Inclined shaft formwork design method based on digital modeling and sliding mode optimization

Abstract

The invention discloses an inclined shaft formwork design method based on digital modeling and sliding mode optimization, and the method comprises the steps: drawing a complete three-dimensional digital model of an inclined shaft through employing a geographic information system and a building information model, obtaining the high-precision inclined shaft data through combining with the technologies of laser scanning, an unmanned aerial vehicle and the like, and guaranteeing the accuracy of the model; an included angle between a tangent line and a normal line of each segment is calculated through an inclined shaft curve equation, and a precise geometric basis is provided for optimization design of the formwork based on the divided pouring areas and bin division starting and ending points; the optimal scheme of sliding mode segmentation is calculated by adopting an optimization algorithm, the structural deformation of the template is emphatically optimized, and the rationality of the position, angle and transition part of each segment is ensured; finally, through the accurate three-dimensional inclined shaft model and optimal design, the overall construction formwork is constructed, the precision and stability of inclined shaft formwork design are improved, it is ensured that in the construction process, stress of the formwork is uniform, deformation is minimized, and the construction efficiency and safety are remarkably improved.

Description

Technical Field

[0001] The invention relates to the technical field of building formwork design, and more specifically to a method for designing an inclined shaft formwork based on digital modeling and sliding form optimization. Background Art

[0002] In modern engineering construction, especially in the construction of inclined shafts of pumped storage power stations, the accuracy and stability of formwork design are crucial to engineering quality and construction efficiency. Pumped storage power stations can effectively regulate the load of the power grid and improve the stability and efficiency of the power system by pumping water to the upper reservoir when the power load is low and releasing water to generate electricity during peak hours. In this process, the lining construction of the inclined shaft is a key link. The lining not only prevents the 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 system (GIS) and laser scanning, 3D digital modeling has become a trend in the industry. These technologies can accurately restore the complex geometric forms of inclined shafts and provide high-precision data support for formwork design. However, how to combine these high-precision digital models with actual construction needs, especially to optimize the design of formwork in complex environments such as inclined shafts, is still a technical problem that needs to be solved urgently.

[0004] In inclined shaft construction, especially when there are curved sections, it is a challenge to reasonably divide the slipform sections and ensure that the structural deformation of each section is minimized to meet the requirements of uniform force and stability. Traditional formwork design methods often rely on manual calculations and experience, resulting in problems such as uneven force and excessive deformation in the structural design of the formwork in the construction of inclined shafts with complex geometric shapes. This not only affects construction safety, but may also lead to delays in construction schedules and additional costs. Therefore, traditional formwork design often finds it difficult to provide effective solutions in these transition sections and complex geometric areas. Summary of the invention

[0005] The purpose of the present invention is to provide an inclined shaft formwork design method based on digital modeling and sliding formwork optimization to address the technical problem that in the construction of inclined shafts with complex geometric shapes, traditional formwork design methods often find it difficult to provide effective solutions in transition sections and complex geometric areas. This method constructs an overall construction formwork through an accurate three-dimensional inclined shaft model and optimized design, which not only improves the accuracy and stability of the formwork design, but also ensures uniform force and minimized deformation during construction, thereby significantly improving construction efficiency and safety.

[0006] The present invention is achieved through the following technical solutions:

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

[0008] Step 1: Draw a complete axis including curved and straight segments, and build a 3D digital model of the entire inclined shaft by combining the geographic information system and building information model;

[0009] Step 2: Use laser scanners, drones or 3D laser radar to obtain 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 well curve model, calculate the tangent of each segment of the inclined well, and calculate the angle between the tangent and the normal based on the transition points of the upper and lower bends;

[0011] Step 4: Divide the casting area and determine the starting and ending points of each compartment according to the geometry of the inclined shaft and the calculation results of the tangent;

[0012] Step 5: Use the optimization algorithm to calculate the optimal solution for the sliding form segmentation, where the optimization goal is to minimize the structural deformation of the template; calculate the position, angle and transition part of each sliding form segment;

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

[0014] The present invention proposes a new inclined shaft formwork design method by combining digital modeling technology with sliding form optimization algorithm, which effectively solves the problems of uneven structural force and excessive deformation in transition sections and complex geometric areas in traditional design methods. First, a complete three-dimensional digital model of the inclined shaft is drawn using geographic information system (GIS) and building information model (BIM), and high-precision inclined shaft data is obtained by combining laser scanning, drones and other technologies to ensure the accuracy of the model. The angle between the tangent and the normal of each segment is calculated by the inclined shaft curve equation, and the casting area and the starting and ending points of the compartments are divided based on this, which provides an accurate geometric basis for the optimization design of the formwork. On this basis, the optimization algorithm is used to calculate the optimal solution of the sliding formwork segmentation, focusing on optimizing the structural deformation of the template to ensure the rationality of the position, angle and transition part of each segment. Finally, through the accurate three-dimensional inclined shaft model and optimization design, the overall construction formwork is constructed, which not only improves the accuracy and stability of the formwork design, but also ensures uniform force and minimized deformation during construction, significantly improving construction efficiency and safety.

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

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

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

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

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

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

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

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

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

[0024] Local surface fitting:

[0025] Assume that each point P in the point cloud data i =(x i ,y i , z i ), select k points in its neighborhood as the local data set 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 j}, where each point P j =(x j ,y j , z j );

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

[0028]

[0029] Where: x j ,y j 、z j Represents P j Coordinates in the x, y, and z axes;

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

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

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

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

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

[0035]

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

[0037]

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

[0039] Global surface fusion and optimization:

[0040] The regional least squares method is used to fuse all local fitting results. The optimization goal is to minimize the difference between the local fitting surfaces. The optimization problem is as follows:

[0041]

[0042] Where: P i =(x i ,y i, z i ) is the i-th point; f(x, y) represents the quadratic surface model; N(i) represents 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 levels. The point cloud data on each slice is processed using adaptive surface fitting. On each layer, a local two-dimensional surface f(x, y) is generated and optimized and merged through the data of adjacent slices.

[0044] For each adjacent slice S i and S i+1 , and fuse the fitting results through three-dimensional interpolation:

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

[0046] Where: λ1 and λ2 are weights calculated according to the slice distance and fitting accuracy;

[0047] Incremental surface optimization: Based on the local surfaces generated by all slices, an incremental optimization method is used to adjust the surface, and the objective function is optimized as follows:

[0048]

[0049] Where: represents the true value;

[0050] Global model generation: By splicing the optimized surfaces at each level, a high-precision three-dimensional inclined well model is obtained.

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

[0052] Step 3.1: Assume that the curve of the inclined well is represented by the following parameterized equation:

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

[0054] Where: t represents the parameter of the curve; x(t), y(t), z(t) represent the coordinates of the curve in the x, y, and z directions in three-dimensional space respectively;

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

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

[0057]

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

[0059] Based on the calculation formula of the tangent vector T(t) above, the tangent direction of the starting point and the end point of each segment is calculated to obtain T1 and T2, which represent the tangent vectors of the starting point and the end point of the segment respectively;

[0060] Determination of transition point: Determine the transition point by calculating the curvature of the inclined well curve:

[0061]

[0062] Where: x′(t), y′(t) are the first-order derivatives of x(t) and y(t) with respect to t; x″(t), y″(t) are the second-order derivatives with respect to t; k(t) represents the curvature;

[0063] The point where the curvature exceeds the threshold is defined as the transition point;

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

[0065] Normal vector: The normal vector is the vector perpendicular to the tangent line and is calculated by the tangent vector T(t) and the normal of the inclined well surface:

[0066]

[0067] Where: B(t) represents the 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 of the vectors:

[0069]

[0070] Where: |T(t)| and |N(t)| represent the modulus lengths of the tangent and normal, respectively.

[0071] Preferably, step 4 comprises the steps of:

[0072] Based on the tangent and normal obtained in step 3, the straight line segment is segmented, wherein the straight line segment is segmented based on fixed length intervals;

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

[0074]

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

[0076]

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

[0078] According to the change of tangent direction, determine the starting and ending points for each sub-bin:

[0079]

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

[0081] Preferably, the 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, that is, a configuration scheme of a sliding mode segment, 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] Where: n represents the number of sliding mode segments; δ i represents the structural deformation of the i-th segment; F i represents the force of the ith segment;

[0086] Update particle position and velocity: Update the particle position and velocity based on the particle's historical optimal solution and the historical optimal solution of all particles:

[0087]

[0088] Where: represents the velocity of the i-th particle at the k-th iteration; w represents the inertia weight; c1 and c2 represent learning factors; r1 and r2 represent random numbers, uniformly distributed between [0,1]; p i represents the best historical position of particle i; g i Represents the best historical position of all particles;

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

[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 met during the iteration process:

[0092] Force uniformity constraint:

[0093]

[0094] Where: F i represents the force of the ith segment; F max Indicates the maximum allowable force for each segment;

[0095] Stability constraints:

[0096]

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

[0098] Geometric constraints: According to construction requirements, the starting point and node points of the segment must be within the geometric boundary of the inclined shaft.

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

[0100] The present invention proposes a new inclined shaft formwork design method by combining digital modeling technology with sliding form optimization algorithm, which effectively solves the problems of uneven structural force and excessive deformation in transition sections and complex geometric areas in traditional design methods. First, a complete three-dimensional digital model of the inclined shaft is drawn using geographic information system (GIS) and building information model (BIM), and high-precision inclined shaft data is obtained by combining laser scanning, drones and other technologies to ensure the accuracy of the model. The angle between the tangent and the normal of each segment is calculated by the inclined shaft curve equation, and the casting area and the starting and ending points of the compartments are divided based on this, which provides an accurate geometric basis for the optimization design of the formwork. On this basis, the optimization algorithm is used to calculate the optimal solution of the sliding formwork segmentation, focusing on optimizing the structural deformation of the template to ensure the rationality of the position, angle and transition part of each segment. Finally, through the accurate three-dimensional inclined shaft model and optimization design, the overall construction formwork is constructed, which not only improves the accuracy and stability of the formwork design, but also ensures uniform force and minimized deformation during construction, significantly improving construction efficiency and safety. BRIEF DESCRIPTION OF THE DRAWINGS

[0101] In order to more clearly illustrate the technical solutions of the exemplary embodiments of the present invention, the following briefly introduces the drawings required for use in the embodiments. It should be understood that the following drawings only illustrate certain embodiments of the present invention and should not be regarded as limiting the scope. For those of ordinary skill in the art, other relevant drawings can be obtained based on these drawings without creative work. In the drawings:

[0102] Figure 1 The present invention is a flow chart of the inclined shaft formwork design method based on digital modeling and sliding form optimization. DETAILED DESCRIPTION

[0103] In order to make the objectives, technical solutions and advantages of the present invention more clearly understood, the present invention is further described in detail below in conjunction with embodiments and drawings. The exemplary embodiments of the present invention and their description 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 technicians in the technical field to which this application belongs; the terms used herein are only for the purpose of describing specific embodiments and are not intended to limit this application; the terms "including" and "having" in the specification and claims of this application and the above-mentioned figure descriptions and any variations thereof are intended to cover non-exclusive inclusions.

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

[0106] Reference to "embodiments" herein means that a particular feature, structure, or characteristic described in conjunction with the embodiments may be included in at least one embodiment of the present application. The appearance of the phrase in various locations in the specification does not necessarily refer to the same embodiment, nor is it an independent or alternative embodiment that is mutually exclusive with other embodiments. It is explicitly and implicitly understood by those skilled in the art that the embodiments described herein may be combined with other embodiments.

[0107] In the description of the embodiments of the present application, the term "and / or" is only a description of the association relationship of associated objects, indicating that three relationships may exist. For example, A and / or B can represent: A exists, A and B exist at the same time, and B exists. In addition, the character " / " in this article generally indicates that the associated objects before and after are in an "or" relationship.

[0108] In the embodiments of the present application, the same reference numerals represent 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 the present application shown in the drawings, as well as the overall thickness, length, width and other dimensions of the integrated device are only exemplary descriptions and should not constitute any limitation to the present application.

[0109] In the description of the embodiments of the present application, the term "multiple" refers to more than two (including two). Similarly, "multiple groups" refers to more than two groups (including two groups), and "multiple pieces" refers to more than two pieces (including two pieces), unless otherwise clearly and specifically defined.

[0110] In the description of the embodiments of the present application, the technical terms "center", "longitudinal", "lateral", "length", "width", "thickness", "up", "down", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inside", "outside", "clockwise", "counterclockwise", "axial", "radial", "circumferential", etc. indicate orientations or positional relationships based on the orientations or positional relationships shown in the accompanying drawings, which are only for the convenience of describing the embodiments of the present application and simplifying the description, and do not indicate or imply that the referred device or element must have a specific orientation, be constructed and operated in a specific orientation, and therefore should not be understood as a limitation on the embodiments of the present application.

[0111] In the description of the embodiments of the present application, unless otherwise clearly specified and limited, technical terms such as "installed", "connected", "connected", "fixed" and the like should be understood in a broad sense. For example, it can be a fixed connection, a detachable connection, or an integral connection; it can be a mechanical connection or an electrical connection; it can be a direct connection or an indirect connection through an intermediate medium, and it can be the internal connection of two elements or the interaction relationship between two elements. For those of ordinary skill in the art, the specific meanings of the above terms in the embodiments of the present application can be understood according to the specific circumstances.

[0112] Please refer to Figure 1 , a method for designing a inclined shaft formwork based on digital modeling and sliding form optimization provided in an embodiment of the present application comprises the following steps:

[0113] Step 1: Draw a complete axis including curved and straight segments, and build a 3D digital model of the entire inclined shaft by combining the geographic information system and building information model;

[0114] Step 2: Use laser scanners, drones or 3D laser radar to obtain 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 well curve model, calculate the tangent of each segment of the inclined well, and calculate the angle between the tangent and the normal based on the transition points of the upper and lower bends;

[0116] Step 4: Divide the casting area and determine the starting and ending points of each compartment according to the geometry of the inclined shaft and the calculation results of the tangent;

[0117] Step 5: Use the optimization algorithm to calculate the optimal solution for the sliding form segmentation, where the optimization goal is to minimize the structural deformation of the template; calculate the position, angle and transition part of each sliding form segment;

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

[0119] The present invention proposes a new inclined shaft formwork design method by combining digital modeling technology with sliding form optimization algorithm, which effectively solves the problems of uneven structural force and excessive deformation in transition sections and complex geometric areas in traditional design methods. First, a complete three-dimensional digital model of the inclined shaft is drawn using geographic information system (GIS) and building information model (BIM), and high-precision inclined shaft data is obtained by combining laser scanning, drones and other technologies to ensure the accuracy of the model. The angle between the tangent and the normal of each segment is calculated by the inclined shaft curve equation, and the casting area and the starting and ending points of the compartments are divided based on this, which provides an accurate geometric basis for the optimization design of the formwork. On this basis, the optimization algorithm is used to calculate the optimal solution of the sliding formwork segmentation, focusing on optimizing the structural deformation of the template to ensure the rationality of the position, angle and transition part of each segment. Finally, through the accurate three-dimensional inclined shaft model and optimization design, the overall construction formwork is constructed, which not only improves the accuracy and stability of the formwork design, but also ensures uniform force and minimized deformation during construction, significantly improving construction efficiency and safety.

[0120] As a 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 center line of the shaft during the excavation of the inclined shaft. It is composed of alternating straight and curved segments, and usually has certain curves and slopes in the vertical and horizontal directions. In order to ensure the geometric accuracy and construction quality of the inclined shaft during the construction process, the first 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 well, and use straight line equations to describe the straight segments in the inclined well. For the intersection of the curved segment and the straight segment, calculate the tangent and angle to ensure smooth connection, and obtain the geometric model of the inclined well axis;

[0123] Exemplary: The curve segment is modeled as follows:

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

[0125] x(t)=R h ·cos(θ(t))+x0;

[0126] y(t)=R h sin(θ(t))+y0;

[0127] Where: x(t) and y(t) represent the coordinates of the points on the curve; R h Indicates the radius of the horizontal curve; θ(t) indicates the angle from the starting point to a certain scale; x0 and y0 indicate the coordinates of the center of the arc;

[0128] Vertical curve segment (arc): A vertical curve is a curve of the shaft axis in the vertical direction:

[0129] z(t)=R v sin(φ(t))+z0;

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

[0131] Horizontal straight line segment: A horizontal straight line segment usually refers to the part of a straight line moving on a horizontal plane:

[0132] y = m x + b;

[0133] Where: x and y are the coordinates on the straight line segment; m represents the slope of the straight line; b represents the intercept of the straight line on the y-axis;

[0134] Vertical straight line segment:

[0135] z=m′·x+b′;

[0136] Where: z represents the vertical coordinate; m' represents the slope of the vertical line; b' represents the intercept of the line on the z axis;

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

[0138] Tangent calculation: There is a tangent problem at the intersection of a curve segment and a straight line segment. In order to ensure a smooth transition, the tangent of each segment needs to be calculated. For example, where a curve meets a straight line, calculate the angle between the tangent of the curve and the normal of the straight line:

[0139]

[0140] Where: T curve , T line Represent the tangent vectors of the curve and straight line segments respectively; |T curve |、|T line | represents the magnitude of the tangent vector 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 a straight line segment and a curve segment, 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 the inclined well. Curve segments (such as arcs) are used to describe the curved parts of the inclined well, and straight line segments are used to describe the straight sections of the inclined well. These mathematical models can help us accurately calculate the position, shape and transition of the inclined well in digital modeling.

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

[0144] In BIM modeling software (such as Revit, Tekla, etc.), we can import GIS data (such as geographic coordinates, terrain height, 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 plug-ins between ESRI ArcGIS and Autodesk Revit), we can embed GIS spatial data (such as ground elevation, road distribution, etc.) directly into the BIM model.

[0145] Geographic coordinate docking: Once the GIS data is imported into the BIM software, we can ensure that the BIM model is docked with the actual geographic coordinate system to ensure that the position of the inclined shaft in the actual environment is accurate. For example, the starting point, turning point, and end point of the inclined shaft will be located according to the real geographic coordinates to avoid deviations in actual construction.

[0146] Integration of terrain and underground environment: In the BIM model, in addition to modeling of surface facilities, underground environmental data (such as groundwater level, rock layer distribution, etc.) can also be introduced for geological modeling. This helps to consider the impact of the underground environment when designing inclined shafts and avoid construction risks.

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

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

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

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

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

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

[0153] Local surface fitting:

[0154] Assume that each point P in the point cloud data i =(x i ,y i ,z i ), select k points in its neighborhood as the local data set P j , where j∈[ik,i+k], and calculate the normal vector n of each point i and curvature k i :

[0155] Calculate the normal vector: construct a data matrix X = {P j}, where each point P j =(x j ,y j ,z j );

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

[0157]

[0158] Where: x j ,y j 、z j Represents P j Coordinates in the x, y, and z axes;

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

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

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

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

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

[0164]

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

[0166]

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

[0168] Global surface fusion and optimization:

[0169] The regional least squares method is used to fuse all local fitting results. The optimization goal is to minimize the difference between the local fitting surfaces. The optimization problem is as follows:

[0170]

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

[0172] The 3D reconstruction can be built incrementally, and the conversion from local point clouds to the global 3D model can be achieved by a step-by-step optimization and interpolation method, which gradually stitches each fitted local surface into a global 3D model.

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

[0174] For each adjacent slice S i and S i+1 , and fuse the fitting results through three-dimensional interpolation:

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

[0176] Where: λ1 and λ2 are weights calculated according to the slice distance and fitting accuracy;

[0177] Incremental surface optimization: Based on the local surfaces generated by all slices, an incremental optimization method is used to adjust the surface, and the objective function is optimized as follows:

[0178]

[0179] Where: represents the true value;

[0180] Global model generation: By splicing the optimized surfaces at each level, a high-precision three-dimensional inclined well model is obtained.

[0181] In this embodiment, a method combining adaptive surface fitting and incremental 3D reconstruction is used. The fitting accuracy is adjusted by weighted least squares method and local curvature adaptively, and each local surface is gradually optimized and spliced ​​to finally generate an accurate 3D inclined well model. This method avoids the deep learning model and can still provide efficient and accurate 3D reconstruction results, which is suitable for complex point cloud data scenarios.

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

[0183] Step 3.1: In step 2, we have obtained high-precision cross-sectional data of the inclined well through laser scanners, drones or 3D laser radars, and obtained a 3D model of the inclined well through data cleaning and fitting; at this stage, our goal is to use these data to obtain the curve equation of the inclined well; assume that the curve of the inclined well is represented by the following parameterized equation:

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

[0185] Where: t represents the parameter 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 the curve at a certain point. For a parameterized curve, the tangent line is calculated by taking the derivative of t:

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

[0188]

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

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

[0191] Determination of transition points: In the curve of the inclined well, especially in the curved part, there may be transition sections. The definition of transition points is usually some key points in the curve, such as places where the curvature changes greatly, or points connecting different segments.

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

[0193]

[0194] Where: x′(t), y′(t) are the first-order derivatives of x(t) and y(t) with respect to t; x″(t), y″(t) are the second-order derivatives with respect to t; k(t) represents the curvature;

[0195] Transition points can be defined as places where the curvature changes greatly, that is, points when 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 template is installed in the correct direction.

[0198] Normal vector: The normal vector is the vector perpendicular to the tangent line and is calculated by the tangent vector T(t) and the normal of the inclined well surface:

[0199]

[0200] Where: B(t) represents the 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 of the vectors:

[0202]

[0203] Where: |T(t)| and |N(t)| represent the modulus lengths of the tangent and normal, respectively.

[0204] In this embodiment, the angle between the tangent and the normal of each segment is calculated by the above method 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 sliding template can be reasonably laid out in each segment of the inclined shaft, and a smooth transition is performed in the transition area to avoid template deformation caused by excessive angles.

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

[0206] Based on the tangent and normal obtained in step 3, the straight line segment is segmented, wherein the straight line segment is segmented based on fixed length intervals;

[0207] The rate of change of the tangent is an important indicator of the change in the curvature of a curve. It indicates the speed of change of the tangent direction at a certain point. The rate of change of the tangent can be described by the relationship between the 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] Where: V(t) represents the rate of change of the tangent calculated at point t; θ(t) represents the angle of the tangent direction;

[0211] In order to ensure smooth transition of the template in the curve segment, we adjust the segment length according to the curvature. Areas with large curvature (faster changes) need to be divided into smaller segments, while areas with small curvature can increase the segment length appropriately.

[0212]

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

[0214] According to the change of tangent direction, determine the starting and ending points for each sub-bin:

[0215]

[0216] Where: t i represents the starting point of the ith segment; V(ti ) represents the rate of change of tangent; L segment (t i ) indicates the adjusted segment length.

[0217] As a possible implementation of this embodiment, the 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, that is, a configuration scheme of a sliding mode segment, 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] Where: n represents the number of sliding mode segments; δ i represents the structural deformation of the i-th segment; F i Represents the force of the i-th segment; Update the particle position and velocity: Update the particle position and velocity according to the historical optimal solution of the particle and the historical optimal solution of all particles:

[0222]

[0223] Where: represents the velocity of the i-th particle at the k-th iteration; w represents the inertia weight; c1 and c2 represent learning factors; r1 and r2 represent random numbers, uniformly distributed between [0,1]; p i represents the best historical position of particle i; g i Represents the best historical position of all particles;

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

[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 met during the iteration process:

[0227] Force uniformity constraint:

[0228]

[0229] Where: F i represents the force of the ith segment; F maxIndicates the maximum allowable force for each segment;

[0230] Stability constraints:

[0231]

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

[0233] Geometric constraints: According to construction requirements, the starting point and node points of the segment must be within the geometric boundary of the inclined shaft.

[0234] In this embodiment, an optimization algorithm (such as a particle swarm optimization algorithm) is introduced to minimize the structural deformation of the sliding formwork, ensuring that the formwork operates stably and efficiently throughout the construction process. By defining a fitness function, setting optimization constraints, and using a suitable optimization algorithm, the optimal position, angle, and length of each sliding form segment can be calculated, thereby ensuring the accuracy of the construction and the smooth transition of the formwork.

[0235] In this embodiment, the present invention significantly solves the problem that traditional design methods cannot effectively handle the complex geometric shapes and transition sections of inclined shafts through a design method that combines digital modeling with sliding form optimization, especially in the upper and lower bends and the overall casting of the inclined shaft. Through accurate three-dimensional digital models and optimization algorithms, each segment of the inclined shaft can be reasonably divided, and the position, angle and transition part of the sliding form segment can be optimized, thereby realizing an integrated upper and lower bend design. This method can support the joint casting of each compartment of the inclined shaft while ensuring structural stability, avoiding the construction discontinuity and potential structural problems caused by segmented casting in traditional methods.

[0236] The particle swarm optimization algorithm can effectively minimize the structural deformation of the formwork, ensuring that each sliding formwork segment reaches the optimal state in terms of structural stress and deformation control. At the same time, the optimized segment design can also reduce the construction difficulty and material waste caused by uneven transition of the upper and lower bends or changes in the shape of the inclined shaft during construction. This design method that integrates compartment casting and integrated upper and lower bends not only improves construction efficiency, but also reduces construction costs, improves the safety and stability of the entire inclined shaft formwork design, and has 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 sliding formwork 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 3D model of the entire inclined shaft construction formwork is generated. According to the construction requirements and joint design of each segment, a formwork system with smooth transition and uniform force is constructed.

[0239] Verification of formwork structure stability: After the design of the construction formwork is completed, its structural stability needs to be verified to ensure that the formwork can remain stable during the construction process and does not deform excessively.

[0240] Stability analysis: Use finite element analysis (FEA) to conduct stability analysis on the entire construction formwork, calculate the stress conditions of each segment, and verify the stability of the formwork; specific analysis formulas and methods can be carried out based on structural mechanics theory.

[0241] In the present invention, a three-dimensional digital model of the entire inclined shaft is established, including curved and straight segments, which provides an accurate basis for integrated design. This model integrates data from the Geographic Information System (GIS) and the Building Information Model (BIM), and can show the spatial structure of the inclined shaft in detail, including the geometry of the upper and lower curved segments.

[0242] Use advanced equipment such as laser scanners, drones or 3D laser radar to obtain cross-sectional data after actual excavation, and import these data into the modeling software. Through data cleaning and fitting, the 3D inclined shaft model can be updated and optimized to ensure that the model is consistent with the actual construction site.

[0243] The curve equation in the inclined shaft curve model is used to calculate the tangent and normal of each segment and determine the angle between the tangent and the normal. This step is crucial to determine the transition point of the curved segment and ensure the smooth transition of the curve during the integrated casting process.

[0244] According to the geometry of the inclined shaft and the tangent calculation results, the pouring area is reasonably divided and the starting and ending points of each compartment are determined. This provides clear construction boundaries and sequences for integrated pouring, ensuring that the curved section and the main structure can be poured as a whole.

[0245] In step 5, the particle swarm optimization algorithm is used to calculate the optimal solution for the sliding form segment, including position, angle and length. This optimization process takes into account the structural deformation and force uniformity, ensuring the stability and structural safety of each segment during the integrated casting process.

[0246] Based on the high-precision three-dimensional inclined shaft model and the optimized structure of the sliding formwork segment, an overall construction formwork was constructed. This formwork design takes into account the special requirements of the integrated upper and lower curved sections, ensuring that the curved section and the main structure can be constructed synchronously during the pouring process.

[0247] The specific implementation methods described above further illustrate the objectives, technical solutions and beneficial effects of the present invention in detail. It should be understood that the above description is only a specific implementation method 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 in the scope of protection of the present invention.

Claims

1. A method for designing inclined shaft formwork based on digital modeling and sliding form optimization, characterized in that: The following steps are involved: Step 1: Draw a complete axis including curved and straight segments, and build a 3D digital model of the entire inclined shaft by combining the geographic information system and building information model; Step 2: Use laser scanners, drones or 3D laser radar to obtain 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 well curve model, calculate the tangent of each segment of the inclined well, and calculate the angle between the tangent and the normal based on the transition points of the upper and lower bends; Step 4: Divide the casting area and determine the starting and ending points of each compartment according to the geometry of the inclined shaft and the calculation results of the tangent; Step 5: Use the optimization algorithm to calculate the optimal solution for the sliding form segmentation, where the optimization goal is to minimize the structural deformation of the template; calculate the position, angle and transition part of each sliding form segment; Step 6: Based on the high-precision three-dimensional inclined shaft model and the optimized structure of the sliding formwork segment, construct the overall construction formwork.

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

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

4. The inclined shaft formwork design method based on digital modeling and sliding form optimization according to claim 3 is characterized in that: The step 2.4 comprises the following steps: Local surface fitting: Assume that each point P in the point cloud data i =(x i ,y i ,z i ), select k points in its neighborhood as the local data set P j , where j∈[ik,i+k], and calculate the normal vector n of each point i and curvature k i : Calculate the normal vector: construct a data matrix X = {P j }, where each point P j =(x j ,y j ,z j ); Calculate the covariance matrix C of the point cloud set: Where: x j ,y j 、z j Represents P j Coordinates in the x, y, and z axes; Perform eigenvalue decomposition on the covariance matrix C to obtain the eigenvalues ​​λ1, λ2, λ3 of the covariance matrix C and the corresponding eigenvectors v1, v2, v3; where the normal vector n i The eigenvector v3 corresponding to the minimum eigenvalue λ3; Curvature calculation: Based on k neighborhood points, principal component analysis is used to obtain; Weighted least squares fitting: For each local region, a quadratic surface model is fitted using weighted least squares: z(x,y)=ax 2 +by 2 +cxy+dx+ey+f; Where: x, y, z represent the coordinate values ​​in the x, y, and z axes respectively; a, b, c, d, e, and f are fitting parameters, which are solved by weighted least squares method based on the neighborhood point cloud data: Where: w i represents the weight of point i; n represents the number of data points; Where: k i represents the local curvature; ρ i represents the density of the local point cloud; α and β represent adjustment parameters; Global surface fusion and optimization: The regional least squares method is used to fuse all local fitting results. The optimization goal is to minimize the difference between the local fitting surfaces. The optimization problem is as follows: Where: P i =(x i ,y i ,z i ) is the i-th point; f(x,y) represents the quadratic surface model; N(i) represents the neighborhood of point i; λ represents the weight of the smoothing term; Incremental modeling and slicing method: The point cloud data is sliced ​​into multiple levels. The point cloud data on each slice is processed using adaptive surface fitting. On each layer, a local two-dimensional surface f(x, y) is generated and optimized and merged through the data of adjacent slices. For each adjacent slice S i and S i+1 , and fuse the fitting results through three-dimensional interpolation: f(x,y,z)=λ1f i (x,y)+λ2f i+1 (x,y); Where: λ1 and λ2 are weights calculated according to the slice distance and fitting accuracy; Incremental surface optimization: Based on the local surfaces generated by all slices, an incremental optimization method is used to adjust the surface, and the objective function is optimized as follows: Where: represents the true value; Global model generation: By splicing the optimized surfaces at each level, a high-precision three-dimensional inclined well model is obtained.

5. The inclined shaft formwork design method based on digital modeling and sliding form optimization according to claim 1 is characterized in that: The step 3 comprises the following steps: Step 3.1: Assume that the curve of the inclined well is represented by the following parameterized equation: r(t)=(x(t),y(t),z(t)); Where: t represents the parameter 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; Step 3.2: For a parameterized curve, calculate the tangent line by taking the derivative with respect to t: The tangent vector T(t) is expressed as follows: Where: T(t) represents the instantaneous direction of the curve at each point t; Based on the calculation formula of the tangent vector T(t) above, the tangent direction of the starting point and the end point of each segment is calculated to obtain T1 and T2, which represent the tangent vectors of the starting point and the end point of the segment respectively; Determination of transition point: Determine the transition point by calculating the curvature of the inclined well curve: Where: x′(t), y′(t) are the first-order derivatives of x(t) and y(t) with respect to t; x″(t), y″(t) are the second-order derivatives with respect to t; k(t) represents the curvature; The point where the curvature exceeds the threshold is defined as the transition point; Calculate the angle between the tangent and the normal: Normal vector: The normal vector is the vector perpendicular to the tangent line and is calculated by the tangent vector T(t) and the normal of the inclined well surface: Where: B(t) represents the auxiliary vector perpendicular to the tangent vector T(t) and the normal direction; Angle calculation: The angle between the tangent and the normal is calculated using the dot product formula of the vectors: Where: |T(t)| and |N(t)| represent the modulus lengths of the tangent and normal, respectively.

6. The inclined shaft formwork design method based on digital modeling and sliding form optimization according to claim 1 is characterized in that: The step 4 comprises the steps of: Based on the tangent and normal obtained in step 3, the straight line segment is segmented, wherein the straight line segment is segmented based on fixed length intervals; For curved segments, the segment length is adjusted according to the rate of change of the tangent and the magnitude of the curvature; Where: V(t) represents the rate of change of the tangent calculated at point t; θ(t) represents the angle of the tangent direction; Where: L0 represents the basic segment length; α represents the adjustment coefficient; L segment (t) represents the adjusted segment length; According to the change of tangent direction, determine the starting and ending points for each sub-bin: Where: t i represents the starting point of the ith segment; V(t i ) represents the rate of change of tangent; L segment (t i ) indicates the adjusted segment length.

7. The inclined shaft formwork design method based on digital formwork and sliding formwork optimization according to claim 1 is characterized in that: The 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, that is, a configuration scheme of a sliding mode segment, 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; Evaluate the fitness function: For each particle, calculate its fitness value: Where: n represents the number of sliding mode segments; δ i represents the structural deformation of the i-th segment; F i represents the force of the ith segment; Update particle position and velocity: Update the particle position and velocity based on the particle's historical optimal solution and the historical optimal solution of all particles: Where: represents the velocity of the i-th particle at the k-th iteration; w represents the inertia weight; c1 and c2 represent learning factors; r1 and r2 represent random numbers, uniformly distributed between [0,1]; p i represents the best historical position of particle i; g i Represents the best historical position of all particles; When the fitness value of the particle swarm reaches the preset threshold, or after a certain number of iterations, the iteration stops; 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 formwork and sliding formwork optimization according to claim 7 is characterized in that: The following constraints need to be met during the iteration process: Force uniformity constraint: Where: F i represents the force of the ith segment; F max Indicates the maximum allowable force for each segment; Stability constraints: Where: i represents the deformation value of the i-th segment; δ max Indicates the maximum allowable deformation value; Geometric constraints: According to construction requirements, the starting point and node points of the segment must be within the geometric boundary of the inclined shaft.

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

10. The inclined shaft formwork design method based on digital formwork and sliding formwork optimization according to claim 9 is characterized in that: In step 6, after the design of the construction formwork is completed, the stability of the entire construction formwork is analyzed using finite element analysis, the stress conditions of each segment are calculated, and the stability of the formwork is verified.

Images