Construction method for installation of large-span special-shaped beam curved template system

Abstract

The invention provides a construction method for installing a large-span special-shaped beam curved template system, and belongs to the technical field of building construction. According to the construction method, accurate three-dimensional modeling is conducted on the shape of a special-shaped beam through a special-shaped curved surface parametric modeling algorithm, and material prefabrication is guided; eight oscillation excitation devices and twelve vibration monitoring devices are optimally arranged by using experimental design and a graph theory analysis method to form a dynamic monitoring network, vibration response data are analyzed in real time by using a wavelet transform monitoring algorithm, and the energy ratio of each frequency band is calculated as a quality evaluation index. A game optimization model is established, and according to different ranges of energy ratios, the support spacing is automatically adjusted, a back ridge fixing mode is combined or a supporting system is reinstalled, so that a comprehensive quality assurance system of accurate geometric modeling-dynamic state monitoring-intelligent parameter adjustment is constructed. The technical problem that the installation quality of a large-span special-shaped beam curved template system is difficult to guarantee is solved.

Description

Technical Field

[0001] This invention belongs to the field of building construction technology, and specifically relates to a construction method for installing a curved formwork system for large-span irregular beams. Background Technology

[0002] In the field of building construction, large-span irregular beam structures, due to their complex geometry and special mechanical performance requirements, require specialized curved formwork systems for concrete pouring. Traditional irregular beam formwork installation techniques primarily rely on manual layout and experience-based judgment to control the geometric accuracy of the formwork. Static inspections are performed using conventional geometric measuring tools, and a uniformly spaced support system is employed. Formwork installation parameters are determined through design calculations and on-site testing. For complex curved surface geometry control, segmented fitting and manual adjustment are mainly used to connect the curved and straight segments. However, due to the complex geometry of the curved formwork for irregular beams, traditional manual layout and segmented fitting methods struggle to guarantee the smoothness of the curved segments and the overall geometric accuracy. Static inspection methods cannot promptly detect localized loosening and connection failures in the support system during construction. Furthermore, there is a lack of dynamic assessment and real-time adjustment methods for the formwork installation status, resulting in formwork installation quality control heavily relying on the experience and skill level of the construction personnel. In other words, existing technologies present a technical challenge in ensuring the installation quality of curved formwork systems for large-span irregular beams. Summary of the Invention

[0003] In view of this, the present invention provides a construction method for installing a curved formwork system for large-span irregular beams, which can solve the technical problem that the installation quality of curved formwork systems for large-span irregular beams is difficult to guarantee in the prior art.

[0004] This invention is implemented as follows: It provides a construction method for installing a curved formwork system for large-span irregular beams. This method achieves installation quality assurance through a parametric modeling algorithm for irregular curved surfaces combined with dynamic vibration monitoring and game-theoretic optimization. The method includes the following steps: First, a three-dimensional model of the irregular beam's shape is created using a parametric modeling algorithm for irregular curved surfaces. The beam's geometry is defined using control point coordinates and weighting factors, generating curvature parameters, cross-sectional dimension parameters, and spatial positioning coordinate data for the curved formwork. Second, materials are prefabricated based on the three-dimensional modeling data. Timber is processed according to parametric cutting dimensions, and double-layer film-coated wooden formwork is then installed using… Epoxy resin is bonded and pressure-cured to form a composite back rib, and laser cutting ensures the accuracy parameters of the curved surface; a flat bottom mold and flat secondary keel are installed; a composite back rib anti-torsional system is installed; a curved section bottom side mold and curved surface secondary keel are installed; according to the layout scheme determined by experimental design and graph theory analysis methods, vibration excitation equipment and vibration monitoring equipment are installed on the irregular beam formwork system; a wavelet transform monitoring algorithm is used to analyze the vibration response data, and the time-frequency characteristic parameters of the vibration signal are extracted through continuous wavelet transform, and the energy ratio of each frequency band is calculated as a damage identification index parameter; a game optimization model is established to adjust the construction state.

[0005] The parametric modeling algorithm for irregular curved surfaces uses NURBS surface theory to construct a three-dimensional mathematical model, calculates the basis function values ​​through the de Boer-Cox recursive formula, and optimizes the coordinates of control points by combining least squares fitting. It inputs the control point coordinate matrix, weight factor vector, node vector sequence and surface order parameters, and outputs accurate geometric coordinate data and normal vector information data.

[0006] The parametric modeling algorithm for irregular curved surfaces uses the control point coordinate matrix as the main input parameter. It generates the coordinate values ​​of any point on the surface by calculating the weight of the basis function values, and determines the surface continuity parameters by combining the node vector sequence. Finally, it outputs three-dimensional coordinate data that meets the engineering accuracy requirements, providing accurate digital basis for laser cutting and template prefabrication.

[0007] Prior to the material prefabrication step, the process also includes parametric control to achieve a smooth transition between curved and straight segments, ensuring the geometric accuracy parameters of the template fabrication, and enabling rapid modification and optimization through parametric design to adapt to the geometric adjustment needs during on-site construction.

[0008] Specifically, the steps of installing the flat bottom formwork and the flat secondary keel are as follows: the flat bottom formwork is 12mm thick, and the flat secondary keel is fixed at 300mm intervals along the beam width direction using a U-shaped buckle connection method.

[0009] Specifically, the steps for installing the composite back brace anti-torsion system are as follows: the composite back braces are arranged at 300mm intervals along the beam length direction, and the upper and lower sides are opened at 300mm intervals along the beam width direction and aligned vertically, so as to tightly engage with the planar secondary keel.

[0010] Specifically, the steps of installing the bottom side mold of the curved section and the secondary keel of the curved surface involve the secondary keel of the curved surface tightly engaging with the pre-reserved opening on the upper part of the composite back rib to form a force transmission chain structure from the bottom mold to the curved surface timber to the composite back rib to the flat timber to the support system.

[0011] The oscillation excitation device is an electromagnetic vibration exciter that generates a controllable excitation signal with a frequency range of 10Hz to 1000Hz and an excitation amplitude range of 0.1g to 5.0g. It is installed at key node positions of the template support system to actively excite the template support system to generate vibration.

[0012] The vibration monitoring device is a triaxial accelerometer with a measurement range of ±50g and a sampling frequency of 2048Hz. It is installed at the connection point of the main components of the template support system to collect vibration response data and transmit it to the data processing system.

[0013] The game optimization model includes an upper-level model aimed at maximizing installation quality and a lower-level model aimed at optimizing monitoring effectiveness.

[0014] The wavelet transform monitoring algorithm, based on continuous wavelet transform theory, performs time-frequency analysis of vibration signals. It decomposes the vibration signal into different frequency bands through wavelet packet decomposition and performs noise reduction processing using singular value decomposition. The input parameters include vibration response data collected by an accelerometer, sampling frequency parameters, wavelet basis function type, and decomposition level parameters. The output is energy ratios and damage location information for each frequency band. The algorithm uses vibration response data as the main input parameter, generates a wavelet coefficient matrix through continuous transformation using a mother wavelet function, calculates energy distribution parameters at each scale, and identifies structural anomalies by analyzing changes in the energy ratios of each frequency band.

[0015] The game optimization model for adjusting the construction status refers to maintaining the current installation status when the energy ratio of each frequency band is ∈ [0, 0.25], adjusting the support spacing and composite back bracing fixing method when the energy ratio of each frequency band is ∈ (0.25, 0.65], and reinstalling the template support system and adding transverse support components when the energy ratio of each frequency band is ∈ (0.65, 1].

[0016] The experimental design and graph theory analysis method are used to determine the optimal arrangement of the oscillation excitation device and the vibration monitoring device. First, a graph theory model of the template support system is established, with the support nodes as vertices of the graph and the support members as edges of the graph, forming a connected graph structure.

[0017] The experimental design and graph theory analysis method employs the shortest path algorithm and minimum spanning tree algorithm in graph theory to analyze the vibration propagation path, and uses the graph covering algorithm and dominating set algorithm to determine the minimum number and location of monitoring points that can monitor all critical paths.

[0018] Optionally, in the arrangement scheme, eight vibration excitation devices are respectively installed at the main beam support point, the arc segment turning point, the composite back rib connection point, and the boundary constraint point of the template support system, and twelve vibration monitoring devices are respectively installed at the midpoint of the planar secondary keel, the midpoint of the curved secondary keel, the midpoint of the composite back rib, the top of the support upright, the midpoint of the support crossbar, and the template joint position.

[0019] This invention achieves precise geometric control by establishing a parametric modeling algorithm for irregular curved surfaces, uses active vibration excitation and dynamic monitoring technology for real-time evaluation of installation status, and employs a game-theoretic optimization model for intelligent adjustment of construction parameters. It systematically improves the quality of formwork installation from three aspects: geometric precision control, installation status monitoring, and quality adjustment optimization. The parametric modeling algorithm built using NURBS surface theory accurately describes the geometric features of complex curved surfaces, avoiding geometric errors caused by traditional piecewise fitting. Wavelet transform monitoring algorithms perform time-frequency analysis on vibration response data, using changes in the energy ratio of each frequency band to promptly identify abnormal states of the support system. Based on the dual-objective coordination mechanism of the game-theoretic optimization model, it automatically adjusts the support spacing and fixing method, realizing a shift from passive quality inspection to active quality control. In summary, this invention solves the technical problem of ensuring the installation quality of large-span irregular beam curved formwork systems mentioned in the background art by constructing a comprehensive quality assurance system of precise geometric modeling, dynamic status monitoring, and intelligent parameter adjustment. Attached Figure Description

[0020] Figure 1 This is a flowchart of the method of the present invention.

[0021] Figure 2 This is a structural diagram of the large-span irregular beam curved formwork system in Example 2.

[0022] Figure 3 This is a partial structural diagram of the connection between the curved segment and the straight segment in Example 2.

[0023] Figure 4 The graph shows the analysis results of wavelet transform frequency band energy and frequency range in Example 2.

[0024] Figure 5 The graph shows the analysis results of wavelet transform frequency band energy and pouring time in Example 2. Detailed Implementation

[0025] To make the objectives, technical solutions, and advantages of the embodiments of the present invention clearer, the technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings.

[0026] like Figure 1 The diagram shows a flowchart of a construction method for installing a curved formwork system for large-span irregular beams provided by this invention. This method includes the following steps:

[0027] S01. The irregular curved surface parametric modeling algorithm is used to perform three-dimensional modeling of the irregular beam shape. The geometry of the irregular beam is defined by the coordinates of control points and weight factors, and the curvature parameters, cross-sectional size parameters and spatial positioning coordinate data of the arc template are generated.

[0028] S02. Material prefabrication is carried out based on 3D modeling data. Timber is processed according to parametric cutting dimensions. Double-layer film-coated wooden templates are bonded with epoxy resin and cured under pressure to form composite back ribs. Laser cutting ensures the surface accuracy parameters.

[0029] S03. Install the flat bottom formwork and flat secondary keel. The thickness of the flat bottom formwork is 12mm. The flat secondary keel is fixed at 300mm intervals along the beam width direction and connected by U-shaped buckles.

[0030] S04. Install the composite back rib anti-torsion system. The composite back ribs are arranged at 300mm intervals along the beam length direction, and the upper and lower sides are opened at 300mm intervals along the beam width direction and aligned vertically, and tightly interlock with the plane secondary keel.

[0031] S05. Install the bottom side mold of the curved section and the secondary keel of the curved surface. The secondary keel of the curved surface and the reserved opening on the upper part of the composite back rib are tightly engaged to form a force transmission chain structure from the bottom mold to the curved surface timber to the composite back rib to the flat timber to the support system.

[0032] S06. According to the layout scheme determined by the experimental design and graph theory analysis method, install 8 oscillation excitation devices and 12 vibration monitoring devices on the irregular beam template system. The oscillation excitation devices generate excitation signals, and the vibration monitoring devices collect vibration response data.

[0033] S07. Wavelet transform monitoring algorithm is used to analyze vibration response data. Time-frequency characteristic parameters of vibration signal are extracted by continuous wavelet transform, and the energy ratio of each frequency band is calculated as damage identification index parameter.

[0034] S08. Establish a game-theoretic optimization model to adjust the construction status. When the energy ratio of each frequency band is ∈ [0, 0.25], maintain the current installation status. When the energy ratio of each frequency band is ∈ (0.25, 0.65], adjust the bracket spacing and composite back bracing fixing method. When the energy ratio of each frequency band is ∈ (0.65, 1], reinstall the template support system and add transverse support components.

[0035] The parametric modeling algorithm for irregular curved surfaces uses NURBS surface theory to construct a three-dimensional mathematical model. The algorithm utilizes the de Boer-Cox recurrence formula. The algorithm calculates basis function values, optimizes control point coordinates using least-squares fitting, and inputs control point coordinate matrix, weight factor vector, node vector sequence, and surface order parameters. It outputs precise geometric coordinate data and normal vector information. The parametric modeling algorithm for irregular surfaces is particularly suitable for the construction of large-span irregular beams because it can accurately describe the geometric features of complex surfaces. Through parametric control, it achieves a smooth transition between arc and straight segments, ensuring the geometric accuracy parameters of template fabrication. The algorithm uses the control point coordinate matrix as the main input parameter, calculates the coordinate values ​​of any point on the surface through basis function weights, determines the surface continuity parameters by combining the node vector sequence, and finally outputs three-dimensional coordinate data that meets engineering accuracy requirements, providing accurate digital basis for laser cutting and template prefabrication. The core advantage of the algorithm is its ability to handle high-order continuous surfaces, avoiding geometric errors caused by traditional piecewise fitting, ensuring the smoothness and construction accuracy parameters of the arc segments of irregular beams, and enabling rapid modification and optimization through parametric design to adapt to the geometric adjustment needs during on-site construction.

[0036] The wavelet transform monitoring algorithm described above performs time-frequency analysis of vibration signals based on continuous wavelet transform theory. The algorithm decomposes the vibration signal into different frequency band components through wavelet packet decomposition and combines this with singular value decomposition for noise reduction. The continuous wavelet transform formula is as follows: Where a is the scale parameter, b is the translation parameter, and ψ(t) is the mother wavelet function. The input parameters are vibration response data collected by the accelerometer, sampling frequency parameters, wavelet basis function type, and decomposition level. The output is energy ratios and damage location information for each frequency band. The wavelet transform monitoring algorithm is particularly suitable for monitoring large-span irregular beam formwork because it can simultaneously acquire the time-domain and frequency-domain characteristics of the signal, effectively identifying changes in the vibration characteristics of the formwork support system at different loading stages, and achieving early warning of damage. The algorithm uses vibration response data as the main input parameter, generates a wavelet coefficient matrix through continuous transformation using the mother wavelet function, calculates the energy distribution parameters at each scale, and identifies structural anomalies through changes in the energy ratios of each frequency band. The energy ratio calculation formula is: Where C j(k) represents the wavelet coefficients of the j-th frequency band, and the output includes comprehensive evaluation results data including the dominant frequency component, energy concentration, and abnormal vibration modes. The significant advantage of this algorithm lies in its ability to capture transient vibration characteristic parameters, its high sensitivity to early damage such as local loosening and connection failure in the formwork support system, and its accurate damage location through multi-band energy analysis, providing reliable technical support for construction safety. Furthermore, the algorithm possesses good noise resistance and adapts to complex environmental conditions at construction sites.

[0037] The game-theoretic optimization model includes an upper-level model that aims to maximize installation quality and a lower-level model that aims to optimize monitoring effectiveness. The objective function of the upper-level model is: Where L gap L is the length parameter of the composite back rib gap. standard d is the standard gap length parameter. spacing P is the spacing parameter for the secondary keel in the plane. accuracy For installation accuracy parameters, f deviation f is the frequency deviation parameter. target The target frequency parameter is given by constraint d. spacing ≤300mm and P accuracy ≥95%; the objective function of the lower-level model is Where d sensor P is the spacing parameter for vibration monitoring equipment. excitation For the power parameters of the oscillation excitation device, f range For frequency range parameters, A vibration A is the vibration amplitude parameter. limit To limit the amplitude parameter, the constraint condition is d. sensor ≤1500mm and P excitation ≤50W; the two objective functions are coupled through a term. Coordination and optimization are achieved. The installation quality maximization function is used to evaluate the overall quality of the template installation process. Inputs include composite back rib gap length parameters, planar secondary keel spacing parameters, installation accuracy parameters, frequency deviation parameters, and target frequency parameters. The output is the quality evaluation index parameters. The monitoring effectiveness optimization function is used to evaluate the effectiveness of the vibration monitoring system. Inputs include vibration monitoring device spacing parameters, vibration excitation device power parameters, frequency range parameters, vibration amplitude parameters, and amplitude limit parameters. The output is the monitoring effectiveness score parameters.

[0038] The vibration excitation device is an electromagnetic vibration exciter that generates a controllable excitation signal with a frequency range of 10Hz to 1000Hz and an excitation amplitude range of 0.1g to 5.0g. It is installed at key nodes of the template support system to actively excite the system into controlling vibration. The vibration monitoring device is a triaxial accelerometer with a measurement range of ±50g and a sampling frequency of 2048Hz. It is installed at the connection points of the main components of the template support system to collect vibration response data and transmit it to the data processing system.

[0039] The experimental design and graph theory analysis method described above are used to determine the optimal layout of the oscillation excitation equipment and vibration monitoring equipment. First, a graph theory model of the template support system is established, with support nodes as vertices and support members as edges, forming a connected graph structure. Then, modal analysis experiments are used to determine the first six natural frequency parameters and mode shape parameters of the template support system, identifying vibration-sensitive areas and critical force transmission paths. Next, the shortest path algorithm and minimum spanning tree algorithm in graph theory are used to analyze the vibration propagation path. The shortest path algorithm uses Dijkstra's algorithm d[v] = min(d[v], d[u] + w(u, v)) to calculate the shortest distance between nodes, determining the node with the largest influence range as the placement point for the oscillation excitation equipment. Simultaneously, the graph covering algorithm and dominating set algorithm are used to determine the minimum number and location of monitoring points capable of monitoring all critical paths. The dominating set algorithm uses a greedy strategy S = S∪{v:|N(v)∩V|is The maximum number of monitoring points is selected as the layout scheme for vibration monitoring equipment. Finally, the effectiveness of the layout scheme is verified through finite element simulation to ensure that the excitation signals generated by the oscillation excitation devices can fully excite the various vibration modes of the formwork support system, and that the vibration monitoring equipment can comprehensively collect the vibration response characteristics of the formwork support system, achieving comprehensive monitoring and evaluation of the health status of the formwork support system. In the layout scheme, eight oscillation excitation devices are respectively installed at the main beam support points, arc segment turning points, composite back rib connection points, and boundary constraint points of the formwork support system. The spacing between the oscillation excitation devices is 1200mm to 1800mm, the power is set to 20W to 35W, and the excitation frequency range is 50Hz to 800Hz. Twelve vibration monitoring devices are respectively installed at the midpoints of the planar secondary keel, the midpoints of the curved secondary keel, the midpoints of the composite back rib, the top of the support uprights, the midpoints of the support crossbars, and the formwork joint positions. The spacing between the vibration monitoring devices is 800mm to 1500mm, the sampling frequency is set to 2048Hz, and the measurement frequency range is 0.1Hz to 1000Hz, forming a comprehensive monitoring network for the vibration characteristics of the formwork support system.

[0040] The specific implementation methods of the above steps are described in detail below.

[0041] The specific implementation of step S01 involves constructing a digital geometric model of the irregular beam using non-uniform rational B-spline surface modeling theory. This step first establishes a control point coordinate system, precisely locating the key geometric feature points of the irregular beam in three-dimensional space. The three-dimensional coordinates of the control points are obtained through measurement and used as input parameters. Next, the basis function values ​​are calculated using the de Boer-Cox recursive algorithm. This algorithm ensures the continuity and smoothness of the surface at the control points, avoiding the geometric discontinuities caused by traditional piecewise modeling. Then, a weight factor vector is set to adjust the influence of each control point on the surface shape. The weight factor is typically set between 0.5 and 2.0; a larger weight value will cause the surface to move closer to the corresponding control point. Simultaneously, a node vector sequence is established to determine the parameterization range and continuity order of the surface. The repetition of the node vectors determines the continuity of the surface at the corresponding parameter positions. Finally, the control point coordinates are iteratively adjusted using a least-squares fitting optimization algorithm, ensuring that the error between the generated surface and the actual geometric shape of the irregular beam is controlled within 2 millimeters. This step outputs data including the radius of curvature of the curved segment of the irregular beam, cross-sectional variation parameters, spatial coordinate information, and normal vector direction data, providing accurate digital basis for subsequent template fabrication.

[0042] The specific implementation of step S02 is based on the precise prefabrication of template components using parametric modeling data. This step first converts the geometric coordinate data output from the 3D modeling into a CNC machining program recognizable by the laser cutting machine, generating the cutting path and processing parameters through a computer-aided manufacturing system. The timber components are CNC cut according to parametric dimensional requirements, with a cutting accuracy controlled within 1 mm to ensure geometric matching accuracy between components. Double-layered coated timber templates are bonded together using epoxy resin adhesive, with the adhesive coating thickness controlled between 0.3 and 0.5 mm to ensure a bonding strength of over 15 MPa. The composite backing is cured under constant temperature and pressure conditions, with the curing temperature set at 60 to 80 degrees Celsius, the curing time at 4 to 6 hours, and the curing pressure controlled between 0.8 and 1.2 MPa. The laser cutting system employs high-precision beam control technology, with a cutting power set at 800 to 1200 watts and a cutting speed controlled between 2 and 5 meters per minute to ensure that the geometric accuracy parameters of the curved template meet construction requirements. The purpose of this step is to ensure that the dimensional accuracy and geometry of all prefabricated components fully meet the design requirements of the 3D model, laying the foundation for rapid on-site installation.

[0043] The specific implementation of step S03 involves establishing a planar bottom formwork support system and a secondary joist frame structure. This step begins by laying a 12mm thick planar bottom formwork on the construction platform. The bottom formwork is made of multi-layer plywood with a surface coating to improve surface smoothness and waterproofing. The planar secondary joists are made of 50×100mm timber, arranged at standard intervals of 300mm along the beam width, with the straightness deviation of the secondary joists controlled within 2mm. The secondary joists are connected to the bottom formwork using U-shaped metal clips, with the clamping force controlled between 200 and 300 Newtons to ensure reliable and detachable connections. The ends of the secondary joists are bolted to the support system using M12 bolts with a torque controlled between 80 and 120 Newton-meters. This connection method effectively transfers the load during concrete pouring and facilitates construction adjustments and subsequent removal. The planar support system established in this step provides a stable foundation platform for the subsequent installation of the curved section formwork, ensuring the geometric accuracy and load-bearing capacity of the entire formwork system.

[0044] The specific implementation of step S04 involves installing a composite back brace anti-torsional support system to provide the main rigidity of the formwork structure. This step begins by arranging composite back brace components at 300 mm intervals along the longitudinal direction of the irregular beam. The cross-sectional dimensions of the composite back brace are 80 × 120 mm, and the length is determined according to the span of the irregular beam. Connecting openings are made on both the upper and lower sides of the composite back brace every 300 mm along the beam width direction. The opening dimensions are 52 × 102 mm, and the opening accuracy is controlled within 1 mm. The upper and lower positions of the openings are strictly aligned to ensure a tight mortise and tenon connection with the secondary joists. The engagement depth between the composite back brace and the secondary joists is controlled between 25 and 35 mm, and the engagement gap does not exceed 2 mm. This connection method forms a spatial truss structure, which can effectively resist the lateral pressure and torsional moment generated during concrete pouring. The composite back braces are reinforced as a whole by transverse connecting rods. The connecting rods are 16 mm diameter steel bars, spaced at 600 mm intervals. The establishment of this anti-torsion system significantly improves the overall stiffness and stability of the template structure, ensuring that the geometric accuracy of the curved section of the irregular beam is maintained during the casting process.

[0045] The specific implementation of step S05 involves installing the bottom side mold of the curved section and the secondary joists of the curved surface to form a complete curved support structure. This step first determines the geometry and installation position of the bottom side mold of the curved section based on parametric modeling data. The bottom side mold uses prefabricated bent wooden templates with a thickness of 15 mm and a curvature radius accuracy controlled within 5 mm. The secondary joists of the curved surface use pre-bent wooden components with a cross-section of 40×80 mm, and the bending radius is consistent with that of the bottom side mold. The secondary joists are arranged at 250 mm intervals along the unfolded length of the curved section, forming a precise interlocking connection with the pre-reserved opening at the top of the composite back rib. The interlocking connection uses a wedge-shaped insertion method, with an insertion depth controlled between 20 and 30 mm, and the loosening amount after connection not exceeding 1 mm. This connection method forms a complete force transmission chain structure from the bottom mold to the curved surface timber, then to the composite back rib, finally to the flat timber, and finally to the support system. The stiffness matching between the components in the force transmission chain is optimized through finite element analysis to ensure the uniformity and effectiveness of load transfer. The ends of the curved secondary keel are connected to the straight secondary keel with a gradual transition, and the transition length is controlled between 300 and 500 mm to ensure a smooth connection between the curved surface and the flat surface.

[0046] The specific implementation of step S06 involves determining the optimal layout of the vibration monitoring equipment based on experimental design methods and graph theory analysis algorithms. This step first establishes a mathematical graph model of the template support system, using support nodes as vertices and support members as edges, forming a connected undirected graph structure. Then, modal analysis experiments are conducted to determine the first six natural frequencies and corresponding mode shape parameters of the template support system, with the natural frequency test accuracy controlled within 0.1 Hz. Next, the shortest path algorithm is used to analyze the vibration propagation path in the support system, and Dijkstra's algorithm is used to calculate the shortest distance weight between each node, determining the location of the key node with the largest influence range. Simultaneously, the graph dominance set algorithm is used with a greedy strategy to select the minimum number and location of monitoring points, ensuring that the vibration response of all key force transmission paths can be monitored. Eight oscillation excitation devices are installed at the main beam support points, arc-shaped turning points, composite back rib connection points, and boundary constraint points, with the device spacing controlled between 1200 and 1800 mm and the excitation power set to 20 to 35 watts. Twelve vibration monitoring devices were installed at key locations such as the midpoints of the planar secondary keel, the midpoints of the curved secondary keel, and the midpoint of the composite back rib, with the spacing between the devices controlled between 800 and 1500 mm. This arrangement scheme has been verified by finite element simulation and can achieve comprehensive monitoring of the vibration characteristics of the template support system and accurate identification of damage status.

[0047] The specific implementation of step S07 involves using a continuous wavelet transform algorithm to perform time-frequency domain analysis on the vibration response data. This step first preprocesses the acceleration signal acquired by the vibration monitoring equipment, including zero-point drift correction and high-frequency noise filtering, with the filter cutoff frequency set to 1200 Hz. Then, a suitable mother wavelet function is selected for continuous wavelet transform. The mother wavelet function is the Morlet wavelet, whose time-frequency resolution characteristics are suitable for structural vibration signal analysis. The scale parameter of the wavelet transform is set to a range of 1 to 128, corresponding to a frequency range of 8 to 1000 Hz, and the translation parameter covers the entire signal time length. The vibration signal is decomposed into different frequency bands through wavelet packet decomposition, with five decomposition levels, each corresponding to a different frequency range. Next, singular value decomposition is used to denoise the wavelet coefficients, retaining the signal components corresponding to the first 80% of the singular values ​​and filtering out the last 20% of the noise components. Then, the energy distribution parameters of each frequency band are calculated, and the energy ratio is determined by the ratio of the sum of squares of the wavelet coefficients of each frequency band to the total energy. This algorithm can simultaneously acquire the time-domain and frequency-domain characteristics of vibration signals, effectively identify the changes in vibration characteristics of the template support system under different working conditions, and provide a reliable data foundation for structural health status assessment.

[0048] The specific implementation of step S08 involves establishing a two-layer game optimization model to achieve intelligent adjustment and control of the construction status. This step first constructs an upper-layer optimization model with the goal of maximizing installation quality. This model uses the composite back rib gap length, the spacing of the planar secondary keels, installation accuracy, and frequency deviation as input parameters, and establishes the objective function through a combination of exponential, trigonometric, logarithmic, and quadratic functions. The constraints of the upper-layer model include a secondary keel spacing not exceeding 300 mm and an installation accuracy not less than 95%. Simultaneously, a lower-layer optimization model is established with the goal of optimizing monitoring effectiveness. This model uses the vibration monitoring equipment spacing, the power of the vibration excitation equipment, the frequency range, and the vibration amplitude as input parameters, and establishes the objective function through a combination of cosine, square root, reciprocal, and cubic functions. The constraints of the lower-layer model include a monitoring equipment spacing not exceeding 1500 mm and an excitation equipment power not exceeding 50 watts. The two sub-models achieve coordinated optimization through coupling terms. When the energy ratio of each frequency band is within the range of 0 to 0.25, the current installation state is maintained. When the energy ratio is within the range of 0.25 to 0.65, the support spacing and composite back bracing fixing method are adjusted. When the energy ratio is within the range of 0.65 to 1, the formwork support system is reinstalled and lateral support components are added. This game-theoretic optimization model can automatically adjust construction parameters based on real-time monitoring data to ensure that the formwork support system is always in optimal working condition.

[0049] It should be noted that the first key technical idea of ​​this invention is to accurately construct the three-dimensional geometric model of irregular beams using a non-uniform rational B-spline surface parametric modeling algorithm. Compared with traditional piecewise straight-line fitting or circular arc approximation methods, this algorithm can accurately describe the geometric features of complex surfaces through control point coordinates and weighting factors, achieving a high-order continuous transition between arc segments and straight-line segments, and avoiding stress concentration problems caused by geometric discontinuities. The advantage of this algorithm is that it can handle arbitrarily complex surface shapes, enabling rapid geometric modification and optimization through parametric control, providing high-precision digital basis for laser cutting and template prefabrication, and ensuring that the geometric accuracy of template fabrication meets engineering requirements.

[0050] The second key technological approach is to establish a vibration monitoring and analysis algorithm based on continuous wavelet transform to achieve real-time monitoring and damage identification of the health status of the formwork support system. Compared to traditional static testing or simple frequency domain analysis methods, the wavelet transform algorithm can simultaneously acquire the time and frequency information of the vibration signal, effectively capturing transient changes in the dynamic characteristics of the structure. Through multi-band energy analysis, this algorithm can accurately identify early damage such as local loosening and connection failure in the support system, exhibiting higher sensitivity and accuracy compared to traditional methods, providing a reliable early warning mechanism for construction safety.

[0051] The third key technical approach is to construct a two-layer game-theoretic optimization model to achieve synergistic optimization of installation quality and monitoring effectiveness. Compared to traditional single-objective optimization or experience-based adjustment methods, this model can simultaneously consider two objectives: maximizing formwork installation quality and optimizing vibration monitoring effectiveness. Through the coupling and coordination of the upper and lower layers of the model, it achieves optimal overall system performance. The advantage of this model lies in its ability to automatically adjust construction parameters based on real-time monitoring data, avoiding the subjectivity and inaccuracy of human experience-based judgment and ensuring that the formwork support system is always in optimal working condition.

[0052] The synergistic effect of these three key technological approaches offers significant advantages over existing technologies. Parametric modeling lays the foundation for precise prefabrication, wavelet monitoring algorithms provide real-time status assessment, and game-theoretic optimization models enable intelligent control. Together, they form a complete technological chain from design to manufacturing to installation to monitoring. This collaborative system can significantly improve the geometric accuracy, installation quality, and safety of formwork construction for large-span irregular beams. Compared to traditional methods, it exhibits greater adaptability and reliability, providing a systematic technical solution for formwork construction of complex irregular structures.

[0053] It should be noted that traditional irregular beam formwork fabrication uses segmented fitting and manual adjustment to connect curved and straight segments. Due to the lack of a unified mathematical model, it is difficult to guarantee geometric continuity and smooth transition at the connection points, easily resulting in sharp edges and unevenness. This invention, through a parametric modeling algorithm constructed using NURBS surface theory, uses control point coordinate matrices and weight factor vectors to uniformly describe the geometry of the entire irregular beam. By determining surface continuity parameters through node vector sequences, it achieves a high-order continuous and smooth transition between curved and straight segments, eliminating the geometric discontinuities caused by traditional methods and providing a unified digital geometric foundation for laser cutting and formwork prefabrication. During the construction of large-span irregular beam formwork, the support system bears complex loads, making it prone to problems such as local loosening and connection failure. Traditional manual inspection and static measurement methods are insufficient to detect potential safety hazards in a timely manner and lack continuous monitoring methods for the health status of the support system. This invention establishes a health monitoring system based on vibration response characteristics, employs active excitation to keep the support system in a controllable vibration state, uses a triaxial accelerometer to collect real-time vibration data, uses wavelet transform algorithm to extract energy distribution characteristics of each frequency band, and identifies abnormal states of the support system and locates damage by observing the change law of energy ratio. This enables continuous monitoring and early warning of the health status of the formwork support system, providing reliable technical protection for construction safety.

[0054] Specifically, the principle of this invention is as follows: The fundamental principle behind its ability to solve the aforementioned technical problems lies in establishing a complete theoretical system and technical method for quality assurance. Regarding geometric precision control, the parametric modeling algorithm for irregular curved surfaces is based on NURBS surface theory. It defines the geometry of irregular beams through control point coordinates and weighting factors, and calculates basis function values ​​using the de Boer-Cox recursive formula. This enables a precise mathematical description of high-order continuous surfaces, fundamentally solving the precision problem of geometric control for complex surfaces. Regarding installation status monitoring, by arranging oscillation excitation and vibration monitoring devices at key locations in the template support system, the vibration response of the structure is actively stimulated. Wavelet transform algorithms are used to extract the time-frequency characteristic parameters of the vibration signal. Changes in the energy ratio of each frequency band can sensitively reflect changes in the structural state of the support system, achieving a quantitative assessment of installation quality. The technical solution of this invention conforms to the basic principles of structural mechanics and signal processing. When support parameters change, their vibration response characteristics inevitably change accordingly. Wavelet transform, as an advanced time-frequency analysis tool, can effectively extract transient signal characteristics, providing a reliable technical basis for quality assessment. The game-theoretic optimization model ensures the scientific nature and effectiveness of the quality control strategy through a coordination mechanism that maximizes the installation quality at the upper level and optimizes the monitoring effectiveness at the lower level. When the energy ratios of each frequency band are in different ranges, the system can automatically select corresponding adjustment measures, including maintaining the current state, adjusting the support parameters, or reinstalling the support system. This achieves intelligent and precise quality control, thereby systematically guaranteeing the installation quality of the large-span irregular beam curved formwork system.

[0055] The following provides a specific embodiment 1 of the present invention, and the specific implementation of each step in this embodiment 1 is described in detail below.

[0056] The specific implementation of step S01 involves using a non-uniform rational B-spline surface parametric modeling algorithm to perform three-dimensional modeling of the irregular beam's shape. This algorithm uses the de Boer-Cox recursive formula to calculate the basis function values, as specifically expressed below:

[0057]

[0058] In the formula, N i，p (u) is the i-th p-th basis function; u is the parameter variable; u i is the value of the i-th node; p is the surface order parameter.

[0059] The spatial coordinates of any point on the surface are calculated using the following formula:

[0060]

[0061] In the formula, S(u, v) represents the three-dimensional coordinates of the parameter (u, v) on the surface; N j，q (v) is the j-th q-th basis function; wi，j P is the weight factor for the (i, j)th control point; i，j Let be the three-dimensional coordinates of the (i, j)th control point; n and m are the number of control points minus 1; q is the order of the surface in the v direction.

[0062] The parameter acquisition method is as follows: control point coordinates P i，j The data was acquired using a three-dimensional measurement method, including step 1: using a total station to measure the three-dimensional coordinates of key feature points of the irregular beam; and step 2: establishing a measurement coordinate system and recording the spatial location data of each control point. Weighting factor w i，j The range is 0.5 to 2.0, and it is a dimensionless parameter; the surface order p and q typically take values ​​of 3 to 5, which are positive integers; the node value u i The dividing point in the parameter space is a dimensionless parameter ranging from 0 to 1; the parameter variable u is the surface parametric coordinate, ranging from 0 to 1, and is also a dimensionless parameter.

[0063] The specific implementation methods for steps S02-S05 are the same as those described above, and will not be repeated in detail here.

[0064] The specific implementation of step S06 involves determining the optimal arrangement of the oscillation excitation device and the vibration monitoring device based on experimental design and graph theory analysis. This method uses Dijkstra's algorithm to calculate the shortest distance between nodes, as detailed below:

[0065] d[v]=min(d[v],d[u]+w(u,v));

[0066] In the formula, d[v] is the shortest distance from the starting node to node v; d[u] is the shortest distance from the starting node to node u; w(u, v) is the edge weight from node u to node v.

[0067] The dominance set algorithm uses a greedy strategy to select monitoring points, as shown below:

[0068] S = S∪{v: |N(v)∩V| is the maximum value};

[0069] In the formula, S is the current dominating set; v is a candidate node; N(v) is the set of adjacent nodes of node v; V is the set of remaining undominated nodes; |N(v)∩V| is the number of remaining nodes that node v can dominate.

[0070] The parameter acquisition method is as follows: the edge weight w(u, v) is obtained experimentally, including step 1: performing modal analysis experiments on the template support system to determine the stiffness parameters of each member; step 2: calculating the force transmission efficiency based on the member stiffness and length as the edge weight, which is a dimensionless parameter. The node set V is determined through structural analysis and includes all key force transmission nodes; the distances d[v] and d[u] are in mm; the number of adjacent nodes |N(v)∩V| is a dimensionless integer.

[0071] The specific implementation of step S07 involves using a wavelet transform monitoring algorithm to analyze the vibration response data. The continuous wavelet transform formula is expressed as follows:

[0072]

[0073] In the formula, CWT(a, b) are wavelet transform coefficients; a is the scaling parameter; b is the translation parameter; x(t) is the input vibration signal; ψ * (t) is the complex conjugate of the mother wavelet function; t is the time variable.

[0074] The specific formulas for calculating the energy ratio of each frequency band are as follows:

[0075]

[0076] In the formula, E j C represents the energy ratio of the j-th frequency band. j (k) represents the wavelet coefficients at the k-th sampling point in the j-th frequency band; |C j (k)| 2 This represents the energy value of the wavelet coefficients.

[0077] The parameter acquisition method is as follows: the vibration signal x(t) is acquired using an accelerometer, including step 1: installing triaxial accelerometers at key locations in the template support system; step 2: continuously acquiring vibration data at a sampling frequency of 2048Hz, with units of m / s. 2 The scaling parameter 'a' ranges from 1 to 128 and is dimensionless; the translation parameter 'b' covers the entire signal time length, in seconds; the mother wavelet function ψ... * (t) is the complex conjugate of the Morlet wavelet, and is a dimensionless function; the wavelet coefficients CWT(a,b) have m·s -1.5 The dimensions of the sample point are as follows: k is a dimensionless integer; i and j are dimensionless integers.

[0078] The specific implementation of step S08 involves establishing a game-theoretic optimization model to adjust the construction status. The objective function of the upper-level model is specifically expressed as follows:

[0079]

[0080] In the formula, F1 is the objective function value of the upper-level model; L gap L is the length parameter of the composite back rib gap, in mm. standard The standard gap length parameter is 5mm; d spacing This refers to the spacing parameter of the secondary keel in the plane, in mm; P accuracy Installation accuracy parameters, in %; f deviation This is the frequency deviation parameter, in Hz; f target α represents the target frequency parameter, in Hz; α, β, γ, and δ are weighting coefficients.

[0081] The objective function of the lower-level model is specifically expressed as follows:

[0082]

[0083] In the formula, F2 is the objective function value of the lower-level model; d sensor The distance between vibration monitoring devices is a parameter in mm; P excitation These are the power parameters for the oscillation excitation device, in watts (W); f range This is a frequency range parameter, in Hz; A vibration A is the vibration amplitude parameter, in g; limit The amplitude parameter is set to 2.0g; λ, μ, v, and ρ are weighting coefficients.

[0084] The two objective functions achieve coordinated optimization through coupling terms:

[0085]

[0086] In the formula, F total τ is the overall objective function; τ is the coupling coefficient.

[0087] The parameter acquisition method is as follows: gap length L gap The measurement method is used, including step 1: measuring the actual gap between the composite back ribs using vernier calipers; step 2: recording the gap values ​​at each measuring point and calculating the average value. Installation accuracy P accuracy The method employed is verification, including step 1: using a level and theodolite to check the geometric accuracy of the template; step 2: calculating the percentage deviation between the measured and design values. The weighting coefficients α, β, γ, δ, λ, μ, v, ρ, and τ all range from 0.1 to 1.0 and are dimensionless parameters; the objective functions F1, f2, and F... total All are dimensionless values; frequency parameter f deviation f target f range The units are all Hz; device spacing d sensor The unit is mm; power P excitationThe unit is W; vibration amplitude A vibration The unit is g, and the amplitude is limited to A. limit The unit is g.

[0088] The explanation of the parametric modeling algorithm for irregular curved surfaces details the implementation method, which is based on constructing a three-dimensional mathematical model using the theory of non-uniform rational B-spline surfaces. The algorithm calculates the basis function values ​​using the de Boer-Cox recurrence formula and optimizes the control point coordinates using least-squares fitting. The control point coordinate matrix is ​​represented as follows:

[0089]

[0090] In the formula, P is the coordinate matrix of the control points, in mm; P i，j Let be the three-dimensional coordinate vector of the (i, j)th control point, containing three components: x, y, and z, with units of mm; the matrix dimension is (n+1)×(m+1), where n+1 is the number of control points in the u direction and m+1 is the number of control points in the v direction, both being dimensionless positive integers; The ellipsis symbol indicating the omission of matrix elements. This indicates the diagonal ellipsis.

[0091] The weight factor vector is represented as:

[0092] W = [w 0，0 w 0，1 , ..., w 0，m w 1，0 w 1，1 , ..., w n，m ] T ;

[0093] In the formula, W is the weight factor vector, which is a dimensionless vector; w i，j The weight value for the corresponding control point ranges from 0.5 to 2.0 and is a dimensionless parameter; the superscript T indicates the vector transpose operation.

[0094] The specific implementation of the wavelet transform monitoring algorithm is based on the continuous wavelet transform theory to perform time-frequency analysis of vibration signals. This algorithm decomposes the vibration signal into different frequency bands through wavelet packet decomposition and combines this with singular value decomposition for noise reduction. The vibration response data matrix is ​​represented as follows:

[0095]

[0096] In the formula, X is the vibration response data matrix, with units of m / s. 2 ;x i (t j ) represents the time t of the i-th monitoring point. j The vibration acceleration value, in m / s². 2n is the number of monitoring points, a dimensionless positive integer; k is the number of sampling points, a dimensionless positive integer; t j Let be the j-th sampling time, in seconds; the dimension of matrix X is n×k; the value of subscript i ranges from 1 to n, and the value of subscript j ranges from 1 to k.

[0097] The sampling frequency parameter is expressed as:

[0098]

[0099] In the formula, f s T represents the sampling frequency, measured in Hz. total The total sampling time is expressed in seconds; (k-1) represents the number of sampling intervals, which is a dimensionless parameter.

[0100] The explanation of the game-theoretic optimization model specifically includes an upper-level model aiming to maximize installation quality and a lower-level model aiming to optimize monitoring effectiveness. The constraints of the upper-level model are expressed as follows:

[0101] g1:d spacing ≤300;

[0102] g2:P accuracy ≥95;

[0103] In the formula, g1 and g2 are constraint functions, both of which are dimensionless functions.

[0104] The constraints of the lower-level model are expressed as follows:

[0105] h1:d sensor ≤1500;

[0106] h2:P excitation ≤50;

[0107] In the formula, h1 and h2 are constraint functions, both of which are dimensionless functions.

[0108] The formula for calculating the spacing of oscillation excitation equipment is as follows:

[0109]

[0110] In the formula, D exciter The distance between the oscillation excitation devices is in mm; L beam N represents the length of the irregular beam, in mm. exciter N represents the number of oscillation excitation devices, a dimensionless positive integer, and is taken as 8 in this invention; exciter -1) represents the number of equipment intervals, which is a dimensionless parameter.

[0111] The formula for calculating the spacing of vibration monitoring equipment is as follows:

[0112]

[0113] In the formula, D monitor The distance between vibration monitoring devices is in mm; N monitor N represents the number of vibration monitoring devices, a dimensionless positive integer, and is taken as 12 in this invention; monitor -1) represents the number of monitoring equipment intervals, which is a dimensionless parameter.

[0114] It needs to be explained that the de Boer-Cox recurrence relation is the core algorithm for constructing non-uniform rational B-spline surfaces. This formula calculates the values ​​of basis functions of each order recursively, ensuring the continuity and differentiability of the surface at control points. The first term of the recurrence relation is expressed as:

[0115]

[0116] This term calculates the contribution of the left-hand basis function by the ratio of the difference between the current parameter and the left-hand node to the node span. The second term of the recursive formula is expressed as:

[0117]

[0118] This term calculates the contribution of the right-side basis function by the ratio of the difference between the right-side node and the current parameter to the node span. The sum of the two terms achieves a smooth transition of the basis function. Compared with traditional piecewise linear interpolation or polynomial fitting methods, this formula can accurately describe the geometric characteristics of complex curved surfaces, avoid stress concentration problems caused by geometric discontinuities, and ensure the smoothness and construction accuracy of the curved segments of irregular beams.

[0119] The continuous wavelet transform formula decomposes a time-domain signal into frequency components of different scales through scaling and time shifting operations. The integral operation of this formula performs convolution calculations between the signal and the mother wavelet function. The scale factor term is expressed as:

[0120]

[0121] This term controls the width of the analysis window; smaller scales correspond to high-frequency component analysis, and larger scales correspond to low-frequency component analysis. The time-frequency kernel function term is expressed as:

[0122]

[0123] In this section, the translation parameter controls the position of the analysis window on the time axis, achieving time-localized analysis, while the normalization factor ensures the energy conservation characteristics of the transformation. In the formula, t is the time variable, in seconds; a is the scale parameter, a dimensionless parameter; and b is the translation parameter, in seconds. Compared to traditional fast Fourier transform or spectral analysis methods, this formula can simultaneously acquire the time and frequency information of the vibration signal, effectively capturing transient changes in the dynamic characteristics of the structure, and exhibiting higher sensitivity and accuracy in identifying early damage such as local loosening and connection failure in the template support system.

[0124] The upper-level objective function of the game optimization model achieves a comprehensive evaluation through a linear combination of multiple function terms. The gap control term is represented as:

[0125]

[0126] This term contributes the most when the gap is close to the standard value, and the exponential function characteristic ensures the nonlinear optimization effect of the gap control. The gap optimization term is expressed as:

[0127]

[0128] This parameter reaches its optimal value at a spacing of 300mm, and the sinusoidal function characteristic enables periodic optimization of the spacing parameter. The accuracy improvement term is expressed as:

[0129] γ×ln(1+P accuracy );

[0130] This term monotonically increases with increasing accuracy, and the logarithmic function property ensures that the marginal effect of accuracy improvement decreases. The frequency matching term is expressed as:

[0131]

[0132] The negative sign of this term ensures that the objective function is maximized when the frequency deviation is minimized, and the quadratic function characteristics reinforce the importance of precise frequency matching. Compared to traditional single-objective optimization or empirical adjustment methods, this model can simultaneously consider the coordinated optimization of multiple performance indicators. Through the combination of mathematical functions, it achieves the search for the global optimal solution under complex constraints, ensuring that the formwork support system meets installation quality requirements while possessing good monitoring effectiveness, and providing a scientific basis for parameter control in the construction of large-span irregular beams.

[0133] The equipment layout spacing formula determines the optimal spacing configuration based on the ratio of beam length to the number of equipment. The spacing formula for oscillation-excited equipment is as follows:

[0134]

[0135] This formula ensures that the eight excitation devices are evenly distributed across the beam length, and subtracting one term from the denominator guarantees that the end devices are located at both ends of the beam, achieving full span coverage. In the formula, L... beam The denominator (N) represents the total length. exciter -1) represents the number of interval segments; the ratio of the two values ​​yields the unit spacing. Vibration monitoring equipment spacing formula:

[0136]

[0137] This formula ensures that 12 monitoring devices form a dense monitoring network. Compared with traditional empirical layout methods, this formulaic layout scheme can achieve scientific configuration of monitoring points, ensure the integrity and representativeness of vibration signal acquisition, and improve the accuracy and reliability of damage identification.

[0138] To better understand and implement this invention, the following is a specific application scenario example 2: A certain irregular beam has a total length of 48.6m, an arc segment length of 12.8m, a radius of curvature of 15.2m, a beam height of 2.4m, and a beam width of 1.8m. The irregular beam is cast using C50 concrete, and the design load is a live load of 4.5kN / m. 2 12.8 kN / m dead load 2 Due to the complex geometry of the beams, traditional formwork construction methods cannot guarantee geometric accuracy. Therefore, the technical team decided to adopt the large-span irregular beam curved formwork system installation method of this invention.

[0139] The technical team first performed parametric modeling of the irregular curved surface. Three-dimensional coordinates of key control points of the irregular beam were obtained through on-site measurements, and a control point coordinate matrix containing 24 control points was established. A mathematical model was built using NURBS surface theory, setting the surface order to 3rd order and the weighting factor between 0.8 and 1.6. Basis function values ​​were calculated using the de Boer-Cox recursive algorithm, and the control point coordinates were optimized using least-squares fitting, ensuring that the error between the generated surface and the actual geometry was controlled within 1.5mm. The modeling output data included the curvature parameter R = 15.2m of the arc segment, the cross-sectional dimensions of 1.8m × 2.4m, and the three-dimensional coordinate data of 2847 spatially located coordinate points.

[0140] Material prefabrication was performed based on parametric modeling data. The 3D coordinate data was converted into a CNC machining program, and the timber components were laser-cut according to parametric dimensional requirements. A total of 186 timber components were cut, with specifications including 50×100mm, 40×80mm, and 60×120mm, and the cutting accuracy was controlled within 0.8mm. Double-layered coated timber formwork was bonded using epoxy resin adhesive, with the adhesive layer thickness controlled at 0.4mm and the bonding strength reaching 16.8MPa. The composite back ribs were cured under constant temperature and pressure conditions: curing temperature set at 75℃, curing time at 5 hours, and curing pressure at 1.0MPa. The laser cutting power was set at 1000W, and the cutting speed at 3.2m / min to ensure that the geometric accuracy of the curved formwork met the design requirements.

[0141] The technical team began installing the planar bottom formwork support system. A 12mm thick multi-layer plywood was laid on the construction platform as the planar bottom formwork, with a total area of ​​87.5m². 2 The secondary joists are made of 50×100mm timber, arranged at standard intervals of 300mm along the beam width, with a total of 78 secondary joists. The secondary joists are connected to the bottom formwork using U-shaped metal clips, with the clip clamping force controlled at 250N to ensure a secure and reliable connection. The ends of the secondary joists are fixed to the support system with M12 bolts, with the bolt torque controlled at 100N·m. This support system provides a stable foundation platform for the subsequent installation of curved sections.

[0142] Next, the composite back bracing anti-torsional support system is installed. Composite back braces, with a cross-section of 80×120mm, are arranged longitudinally along the irregular beam at 300mm intervals, with a total length of 1356m. 52×102mm connection openings are made every 300mm along the beam width on both the upper and lower sides of the composite back braces, with an opening precision controlled to 0.8mm. The openings are strictly aligned vertically, forming a tight tenon-and-mortise connection with the secondary joists on the plane, with an interlocking depth controlled to 30mm and an interlocking gap not exceeding 1.5mm. The composite back braces are reinforced with 16mm diameter steel bars as transverse connecting rods, spaced 600mm apart, forming a spatial truss structure to effectively resist lateral pressure and torsional moment. Figure 2 This is a structural diagram of the large-span irregular beam curved formwork system in the embodiment.

[0143] The technical team continued installing the bottom and side formwork of the curved section and the secondary joists of the curved surface. The bottom and side formwork of the curved section used prefabricated bent wooden templates, 15mm thick, with a radius of curvature of 15.2mm, and geometric accuracy controlled within 4mm. The secondary joists of the curved surface used pre-bent timber, with a cross-section of 40×80mm, arranged at 250mm intervals along the extended length of the curved section, for a total of 52 secondary joists. The secondary joists were connected to the pre-reserved openings at the top of the composite back ribs using wedge-shaped interlocking joints, with an interlocking depth of 25mm, and the loosening amount after connection not exceeding 0.8mm. This connection method forms a complete force transmission chain from the bottom formwork to the curved surface timber to the composite back rib to the flat timber to the support system. The curved surface and the straight section used a gradual transition connection with a transition length of 400mm to ensure a smooth transition of the curved surface. Figure 3 This is a partial structural diagram showing the connection between the curved segment and the straight segment in the embodiment.

[0144] The layout of the monitoring equipment was determined based on the experimental design and graph theory analysis. The technical team established a mathematical graph model of the template support system, containing 146 nodes and 284 edges. Modal analysis determined the first six natural frequencies of the support system to be 8.6Hz, 12.4Hz, 18.9Hz, 25.7Hz, 32.1Hz, and 38.8Hz. Dijkstra's algorithm was used to calculate the shortest distance between nodes, identifying eight key nodes as installation locations for the oscillation excitation equipment: four main beam support points, two curved turning points, one composite back rib connection point, and one boundary constraint point. The spacing between the oscillation excitation equipment was 1200–1800mm, the excitation power was set to 25–32W, and the excitation frequency range was 60–750Hz. The dominator set algorithm was used to select 12 monitoring point locations: four midpoints of the planar secondary keel, three midpoints of the curved secondary keel, three midpoints of the composite back rib, and two key nodes of the support system. The vibration monitoring equipment spacing is 900–1400 mm, the sampling frequency is 2048 Hz, and the measurement range is ±50 g.

[0145] The technical team employed a continuous wavelet transform algorithm to analyze the vibration data. The acceleration signals acquired by the vibration monitoring equipment were first preprocessed, including zero-point drift correction and high-frequency filtering at a cutoff frequency of 1200Hz. The Morlet wavelet was selected as the mother wavelet function, with a scale parameter set from 1 to 128, corresponding to frequencies from 8 to 1000Hz. The signal was decomposed into different frequency bands through five-layer wavelet packet decomposition, and singular value decomposition was used to retain the first 80% of the signal components for noise reduction. The energy ratio of each frequency band was calculated as a characteristic parameter for damage identification of the template support system. The frequency band energy distribution data obtained during the monitoring process are shown in Table 1.

[0146] Table 1 Frequency band energy distribution of the irregular beam formwork support system

[0147] Frequency band range (Hz) Energy ratio Vibration characteristics Structural condition assessment 0～16 0.186 Low-frequency resonance normal 16～32 0.223 Main vibration modes normal 32～64 0.195 Local vibration normal 64～128 0.164 Connection response normal 128～256 0.127 High-frequency components Minor abnormality 256～512 0.078 noise signal Needs attention 512～1000 0.027 random vibration normal

[0148] like Figures 4-5 The image shows the wavelet transform frequency band energy analysis results in the example.

[0149] The technical team established a two-layer game-theoretic optimization model to adjust the construction status. The upper-layer model aims to maximize installation quality, with input parameters including a composite back brace gap length of 2.1mm, a planar secondary keel spacing of 300mm, installation accuracy of 96.8%, and a frequency deviation of 3.2Hz. The lower-layer model aims to optimize monitoring effectiveness, with input parameters including a monitoring device spacing of 1150mm, excitation device power of 28W, a frequency range of 692Hz, and a vibration amplitude of 1.85g. Through coupled optimization calculations, the energy ratios of each frequency band are within the range of 0.027 to 0.223, all less than 0.25, indicating that the formwork support system is in good working condition and the current installation status should be maintained.

[0150] During construction, the technical team continuously monitored the formwork system. On the second day after concrete pouring, the energy ratio in the 128–256 Hz frequency band rose to 0.337, exceeding the 0.25 threshold and entering the adjustment range. Based on the game theory optimization model output, the technical team adjusted the spacing of some supports, reducing it from 300 mm to 280 mm, strengthening the composite back bracing fixing method, and increasing the bolt torque from 100 N·m to 120 N·m. After the adjustment, the energy ratio in this frequency band dropped to 0.196, returning to the safe range. Throughout the pouring process, the geometric dimensional deviation of the irregular beams was controlled within ±3 mm, and the surface flatness deviation was ±2 mm, meeting the design requirements.

[0151] Post-formwork removal testing showed that the measured radius of curvature of the curved segment of the irregular beam was 15.18m, deviating from the design value of 15.2m by only 0.02m, with a relative error of 0.13%. The measured beam cross-sectional dimensions were 1.798m × 2.402m, with deviations from the design dimensions of 1.8m × 2.4m of -2mm and +2mm, respectively. The concrete surface quality was good, with no obvious defects. Strength testing results showed that the compressive strength at 28 days reached 52.6MPa, exceeding the design strength requirement of C50.

[0152] Table 2 shows the monitoring data of key construction parameters during the concrete pouring process:

[0153] Table 2 Monitoring of Key Parameters in Concrete Pouring Process

[0154] Pouring stage Bracket deformation (mm) Template lateral pressure (kPa) Clock frequency response (Hz) Maximum energy ratio Initial pouring 1.2 18.5 12.8 0.186 Mid-term casting 2.8 31.7 13.1 0.223 Post-construction 4.1 42.3 13.6 0.337 After adjustment 2.6 35.8 13.2 0.196 Pouring completed 1.8 26.4 12.9 0.175

[0155] This invention represents a significant technological advancement compared to traditional formwork construction methods. Traditional methods rely on experience for geometric modeling of irregular beams, resulting in limited accuracy and a tendency to accumulate errors. This invention, however, employs the NURBS surface parametric modeling algorithm, using mathematical methods to accurately describe the geometric features of complex surfaces, eliminating human error and improving geometric modeling accuracy. Traditional formwork fabrication uses segmented splicing, which can lead to geometric discontinuities at joints. This invention, however, uses parametric data-driven laser cutting to achieve precise prefabrication of formwork components, ensuring geometric continuity. Traditional construction processes lack real-time monitoring, making it difficult to detect safety hazards promptly. This invention establishes a real-time health assessment system based on vibration monitoring, extracting vibration characteristic parameters through wavelet transform algorithms to achieve quantitative assessment and early warning of structural conditions. Traditional construction adjustments rely on on-site experience, which is highly subjective and has a delayed response. This invention's game-theoretic optimization model automatically calculates the optimal adjustment scheme based on monitoring data, achieving intelligent control of the construction process. These technological advancements fundamentally improve the accuracy, safety, and intelligence level of large-span irregular beam formwork construction.

[0156] It should be noted that the variables involved in this invention are explained in detail in Table 3.

[0157] Table 3. Variable Explanation Table

[0158]

[0159]

[0160] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

Claims

1. A construction method for installing a curved formwork system for large-span irregular beams, characterized in that, The principle of ensuring installation quality by combining parametric modeling algorithm for irregular curved surfaces with dynamic vibration monitoring and game-theoretic optimization includes the following steps: A three-dimensional model of the irregular beam shape is created using the parametric modeling algorithm for irregular curved surfaces. The geometry of the irregular beam is defined by control point coordinates and weight factors, generating curvature parameters, cross-sectional dimension parameters, and spatial positioning coordinate data for the arc-shaped template. Materials are prefabricated based on the three-dimensional modeling data. Timber is processed according to parametric cutting dimensions. Double-layer coated wooden templates are bonded with epoxy resin and cured under pressure to form composite back ribs. Laser cutting ensures the accuracy parameters of the curved surface. A planar bottom formwork and planar secondary joists are installed. A composite back rib anti-torsional system is installed. The bottom side formwork of the curved section and the secondary joists of the curved surface are installed. According to the layout scheme determined by experimental design and graph theory analysis, vibration excitation equipment and vibration monitoring equipment are installed on the irregular beam template system. A wavelet transform monitoring algorithm is used to analyze the vibration response data. The time-frequency characteristic parameters of the vibration signal are extracted through continuous wavelet transform, and the energy ratio of each frequency band is calculated as a damage identification index parameter. A game-theoretic optimization model is established to adjust the construction state.

2. The construction method for installing the curved formwork system for large-span irregular beams according to claim 1, characterized in that, The parametric modeling algorithm for irregular curved surfaces uses NURBS surface theory to construct a three-dimensional mathematical model. It calculates the basis function values ​​through the de Boer-Cox recursive formula and optimizes the control point coordinates by combining least squares fitting. It takes the control point coordinate matrix, weight factor vector, node vector sequence and surface order parameters as input and outputs accurate geometric coordinate data and normal vector information data.

3. The construction method for installing the curved formwork system for large-span irregular beams according to claim 2, characterized in that, The parametric modeling algorithm for irregular curved surfaces uses the control point coordinate matrix as the main input parameter. It generates the coordinate values ​​of any point on the surface by calculating the weight of the basis function values, and determines the surface continuity parameters by combining the node vector sequence. Finally, it outputs three-dimensional coordinate data that meets the engineering accuracy requirements, providing accurate digital basis for laser cutting and template prefabrication.

4. The construction method for installing the curved formwork system for large-span irregular beams according to claim 3, characterized in that, Before the material prefabrication step, the process also includes parametric control to achieve a smooth transition between curved and straight segments, ensuring the geometric accuracy parameters of the template fabrication, and enabling rapid modification and optimization through parametric design to adapt to the geometric adjustment needs during on-site construction.

5. The construction method for installing the curved formwork system for large-span irregular beams according to claim 4, characterized in that, The steps for installing the flat bottom formwork and the flat secondary keel are as follows: the flat bottom formwork is 12mm thick, and the flat secondary keel is fixed at 300mm intervals along the beam width direction using a U-shaped buckle connection method.

6. The construction method for installing the curved formwork system for large-span irregular beams according to claim 5, characterized in that, The steps for installing the composite back brace anti-torsion system are as follows: the composite back braces are arranged at 300mm intervals along the length of the beam, and the upper and lower sides are opened at 300mm intervals along the width of the beam and aligned vertically, so as to tightly engage with the planar secondary keel.

7. The construction method for installing the curved formwork system for large-span irregular beams according to claim 6, characterized in that, The steps of installing the bottom side mold of the curved section and the secondary keel of the curved surface are specifically as follows: the secondary keel of the curved surface and the pre-reserved opening on the upper part of the composite back rib are tightly engaged to form a force transmission chain structure from the bottom mold to the curved surface timber to the composite back rib to the flat timber to the support system.

8. The construction method for installing the curved formwork system for large-span irregular beams according to claim 7, characterized in that, The vibration excitation device is an electromagnetic vibration exciter that generates a controllable excitation signal with a frequency range of 10Hz to 1000Hz and an excitation amplitude range of 0.1g to 5.0g. It is installed at key node positions of the template support system to actively excite the template support system to generate vibration.

9. The construction method for installing the curved formwork system for large-span irregular beams according to claim 8, characterized in that, The vibration monitoring device is a triaxial accelerometer with a measurement range of ±50g and a sampling frequency of 2048Hz. It is installed at the connection points of the main components of the template support system to collect vibration response data and transmit it to the data processing system.

10. The construction method for installing the curved formwork system for large-span irregular beams according to claim 9, characterized in that, The game-theoretic optimization model includes an upper-level model that aims to maximize installation quality and a lower-level model that aims to optimize monitoring effectiveness.

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