width of the segment, l2 is the width of segment K block, D2 is the outer diameter of the segment ring, θ∈[0,2π] is the rotation angle. In the initial segment lining ring model, the segment has no thickness, so RModel is the outer surface area of ​​a ring segment.

[0022] Optionally, the S200 specifically includes:

[0023] S201. Initialize multiple segment lining ring models [RModel0......RModel n The rotation angle between each ring is δ. i The tunnel model is obtained by sequentially splicing the rings together; where, for the i-th ring segment lining ring model RModel i Current ring RModel i head i With the next ring RModel i+1 tail end face center i+1 Overlapping, current ring RModel i The tail end face and the previous ring RModel i-1 The first end faces coincide;

[0024] S202, Create a multi-segment lining ring model [RModel0......RModel] n The center line segment [TLine0......TLine] in ] nThe tunnel axis TA is formed by connecting the segments sequentially; where, for the i-th ring segment lining ring model RModel i Connect the center of the tail end face. i and the head of the first end face i And through the segment lining ring model RModel i Center i Obtain the center line segment TLine i .

[0025] Optionally, the step of employing an optimization algorithm to progressively adjust each segment of the tunnel axis to fit the correction axis and obtain an optimized tunnel axis includes:

[0026] Set the optimization goal as follows:

[0027]

[0028] Where, d i Indicates the tunnel axis above points Distance to correction axis CTA Global L r The distance;

[0029] Setting constraints includes:

[0030] (1) The center of the first end face of the previous ring is fixed and coincides with the center of the tail end face of the ring to be assembled.

[0031] (2) The x-axis direction of the tail end face of the ring to be assembled is located on the conical surface with the center of the first end face of the previous ring as the vertex and the x-axis of the first end face of the previous ring as the axis of rotation, and is in the same plane as the axis of rotation.

[0032] (3) Meets the requirements of engineering operations;

[0033] A numerical optimization algorithm is used to perform nonlinear optimization on the objective function, so that the tunnel axis fits the correction axis, resulting in an optimized tunnel axis. The optimized tunnel axis is then transformed using a homogeneous coordinate transformation matrix. The solution is obtained by transforming to the local coordinate system {O0}, resulting in the optimized tunnel axis in coordinate system {O0}.

[0034] Wherein, the homogeneous coordinate transformation matrix is

[0035] Optionally, establishing the three-dimensional motion envelope of the tunnel boring machine's tail based on the correction axis, and updating the tunnel model based on the optimized tunnel axis, includes:

[0036] The shield machine is regarded as a cylinder, a three-dimensional envelope surface of the shield machine is moved along the deviation axis in a global coordinate system {Global} based on an expression of the deviation axis in the global coordinate system {Global}, and a three-dimensional motion trajectory is obtained:

[0037] The starting three-dimensional envelope surface is set as:

[0038]

[0039] wherein x i ∈ [0, l], x i The number of the sampling points is set according to the number of sampling points, and l is the distance from the center of the shield tail of the shield machine to the center of the cutter head.

[0040] A direction vector on the deviation axis is obtained:

[0041] V i = [x ri -x ri-1 y ri -y ri-1 z ri -z ri-1 ]

[0042] wherein [x ri-1 , y ri-1 , z ri-1 ] and [x ri , y ri , z ri ] are direction vectors of adjacent two points of the deviation axis .

[0043] The direction vector of the three-dimensional starting envelope surface is:

[0044] T i = [1 0 0]

[0045] The direction vector of the rotation axis of the envelope surface adjusted to the direction of the deviation axis CTA is

[0046] wherein the rotation angle is:

[0047]

[0048] The rotation matrix is constructed as follows:

[0049]

[0050] The three-dimensional envelope surface of the i-th sampling point is calculated as:

[0051] L i = R*L i-1.

[0052] Optionally, the tunnel model is updated based on the optimized tunnel axis, comprising:

[0053] According to the optimized tunnel axis, an angle between each segmental lining ring is obtained, and a plurality of segmental lining ring models [RModel0... RModel n ] are sequentially spliced with each other, and an angle δ i between each segmental lining ring is assigned a value of the angle of the i-th ring of the tunnel axis, so as to obtain an updated tunnel model.

[0054] The updated tunnel model in the coordinate system {O i} is converted to the coordinate system {O0} through the homogeneous coordinate transformation matrix, so as to obtain the updated tunnel model in the coordinate system {O0}.

[0055] Optionally, the updated tunnel model and the three-dimensional movement envelope surface of the shield tail are discretely processed, and the obtained point cloud data are compared, and the shield tail gap is detected in the ring direction at each ring, comprising:

[0056] The points on the surface of the i-th segmental lining ring and the envelope surface of the surrounding shield tail are converted to the local coordinate system of the segmental lining ring through the transformation matrix, so as to obtain

[0057] The polar angle θ of the i-th segmental lining ring is calculated:

[0058] θ = atan2 (Y, Z)

[0059]

[0060] The position of the segmental lining ring in the cross section is determined through the polar angle θ, and whether the X coordinate of the point of the envelope surface of the shield tail is within the range is determined:

[0061] X ∈ [x min , x max ]

[0062] Whether the Y and Z coordinates of the point of the envelope surface of the shield tail are within the circular cross section is determined:

[0063]

[0064] If the point of the envelope surface of the shield tail satisfies X ∈ [x min , x max ] and , the shield tail gap is less than the warning threshold.

[0065] Optionally, the tunnel deviation rectification path optimization algorithm comprises:

[0066] For the i-th lining ring, set the assemblable point x as the decision variable, and the objective function is:

[0067] min x (w1·E total (x)+w2·E maxdev (x)+w3·E variance (x))

[0068] Wherein, the assemblable point x is the assemblage position of the wedge-shaped ring K block, and the homogeneous transformation matrix of the i-th lining ring relative to the starting lining ring is determined and the direction of the center line segment TLine i ; E total (x) is the total distance deviation of the points on the i-th lining ring center axis to the target curve CTA, expressed as the sum of all distance deviations; E max dev (x) represents the maximum distance deviation, that is, the maximum value in all distance errors; E variance (x) is the standard deviation of the distance deviation, which measures the uniformity of the distance distribution; w1, w2 and w3 are weight coefficients for balancing the importance of each target, and should satisfy w1+w2+w3=1 to ensure the normalization of the weight.

[0069] In the second aspect, the application further provides a shield construction path optimization device considering the shield tail gap constraint and the segment arrangement, comprising:

[0070] The deviation rectification axis construction module is configured to obtain preset posture data of the shield machine at each sampling point on a preset line, calculate a design axis of the shield machine according to the preset posture data, obtain current posture data of the shield machine, generate an original deviation rectification axis of the shield machine according to the current posture data and the preset posture data at each sampling point by using an interpolation algorithm, and convert the original deviation rectification axis to a geodetic coordinate system to obtain a deviation rectification axis.

[0071] The tunnel axis construction module is configured to initialize a segment lining ring model, splice the tunnel model according to the rule that adjacent rings are connected end to end and the center points of adjacent end faces coincide, and connect the center points of the head end face and the tail end face of each ring to form a tunnel axis of the shield machine.

[0072] The curve optimization module is configured to fit the tunnel axis to the deviation rectification axis by using an optimization algorithm, establish a shield tail three-dimensional motion envelope surface of the shield machine based on the deviation rectification axis, and establish a tunnel model based on the tunnel axis.

[0073] The detection module is used for discretizing the updated tunnel model and the three-dimensional movement envelope surface of the shield tail, and comparing the obtained point cloud data to detect the shield tail gap at the measuring point of each ring; if the shield tail gap is less than the early warning threshold, the tunnel deviation correction path optimization algorithm is called to obtain the rotation angle of the tail end surface of each ring when the tail end surface is closest to the design axis, to obtain an initial angle sequence, and the initial angle sequence is set as the initial solution of the optimization algorithm, and the process jumps to the curve optimization module; if the shield tail gap is greater than or equal to the early warning threshold, the process jumps to the output module.

[0074] The output module is used for outputting the optimized shield construction path and the segment arrangement scheme based on the optimized tunnel axis.

[0075] The above technical scheme conceived by the present application can achieve the following beneficial effects compared with the prior art:

[0076] 1. The present application provides a shield construction path optimization method considering shield tail gap constraint and segment arrangement, which automatically fits the segment layout through the deviation correction axis, and judges whether the layout result meets the engineering specification, and if not, the layout is re-performed. The deviation correction curve determines the movement path of the shield machine, which can reflect the shield machine posture adjustment process, and the tunnel axis determines the segment assembly layout scheme. In the present scheme, the numerical optimization algorithm is used to fit the tunnel axis and the deviation correction axis, and the process of adjusting the tunnel axis according to the deviation correction curve reflects the collaborative optimization of the shield machine posture adjustment process and the segment assembly layout scheme. The shield tail gap is detected ring by ring, which can effectively avoid the shield tail collision in shield construction; by limiting the total deviation, the optimal strategy for fitting the deviation correction axis is obtained, and the tunnel axis meeting the kinematics of the shield machine and the constraint conditions is generated. The present application solves the problem that the previous automatic segment layout takes the total deviation as the main purpose, lacks the actual engineering limiting factors such as shield tail gap and minimum turning radius, and comprehensively considers the segment assembly quality and the shield machine movement process, thereby reducing the risk of segment rupture caused by collision between segment and shield tail, ensuring safety, saving the time of workers for correcting each ring according to experience, and having important economic value for shortening the construction period and saving cost.

[0077] 2. The present application provides a shield construction path optimization method considering shield tail gap constraint and segment arrangement. In the present scheme, the Euler spiral generated by interpolation is used as the deviation correction axis, thereby solving the problem that the traditional deviation correction axis does not meet the curvature continuity at the start and end points, improving the smoothness of the deviation correction axis, and reducing the construction risk to ensure safety on the clothoid curve. BRIEF DESCRIPTION OF DRAWINGS

[0078] Figure 1 is a flow chart of shield dynamic path optimization in the embodiment of the present application;

[0079] Figure 2is a schematic diagram of a coordinate system established on a segment ring in an embodiment of the present application; which includes a head end face coordinate system, a centroid coordinate system and a tail end face coordinate system;

[0080] Figure 3 is a schematic diagram of a tunnel model constructed in an embodiment of the present application, different colors represent different wedge-shaped rings;

[0081] Figure 4 is a schematic diagram of fitting a tunnel axis to a deviation correction axis in an embodiment of the present application;

[0082] Figure 5 is a schematic diagram of a shield tail gap area that is too small in an embodiment of the present application. DETAILED DESCRIPTION

[0083] In order to make the purpose, technical scheme and advantages of the present application clearer and more apparent, the present application will be further described in detail below in combination with the drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present application and do not limit the present application. In addition, the technical features involved in each embodiment of the present application described below can be combined with each other as long as they do not conflict with each other.

[0084] The content involved in the above embodiments will be described below in combination with a preferred embodiment.

[0085] Embodiment one

[0086] As shown in Figure 1 , a shield construction path optimization method considering shield tail gap constraints and segment arrangement, comprising:

[0087] S100, obtaining preset attitude data of a shield machine at each sampling point on a preset line, calculating a design axis of the shield machine according to the preset attitude data; obtaining current attitude data of the shield machine, generating an original deviation correction axis of the shield machine at each sampling point according to the current attitude data and the preset attitude data by using an interpolation algorithm, and converting it to a geodetic coordinate system to obtain a deviation correction axis;

[0088] S200, initializing a plurality of segment lining ring models, splicing to obtain a tunnel model according to the rule that adjacent rings are connected end to end and the center points of adjacent end faces coincide, and the center points of the head end face and the tail end face of each ring are connected to form a tunnel axis of the shield machine;

[0089] S300, using an optimization algorithm to gradually adjust each segment of the tunnel axis, so that the tunnel axis fits the deviation correction axis to obtain an optimized tunnel axis; based on the deviation correction axis, establishing a three-dimensional movement envelope surface of the shield tail of the shield machine, and updating the tunnel model based on the optimized tunnel axis;

[0090] S400: Discretize the updated tunnel model and the three-dimensional motion envelope of the shield tail, and compare the obtained point cloud data. Detect the shield tail gap ring by ring at the circumferential measurement points. If the shield tail gap is less than the warning threshold, call the tunnel correction path optimization algorithm to obtain the rotation angle of each ring segment when the tail end face is closest to the design axis, obtain the initial angle sequence, and set it as the initial solution of the optimization algorithm, then return to S300. If the shield tail gap is greater than or equal to the warning threshold, then execute S500.

[0091] S500, the optimized tunnel boring machine construction path and segment layout scheme based on the optimized tunnel axis output.

[0092] Based on the kinematics of the tunnel boring machine (TBM) fitting the tunnel axis and the requirements for segment assembly quality, this project ensures that the tail clearance is within a safe range and guarantees segment assembly quality, thereby further ensuring the safe operation of the TBM. It addresses the problems in existing TBM construction processes, such as the reliance on operator experience for TBM correction path planning, insufficient consideration of tail clearance constraints, and lack of coordinated optimization between the TBM attitude adjustment process and the segment assembly layout plan.

[0093] Using the current position and posture parameters of the tunnel boring machine, the original correction axis L is obtained by interpolation through the Euler spiral in the horizontal plane and the Euler spiral in the vertical plane, respectively. o (s) = (x, y, z). Where s is the length of the correction axis, (x, y, z) are the three-dimensional spatial coordinates of the correction axis corresponding to the arc length s, and the total arc length of the correction axis is S. The segment lining ring model adopts a wedge-shaped ring model. To construct the representation model of the wedge-shaped ring, the origin O is taken as the center of the wedge-shaped ring, the x-axis is the direction from the center of the tail end face to the center of the head end face, the y-axis is the direction from the center of the wedge-shaped ring K block, and the z-axis is determined by the right-hand screw rule, forming a coordinate system {O}. The segment lining ring model is then assembled according to the preset splicing rules to obtain the tunnel model, thus obtaining the tunnel axis. Finally, a numerical optimization algorithm is used to fit the correction axis to the tunnel axis, thereby obtaining the optimized tunnel curve. The optimized tunnel curve needs to be validated. The validation method involves using segment layout to check the shield tail gap ring by ring for the segment arrangement corresponding to the optimized tunnel curve. When the shield tail gap does not meet the preset threshold, the tunnel deviation correction path optimization algorithm is invoked to further optimize the optimized tunnel axis, update the tunnel model, and comprehensively consider the segment assembly quality and the tunnel boring machine (TBM) movement process. The optimized TBM construction path and segment arrangement scheme are then output. By comprehensively considering the shield tail gap constraint and the segment ring assembly quality in the TBM deviation correction path planning, dynamic adjustment of the deviation correction path is achieved to ensure the stable operation of the TBM and cope with complex and highly uncertain geological environments. This is of great significance for ensuring tunnel construction quality, controlling project progress, and ensuring the safety of construction personnel and equipment.

[0094] Optionally, S1 specifically includes:

[0095] S101, obtain preset posture data of the shield tunneling machine at each sampling point on a preset line, calculate spatial coordinates of the shield tunneling machine at each sampling point, and sequentially connect the spatial coordinates to obtain a design axis;

[0096] S102, obtain current posture data of the shield tunneling machine, and generate an original deviation correction axis of the shield tunneling machine according to the current posture data and the preset posture data at each sampling point by using a second-order continuous interpolation algorithm;

[0097] S103, rotate the original deviation correction axis to a geodetic coordinate system in which the shield tunneling machine is located according to a rotation matrix to obtain a deviation correction axis:

[0098] Global L r =R*L o

[0099] wherein, L o represents an initial deviation correction axis, L r represents the deviation correction axis, Global L r represents L r in the world coordinate system, and R is a rotation matrix;

[0100] On the basis of the above, the second-order continuous interpolation algorithm in step S1 satisfies a second-order continuous condition. Specifically, the second-order continuous interpolation algorithm realizes construction of an Euler spiral. The Euler spiral is a parameterized planar curve (x(s), y(s)); wherein, s is an arc length. Six real number parameters: an initial point (x0, y0), an initial angle θ0, a starting curvature κ0, a starting value κ'0 of a derivative of the starting curvature, and a length L.

[0101] The spatial coordinates, the angle, and the curvature corresponding to the arc length s on the spiral are determined by the following integrals:

[0102]

[0103] Further, the curve is given by a finite set of real number parameters 0 = s0 < s1 < … < s N and (p i , θ i , κ i , κ' i ), and the parameters of the spline should satisfy the following continuity conditions between i and i+1 segments:

[0104]

[0105] wherein, L i = s i+1 -s i > 0, i = 0, 1, …, N-1.

[0106] L o Further, in order to convert the rectification axis in the current coordinate system to the geodetic coordinate system measured by the shield machine, coordinate transformation needs to be performed on the original rectification axis L o (s). Let the original rectification path The rotation matrix R is constructed to rotate the rectification axis L

[0107] The constructed rotation matrix R satisfies the following conditions:

[0108] The starting tangent direction: V start = [x o2 -x o1 y o2 -y o1 z o2 -z o1 ];

[0109] Wherein, x oi represents the x coordinate of the i-th point on the initial rectification axis L o , y oi represents the y coordinate of the i-th point on the initial rectification axis L o , and z oi represents the z coordinate of the i-th point on the initial rectification axis L o ;

[0110] The target direction: T target = [1 0 0]

[0111] Rotation axis:

[0112] Wherein, r1, r2, r3 represent the three components of r, and norm represents the modulus operation.

[0113] Rotation angle:

[0114] Based on the above conditions, the intermediate matrix k is constructed:

[0115]

[0116] The rotation matrix R is constructed:

[0117]

[0118] Further, as Figure 2As shown, the model of the wedge-shaped ring is a pipe lining ring RModel. To construct the representation model of the wedge-shaped ring, the center of the wedge-shaped ring is taken as the origin O, the center of the tail end surface is taken as the x-axis, the center of the wedge-shaped ring K block is taken as the y-axis, and the z-axis is determined according to the right-hand screw rule, to form a coordinate system {O}.

[0119] Optionally, the expression of the pipe lining ring model is as follows:

[0120]

[0121] wherein l1 is the standard ring width of the pipe, l2 is the K block width of the pipe, D2 is the outer diameter of the pipe ring, and θ ∈ [0, 2π] is the rotation angle. The initial pipe lining ring model has no thickness, and thus RModel is the outer surface area of a ring pipe.

[0122] The tunnel axis TA is spliced based on the center line TLine of the multi-ring RModel. Specifically, for the i-th ring RModel i , the center line segment TLine i is a line segment connecting the tail end surface center tail i , the head end surface center head i of the lining ring RModel i , and passing through the center Center i of the lining ring RModel i . The center line of RModel i is represented by the tail end surface center tail i and the head end surface center head i , and TLine i = [tail i , head i ]. Further, [tail i , head i ] is the coordinate of the tail end surface center tail i and the head end surface center head i in the coordinate system {O i} constructed with the center of the lining ring RModel i as the origin, wherein l1 is the standard ring width of the pipe, and l2 is the K block width of the pipe.

[0123] Optionally, S200 specifically includes:

[0124] S201, initializing a plurality of pipe lining ring models [RModel0......RModel n ], and the rotation angle between each ring is δ i S202, sequentially splicing the rings to obtain a tunnel model; wherein for the i-th ring pipe lining ring model RModel iCurrent ring RModel i head i With the next ring RModel i+1 tail end face center i+1 Overlapping, current ring RModel i The tail end face and the previous ring RModel i-1 The first end faces coincide;

[0125] S202, Create a multi-segment lining ring model [RModel0......RModel] n The center line segment [TLine0......TLine] in ] n The tunnel axis TA is formed by connecting the segments sequentially; where, for the i-th ring segment lining ring model RModel i Connect the center of the tail end face. i and the head of the first end face i And through the segment lining ring model RModel i Center i Obtain the center line segment TLine i .

[0126] Furthermore, the tunnel axis TA (Tunnel Axis) can be represented as... Wherein, Center0 represents the center of the initial lining ring. Further, the point set refers to coordinates within a coordinate system {O0} constructed with the center of the initial lining ring. Further, to calculate the RModel of the i-th lining ring... i Head i The representation in coordinate system {O0} requires calculating RModel. i First end face coordinate system {H i}、Tail end face coordinate system {E i} and the central coordinate system {O i The homogeneous transformation matrix relative to coordinate system {O}. Furthermore, {O} i Homogeneous transformation matrix relative to coordinate system {O0} Furthermore, for each ring RModel i First end face coordinate system {H i The method for establishing this is as follows: taking the direction perpendicular to the first end face outwards from the lining ring as the x-axis, and the direction parallel to the first end face pointing towards segment K, and aligning with {O}. i The y-axis direction of} lies in the same plane as {H}. i The y-axis of} is determined using the right-hand rule to determine the z-axis; for each ring RModel i Tail end face coordinate system {E i}, the establishment method is: taking the vertical tail end surface direction into the lining ring as the x axis, taking the direction parallel to the tail end surface direction and pointing to the K block segment direction as the y axis of {O i}, and taking the z axis in the right-hand rule. i

[0127] Suppose that the tunnel is composed of n lining rings [RModel0... RModel n ], the rotation angle of each ring relative to the previous ring is δ i+1 , the y axis of {H i} rotates relative to {H i} around the x axis of {H i . n The n lining rings [RModel0... RModel i ] contain n angle transformations: δ = [δ1... δ n ].

[0128] Further, for each ring segment RModel i in the tunnel, the coordinates of the segment in the starting lining ring coordinate system {O0} are Wherein: The calculation method is as follows:

[0129]

[0130] Wherein, θ is determined by the wedge amount of the segment is the standard ring width of the segment, l2 is the K block width of the segment, and D2 is the outer diameter of the segment ring.

[0131] The calculation method is as follows:

[0132]

[0133]

[0134] The calculation method is as follows:

[0135]

[0136] Further, through the above construction scheme, the tunnel axis composed of n lining rings [RModel0... RModel n ] can be obtained .

[0137] ​​Based on the above, the required number of tunnel segments is further calculated using the obtained CTA arc length of the correction axis and the parameters of the wedge-shaped ring RModel model.

[0138] Furthermore, the tunnel model is composed of each ring of RModel connected end to end, such as... Figure 3 As shown, that is, {E i The origin of} and {H i-1 The origins of the rings coincide, and the rotation angle of each ring relative to the previous ring is:

[0139] δ=[… δ i …] N

[0140] Specifically, δ i E represents i x-axis around H i-1 The angle of rotation along the x-axis. Where, E i x-axis and H i-1 The angle between the x-axis and the x-axis is determined by the unilateral wedge amount of the wedge ring RModel model.

[0141] Optional, such as Figure 4 As shown, the optimization algorithm is used to gradually adjust each segment of the tunnel axis to make the tunnel axis fit the correction axis, thereby obtaining an optimized tunnel axis, including:

[0142] Set the optimization goal as follows:

[0143]

[0144] Where, d i Indicates the tunnel axis above points Distance to correction axis CTA Global L r The distance;

[0145] Setting constraints includes:

[0146] (1) The center of the first end face of the previous ring is fixed and coincides with the center of the tail end face of the ring to be assembled.

[0147] (2) The x-axis direction of the tail end face of the ring to be assembled is located on the conical surface with the center of the first end face of the previous ring as the vertex and the x-axis of the first end face of the previous ring as the axis of rotation, and is in the same plane as the axis of rotation.

[0148] (3) Meets the requirements of engineering operations;

[0149] Among them, (3) specifically includes: (31) meeting the requirements for bolt hole position and through joint and staggered joint of segment ring assembly; (32) meeting the requirements for staggered joint between segment rings;

[0150] A numerical optimization algorithm is used to perform nonlinear optimization on the objective function, so that the tunnel axis is fitted to the correction axis to obtain an optimized tunnel axis, and the optimized tunnel axis is converted to a local coordinate system {O0} through a homogeneous coordinate transformation matrix to obtain the optimized tunnel axis in the coordinate system {O0};

[0151] The homogeneous coordinate transformation matrix is

[0152] Before establishing the three-dimensional movement envelope surface of the shield tail of the shield tunneling machine, the method further comprises a two-dimensional movement envelope surface solving process of the shield tunneling machine.

[0153] The two-dimensional envelope surface is an envelope surface formed by moving a shield tunneling machine as a rectangle on a plane. The center of the rectangle is the center of the shield tunneling machine, and the envelope surface formed by moving the center of the rectangle on the plane is established in the following manner: let f(x) be a motion trajectory equation of the center of the rectangle on a two-dimensional plane, then a tangent vector and a normal vector of the motion trajectory f(x) of the center of the rectangle can be represented as:

[0154]

[0155] where f'(x) represents the derivative of f(x);

[0156] The positions of the four corner points P1, P2, P3, and P4 of the rectangle are:

[0157]

[0158] When the center of the rectangle moves on an arbitrary curve in space, the left and right edges l1 and l2 are represented as:

[0159]

[0160] where s represents the movement distance, and k represents the edge number.

[0161] Optionally, the method further comprises:

[0162] The shield tunneling machine is regarded as a cylinder, a three-dimensional envelope surface of the shield tunneling machine is moved along the correction axis in the geodetic coordinate system {Global} based on the expression of the correction axis in the geodetic coordinate system {Global}, and a three-dimensional movement trajectory is obtained:

[0163] The initial three-dimensional envelope surface is set as:

[0164]

[0165] wherein x i ∈ [0, l], x i is the number of sampling points, and l is the distance from the center of the tail shield to the center of the cutter head of the tunneling machine.

[0166] Obtain a direction vector on the correction axis:

[0167] V i = [x ri -x ri-1 y ri -y ri-1 z ri -z ri-1 ]

[0168] wherein [x ri-1 ,y ri-1 ,z ri-1 ] and [x ri ,y ri ,z ri ] are direction vectors of two adjacent points on the correction axis .

[0169] The direction vector of the three-dimensional starting envelope surface is:

[0170] T i = [1 0 0]

[0171] The direction vector of the rotation axis of the envelope surface adjusted to the direction of the correction axis CTA is

[0172] wherein the rotation angle is:

[0173]

[0174] The rotation matrix is constructed as follows:

[0175]

[0176] The three-dimensional envelope surface of the i-th sampling point is calculated as:

[0177] L i = R*L i-1 .

[0178] After the three-dimensional envelope surface of the tunneling machine is solved, the point set on the tail shield envelope surface is obtained by sampling the points on the tail shield envelope surface, which is used for subsequent tail shield gap detection.

[0179] Optionally, the tunnel model is updated based on the optimized tunnel axis, comprising:

[0180] According to the optimized tunnel axis, an angle between each segment lining ring is obtained, a plurality of segment lining ring models [RModel0...RModel n ] are sequentially spliced with each other, and an angle δ i between each segment of each ring is assigned as a turning angle of the i-th ring of the tunnel axis, and an updated tunnel model is obtained;

[0181] The updated tunnel model in the coordinate system {O i} is converted to the coordinate system {O0} through the homogeneous coordinate transformation matrix to obtain an updated tunnel model in the coordinate system {O0}.

[0182] Optionally, as shown in Figure 5 , the updated tunnel model and the shield tail three-dimensional motion envelope surface are discretized, and the obtained point cloud data are compared, and shield tail gap detection is performed on the ring measuring points, including:

[0183] The points on the surface of the i-th ring segment and the surrounding shield tail envelope surface are converted to the local coordinate system of the ring segment through a transformation matrix, to obtain

[0184] The polar angle θ of the i-th ring segment is calculated:

[0185] θ=atan2(Y,Z)

[0186]

[0187] The cross-sectional position of the segment ring is determined by the polar angle θ, and whether the X coordinate of the point of the shield tail envelope surface is within the range is determined:

[0188] X∈[x min ,x max ]

[0189] Whether the Y and Z coordinates of the point of the shield tail envelope surface are within the circular cross-section is determined:

[0190]

[0191] If the point of the shield tail envelope surface satisfies X∈[x min ,x max ] and , the shield tail gap is less than the warning threshold.

[0192] Wherein, the point of the surrounding shield tail envelope surface is searched for the i-th ring segment.The octree is used for data storage to accelerate the searching speed. After being converted into the local coordinate system of the i-th segment, the position of the segment ring is determined by the polar angle θ, so as to determine the shield tail gap.

[0193] Optionally, the tunnel deviation rectification path optimization algorithm comprises:

[0194] For the i-th segment lining ring, the point position x that can be assembled is a decision variable, and the objective function is:

[0195] min x (w1·E total (x)+w2·E maxdev (x)+w3·E variance (x))

[0196] wherein the point position x that can be assembled is the assembling position of the wedge-shaped ring K block, and the homogeneous transformation matrix of the i-th segment relative to the starting segment is determined and the direction of the center line segment TLine i ; E total (x) is the total distance deviation of the point on the i-th segment lining ring center axis to the target curve CTA, which is expressed as the sum of all distance deviations; E max dev (x) represents the maximum distance deviation, that is, the maximum value in all distance errors; E variance (x) is the standard deviation of the distance deviation, which measures the uniformity of the distance distribution; w1, w2 and w3 are weight coefficients for balancing the importance of each target, and should satisfy w1+w2+w3=1 to ensure the normalization of the weight.

[0197] wherein the tunnel deviation rectification path optimization algorithm is the adjustment of the assembling point position of each segment. In this embodiment, 0.7, 0.2 and 0.1 are respectively set; in this embodiment, the staggered jointing condition needs to be met, the bolt hole position or the assembling point position meets the constraint of 22.5°, that is, the rotation angle δ i in step S2 can only be a multiple of 22.5°.

[0198] Finally, the optimized shield construction path and segment arrangement scheme are output according to the optimized tunnel axis. In addition, the optimized tunnel axis needs to be qualitatively verified according to the finally obtained deviation rectification axis, whether the optimized tunnel axis surrounds the deviation rectification axis or whether the deviation range is within the preset threshold is observed through the visual window.

[0199] The deviation rectification axis CTA final is the finally adjusted The segment arrangement scheme based on the optimized tunnel axis TA refers to the assembling point position of the N-th segment.

[0200] The deviation correction axis is the construction path of the shield machine, that is, the movement trajectory of the shield machine; and the segment arrangement is arranged according to the turning angle between each ring given by the optimized tunnel axis.

[0201] In the embodiment, the segment arrangement is automatically fitted by the deviation correction axis, and whether the arrangement result meets the engineering specification is judged, and if not, how to re-arrange is determined. The numerical optimization algorithm is used to fit the tunnel axis and the deviation correction axis, which can solve the problem that the traditional deviation correction axis does not meet or does not meet the curvature continuity at the start and end points, improve the smoothness of the deviation correction axis, reduce the construction risk, and ensure the safety on the easement trajectory. The shield tail gap is detected ring by ring, which can effectively avoid the shield tail collision in the shield construction; the optimal strategy of fitting the deviation correction axis is obtained by limiting the total deviation size, and the tunnel axis meeting the kinematics and constraint conditions of the shield machine is generated. The shield machine deviation path planning depends on the subjective experience of the operator, the automatic segment arrangement takes the total deviation size as the main purpose, and lacks the actual engineering limiting factors such as the shield tail gap and the minimum turning radius, the segment assembly quality and the shield machine movement process are comprehensively considered, the risk of segment rupture caused by the collision of segments and shield tail is reduced, and the safety is ensured. Automatic arrangement saves the time of workers for correcting each ring according to experience, has important economic value for shortening the construction period and saving the cost.

[0202] Embodiment two

[0203] The application also provides a shield construction path optimization device considering shield tail gap constraint and segment arrangement, comprising:

[0204] The deviation correction axis construction module is used for acquiring preset posture data of the shield machine at each sampling point on a preset line, calculating a design axis of the shield machine according to the preset posture data, acquiring current posture data of the shield machine, generating an original deviation correction axis of the shield machine at each sampling point according to the current posture data and the preset posture data by using an interpolation algorithm, and converting the original deviation correction axis to a geodetic coordinate system to obtain a deviation correction axis.

[0205] The tunnel axis construction module is used for initializing a segment lining ring model, splicing the tunnel model according to the rule that adjacent rings are connected end to end and the center points of adjacent end faces coincide, and connecting the center points of the head end face and the tail end face of each ring to form a tunnel axis of the shield machine.

[0206] The curve optimization module is used for fitting the tunnel axis to the deviation correction axis by using an optimization algorithm; a shield tail three-dimensional movement envelope surface of the shield machine is established based on the deviation correction axis, and a tunnel model is established based on the tunnel axis.

[0207] The detection module is configured to discretize the updated tunnel model and the three-dimensional movement envelope surface of the shield tail, compare the obtained point cloud data, and detect the shield tail gap at each ring of the measurement points in the ring direction; if the shield tail gap is less than a warning threshold, a tunnel deviation correction path optimization algorithm is called to obtain the rotation angle of each ring of segments when the tail end surface of each ring is closest to the design axis, obtain an initial angle sequence, and set the initial angle sequence as an initial solution of the optimization algorithm, and jump to the curve optimization module; if the shield tail gap is greater than or equal to the warning threshold, the output module is jumped to.

[0208] The output module is configured to output the optimized shield construction path and the segment arrangement scheme based on the optimized tunnel axis.

[0209] The shield construction path optimization device considering the shield tail gap constraint and the segment arrangement provided by the embodiment of the present application is used to execute the shield construction path optimization method considering the shield tail gap constraint and the segment arrangement provided by any embodiment of the present application, and has the corresponding beneficial effects.

[0210] Those skilled in the art can easily understand that the above description is only a preferred embodiment of the present application, and is not intended to limit the present application, and any modification, equivalent replacement and improvement made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method for optimizing the tunnel boring machine (TBM) construction path considering tail clearance constraints and segment arrangement, characterized in that, include: S100: Obtain the preset attitude data of the tunnel boring machine at each sampling point on the preset line, and calculate the design axis of the tunnel boring machine based on the preset attitude data; The current attitude data of the tunnel boring machine is obtained. An interpolation algorithm is used to generate the original correction axis of the tunnel boring machine at each sampling point based on the current attitude data and the preset attitude data. The original axis is then converted to the geodetic coordinate system to obtain the correction axis. S200. Initialize multiple segment lining ring models and splice them together according to the rule that the beginning and end of adjacent rings are connected and the center points of adjacent end faces coincide to obtain the tunnel model. At the same time, the line connecting the center points of the beginning and end faces of each ring together constitutes the tunnel axis of the shield machine. S300. Using an optimization algorithm, each segment of the tunnel axis is gradually adjusted to make the tunnel axis fit the correction axis, thus obtaining an optimized tunnel axis. Based on the aforementioned correction axis, a three-dimensional motion envelope surface of the shield tail of the tunnel boring machine is established, and the tunnel model is updated based on the optimized tunnel axis. S400: Discretize the updated tunnel model and the three-dimensional motion envelope of the shield tail, and compare the obtained point cloud data. Detect the shield tail gap ring by ring at the circumferential measurement points. If the shield tail gap is less than the warning threshold, call the tunnel correction path optimization algorithm to obtain the rotation angle of each ring segment when the tail end face is closest to the design axis, obtain the initial angle sequence, and set it as the initial solution of the optimization algorithm, then return to S300. If the shield tail gap is greater than or equal to the warning threshold, then execute S500. S500, Based on the optimized tunnel axis output, the shield machine construction path and segment layout scheme are optimized. The step of employing an optimization algorithm to progressively adjust each segment of the tunnel axis to fit the correction axis and obtain an optimized tunnel axis includes: Set the optimization goal as follows: in, Indicates the tunnel axis above points Distance to correction axis CTA The distance; Setting constraints includes: (1) The center of the first end face of the previous ring is fixed and coincides with the center of the tail end face of the ring to be assembled. (2) The tail end face of the ring to be assembled The axial direction is located with the center of the first end face of the previous ring as the vertex, and the first end face of the previous ring... The axis is on the conical surface of the axis of rotation, and lies in the same plane as the axis of rotation; (3) Meets the requirements of engineering operations; A numerical optimization algorithm is used to perform nonlinear optimization on the objective function, so that the tunnel axis fits the correction axis, resulting in an optimized tunnel axis. The optimized tunnel axis is then transformed using a homogeneous coordinate transformation matrix. Transform to local coordinate system Solve the following to obtain the coordinate system. Optimize the tunnel axis below; Wherein, the homogeneous coordinate transformation matrix is .

2. The method as described in claim 1, characterized in that, S1 specifically includes: S101. Obtain the preset attitude data of the tunnel boring machine at each sampling point on the preset line, calculate the spatial coordinates of the tunnel boring machine at each sampling point, and connect them sequentially to obtain the design axis. S102. Obtain the current attitude data of the tunnel boring machine and use a second-order continuous interpolation algorithm to generate the original correction axis of the tunnel boring machine at each sampling point based on the current attitude data and the preset attitude data. S103. Based on the rotation matrix, rotate the original correction axis to the geodetic coordinate system where the tunnel boring machine is located to obtain the correction axis: in, Indicates the initial correction axis. Indicates the correction axis. express In the world coordinate system, It is a rotation matrix.

3. The method as described in claim 1, characterized in that, The expression for the segment lining ring model is as follows: in: This refers to the standard ring width of the tunnel lining segment. The width of segment K is given. The outer diameter of the segment ring, Because of the rotation angle, the segments in the initial segment lining ring model have no thickness, therefore This refers to the outer surface area of ​​a ring-shaped segment.

4. The method as described in claim 3, characterized in that, S200 specifically includes: S201. Initialize multiple segment lining ring models The rotation angle between each ring is By sequentially splicing the rings together, a tunnel model is obtained; where, for the Ring model of segment lining Current ring The center of the first end face With the next link Tail end face center Overlap, current ring The tail end face and the previous ring The first end faces coincide; S202, Model of multiple tunnel segment lining rings The center line segment Connected sequentially to form the tunnel axis Among them, for the first Ring model of segment lining Connect the center of the tail end face and the center of the first end face And through the segment lining ring model center Obtain the center line segment .

5. The method as described in claim 1, characterized in that, The process of establishing a three-dimensional motion envelope surface for the shield tail of the tunnel boring machine based on the correction axis, and updating the tunnel model based on the optimized tunnel axis, includes: The tunnel boring machine is considered as a cylinder, and the correction axis is used in the geodetic coordinate system. The expression represents the three-dimensional envelope of the tunnel boring machine in the geodetic coordinate system. Moving along the correction axis, the three-dimensional motion trajectory is obtained: Set the initial 3D envelope surface as follows: in, , The number of sampling points is set according to the number of sampling points. The distance from the center of the shield tail to the center of the cutterhead of the tunnel boring machine; Obtain the direction vector on the correction axis: in, and CTA for correcting axis deviation The direction vectors of two adjacent points; The direction vector of the three-dimensional initial envelope surface is: The envelope surface is adjusted to align with the rotation axis direction vector along the CTA (Correction Axis) axis. = ; Wherein, rotation angle: The rotation matrix is ​​constructed as follows: The 3D envelope surface of the i-th sampling point is represented as: 。 6. The method as described in claim 5, characterized in that, The process of updating the tunnel model based on the optimized tunnel axis includes: Based on the optimized tunnel axis, the rotation angle between each segment lining ring is obtained, and several segment lining ring models are generated. The segments are spliced ​​together sequentially, and the included angle between each ring of segments is... The value is assigned as the rotation angle of the i-th ring of the tunnel axis, and the tunnel model is updated. coordinate system The updated tunnel model is transformed to the coordinate system using the homogeneous coordinate transformation matrix. Below, we obtain the coordinate system. The updated tunnel model.

7. The method as described in claim 1, characterized in that, The process involves discretizing the updated tunnel model and the three-dimensional motion envelope of the shield tail, comparing the resulting point cloud data, and performing shield tail gap detection ring by ring at the circumferential measurement points, including: For the surface of the i-th ring segment and points on the surrounding shield tail envelope By transforming the matrix Transform to the local coordinate system of the ring segment to obtain , ; Calculate the polar angle of the i-th ring segment. : via polar angle Determine the cross-sectional location of the segment ring and identify the points on the shield tail envelope. of Are the coordinates within range? Simultaneously determine the points on the shield tail envelope. of and Is it within a circular cross-section? If the points on the shield tail envelope satisfy and If the shield tail gap is less than the warning threshold, then...

8. The method as described in claim 1, characterized in that, The tunnel correction path optimization algorithm includes: For the i-th lining ring, the points where assembly is possible are defined. Let be the decision variables, and the objective function be: Among them, the assembly points This refers to the assembly position of the wedge-shaped ring K block, which determines the homogeneous transformation matrix of the i-th ring segment relative to the initial ring segment. With the center line segment The direction; It is the total distance deviation from the point on the central axis of the i-th ring lining ring to the target curve CTA, expressed as the sum of all distance deviations; This represents the maximum distance deviation, which is the maximum value among all distance errors; It is the standard deviation of the distance deviation, which measures the uniformity of the distance distribution; , , These are weighting coefficients used to balance the importance of each objective, and they should satisfy... This is to ensure the normalization of weights.

9. A shield tunneling path optimization device considering shield tail gap constraints and segment arrangement, characterized in that, include: The alignment correction axis construction module is used to acquire the preset attitude data of the tunnel boring machine at each sampling point on the preset line, and to calculate the design axis of the tunnel boring machine based on the preset attitude data; The current attitude data of the tunnel boring machine is obtained. An interpolation algorithm is used to generate the original correction axis of the tunnel boring machine at each sampling point based on the current attitude data and the preset attitude data. The original axis is then converted to the geodetic coordinate system to obtain the correction axis. The tunnel axis construction module is used to initialize multiple segment lining ring models. The tunnel model is obtained by splicing the adjacent rings according to the rule that the beginning and end of the adjacent rings are connected and the center points of the adjacent end faces coincide. At the same time, the line connecting the center points of the beginning and end faces of each ring together constitutes the tunnel axis of the shield machine. The curve optimization module is used to employ an optimization algorithm to fit the tunnel axis to the correction axis. A three-dimensional motion envelope of the shield tail of the tunnel boring machine is established based on the correction axis, and a tunnel model is established based on the tunnel axis. The detection module is used to discretize the updated tunnel model and the three-dimensional motion envelope of the shield tail, and compare the obtained point cloud data. It performs shield tail gap detection ring by ring at the circumferential measurement points. If the shield tail gap is less than the warning threshold, the tunnel deviation correction path optimization algorithm is called to obtain the rotation angle of each ring segment when the tail end face is closest to the design axis, obtain the initial angle sequence, and set it as the initial solution of the optimization algorithm, and jump to the curve optimization module. If the shield tail gap is greater than or equal to the warning threshold, then jump to the output module; The output module is used to output the optimized tunnel boring machine construction path and segment layout scheme based on the optimized tunnel axis. The step of employing an optimization algorithm to progressively adjust each segment of the tunnel axis to fit the correction axis and obtain an optimized tunnel axis includes: Set the optimization goal as follows: in, Indicates the tunnel axis above points Distance to correction axis CTA The distance; Setting constraints includes: (1) The center of the first end face of the previous ring is fixed and coincides with the center of the tail end face of the ring to be assembled. (2) The tail end face of the ring to be assembled The axial direction is located with the center of the first end face of the previous ring as the vertex, and the first end face of the previous ring... The axis is on the conical surface of the axis of rotation, and lies in the same plane as the axis of rotation; (3) Meets the requirements of engineering operations; A numerical optimization algorithm is used to perform nonlinear optimization on the objective function, so that the tunnel axis fits the correction axis, resulting in an optimized tunnel axis. The optimized tunnel axis is then transformed using a homogeneous coordinate transformation matrix. Transform to local coordinate system Solve the following to obtain the coordinate system. Optimize the tunnel axis below; Wherein, the homogeneous coordinate transformation matrix is .

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