Large-span dome suspended ceiling parameterization rhombus module grading optimization construction method
By using parametric modeling and hierarchical optimization, large-span dome ceilings are divided into standardized templates. Combined with dynamic adjustment technology, this solves the problems of numerous module types and installation errors in existing construction, achieving efficient and aesthetically pleasing ceiling construction.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Applications(China)
- Current Assignee / Owner
- SHANGHAI BUILDING DECORATION ENG GRP CO LTD
- Filing Date
- 2025-12-17
- Publication Date
- 2026-04-17
AI Technical Summary
Existing construction methods for large-span dome ceilings suffer from problems such as a wide variety of modules, complex processing, high transportation costs, and difficulty in correcting installation errors, which affect construction efficiency and aesthetics.
Using parametric modeling and hierarchical optimization methods, the dome surface is divided into rhombic mesh units. Through curvature determination and energy function optimization, it is divided into eight types of standardized templates. Combined with laser scanning and total station, dynamic adjustments are made to achieve efficient module installation.
It significantly reduces the types of panels, lowers processing and transportation costs, improves construction efficiency and overall aesthetics, and ensures installation accuracy and structural continuity.
Smart Images
Figure CN121881607A_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of building construction technology, and more specifically, to a parametric diamond-shaped module hierarchical optimization construction method for large-span dome ceilings. Background Technology
[0002] With the continuous construction of large public buildings such as airport terminals, convention centers, and stadiums, interior ceilings in large-span spaces are gradually developing towards curved, irregular, and artistic designs. As an important component of the spatial environment, dome ceilings need to meet both structural safety and construction feasibility requirements, while also creating a continuous, smooth, and rhythmic curved form visually. Therefore, in practical engineering, aluminum alloy panels, light steel keel, and parametric modeling technology are typically used to design and construct complex ceilings.
[0003] However, existing construction methods for large-span dome ceilings still have several shortcomings in practical applications. First, traditional ceiling designs often employ a uniform grid division method, resulting in a wide variety of panel types. This is especially true in hyperbolic areas, where significant differences exist between modules, leading to a large number of panels, complex processing molds, and high transportation and installation costs. Second, the lack of unified optimization standards for module classification often results in unreasonable unit division, excessive gaps between panels, or uneven splicing, affecting the overall aesthetics. Third, during the construction phase, the lack of a dynamic adjustment mechanism based on parametric feedback makes it difficult to correct errors in real time. This often necessitates manual repairs or forced splicing, reducing construction efficiency and impacting structural continuity and safety.
[0004] Therefore, there is an urgent need for a parameterized rhomboid module hierarchical optimization construction method for large-span dome ceilings to solve the above problems. Summary of the Invention
[0005] The purpose of this invention is to solve the technical problems mentioned in the background section and to provide a parameterized rhomboid module hierarchical optimization construction method for large-span dome ceilings, comprising the following steps:
[0006] S1 Parametric Modeling: A 3D model of the dome target surface is performed, extracting the principal curvature parameters k1(u,v) and k2(u,v). Based on the geometric constraints of the element side length l and acute angle θ, the surface is divided into several rhombic mesh elements C. i ;
[0007] S2 Initial Grouping: Based on the curvature parameters of each unit, it is divided into hyperbolic plates, monobolic plates, or flat plates to obtain the initial grouping results.
[0008] S3 Hierarchical Optimization: Based on the initial grouping in step S2, an energy function E is established for the geometric deviation of each unit.i (P i Furthermore, by employing clustering and template assignment methods, the complex and diverse blocks are simplified into eight standardized templates, including two types of hyperbolic plates, two types of single-curved plates, and four types of flat plates, resulting in optimized grouping t. i ;
[0009] S4 Module Processing: Based on the template type obtained in step S3, calculate the bending radius R of the single-curved board. i The hot-pressing radius (R) of the hyperbolic plate 1i ,R 2i The flat plate is then cut into shape.
[0010] S5 module installation: Install the processed modules on the graded keel system. The gap-fitting method leaves a gap width g at the edge of the module, while the tight-fitting method achieves a seamless connection through concave edge fastening.
[0011] S6 Dynamic Adjustment: During installation, measured point cloud data is collected using laser scanning or a total station and compared with the parametric design model to calculate the keel node correction amount Δx. j The node positions are dynamically adjusted to ensure that the overall installation deviation does not exceed the preset limit.
[0012] As a preferred embodiment of the present invention, the rhombic mesh division in step S1 satisfies the following formula:
[0013] ||e1||=||e2||=l,∠(e1,e2)=θ,
[0014] Where e1 and e2 are the two diagonals of the rhombic element, l is the element side length, and θ is the acute angle of the rhombus. This partitioning result provides geometric input for subsequent curvature classification and optimization.
[0015] As a preferred technical solution of the present invention, the initial grouping in step S2 is based on the following curvature determination condition:
[0016]
[0017] Where k1 and k2 are principal curvature parameters, and τ K τ is the Gaussian curvature threshold. D τ is the curvature difference threshold. S This is the curvature amplitude threshold. Judgment result. It will be used as input for hierarchical optimization.
[0018] As a preferred technical solution of the present invention, the hierarchical optimization in step S3 is achieved through an energy function:
[0019]
[0020] For unit Ci The geometric distortion is quantized, where P i For the set of unit parameters, Indicates isometric distortion. Indicates area deviation The boundary discontinuity is represented by α, β, and γ, which are weighting factors. The result of this energy function will be used as input for clustering and template assignment.
[0021] As a preferred technical solution of the present invention, the S3 template assignment adopts the following optimization model:
[0022]
[0023] Among them, T k For the k-th type template, z ik Assign a variable to the unit, which takes the value 0 or 1, ε i (T k The error is the fitting error between the unit and the template. The optimization model outputs eight types of templates. As the basis for module processing.
[0024] As a preferred technical solution of the present invention, the module processing parameters in step S4 are obtained by the following formula:
[0025] Single-curved board bending radius:
[0026] Hyperbolic plate hot pressing radius:
[0027] Among them, κ max (p) is the function for the maximum curvature, κ max (p)=max(|k1|,|k2|),p∈C i For grid cell C i The sampling points on the surface are k1 and k2, which are the two principal curvature parameters of the surface at the sampling point p. R1 and R2 are the optimal bending radius for the single-curved plate, and the fitted radius variables for the hyperbolic plate in the two principal directions. Let C be the two principal radii of curvature of the hyperbolic plate. i : The i-th rhombic mesh element; R: The bending radius variable of the single-curved plate; The optimal bending radius for a single-curved board; The optimal radius of curvature solution for the hyperboloid in the two principal directions; argmin optimization operator, which represents taking the parameter value that minimizes the objective function.
[0028] As a preferred technical solution of the present invention, the seam width g in step S5 satisfies the thermal expansion and contraction check condition:
[0029] g≥αT LΔT+δ,
[0030] Where, α T Let L be the coefficient of linear expansion of the material, L be the characteristic length of the module, ΔT be the temperature difference range, and δ be the construction allowance. The calculated joint width is used as the input parameter for gap installation.
[0031] As a preferred technical solution of the present invention, the dynamic adjustment in step S6 adopts least squares optimization:
[0032]
[0033] in, For actual point cloud measurements, For the design model, Δx j The correction amount for the keel node is given by the constraint ||Δx. j ||≤η, where η represents the allowable adjustable stroke.
[0034] As a preferred embodiment of the present invention, the keel system is a hierarchical keel structure, including a main keel, a secondary keel, and hangers. The hangers are length-adjustable hangers used to achieve node correction Δx. j Fine-tuning.
[0035] As a preferred technical solution of the present invention, the method is applicable to large-span public buildings such as airport terminals, convention centers, and stadiums. While reducing the types of modules and lowering processing costs, it ensures the structural safety, construction accuracy, and spatial aesthetics of the dome ceiling.
[0036] Beneficial effects: This invention models the curved surface of a large-span dome ceiling using a parametric design method, and combines curvature determination and hierarchical optimization techniques to merge complex module division results into a small number of standardized modules. This method effectively reduces the types of panels, lowers the complexity of molds and processing procedures, thereby improving the efficiency of the connection between design and construction, and significantly enhancing overall feasibility.
[0037] In the modular manufacturing stage, this invention uses mathematical formulas to determine the forming parameters of single-curved and double-curved panels, ensuring geometric continuity and consistency among different types of modules. Combined with parametric constraints, the seams between modules are more uniform, surface transitions are smoother, and the overall ceiling exhibits greater aesthetic integrity and consistency, meeting the visual and spatial experience requirements of large public spaces.
[0038] This invention introduces a dynamic adjustment mechanism during the installation process. By comparing measured data with the design model, it enables real-time correction of the ceiling node positions, ensuring the accuracy and controllability of the installation process. This mechanism avoids the splicing problems caused by error accumulation in traditional methods, improving the reliability and safety of ceiling construction, and enhancing the overall performance and stability of the dome ceiling while ensuring construction efficiency. Attached Figure Description
[0039] Figure 1 A schematic diagram of the hyperbolic grid layout for a large-span dome ceiling;
[0040] Figure 2 A schematic diagram of the subdivision of the rhomboid grid unit;
[0041] Figure 3 A schematic diagram illustrating the hierarchical optimization of a full hyperboloid aluminum plate into 2 hyperboloids, 2 single-curves, and 4 flat plates;
[0042] Figure 4 This is a rendering of the overall effect of a large-span dome ceiling.
[0043] Figure 5 A comparative diagram illustrating the dynamic adjustment of ceiling module specifications for parametric design;
[0044] Figure 6 This is a schematic diagram illustrating the construction process of the open-joint method and the tight-joint method;
[0045] Figure 7 A schematic diagram showing the splicing details of a single module under both open-seam and close-seam construction methods;
[0046] Figure 8 A flowchart for the hierarchical optimization construction method of parametric diamond-shaped modules for span dome ceilings. Detailed Implementation
[0047] To make the objectives, technical solutions, and advantages of this invention clearer, the following description is provided in conjunction with the appendix. Figure 1-2 The present invention will be further described in detail below with reference to embodiments. It should be understood that the specific embodiments described herein are merely illustrative of the invention and are not intended to limit the invention.
[0048] Example 1: See Figure 1-8 This invention provides a parameterized rhomboid module hierarchical optimization construction method for large-span dome ceilings, aiming to solve the problems of numerous module types, high processing costs, and difficulty in guaranteeing installation accuracy in the construction of ceilings in large public buildings. The technical solution of this invention will be further described below with reference to the accompanying drawings and embodiments.
[0049] In this method, the target building dome is first parametrically modeled. Let the dome surface be S(u,v), where u,v are the surface parametric coordinates. The two principal curvatures k1(u,v) and k2(u,v) of the surface can be extracted using differential geometry. During the mesh generation stage, the surface is decomposed into several rhombic mesh elements C. i Each rhombic element needs to satisfy the basic geometric constraints, namely...
[0050] ||e1||=||e2||=l,∠(e1,e2)=θ,
[0051] Where e1 and e2 are the two diagonals of the element, l is the side length of the rhombus, and θ is the acute angle. This geometric constraint ensures the uniformity of the module distribution and the continuity of the structure. After obtaining the mesh, the curvature characteristics of each element need to be analyzed, and they are initially grouped according to the magnitude of curvature. The judgment criteria are as follows:
[0052]
[0053] Where, τ K τ is the Gaussian curvature threshold. D τ is the curvature difference threshold. S This is the curvature amplitude threshold. Based on this determination, each unit obtains an initial grouping. This serves as input for subsequent optimization. However, if the initial grouping is used directly, there will be too many panel types, making processing and transportation uneconomical. Based on this, the present invention introduces a hierarchical optimization step, first defining an energy function for each unit:
[0054]
[0055] Among them, P i For the set of unit parameters, Represents an isometric distortion measure. Indicates area deviation. The discontinuity with the boundary of adjacent modules is represented by α, β, and γ, which are weighting factors. The result of this energy function is used as the clustering input. A template assignment model is then employed.
[0056]
[0057] Among them, T k For the k-th type template, z ik For the assignment variable (taking 0 or 1), ε i (T k The value represents the fitting error between the unit and the template. Through this optimization, the original 19 complex modules were finally merged into eight standardized templates, namely, two hyperbolic templates, two single-curved templates, and four flat templates.
[0058] After optimization, the module processing stage begins. The single-curved board is processed by fitting the optimal bending radius. The optimal formula for determining the machining mold is as follows:
[0059]
[0060] Among them, κ max (p) = max(|k1|,|k2|) represents the function for maximizing curvature, where R is the candidate radius variable. For hyperbolic plates, the curvature radii need to be fitted along the two principal directions. The calculation formula is as follows:
[0061]
[0062] Where R1 and R2 are the curvature radii variables in the two principal directions, and the optimal solution... These are the parameters for hot pressing molds. Flat plates, on the other hand...
[0063] It is directly shaped through CNC cutting.
[0064] During installation, the modules are suspended and secured using a keel system. For gap-joint installations, a gap width g needs to be reserved at the edge of the module, and this width must meet certain requirements.
[0065] Thermal expansion and contraction check conditions:
[0066] g≥α T LΔT+δ,
[0067] Where, α T Let L be the coefficient of linear expansion of the material, ΔT be the characteristic length of the module, ΔT be the possible temperature difference range, and δ be the construction allowance, typically 10mm as the preferred value. For close-fitting construction, the edges of adjacent modules are machined into concave edges and interlocked to achieve a seamless connection. Throughout the construction process, to ensure the overall continuity and installation accuracy of the ceiling, this method introduces a dynamic adjustment mechanism. Measured point clouds are obtained through laser scanning or a total station. and with the design model A comparison is performed. Let the correction amount for the keel node be Δx. j The optimization problem can then be expressed as:
[0068]
[0069] And constrain ||Δx j||≤η, where η is the adjustable stroke. By iteratively adjusting the node positions, the installation deviation is ultimately controlled within 5mm. The above implementation method fully covers the entire process from surface modeling, module classification, parametric optimization, processing parameter solving, construction and installation to dynamic adjustment. Each step is linked through parameter transfer and formula calculation: curvature k1 and k2 are used for classification, grouping results are entered into the energy function and template assignment, the optimized template determines the processing radius, the calculated processing parameters are used for module forming, joint width verification ensures installation safety, and final dynamic adjustment brings the error to convergence. The entire process ensures both the complexity and aesthetics of the ceiling design, while reducing the types of modules and processing costs and improving construction accuracy and controllability.
[0070] Example 2: Figure 1 As shown, this embodiment uses a large transportation hub hall as the application object. First, the overall curved surface S(u,v) of the dome is parametrically modeled. Utilizing the distribution patterns of the principal curvatures k1(u,v) and k2(u,v), the surface is divided into several rhombic mesh elements C. i , forming as Figure 1 The hyperbolic mesh structure shown in green requires each element to satisfy ||e1||=||e2||=l, ∠(e1,e2)=θ, where e1 and e2 are diagonals, l is the side length, and θ is the acute angle. This mesh provides the basic geometric conditions for subsequent module classification and optimization.
[0071] like Figure 2 As shown, a typical rhomboid unit is subdivided, resulting in 8 panels in the initial division. To reduce the variety and processing difficulty, this embodiment uses a threshold determination for curvature: when |k1k2|>τ K And |k1-k2|>τ D It is classified as a hyperbolic plate when |k1k2|≤τ K And max(|k1|,|k2|)>τ s The ones that are categorized as single-curved boards are classified as flat boards, and the rest as flat boards. This results in the initial grouping. There are many varieties, making them difficult to process directly.
[0072] like Figure 3 As shown, a hierarchical optimization method is used to cluster the above panels, and an energy function is established:
[0073]
[0074] And optimize by combining template assignment:
[0075]
[0076] The original 19 types of panels were eventually simplified into eight standardized modules: two hyperbolic panels, two single-curved panels, and four flat panels.
[0077] Figure 3 The different colored panels correspond to different types of templates, indicating the result of optimizing the full hyperbolic curve into a combination of multiple categories.
[0078] like Figure 4 As shown, after the optimization design was completed, the resulting ceiling exhibits a large-scale, continuous spatial effect. To guide actual manufacturing, the forming parameters of the single-curved and double-curved panels were calculated, including the bending radius of the single-curved panel. Through formula
[0079]
[0080] Determined, where κ max (p) = max(|k1|,|k2|).
[0081] For hyperbolic plates, the hot-pressing radii in the two principal directions need to be calculated. satisfy:
[0082]
[0083] During the processing, single-curved boards are bent using CNC, double-curved boards are formed using hot pressing molds, and flat boards are obtained directly through CNC cutting.
[0084] like Figure 5 As shown, the introduction of parametric dynamic adjustment technology in the construction design optimized the original 19 different specifications of diamond-shaped ceiling modules into 8 modules, greatly reducing the processing complexity. The left side of the figure shows the situation before optimization, and the right side shows the situation after optimization, clearly demonstrating the convergence effect of different types.
[0085] like Figure 6 and Figure 7 As shown, two methods can be selected during installation: one is gap installation, where a gap width g is reserved at the edge of the module, which must meet the requirements of thermal expansion and contraction.
[0086] g≥α T LΔT+δ,
[0087] Where α T Where L is the coefficient of thermal expansion of the material, ΔT is the characteristic length of the module, ΔT is the construction temperature difference, and δ is the construction allowance. In this embodiment, g is preferably 10mm, and a concealed joint sealing strip is embedded in the joint. Secondly, a tight-fitting installation is adopted, with concave edges processed on the edges of adjacent modules, which interlock during installation to ensure a seamless visual effect.
[0088] A dynamic adjustment mechanism is introduced during the final installation phase. Measured point clouds are acquired via laser scanning. With design model Comparison, constructing optimization problems:
[0089]
[0090] Where Δx j The correction amount for the keel node is constrained by ||Δx j ||≤η. In this embodiment, the hanger has a 20mm telescopic adjustment capability, and through multiple iterative corrections, the overall installation deviation is controlled within 5mm.
[0091] In summary, the construction process corresponding to this embodiment is as follows: Figures 1-7 As shown: Modeled by mesh ( Figure 1 ), unit division ( Figure 2 ), Module optimization Figure 3 ), Effect presentation ( Figure 4 ), parameterized dynamic adjustment ( Figure 5 ), gap seam and tight stitching methods ( Figure 6 , Figure 7 This led to the development of an efficient, controllable, and aesthetically pleasing method for constructing large-span dome ceilings. This method significantly reduces the types of panels used, lowers processing and transportation costs, and ensures construction accuracy and structural continuity through dynamic adjustments.
[0092] The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, and improvements made within the spirit and principles of the present invention should be included within the protection scope of the present invention.
Claims
1. A method for hierarchical optimization of parametric diamond-shaped module construction for large-span dome ceilings, characterized in that, Includes the following steps: S1 Parametric Modeling: A 3D model of the dome target surface is performed, extracting the principal curvature parameters k1(u,v) and k2(u,v). Based on the geometric constraints of the element side length l and acute angle θ, the surface is divided into several rhombic mesh elements C. i ; S2 Initial Grouping: Based on the curvature parameters of each unit, it is divided into hyperbolic plates, monobolic plates, or flat plates to obtain the initial grouping results. S3 Hierarchical Optimization: Based on the initial grouping in step S2, an energy function E is established for the geometric deviation of each unit. i (P i Furthermore, by employing clustering and template assignment methods, the complex and diverse blocks are simplified into eight standardized templates, including two types of hyperbolic plates, two types of single-curved plates, and four types of flat plates, resulting in optimized grouping t. i ; S4 Module Processing: Based on the template type obtained in step S3, calculate the bending radius R of the single-curved board. i The hot-pressing radius (R) of the hyperbolic plate 1i ,R 2i The flat plate is then cut into shape. S5 module installation: Install the processed modules on the graded keel system. The gap-fitting method leaves a gap width g at the edge of the module, while the tight-fitting method achieves a seamless connection through concave edge fastening. S6 Dynamic Adjustment: During installation, measured point cloud data is collected using laser scanning or a total station and compared with the parametric design model to calculate the keel node correction amount Δx. j The node positions are dynamically adjusted to ensure that the overall installation deviation does not exceed the preset limit.
2. The method for hierarchical optimization construction of a parametric rhombic module for a large-span dome ceiling according to claim 1, characterized in that, The rhombic mesh division in step S1 satisfies the following formula: ||e1||=||e2||=l,∠(e1,e2)=θ, Where e1 and e2 are the two diagonals of the rhombus unit, l is the side length of the unit, and θ is the acute angle of the rhombus.
3. The method for hierarchical optimization construction of a parametric rhombic module for a large-span dome ceiling according to claim 1, characterized in that, The initial grouping in step S2 is based on the following curvature determination criteria: Where k1 and k2 are principal curvature parameters, and τ K τ is the Gaussian curvature threshold. D τ is the curvature difference threshold. S The determination result is based on the curvature amplitude threshold. It will be used as input for hierarchical optimization.
4. The method for hierarchical optimization construction of a parametric diamond-shaped module for a large-span dome ceiling according to claim 1, characterized in that, The hierarchical optimization in step S3 is achieved through an energy function: For unit C i The geometric distortion is quantized, where P i For the set of unit parameters, Indicates isometric distortion. Indicates area deviation The boundary discontinuity is represented by α, β, and γ, which are weighting factors. The result of this energy function will be used as the input for clustering and template assignment.
5. The method for hierarchical optimization construction of a large-span dome ceiling with parametric diamond-shaped modules according to claim 4, characterized in that, The S3 template assignment adopts the following optimization model: Among them, T k For the k-th type template, z ik Assign a variable to the unit, which takes the value 0 or 1, ε i (T k The error is the fitting error between the unit and the template. The optimization model outputs eight types of templates. As the basis for module processing.
6. The method for hierarchical optimization construction of a parametric diamond-shaped module for a large-span dome ceiling according to claim 1, characterized in that, The module processing parameters in step S4 are obtained using the following formula: Single-curved board bending radius: Hyperbolic plate hot pressing radius: Among them, κ max (p) is the function for the maximum curvature, κ max (p)=max(|k1|,|k2|),p∈C i For grid cell C i The sampling points on the surface are k1 and k2, which are the two principal curvature parameters of the surface at the sampling point p. R1 and R2 are the optimal bending radius for the single-curved plate, and the fitted radius variables for the hyperbolic plate in the two principal directions. Let C be the two principal radii of curvature of the hyperbolic plate. i : The i-th rhombic mesh element; R: The bending radius variable of the single-curved plate; The optimal bending radius for a single-curved board; The optimal radius of curvature solution for the hyperboloid in the two principal directions; argmin optimization operator, which represents taking the parameter value that minimizes the objective function.
7. The method for hierarchical optimization construction of a parametric diamond-shaped module for a large-span dome ceiling according to claim 1, characterized in that, The seam width g in step S5 satisfies the thermal expansion and contraction check condition: g≥a T LΔT+δ, Where, α T δ is the coefficient of linear expansion of the material, L is the characteristic length of the module, ΔT is the temperature difference range, and δ is the construction allowance. The calculated joint width is used as the input parameter for jointless installation.
8. The method for hierarchical optimization construction of a parametric diamond-shaped module for a large-span dome ceiling according to claim 1, characterized in that, The dynamic adjustment in step S6 employs least squares optimization: in, For actual point cloud measurements, For the design model, Δx j The correction amount for the keel node is given by the constraint ||Δx. j ||≤η, where η represents the allowable adjustable stroke.
9. The method for hierarchical optimization construction of a parametric diamond-shaped module for a large-span dome ceiling according to claim 1, characterized in that, The keel system is a hierarchical keel structure, including main keels, secondary keels, and hangers. The hangers are adjustable in length and are used to achieve node correction Δx. j Fine-tuning.
10. The method for hierarchical optimization construction of a parametric diamond-shaped module for a large-span dome ceiling according to claim 1, characterized in that, The method is applicable to large-span public buildings such as airport terminals, convention centers, and stadiums. While reducing the types of modules and lowering processing costs, it ensures the structural safety, construction precision, and spatial aesthetics of the dome ceiling.