A Design Method for Inclined Shaft Formwork Based on Digital Modeling and Slip Mode Optimization

Abstract

This invention discloses a design method for inclined shaft formwork based on digital modeling and slipform optimization. This method utilizes Geographic Information System (GIS) and Building Information Modeling (BIM) to create a complete 3D digital model of the inclined shaft, and combines laser scanning and UAV technologies to acquire high-precision inclined shaft data, ensuring model accuracy. The method calculates the angle between the tangent and normal of each segment using the inclined shaft curve equation, and uses this to divide the pouring area and the start and end points of each section, providing precise geometric basis for the optimized design of the formwork. An optimization algorithm is used to calculate the optimal solution for the slipform segments, focusing on optimizing the structural deformation of the formwork to ensure the rationality of the position, angle, and transition of each segment. Finally, through a precise 3D inclined shaft model and optimized design, an overall construction formwork is constructed, which not only improves the accuracy and stability of the inclined shaft formwork design but also ensures uniform stress and minimizes deformation during construction, significantly improving construction efficiency and safety.

Description

Technical Field

[0001] This invention relates to the field of building formwork design technology, and more specifically, to a method for designing inclined shaft formwork based on digital modeling and slipform optimization. Background Technology

[0002] In modern engineering construction, especially in the construction of inclined shafts for pumped storage power stations, the precision and stability of the formwork design are crucial to project quality and construction efficiency. Pumped storage power stations effectively regulate grid load and improve the stability and efficiency of the power system by pumping water to an upper reservoir during off-peak hours and releasing it to generate electricity during peak periods. In this process, the lining construction of the inclined shaft is a critical step; the lining not only prevents deformation or collapse of the surrounding rock but also ensures the safety and durability of the project.

[0003] With the widespread application of digital technologies such as Building Information Modeling (BIM), Geographic Information Systems (GIS), and laser scanning, 3D digital modeling has become a trend in the industry. These technologies can accurately reproduce the complex geometry of inclined shafts, providing high-precision data support for formwork design. However, how to combine these high-precision digital models with actual construction needs, especially for optimizing formwork design in complex environments like inclined shafts, remains a pressing technical challenge.

[0004] In inclined shaft construction, especially in areas with curved sections, rationally dividing the slipform into segments and ensuring minimal structural deformation in each segment while meeting the requirements of uniform stress and stability is a challenge. Traditional formwork design methods often rely on manual calculations and experience, leading to problems such as uneven stress and excessive deformation in the structural design of formwork in inclined shafts with complex geometries. This not only affects construction safety but may also lead to project delays and increased costs. Therefore, traditional formwork designs often struggle to provide effective solutions in these transition sections and complex geometric areas. Summary of the Invention

[0005] The purpose of this invention is to address the technical problem that traditional formwork design methods often fail to provide effective solutions in transition sections and complex geometric areas during the construction of inclined shafts with complex geometries. This invention provides an inclined shaft formwork design method based on digital modeling and slipform optimization. This method constructs an overall construction formwork through a precise three-dimensional inclined shaft model and optimized design. This not only improves the accuracy and stability of the formwork design, but also ensures uniform stress and minimizes deformation during construction, significantly improving construction efficiency and safety.

[0006] This invention is achieved through the following technical solution:

[0007] This invention provides a method for designing inclined shaft formwork based on digital modeling and sliding mode optimization, comprising the following steps:

[0008] Step 1: Draw the complete axis line containing curve segments and straight line segments, and combine the geographic information system and building information model to establish a three-dimensional digital model of the entire inclined shaft;

[0009] Step 2: Use a laser scanner, drone or 3D LiDAR to acquire cross-sectional data after the inclined shaft is excavated, and import it into the modeling software. After data cleaning and fitting, a high-precision 3D inclined shaft model is obtained.

[0010] Step 3: Using the curve equation in the inclined shaft curve model, calculate the tangent of each segment of the inclined shaft, and calculate the angle between the tangent and the normal based on the transition points of the upper and lower bends;

[0011] Step 4: Based on the geometry of the inclined shaft and the calculation results of the tangent, divide the pouring area and determine the start and end points of each compartment;

[0012] Step 5: Calculate the optimal solution for sliding mode segmentation using an optimization algorithm, where the optimization objective is to minimize the structural deformation of the template; calculate the position, angle, and transition portion of each sliding mode segment;

[0013] Step 6: Based on the obtained high-precision three-dimensional inclined shaft model and the optimized structure of the slipform segment, construct the overall construction formwork.

[0014] This invention proposes a novel design method for inclined shaft formwork by combining digital modeling technology with slipform optimization algorithms. This method effectively solves problems such as uneven structural stress and excessive deformation in transition sections and complex geometric areas, which are inherent in traditional design methods. First, a complete 3D digital model of the inclined shaft is created using Geographic Information System (GIS) and Building Information Modeling (BIM). High-precision data of the inclined shaft is obtained using technologies such as laser scanning and drones to ensure model accuracy. The angle between the tangent and normal of each segment is calculated using the inclined shaft curve equation. Based on this, the pouring area and the start and end points of each section are delineated, providing a precise geometric basis for the optimized design of the formwork. On this basis, an optimization algorithm is used to calculate the optimal solution for the slipform segments, focusing on optimizing the structural deformation of the formwork to ensure the rationality of the position, angle, and transition of each segment. Finally, through a precise 3D inclined shaft model and optimized design, an overall construction formwork is constructed. This not only improves the accuracy and stability of the formwork design but also ensures uniform stress and minimizes deformation during construction, significantly improving construction efficiency and safety.

[0015] Preferably, step 1 includes the following steps:

[0016] Step 1.1: Use geometric curve equations to describe the curved segments of the inclined shaft and straight line equations to describe the straight segments in the inclined shaft. For the intersection of the curved segments and the straight segments, calculate the tangent and angle to ensure a smooth connection and obtain the geometric model of the inclined shaft axis.

[0017] Step 1.2: Collect topographic and address data of the actual area through a geographic information system, and embed the collected topographic and address data into the BIM model in the BIM modeling software; then import the inclined shaft axis geometric model into the BIM model; by combining the actual topographic and address data with the inclined shaft axis geometric model, a three-dimensional digital model with geospatial positioning is generated.

[0018] Preferably, step 2 includes the following steps:

[0019] Step 2.1: Use a laser scanner, drone, or 3D lidar to acquire cross-sectional data after the inclined shaft is excavated, and obtain point cloud data;

[0020] Step 2.2: Convert the acquired point cloud data into a data format that BIM modeling software can process;

[0021] Step 2.3: Remove noise from the point cloud data and remove holes, then use the voxel mesh method to downsample the point cloud data to obtain preprocessed point cloud data;

[0022] Step 2.4: Based on adaptive surface fitting and incremental 3D reconstruction, the preprocessed point cloud data and 3D digital model are used for optimization to obtain a high-precision 3D inclined shaft model.

[0023] Preferably, step 2.4 includes the following steps:

[0024] Local surface fitting:

[0025] Let each point P in the point cloud data i =(x i y i , z i Select k points within its neighborhood as the local dataset P. j Where j∈[ik, i+k], and calculate the normal vector n for each point. i and curvature k i :

[0026] Calculate the normal vector: Construct a data matrix X = {P} for the selected k points. j}, where each point P j =(x j y j , z j );

[0027] Calculate the covariance matrix C of the point cloud:

[0028]

[0029] In the formula: x j y j z j Representing P respectively j Coordinates on the x, y, and z axes;

[0030] Eigenvalue decomposition is performed on the covariance matrix C to obtain the eigenvalues ​​λ1, λ2, λ3 and the corresponding eigenvectors v1, v2, v3; where the normal vector n i The eigenvector v3 corresponds to the smallest eigenvalue λ3;

[0031] Curvature calculation: Based on k neighborhood points, principal component analysis is used to obtain the curvature.

[0032] Weighted least squares fitting: For each local region, a quadratic surface model is fitted using the weighted least squares method.

[0033] z(x, y) = ax 2 +by 2 +cxy+dx+ey+f;

[0034] In the formula: x, y, z represent the coordinate values ​​on the x, y, and z axes, respectively; a, b, c, d, e, and f are fitting parameters, solved using the weighted least squares method based on neighborhood point cloud data.

[0035]

[0036] In the formula: w i Indicates the weight of point i; n represents the number of data points;

[0037]

[0038] In the formula: k i Represents local curvature; ρ i α represents the density of the local point cloud; α and β represent adjustment parameters.

[0039] Global surface blending and optimization:

[0040] The local least squares method is used to fuse all local fitting results. The optimization objective is to minimize the differences between the local fitted surfaces, where the optimization problem takes the following form:

[0041]

[0042] In the formula: P i =(x i y i, z i Let f(x, y) be the i-th point; f(x, y) represent the quadratic surface model; N(i) represent the neighborhood of point i; λ represents the weight of the smoothing term;

[0043] Incremental modeling and slicing method: The point cloud data is sliced ​​into multiple layers. The point cloud data in each slice is processed using adaptive surface fitting. At each layer, a local two-dimensional surface f(x, y) is generated, and the data from adjacent slices are optimized and merged.

[0044] For each adjacent slice S i and S i+1 The fitting results are then fused using three-dimensional difference:

[0045] f(x, y, z) = λ1f i (x, y) + λ2f i+1 (x, y);

[0046] In the formula: λ1 and λ2 are the weights calculated based on the slice distance and fitting accuracy;

[0047] Incremental surface optimization: Based on the local surfaces generated from all slices, an incremental optimization method is used for adjustment, with the following optimization objective function:

[0048]

[0049] In the formula: Represents the actual value;

[0050] Global model generation: By stitching together the optimized surfaces at various levels, a high-precision 3D inclined shaft model is obtained.

[0051] Preferably, step 3 includes the following steps:

[0052] Step 3.1: Suppose the curve of the inclined shaft is represented by the following parametric equation:

[0053] r(t)=(x(t),y(t),z(t));

[0054] In the formula: t represents the parameters of the curve; x(t), y(t), z(t) represent the coordinate values ​​of the curve in the x, y, and z directions in three-dimensional space, respectively;

[0055] Step 3.2: For the parametric curve, calculate the tangent line by taking the derivative with respect to t:

[0056] The tangent vector T(t) is represented as follows:

[0057]

[0058] In the formula: T(t) represents the instantaneous direction of the curve at each point t;

[0059] Based on the above formula for calculating the tangent vector T(t), the tangent directions at the start and end of each segment are calculated to obtain T1 and T2, which represent the tangent vectors at the start and end of the segment, respectively.

[0060] Determining the transition point: The transition point is determined by calculating the curvature of the inclined shaft curve.

[0061]

[0062] In the formula: x′(t) and y′(t) are the first derivatives of x(t) and y(t) with respect to t, respectively; x″(t) and y″(t) represent the second derivatives with respect to t, respectively; k(t) represents the curvature.

[0063] Points where the curvature exceeds a threshold are defined as transition points;

[0064] Calculate the angle between the tangent and the normal:

[0065] Normal vector: The normal vector is a vector perpendicular to the tangent, calculated using the tangent vector T(t) and the normal vector to the inclined well surface.

[0066]

[0067] In the formula: B(t) represents an auxiliary vector perpendicular to the tangent vector T(t) and the normal direction;

[0068] Angle calculation: The angle between the tangent and the normal is calculated using the dot product formula for vectors.

[0069]

[0070] In the formula: |T(t)| and |N(t)| represent the magnitudes of the tangent and normal, respectively.

[0071] Preferably, step 4 includes the following steps:

[0072] Based on the tangent and normal obtained in step 3, the line segment is divided into segments, wherein the segmentation of the line segment is based on a fixed length interval;

[0073] For curve segments, the segment length is adjusted according to the rate of change of the tangent and the magnitude of the curvature;

[0074]

[0075] In the formula: V(t) represents the rate of change of the tangent at point t; θ(t) represents the angle of the tangent direction;

[0076]

[0077] In the formula: L0 represents the basic segment length; α represents the adjustment coefficient; L segment (t) represents the adjusted segment length;

[0078] Based on the change in tangent direction, determine the start and end points for each sub-compartment:

[0079]

[0080] In the formula: t i V(t) represents the starting point of the i-th segment; i ) represents the rate of change of the tangent; L segment (t i ) indicates the adjusted segment length.

[0081] Preferably, step 5 uses a particle swarm optimization algorithm to calculate the optimal solution for sliding mode segmentation:

[0082] Initialize the particle swarm: Each particle represents a solution, i.e., a sliding mode segmentation configuration scheme, and the dimension of each particle is (x...). i ,y i ,θ i ,L i () represents the position, angle, and length of a sliding mode segment;

[0083] Evaluate the fitness function: For each particle, calculate its fitness value:

[0084]

[0085] In the formula: n represents the number of sliding mode segments; δ i F represents the structural deformation of the i-th segment; i This represents the force on the i-th segment;

[0086] Update particle position and velocity: Based on the particle's historical best solution and the historical best solutions of all particles, update the particle's position and velocity.

[0087]

[0088] In the formula: The velocity of the i-th particle in the k-th iteration is represented by: w; inertia weight; c1 and c2; learning factors; r1 and r2; random numbers uniformly distributed between [0,1]; p i Represents the historical best position of particle i; g i Represents the historical best position of all particles;

[0089] The iteration stops when the fitness value of the particle swarm reaches a preset threshold, or after a certain number of iterations.

[0090] After multiple iterations, the optimal configuration of each sliding mode segment is obtained, including position, angle and length;

[0091] The following constraints need to be satisfied during the iteration process:

[0092] Force uniformity constraint:

[0093]

[0094] In the formula: F i F represents the force on the i-th segment. max This indicates the maximum allowable force for each segment;

[0095] Stability constraints:

[0096]

[0097] Where: δ i δ represents the deformation value of the i-th segment. max Indicates the maximum allowable deformation value;

[0098] Geometric constraints: According to construction requirements, the starting point and number of sections must be within the geometric boundaries of the inclined shaft.

[0099] Compared with the prior art, the present invention has the following advantages and beneficial effects:

[0100] This invention proposes a novel design method for inclined shaft formwork by combining digital modeling technology with slipform optimization algorithms. This method effectively solves problems such as uneven structural stress and excessive deformation in transition sections and complex geometric areas, which are inherent in traditional design methods. First, a complete 3D digital model of the inclined shaft is created using Geographic Information System (GIS) and Building Information Modeling (BIM). High-precision data of the inclined shaft is obtained using technologies such as laser scanning and drones to ensure model accuracy. The angle between the tangent and normal of each segment is calculated using the inclined shaft curve equation. Based on this, the pouring area and the start and end points of each section are delineated, providing a precise geometric basis for the optimized design of the formwork. On this basis, an optimization algorithm is used to calculate the optimal solution for the slipform segments, focusing on optimizing the structural deformation of the formwork to ensure the rationality of the position, angle, and transition of each segment. Finally, through a precise 3D inclined shaft model and optimized design, an overall construction formwork is constructed. This not only improves the accuracy and stability of the formwork design but also ensures uniform stress and minimizes deformation during construction, significantly improving construction efficiency and safety. Attached Figure Description

[0101] To more clearly illustrate the technical solutions of the exemplary embodiments of the present invention, the accompanying drawings used in the embodiments will be briefly described below. It should be understood that the following drawings only show some embodiments of the present invention and should not be considered as a limitation of the scope. For those skilled in the art, other related drawings can be obtained based on these drawings without creative effort. In the drawings:

[0102] Figure 1 This is a flowchart of the inclined shaft formwork design method based on digital modeling and sliding mode optimization in this invention. Detailed Implementation

[0103] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the embodiments and accompanying drawings. The illustrative embodiments and descriptions of the present invention are only used to explain the present invention and are not intended to limit the present invention.

[0104] Unless otherwise defined, all technical and scientific terms used herein have the same meaning as commonly understood by one of ordinary skill in the art to which this application pertains; the terminology used herein is for the purpose of describing particular embodiments only and is not intended to limit the application; the terms “comprising” and “having”, and any variations thereof, in the specification, claims, and foregoing description of the drawings are intended to cover non-exclusive inclusion.

[0105] In the description of the embodiments of this application, technical terms such as "first" and "second" are used only to distinguish different objects and should not be construed as indicating or implying relative importance or implicitly indicating the number, specific order, or primary and secondary relationship of the indicated technical features.

[0106] In this document, the term "embodiment" means that a particular feature, structure, or characteristic described in connection with an embodiment may be included in at least one embodiment of this application. The appearance of this phrase in various places throughout the specification does not necessarily refer to the same embodiment, nor is it a separate or alternative embodiment mutually exclusive with other embodiments. It will be explicitly and implicitly understood by those skilled in the art that the embodiments described herein can be combined with other embodiments.

[0107] In the description of the embodiments in this application, the term "and / or" is merely a description of the relationship between related objects, indicating that three relationships can exist. For example, A and / or B can represent three cases: A exists, A and B exist simultaneously, and B exists. In addition, the character " / " in this document generally indicates that the related objects before and after it have an "or" relationship.

[0108] In the embodiments of this application, the same reference numerals denote the same components, and for the sake of brevity, detailed descriptions of the same components are omitted in different embodiments. It should be understood that the thickness, length, width, and other dimensions of various components in the embodiments of this application shown in the accompanying drawings, as well as the overall thickness, length, width, and other dimensions of the integrated device, are merely illustrative and should not constitute any limitation on this application.

[0109] In the description of the embodiments of this application, the term "multiple" refers to two or more (including two), similarly, "multiple sets" refers to two or more (including two sets), and "multiple pieces" refers to two or more (including two pieces), unless otherwise explicitly specified.

[0110] In the description of the embodiments of this application, the technical terms "center," "longitudinal," "lateral," "length," "width," "thickness," "upper," "lower," "front," "rear," "left," "right," "vertical," "horizontal," "top," "bottom," "inner," "outer," "clockwise," "counterclockwise," "axial," "radial," and "circumferential" indicate the orientation or positional relationship based on the orientation or positional relationship shown in the accompanying drawings. They are only for the convenience of describing the embodiments of this application and simplifying the description, and are not intended to indicate or imply that the device or element referred to must have a specific orientation, or be constructed and operated in a specific orientation. Therefore, they should not be construed as limitations on the embodiments of this application.

[0111] In the description of the embodiments of this application, unless otherwise expressly specified and limited, technical terms such as "installation," "connection," "joining," and "fixing" should be interpreted broadly. For example, they can refer to a fixed connection, a detachable connection, or an integral part; they can refer to a mechanical connection or an electrical connection; they can refer to a direct connection or an indirect connection through an intermediate medium; they can refer to the internal communication of two components or the interaction between two components. For those skilled in the art, the specific meaning of the above terms in the embodiments of this application can be understood according to the specific circumstances.

[0112] Please refer to Figure 1 The present application provides a method for designing inclined shaft formwork based on digital modeling and sliding mode optimization, which includes the following steps:

[0113] Step 1: Draw the complete axis line containing curve segments and straight line segments, and combine the geographic information system and building information model to establish a three-dimensional digital model of the entire inclined shaft;

[0114] Step 2: Use a laser scanner, drone or 3D LiDAR to acquire cross-sectional data after the inclined shaft is excavated, and import it into the modeling software. After data cleaning and fitting, a high-precision 3D inclined shaft model is obtained.

[0115] Step 3: Using the curve equation in the inclined shaft curve model, calculate the tangent of each segment of the inclined shaft, and calculate the angle between the tangent and the normal based on the transition points of the upper and lower bends;

[0116] Step 4: Based on the geometry of the inclined shaft and the calculation results of the tangent, divide the pouring area and determine the start and end points of each compartment;

[0117] Step 5: Calculate the optimal solution for sliding mode segmentation using an optimization algorithm, where the optimization objective is to minimize the structural deformation of the template; calculate the position, angle, and transition portion of each sliding mode segment;

[0118] Step 6: Based on the obtained high-precision three-dimensional inclined shaft model and the optimized structure of the slipform segment, construct the overall construction formwork.

[0119] This invention proposes a novel design method for inclined shaft formwork by combining digital modeling technology with slipform optimization algorithms. This method effectively solves problems such as uneven structural stress and excessive deformation in transition sections and complex geometric areas, which are inherent in traditional design methods. First, a complete 3D digital model of the inclined shaft is created using Geographic Information System (GIS) and Building Information Modeling (BIM). High-precision data of the inclined shaft is obtained using technologies such as laser scanning and drones to ensure model accuracy. The angle between the tangent and normal of each segment is calculated using the inclined shaft curve equation. Based on this, the pouring area and the start and end points of each section are delineated, providing a precise geometric basis for the optimized design of the formwork. On this basis, an optimization algorithm is used to calculate the optimal solution for the slipform segments, focusing on optimizing the structural deformation of the formwork to ensure the rationality of the position, angle, and transition of each segment. Finally, through a precise 3D inclined shaft model and optimized design, an overall construction formwork is constructed. This not only improves the accuracy and stability of the formwork design but also ensures uniform stress and minimizes deformation during construction, significantly improving construction efficiency and safety.

[0120] As one possible implementation of this embodiment, step 1 includes the following steps:

[0121] It should be noted that the inclined shaft axis refers to the spatial path formed along the centerline of the shaft during the excavation process. It consists of alternating straight and curved segments, typically exhibiting curves and slopes in both the vertical and horizontal directions. To ensure the geometric accuracy and construction quality of the inclined shaft during construction, the primary task is to accurately draw the complete inclined shaft axis.

[0122] Step 1.1: Use geometric curve equations to describe the curved segments of the inclined shaft and straight line equations to describe the straight segments in the inclined shaft. For the intersection of the curved segments and the straight segments, calculate the tangent and angle to ensure a smooth connection and obtain the geometric model of the inclined shaft axis.

[0123] For example: the curve segment is modeled as follows:

[0124] Horizontal curve segment (circular arc): A horizontal curve is usually a bend in a horizontal plane and can be represented by the following equation for a circular arc:

[0125] x(t)=R h ·cos(θ(t))+x0;

[0126] y(t)=R h sin(θ(t))+y0;

[0127] In the formula: x(t) and y(t) represent the coordinates of a point on the curve; R h The radius of the horizontal curve is represented by θ(t); the angle from the starting point to a certain scale mark is represented by x0 and y0; the coordinates of the center of the arc are represented by x0 and y0.

[0128] Vertical curve segment (circular arc): The vertical curve is the curve of the inclined shaft axis in the vertical direction.

[0129] z(t) = R v sin(φ(t))+z0;

[0130] In the formula: z(t) represents the position of the curve in the vertical direction; R v φ(t) represents the radius of the vertical curve; φ(t) represents the angle from the starting point to a certain scale mark, which is related to the change in slope in the vertical direction; z0 represents the height of the center of the vertical curve.

[0131] Horizontal straight segment: A horizontal straight segment usually refers to the part that moves in a straight line on a horizontal plane.

[0132] y = m·x + b;

[0133] In the formula: x and y are the coordinates of the line segment; m represents the slope of the line; b represents the y-intercept of the line.

[0134] Perpendicular line segment:

[0135] z = m′·x + b′;

[0136] In the formula: z represents the coordinate in the vertical direction; m′ represents the slope of the vertical line; b′ represents the intercept of the line on the z-axis;

[0137] Connecting curved and straight segments: In actual inclined shaft construction, the axis of the inclined shaft is usually composed of multiple straight and curved segments;

[0138] Tangent calculation: At the intersection of a curve segment and a straight line segment, there is a tangent problem. To ensure a smooth transition, it is necessary to calculate the tangent for each segment. For example, at the junction of a curve and a straight line, calculate the angle between the tangent to the curve and the normal to the straight line:

[0139]

[0140] In the formula: T curve T line Represent the tangent vectors of the curve and the line segment, respectively; |T curve |、|T line | represents the magnitude of the tangent vectors of the curve and the line, respectively;

[0141] Smooth transition of transition segments: If there is a connection between curve segments, or a smooth transition is required between straight line segments and curve segments, an interpolation algorithm (such as spline interpolation) can be used to achieve the transition.

[0142] By using geometric curve equations and straight line equations, we can accurately describe the axis of an inclined shaft. Curved segments (such as circular arcs) are used to describe the curved sections of the inclined shaft, while straight line segments are used to describe the straight sections. These mathematical models help us accurately calculate the location, shape, and transitions of the inclined shaft in digital modeling.

[0143] Step 1.2: Collect topographic and address data of the actual area through a geographic information system, and embed the collected topographic and address data into the BIM model in the BIM modeling software; then import the inclined shaft axis geometric model into the BIM model; by combining the actual topographic and address data with the inclined shaft axis geometric model, a three-dimensional digital model with geospatial positioning is generated.

[0144] In BIM modeling software (such as Revit, Tekla, etc.), we can import GIS data (such as geographic coordinates, terrain elevation, soil type, etc.) into the BIM model to ensure that the design of buildings and infrastructure conforms to the actual geographical environment. Through professional software interfaces (such as the plugin between ESRI ArcGIS and Autodesk Revit), we can directly embed GIS spatial data (such as ground elevation, road distribution, etc.) into the BIM model.

[0145] Geographic coordinate alignment: Once the GIS data is imported into the BIM software, we can ensure that the BIM model is aligned with the actual geographic coordinate system, ensuring the accurate location of the inclined shaft in the actual environment. For example, the starting point, turning points, and ending points of the inclined shaft will be located according to the actual geographic coordinates, avoiding deviations during actual construction.

[0146] Integrating Topography and Subsurface Environment: In addition to modeling surface facilities, BIM models can also incorporate subsurface environmental data (such as groundwater levels and rock strata distribution) for geological modeling. This helps to consider the impact of the subsurface environment during the design of inclined shafts, thus avoiding construction risks.

[0147] As one possible implementation of this embodiment, step 2 includes the following steps:

[0148] Step 2.1: Use a laser scanner, drone, or 3D lidar to acquire cross-sectional data after the inclined shaft is excavated, and obtain point cloud data;

[0149] Step 2.2: Convert the acquired point cloud data into a data format that BIM modeling software can process;

[0150] Step 2.3: Remove noise from the point cloud data and remove holes, then use the voxel mesh method to downsample the point cloud data to obtain preprocessed point cloud data;

[0151] Step 2.4: Based on adaptive surface fitting and incremental 3D reconstruction, the preprocessed point cloud data and 3D digital model are used for optimization to obtain a high-precision 3D inclined shaft model.

[0152] As one possible implementation of this embodiment, step 2.4 includes the following steps:

[0153] Local surface fitting:

[0154] Let each point P in the point cloud data i =(x i ,y i ,z i Select k points within its neighborhood as the local dataset P. j Where j∈[ik,i+k], and calculate the normal vector n for each point. i and curvature k i :

[0155] Calculate the normal vector: Construct a data matrix X = {P} for the selected k points. j}, where each point P j =(x j ,y j ,z j );

[0156] Calculate the covariance matrix C of the point cloud:

[0157]

[0158] In the formula: x j y j z j Representing P respectively j Coordinates on the x, y, and z axes;

[0159] Eigenvalue decomposition is performed on the covariance matrix C to obtain the eigenvalues ​​λ1, λ2, λ3 and the corresponding eigenvectors v1, v2, v3; where the normal vector n i The eigenvector v3 corresponds to the smallest eigenvalue λ3;

[0160] Curvature calculation: Based on k neighborhood points, principal component analysis is used to obtain the curvature.

[0161] Weighted least squares fitting: For each local region, a quadratic surface model is fitted using the weighted least squares method.

[0162] z(x,y)=ax 2 +by 2 +cxy+dx+ey+f;

[0163] In the formula: x, y, z represent the coordinate values ​​on the x, y, and z axes, respectively; a, b, c, d, e, and f are fitting parameters, solved using the weighted least squares method based on neighborhood point cloud data.

[0164]

[0165] In the formula: w i Indicates the weight of point i; n represents the number of data points;

[0166]

[0167] In the formula: k i Represents local curvature; ρ i α represents the density of the local point cloud; α and β represent adjustment parameters.

[0168] Global surface blending and optimization:

[0169] The local least squares method is used to fuse all local fitting results. The optimization objective is to minimize the differences between the local fitted surfaces, where the optimization problem takes the following form:

[0170]

[0171] In the formula: P i =(x i ,y i ,z i Let f(x,y) be the i-th point; f(x,y) represent the quadratic surface model; N(i) represent the neighborhood of point i; λ represents the weight of the smoothing term;

[0172] 3D reconstruction can be built incrementally, and the transformation from a local point cloud to a global 3D model can be achieved through progressive optimization and interpolation methods. This method progressively stitches together each fitted local surface into a global 3D model.

[0173] Incremental modeling and slicing method: The point cloud data is sliced ​​into multiple layers. The point cloud data in each slice is processed using adaptive surface fitting. At each layer, a local two-dimensional surface f(x,y) is generated, and the data from adjacent slices are optimized and merged.

[0174] For each adjacent slice S i and S i+1 The fitting results are then fused using three-dimensional difference:

[0175] f(x,y,z)=λ1f i (x,y)+λ2f i+1 (x,y);

[0176] In the formula: λ1 and λ2 are the weights calculated based on the slice distance and fitting accuracy;

[0177] Incremental surface optimization: Based on the local surfaces generated from all slices, an incremental optimization method is used for adjustment, with the following optimization objective function:

[0178]

[0179] In the formula: Represents the actual value;

[0180] Global model generation: By stitching together the optimized surfaces at various levels, a high-precision 3D inclined shaft model is obtained.

[0181] In this embodiment, an adaptive surface fitting and incremental 3D reconstruction method is adopted. By using weighted least squares and adaptive adjustment of local curvature to improve the fitting accuracy, each local surface is gradually optimized and stitched together to finally generate an accurate 3D inclined well model. This method avoids deep learning models while still providing efficient and accurate 3D reconstruction results, and is suitable for complex point cloud data scenarios.

[0182] As one possible implementation of this embodiment, step 3 includes the following steps:

[0183] Step 3.1: In Step 2, we have acquired high-precision cross-sectional data of the inclined shaft using a laser scanner, UAV, or 3D LiDAR, and obtained a 3D model of the inclined shaft through data cleaning and fitting. At this stage, our goal is to use this data to obtain the curve equation of the inclined shaft. Let the curve of the inclined shaft be represented by the following parametric equation:

[0184] r(t) = (x(t), y(t), z(t));

[0185] In the formula: t represents the parameters of the curve; x(t), y(t), z(t) represent the coordinate values ​​of the curve in the x, y, and z directions in three-dimensional space, respectively;

[0186] Step 3.2: The tangent line is the instantaneous rate of change of a curve at a certain point. For a parametric curve, the tangent line is calculated by differentiating it with respect to t.

[0187] The tangent vector T(t) is represented as follows:

[0188]

[0189] In the formula: T(t) represents the instantaneous direction of the curve at each point t;

[0190] The curve is divided into several segments. Based on the above formula for calculating the tangent vector T(t), the tangent direction at the start and end of each segment is calculated to obtain T1 and T2, which represent the tangent vectors at the start and end of the segment, respectively.

[0191] Determining transition points: In the curves of inclined shafts, especially in the curved sections, there may be transition segments. Transition points are typically defined as key points on the curve, such as places with significant changes in curvature, or points connecting different segments.

[0192] The transition point can be determined by calculating the curvature of the inclined shaft curve; the transition point can be determined by calculating the curvature of the inclined shaft curve:

[0193]

[0194] In the formula: x′(t) and y′(t) are the first derivatives of x(t) and y(t) with respect to t, respectively; x″(t) and y″(t) represent the second derivatives with respect to t, respectively; k(t) represents the curvature.

[0195] A transition point can be defined as a point where the curvature changes significantly, that is, a point where the derivative of the curvature changes significantly.

[0196] Calculate the angle between the tangent and the normal:

[0197] In the design of inclined shafts, the angle between the tangent and the normal needs to be considered to ensure that the installation direction of the formwork is correct.

[0198] Normal vector: The normal vector is a vector perpendicular to the tangent, calculated using the tangent vector T(t) and the normal vector to the inclined well surface.

[0199]

[0200] In the formula: B(t) represents an auxiliary vector perpendicular to the tangent vector T(t) and the normal direction;

[0201] Angle calculation: The angle between the tangent and the normal is calculated using the dot product formula for vectors.

[0202]

[0203] In the formula: |T(t)| and |N(t)| represent the magnitudes of the tangent and normal, respectively.

[0204] In this embodiment, the angle between the tangent and normal of each segment is calculated using the method described above to determine the installation direction of the template and the optimized structure of the transition section. Through these geometric calculations, we can ensure that the slipform template is reasonably laid out in each segment of the inclined shaft and that there is a smooth transition in the transition area, avoiding template deformation caused by excessive angles.

[0205] As one possible implementation of this embodiment, step 4 includes the following steps:

[0206] Based on the tangent and normal obtained in step 3, the line segment is divided into segments, wherein the segmentation of the line segment is based on a fixed length interval;

[0207] The rate of change of the tangent is an important indicator of the degree of curvature of a curve. It represents the speed at which the tangent changes direction at a given point. The rate of change of the tangent can be described by the relationship between curvature and the tangent.

[0208] The rate of change of the tangent direction is determined by the change of curvature. Suppose we want to calculate the rate of change of the tangent near point t:

[0209]

[0210] In the formula: V(t) represents the rate of change of the tangent at point t; θ(t) represents the angle of the tangent direction;

[0211] To ensure a smooth transition of the template across curve segments, we adjust the segment length based on the curvature. Regions with higher curvature (rapid changes) need to be divided into smaller segments, while regions with lower curvature can have their segment lengths increased appropriately.

[0212]

[0213] In the formula: L0 represents the basic segment length; α represents the adjustment coefficient; L segment (t) represents the adjusted segment length;

[0214] Based on the change in tangent direction, determine the start and end points for each sub-compartment:

[0215]

[0216] In the formula: t i V(t) represents the starting point of the i-th segment;i ) represents the rate of change of the tangent; L segment (t i ) indicates the adjusted segment length.

[0217] As one possible implementation of this embodiment, step 5 uses a particle swarm optimization algorithm to calculate the optimal solution for sliding mode segmentation:

[0218] Initialize the particle swarm: Each particle represents a solution, i.e., a sliding mode segmentation configuration scheme, and the dimension of each particle is (x...). i ,y i ,θ i ,L i () represents the position, angle, and length of a sliding mode segment;

[0219] Evaluate the fitness function: For each particle, calculate its fitness value:

[0220]

[0221] In the formula: n represents the number of sliding mode segments; δ i F represents the structural deformation of the i-th segment; i Indicate the force on the i-th segment; Update particle position and velocity: Based on the particle's historical best solution and the historical best solutions of all particles, update the particle's position and velocity:

[0222]

[0223] In the formula: The velocity of the i-th particle in the k-th iteration is represented by: w; inertia weight; c1 and c2; learning factors; r1 and r2; random numbers uniformly distributed between [0,1]; p i Represents the historical best position of particle i; g i Represents the historical best position of all particles;

[0224] The iteration stops when the fitness value of the particle swarm reaches a preset threshold, or after a certain number of iterations.

[0225] After multiple iterations, the optimal configuration of each sliding mode segment is obtained, including position, angle and length;

[0226] The following constraints need to be satisfied during the iteration process:

[0227] Force uniformity constraint:

[0228]

[0229] In the formula: F i F represents the force on the i-th segment. maxThis indicates the maximum allowable force for each segment;

[0230] Stability constraints:

[0231]

[0232] Where: δ i δ represents the deformation value of the i-th segment. max Indicates the maximum allowable deformation value;

[0233] Geometric constraints: According to construction requirements, the starting point and number of sections must be within the geometric boundaries of the inclined shaft.

[0234] In this embodiment, an optimization algorithm (such as particle swarm optimization) is introduced to minimize the structural deformation of the slipform template, ensuring stable and efficient operation of the template throughout the construction process. By defining a fitness function, setting optimization constraints, and employing a suitable optimization algorithm, the optimal position, angle, and length of each slipform segment can be calculated, thereby ensuring construction accuracy and smooth template transition.

[0235] In this embodiment, the present invention, through a design method combining digital modeling and slipform optimization, significantly solves the problem that traditional design methods cannot effectively handle the complex geometry and transition sections of inclined shafts, especially exhibiting unique advantages in the upper and lower bends and the overall casting of the inclined shaft. Through precise three-dimensional digital models and optimization algorithms, each segment of the inclined shaft can be rationally divided, optimizing the position, angle, and transition parts of the slipform segments, thereby achieving integrated upper and lower bend design. This method can support the simultaneous casting of various sections of the inclined shaft while ensuring structural stability, avoiding the construction discontinuity and potential structural problems caused by segmented casting in traditional methods.

[0236] By employing particle swarm optimization (PSO) algorithms, the structural deformation of the formwork can be effectively minimized, ensuring that each slipform segment achieves optimal performance in terms of structural stress and deformation control. Furthermore, the optimized segment design reduces construction difficulties and material waste caused by uneven transitions between upper and lower bends or changes in the shape of the inclined shaft. This integrated design method, combining compartmentalized casting with unified upper and lower bends, not only improves construction efficiency but also reduces construction costs and enhances the safety and stability of the entire inclined shaft formwork design, demonstrating significant technical advantages and economic benefits.

[0237] In step 6, after completing the optimized design of the transition section and the smooth transition of the slipform segments, we can construct the overall construction formwork based on these data.

[0238] Overall formwork design: By combining the position information, angles, and lengths of all segments, a three-dimensional model of the entire inclined shaft construction formwork is generated. Based on the construction requirements and joint design of each segment, a formwork system with smooth transitions and uniform stress distribution is constructed.

[0239] Formwork structure stability verification: After the construction formwork is designed, its structural stability needs to be verified to ensure that the formwork can remain stable during construction and will not undergo excessive deformation.

[0240] Stability analysis: The stability of the entire construction formwork is analyzed using finite element analysis (FEA), the stress on each segment is calculated, and the stability of the formwork is verified; the specific analysis formulas and methods can be based on structural mechanics theory.

[0241] In this invention, a precise basis for integrated design is provided by establishing a three-dimensional digital model of the entire inclined shaft, including curved and straight sections. This model integrates data from Geographic Information System (GIS) and Building Information Modeling (BIM), and can display the spatial structure of the inclined shaft in detail, including the geometry of the upper and lower curved sections.

[0242] Advanced equipment such as laser scanners, drones, or 3D LiDAR are used to acquire cross-sectional data after actual excavation, and this data is imported into modeling software. Through data cleaning and fitting, the 3D inclined shaft model can be updated and optimized to ensure that the model conforms to the actual construction site.

[0243] The tangent and normal lines for each segment are calculated using the curve equation in the inclined shaft curve model, and the angle between the tangent and normal lines is determined. This step is crucial for determining the transition points of the bends and ensuring a smooth transition of the curve during the integrated casting process.

[0244] Based on the geometry of the inclined shaft and the tangent calculation results, the pouring area was rationally divided, and the start and end points of each section were determined. This provided clear construction boundaries and sequence for integrated pouring, ensuring that the curved section and the main structure could be poured as a whole.

[0245] In step 5, the optimal solution for the sliding formwork segment is calculated using a particle swarm optimization algorithm, including its position, angle, and length. This optimization process considers structural deformation and stress uniformity, ensuring the stability and structural safety of each segment during the integrated casting process.

[0246] Based on a high-precision 3D inclined shaft model and an optimized slipform segment structure, an integrated construction formwork was constructed. This formwork design took into account the special requirements of the integrated upper and lower curved sections, ensuring that the curved sections and the main structure could be constructed synchronously during the pouring process.

[0247] The specific embodiments described above further illustrate the purpose, technical solution, and beneficial effects of the present invention. It should be understood that the above description is only a specific embodiment of the present invention and is not intended to limit the scope of protection of the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the scope of protection of the present invention.

Claims

1. A method for designing inclined shaft formwork based on digital modeling and sliding mode optimization, characterized in that, Includes the following steps: Step 1: Draw the complete axis line containing curve segments and straight line segments, and combine the geographic information system and building information model to establish a three-dimensional digital model of the entire inclined shaft; Step 2: Use a laser scanner, drone or 3D LiDAR to acquire cross-sectional data after the inclined shaft is excavated, and import it into the modeling software. After data cleaning and fitting, a high-precision 3D inclined shaft model is obtained. Step 3: Using the curve equation in the inclined shaft curve model, calculate the tangent of each segment of the inclined shaft, and calculate the angle between the tangent and the normal based on the transition points of the upper and lower bends; Step 4: Based on the geometry of the inclined shaft and the calculation results of the tangent, divide the pouring area and determine the start and end points of each compartment; Step 5: Calculate the optimal solution for sliding mode segmentation using an optimization algorithm, where the optimization objective is to minimize the structural deformation of the template; calculate the position, angle, and transition portion of each sliding mode segment; Step 6: Based on the obtained high-precision three-dimensional inclined shaft model and the optimized structure of the slipform segment, construct the overall construction formwork.

2. The inclined shaft formwork design method based on digital modeling and sliding mode optimization according to claim 1, characterized in that, Step 1 includes the following steps: Step 1.1: Use geometric curve equations to describe the curved segments of the inclined shaft and straight line equations to describe the straight segments in the inclined shaft. For the intersection of the curved segments and the straight segments, calculate the tangent and angle to ensure a smooth connection and obtain the geometric model of the inclined shaft axis. Step 1.2: Collect topographic and address data of the actual area through a geographic information system, and embed the collected topographic and address data into the BIM model in the BIM modeling software; then import the inclined shaft axis geometric model into the BIM model; by combining the actual topographic and address data with the inclined shaft axis geometric model, a three-dimensional digital model with geospatial positioning is generated.

3. The inclined shaft formwork design method based on digital modeling and sliding mode optimization according to claim 1, characterized in that, Step 2 includes the following steps: Step 2.1: Use a laser scanner, drone, or 3D lidar to acquire cross-sectional data after the inclined shaft is excavated, and obtain point cloud data; Step 2.2: Convert the acquired point cloud data into a data format that BIM modeling software can process; Step 2.3: Remove noise from the point cloud data and remove holes, then use the voxel mesh method to downsample the point cloud data to obtain preprocessed point cloud data; Step 2.4: Based on adaptive surface fitting and incremental 3D reconstruction, the preprocessed point cloud data and 3D digital model are used for optimization to obtain a high-precision 3D inclined shaft model.

4. The inclined shaft formwork design method based on digital modeling and sliding mode optimization according to claim 3, characterized in that, Step 2.4 includes the following steps: Local surface fitting: Let each point in the point cloud data Select k points within its neighborhood as local datasets ,in And calculate the normal vector of each point. and curvature : Calculate the normal vector: construct a data matrix from the selected k points. , where each point ; Calculate the covariance matrix C of the point cloud: ； In the formula: , , Represent Coordinates on the x, y, and z axes; Perform eigenvalue decomposition on the covariance matrix C to obtain the eigenvalues ​​of the covariance matrix C. , , and the corresponding feature vectors , , ; where the normal vector Corresponding minimum eigenvalue eigenvectors ; Curvature calculation: Based on k neighborhood points, principal component analysis is used to obtain the curvature. Weighted least squares fitting: For each local region, a quadratic surface model is fitted using the weighted least squares method. ； In the formula: x, y, z represent the coordinate values ​​on the x, y, and z axes, respectively; a, b, c, d, e, and f are fitting parameters, solved using the weighted least squares method based on neighborhood point cloud data. ； In the formula: Indicates the weight of point i; n represents the number of data points; ； In the formula: Indicates local curvature; This indicates the density of a local point cloud. as well as Indicates the adjustment parameter; Global surface blending and optimization: The local least squares method is used to fuse all local fitting results. The optimization objective is to minimize the differences between the local fitted surfaces, where the optimization problem takes the following form: ； In the formula: Let i be the i-th point; Represents a quadratic surface model; Let i represent the neighborhood of point i; Indicates the weight of the smoothing term; Incremental modeling and slicing method: The point cloud data is sliced ​​into multiple layers. The point cloud data in each slice is processed using adaptive surface fitting. At each layer, a local two-dimensional surface is generated. And optimize and merge data from adjacent slices; For each adjacent slice and The fitting results are then fused using three-dimensional difference: ； In the formula: and The weights are calculated based on slice distance and fitting accuracy. Incremental surface optimization: Based on the local surfaces generated from all slices, an incremental optimization method is used for adjustment, with the following optimization objective function: ； In the formula: Represents the actual value; Global model generation: By stitching together the optimized surfaces at various levels, a high-precision 3D inclined shaft model is obtained.

5. The inclined shaft formwork design method based on digital modeling and sliding mode optimization according to claim 1, characterized in that, Step 3 includes the following steps: Step 3.1: Suppose the curve of the inclined shaft is represented by the following parametric equation: ； In the formula: t represents the parameters of the curve; These represent the coordinates of the curve in the x, y, and z directions in three-dimensional space, respectively. Step 3.2: For the parametric curve, calculate the tangent line by taking the derivative with respect to t: Tangent vector It is expressed as follows: ； In the formula: This indicates the instantaneous direction of the curve at each point t; Based on the above tangent vectors The calculation formula is used to calculate the tangent direction at the start and end of each segment, resulting in... and , represent the tangent vectors at the start and end points of the segment, respectively; Determining the transition point: The transition point is determined by calculating the curvature of the inclined shaft curve. ； In the formula: , They are respectively The first derivative with respect to t; , Let and denote the second derivatives with respect to t; Indicates curvature; Points where the curvature exceeds a threshold are defined as transition points; Calculate the angle between the tangent and the normal: Normal vector: The normal vector is a vector perpendicular to the tangent line and passes through the tangent vector. Calculation of the surface normal of the inclined shaft: ； In the formula: Represents the tangent vector An auxiliary vector perpendicular to the normal direction; Angle calculation: The angle between the tangent and the normal is calculated using the dot product formula for vectors. ； In the formula: and These represent the magnitudes of the tangent and normal, respectively.

6. The inclined shaft formwork design method based on digital modeling and sliding mode optimization according to claim 1, characterized in that, Step 4 includes the following steps: Based on the tangent and normal obtained in step 3, the line segment is divided into segments, wherein the segmentation of the line segment is based on a fixed length interval; For curve segments, the segment length is adjusted according to the rate of change of the tangent and the magnitude of the curvature; ； ； In the formula: This represents the rate of change of the tangent at point t. An angle indicating the direction of the tangent; ； In the formula: Indicates the basic segment length; Indicates the adjustment factor; Indicates the adjusted segment length; Based on the change in tangent direction, determine the start and end points for each sub-compartment: ； In the formula: This indicates the starting point of the i-th segment; Indicates the rate of change of the tangent; This indicates the adjusted segment length.

7. The inclined shaft formwork design method based on digital modeling and sliding mode optimization according to claim 1, characterized in that, Step 5 uses the particle swarm optimization algorithm to calculate the optimal solution for sliding mode segmentation: Initialize the particle swarm: Each particle represents a solution, i.e., a sliding mode segmentation configuration scheme, and the dimension of each particle is... This represents the position, angle, and length of a sliding mode segment; Evaluate the fitness function: For each particle, calculate its fitness value: ； In the formula: n represents the number of sliding mode segments; This represents the structural deformation of the i-th segment; This represents the force on the i-th segment; Update particle position and velocity: Based on the particle's historical best solution and the historical best solutions of all particles, update the particle's position and velocity. ； In the formula: represents the velocity of the i-th particle in the k-th iteration; w represents the inertia weight; and Indicates the learning factor; and This represents a random number, uniformly distributed between [0,1]. This represents the historical best position of particle i; Represents the historical best position of all particles; The iteration stops when the fitness value of the particle swarm reaches a preset threshold, or after a certain number of iterations. After multiple iterations, the optimal configuration of each sliding mode segment is obtained, including position, angle and length.

8. The inclined shaft formwork design method based on digital modeling and sliding mode optimization according to claim 7, characterized in that, The following constraints need to be satisfied during the iteration process: Force uniformity constraint: ； In the formula: This represents the force on the i-th segment; This indicates the maximum allowable force for each segment; Stability constraints: ； In the formula: This represents the deformation value of the i-th segment; Indicates the maximum allowable deformation value; Geometric constraints: According to construction requirements, the starting point and number of sections must be within the geometric boundaries of the inclined shaft.

9. The inclined shaft formwork design method based on digital modeling and sliding mode optimization according to claim 1, characterized in that, In step 6, by combining the position information, angle and length of all segments, a three-dimensional model of the entire inclined shaft construction formwork is generated. Based on the construction requirements and joint design of each segment, a formwork system with smooth transition and uniform stress is constructed.

10. The inclined shaft formwork design method based on digital modeling and sliding mode optimization according to claim 9, characterized in that, In step 6, after the construction formwork design is completed, finite element analysis is used to perform stability analysis on the entire construction formwork, calculate the stress on each segment, and verify the stability of the formwork.

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