Bridge prefabricated component size deviation intelligent matching method based on BIM technology

Abstract

The application provides a bridge prefabricated component size deviation intelligent matching method based on BIM technology, and relates to the technical field of intelligent matching. The method comprises the following steps: obtaining BIM design models of each prefabricated component; in the BIM design model, three identification nodes are marked for each prefabricated component, and the three identification nodes are respectively defined in a top centroid area, a bottom centroid area and a normal projection extreme area of a middle segment lateral contour surface of the corresponding prefabricated component; according to the assembly correlation topological relationship of each prefabricated component and the three identification nodes on each prefabricated component, a first assembly base point and a second assembly base point are respectively calculated in two adjacent prefabricated components to be assembled, and a space positioning origin point is determined. The application can determine the component deviation and intelligently adjust the BIM model geometric contour, realize the matching of the size deviation of the bridge prefabricated component before assembly, improve the assembly efficiency and precision, and reduce the on-site construction adjustment cost.

Description

Technical Field

[0001] This invention relates to the field of intelligent matching technology, and in particular to an intelligent matching method for dimensional deviations of prefabricated bridge components based on BIM technology. Background Technology

[0002] In the assembly process of existing precast bridge components, the control of dimensional deviations usually focuses on individual inspections before leaving the factory or trial assembly adjustments during on-site installation. A common method is to use a total station or laser scanner to perform single-point measurements on key parts of the component in the prefabrication plant, and then compare the measurement results with the design values ​​to determine whether the component's processing accuracy meets the requirements. However, this approach still has room for improvement in practical applications.

[0003] Taking the assembly of precast piers and cap beams as an example, existing technologies typically focus more on the local geometric dimensions of the connection areas at the ends of components, such as end face flatness or center point offset. However, in actual engineering, during the processing, storage, and transportation of precast components, the lateral contour of the middle section may undergo certain deformation due to differences in concrete shrinkage or minor collisions. While such deformation may still be within the tolerance range of a single component during single-component inspection, when two components are spatially aligned and assembled, minute deviations in non-connected areas may be transmitted through the spatial orientation of the components, causing nonlinear coupling deviations in the pre-designed assembly reference points (such as the component's centroidal axis) during actual installation. Currently, there is a lack of an auxiliary method to perform overall envelope matching of multiple precast components in virtual space and to comprehensively quantify assembly deviations from multi-dimensional marker nodes. This makes it difficult to fully predict assembly interference or uneven gaps that may be caused by deviations in the middle section contour of the components before hoisting. Sometimes, temporary repairs or adjustments are still necessary on-site, which may have a certain impact on assembly efficiency and structural stress performance. Summary of the Invention

[0004] This invention provides an intelligent matching method for dimensional deviations of prefabricated bridge components based on BIM technology, which can comprehensively reflect the overall dimensional deviations of the components and effectively avoid omissions in deviation detection caused by local inspections.

[0005] To solve the above-mentioned technical problems, the technical solution of the present invention is as follows:

[0006] A method for intelligent matching of dimensional deviations in prefabricated bridge components based on BIM technology, the method comprising:

[0007] Step 1: Obtain the BIM design model of each prefabricated component. In the BIM design model, three identification nodes are marked for each prefabricated component. The three identification nodes are respectively defined in the top centroid region, bottom centroid region and the normal projection extreme value region of the middle lateral contour surface of the corresponding prefabricated component.

[0008] Step 2: Based on the assembly association topology of each prefabricated component and the three identification nodes on each prefabricated component, calculate the first assembly base point and the second assembly base point in two adjacent prefabricated components to be assembled, and determine the spatial positioning origin.

[0009] Step 3: Based on the spatial positioning origin, construct the first spatial envelope and the second spatial envelope respectively. Perform spatial topological overlap operation on the first spatial envelope and the second spatial envelope to obtain the spatial boundary curve of the overlap domain. Extract several discrete boundary feature nodes on the spatial boundary curve, and sequentially perform spatial vector mapping between the boundary feature nodes and the first assembly base point and the second assembly base point to obtain the first deviation vector set and the second deviation vector set.

[0010] Step 4: Based on the first set of deviation vectors and the second set of deviation vectors, calculate the coupling deviation metric between the first assembly base point and the second assembly base point;

[0011] Step 5: Compare the coupling deviation metric with the preset deviation tolerance threshold. If the coupling deviation metric exceeds the deviation tolerance threshold, adjust the spatial geometric contour of the prefabricated component in the BIM design model to achieve intelligent matching of dimensional deviations before assembly.

[0012] The above-described solution of the present invention has at least the following beneficial effects:

[0013] This invention achieves full-domain localization of key assembly features of precast components by setting marker nodes at the top centroid, bottom centroid, and extreme value areas of the mid-section lateral contour. This overcomes the limitations of detection that only focuses on the end connection area and ignores the influence of mid-section contour deformation, comprehensively reflecting the overall dimensional deviation of the component and effectively avoiding missed deviations caused by local detection. This reduces assembly risks caused by nonlinear coupling deviations from the source. Utilizing BIM virtual modeling and spatial envelope topology calculations, a comprehensive quantitative analysis of spatial deviations between adjacent components can be completed in the early stages of assembly. Assembly interference and uneven gaps can be predicted without relying on on-site trial assembly, reducing on-site temporary adjustments and repeated debugging, and improving the efficiency of precast component assembly construction. By employing deviation vector mapping and coupled deviation measurement, accurate characterization and evaluation of assembly deviations between components are achieved, which is more objective and accurate than manual experience judgment. Furthermore, by intelligently pre-adapting and adjusting the geometric contour of the BIM model based on the deviation results, dimensional deviation matching optimization can be completed in a virtual environment, improving the standardization of bridge prefabricated construction. Attached Figure Description

[0014] Figure 1 This is a flowchart illustrating the intelligent matching method for dimensional deviations of prefabricated bridge components based on BIM technology, provided in an embodiment of the present invention.

[0015] Figure 2This is a schematic flowchart of an embodiment of the present invention, which shows how to perform spatial topological overlap operation on a first spatial envelope and a second spatial envelope to obtain the spatial boundary curve of the overlap region.

[0016] Figure 3 This is the polar coordinate diagram of the first set of deviation vectors.

[0017] Figure 4 This is the polar coordinate plot of the second set of deviation vectors.

[0018] Figure 5 This is a curve showing the relationship between the coupling deviation metric and the assembly pass rate / on-site adjustment rate. Detailed Implementation

[0019] Exemplary embodiments of the present disclosure will now be described in more detail with reference to the accompanying drawings. While exemplary embodiments of the present disclosure are shown in the drawings, it should be understood that the present disclosure may be implemented in various forms and should not be limited to the embodiments set forth herein. Rather, these embodiments are provided so that this disclosure will be thorough and complete, and will fully convey the scope of the disclosure to those skilled in the art.

[0020] like Figure 1 As shown in the figure, an embodiment of the present invention proposes an intelligent matching method for dimensional deviations of prefabricated bridge components based on BIM technology. The method includes the following steps:

[0021] Step 1: Obtain the BIM design model of each prefabricated component. In the BIM design model, three identification nodes are marked for each prefabricated component. The three identification nodes are respectively defined in the top centroid region, bottom centroid region and the normal projection extreme value region of the middle lateral contour surface of the corresponding prefabricated component.

[0022] Step 2: Based on the assembly association topology of each prefabricated component and the three identification nodes on each prefabricated component, calculate the first assembly base point and the second assembly base point in two adjacent prefabricated components to be assembled, and determine the spatial positioning origin.

[0023] Step 3: Based on the spatial positioning origin, construct the first spatial envelope and the second spatial envelope respectively. Perform spatial topological overlap operation on the first spatial envelope and the second spatial envelope to obtain the spatial boundary curve of the overlap domain. Extract several discrete boundary feature nodes on the spatial boundary curve, and sequentially perform spatial vector mapping between the boundary feature nodes and the first assembly base point and the second assembly base point to obtain the first deviation vector set and the second deviation vector set.

[0024] Step 4: Based on the first set of deviation vectors and the second set of deviation vectors, calculate the coupling deviation metric between the first assembly base point and the second assembly base point;

[0025] Step 5: Compare the coupling deviation metric with the preset deviation tolerance threshold. If the coupling deviation metric exceeds the deviation tolerance threshold, adjust the spatial geometric contour of the prefabricated component in the BIM design model to achieve intelligent matching of dimensional deviations before assembly.

[0026] In this embodiment of the invention, by setting marker nodes in the extreme value areas of the top centroid, bottom centroid, and middle lateral contour of the precast component, the invention achieves full-domain positioning of key assembly features of the component. This overcomes the limitations of detection that only focuses on the end connection area and ignores the influence of the middle contour deformation, and can comprehensively reflect the overall dimensional deviation of the component, effectively avoiding the omission of deviations caused by local detection, and reducing the assembly risk caused by nonlinear coupling deviations from the source. With the help of BIM virtual modeling and spatial envelope topology calculation, the overall quantitative analysis of spatial deviations between adjacent components can be completed in the early stage of assembly. Assembly interference and uneven gap problems can be predicted without relying on on-site trial assembly, reducing on-site temporary repairs and repeated debugging, and improving the efficiency of precast component assembly construction. By adopting deviation vector mapping and coupled deviation measurement, the invention achieves accurate characterization and evaluation of assembly deviations between components, which is more objective and accurate than manual experience judgment. At the same time, by intelligently pre-adapting and adjusting the geometric contour of the BIM model based on the deviation results, dimensional deviation matching optimization can be completed in the virtual environment, improving the standardization of bridge prefabricated construction.

[0027] In a preferred embodiment of the present invention, step 1 involves obtaining the BIM design model of each prefabricated component. In the BIM design model, three identifier nodes are labeled for each prefabricated component. The three identifier nodes are respectively defined in the top centroid region, the bottom centroid region, and the extreme value region of the normal projection of the middle lateral contour surface of the corresponding prefabricated component, including:

[0028] In this embodiment of the invention, firstly, based on the overall design drawings of the bridge project, the prefabricated component processing drawings, and the assembly construction plan, a three-dimensional solid model of each prefabricated component to be assembled is established according to the design parameters. By integrating component dimensions, material properties, assembly constraints, and installation positioning information, a complete and parameterized BIM design model of the bridge prefabricated component is formed. The preset theoretical installation posture information specifically includes the spatial orientation of the prefabricated component's design axis in the overall bridge structure, such as extending along the positive direction of the global coordinate system X-axis, with an angle not exceeding 3° with the X-axis; the design vertical inclination angle (the vertical inclination angle of conventional prefabricated piers is 0°, while the vertical inclination angle of prefabricated components for skew bridges is controlled between 3° and 8°); the design lateral deviation angle (not greater than the deviation angle corresponding to 5mm, approximately 0.1°); the design elevation benchmark value, based on the design top surface elevation of the bridge pier, such as 120.500m, with the elevation deviation of the top end face of the prefabricated component controlled within ±3mm; and the design horizontal rotation angle (not greater than 0.2m). The system includes the following parameters: vertical rotation angle (not greater than 0.15°), theoretical translation components along the X, Y, and Z axes in the global coordinate system (controlled within ±2mm, ±2mm, and ±3mm respectively), and theoretical rotation angles around the three axes (rotation angles around the X and Y axes not greater than 0.1°, and rotation angles around the Z axis not greater than 0.2°). It also includes the design assembly gap value between adjacent components, which is usually 2mm to 5mm and is adjusted according to the component type. For example, the assembly gap between the precast cap beam and the pier column is 3mm, the end face normal fit constraint condition (the angle between the end face normal and the component design axis is not greater than 0.05°), the component axis coaxiality requirement (coaxiality deviation not greater than 4mm / m), the flatness constraint of the end face contact area (flatness not greater than 0.3mm / m), and the spatial alignment limit relationship (limit deviation not greater than 2mm). These parameters are used to uniquely determine the standard installation posture, spatial positioning relationship, and theoretical assembly state of the precast component in the global coordinate system.

[0029] The generated BIM design models of each prefabricated component to be assembled are retrieved. These models fully contain the spatial geometric morphology information of each prefabricated component, the assembly topology information between components, and the theoretical installation pose information preset during the design phase. Based on this model data, a unified spatial calculation benchmark is established using the global coordinate system built into the BIM design model. This global coordinate system is defined as O-XYZ, and the spatial position of any geometric point within the spatial range is uniquely represented by three-dimensional rectangular coordinates P(x, y, z), where x, y, and z represent the coordinate components of the geometric point along the X, Y, and Z axes in the global coordinate system, respectively. For a single prefabricated component in the BIM design model, the built-in geometric analysis engine is used to perform solid analysis on the prefabricated component, fully extracting its three-dimensional solid contour features, end face boundary information, and spatial geometric parameters of each surface. Geometric centroid calculation is then performed on the top end face region of the prefabricated component, calculating the three-dimensional centroid coordinates of this region in the global coordinate system, i.e.:

[0030] ;

[0031] In the formula, x c y c These are the centroid coordinate components of the top end face in the plane, z and z'. c Here, denoted by dA, represents the centroid coordinate component along the height direction of the top end face region; A represents the planar projected area of ​​the top end face of the precast component, which is the area of ​​the closed region enclosed by the contour of the end face; V represents the volume of the local solid region corresponding to the top end face, which is the size of the space occupied by the local solid extending downward from the top end face; dA is the area of ​​a micro-element in the plane of the end face, and dV is the volume of a micro-element in the local space. By performing numerical integration on the above formulas, the geometric centroid coordinates of the top end face region are obtained, and this coordinate point is marked as the top centroid region identifier node of the current precast component. Using the same solution method and calculation formula as the top centroid region, the geometric centroid of the bottom end face region of the precast component is solved, and the three-dimensional centroid coordinates of the bottom end face region in the global coordinate system are obtained. This centroid coordinate point is marked as the bottom centroid region identifier node of the precast component. After indexing the centroid nodes at the upper and lower ends, normal projection and extreme value calculation analysis are performed on the lateral profile surface of the middle section of the precast component. First, based on the geometric characteristics of the middle section of the component, the spatial surface function of the lateral profile surface of the middle section is determined, namely:

[0032] ;

[0033] Where a, b, c, d, e, f, g, h, i, and j are constant coefficients obtained by fitting the geometric dimensions of the lateral profile of the middle section of the component. This function completely describes the spatial coordinate constraint relationship of any point on the lateral profile surface of the middle section. Orthogonal projection operations are performed on the lateral profile surface of the middle section along the three coordinate axes X, Y, and Z of the global coordinate system. When orthogonally projecting onto the YOZ plane, the coordinate x=0 is fixed to obtain the two-dimensional projection curve. When projecting orthogonally onto the XOZ plane, with the coordinate y=0 fixed, a two-dimensional projection curve is obtained. When projecting orthogonally onto the XOY plane, the coordinates are fixed. =0, thus obtaining the two-dimensional projection curve. Through the above projection, three corresponding contour projection curves are obtained. Then, using spatial partial derivatives as constraints, the curvature extrema and coordinate extrema of each projection curve are solved. The extrema calculation expression is:

[0034] ;

[0035] In the formula, Let be the first-order partial derivatives of the surface function along the X, Y, and Z axes, respectively. A partial derivative of zero indicates a sudden change in the slope of the curve along the corresponding direction, suggesting the existence of a local extremum. Solving the above system of equations simultaneously yields the two-dimensional projected coordinates of the extremum points on each projected curve. Substituting these two-dimensional projected coordinates of the extremum points back into the spatial surface function along the original projection normal... The missing coordinate components of the coordinate axes are supplemented, and the complete three-dimensional spatial coordinates of the extreme point in the global coordinate system are obtained, so that the point falls back on the middle section lateral contour surface of the prefabricated component. This point is the spatial location of the extreme value region of the normal projection of the middle section lateral contour surface, and it is marked as the identification node of the extreme value region of the normal projection of the middle section lateral contour surface of the prefabricated component. Following the above unified process, the top centroid calculation, bottom centroid calculation, middle section lateral contour surface normal projection extreme value calculation, and corresponding identification node calibration operations are performed on all prefabricated components to be assembled in the BIM design model in sequence, finally completing the standardized indexing of three identification nodes on each prefabricated component. The spatial coordinates of all identification nodes are uniformly attributed to the global assembly coordinate system for recording and storage, forming a standardized node coordinate dataset.

[0036] In a preferred embodiment of the present invention, step 2, based on the assembly association topology of each prefabricated component and the three identification nodes on each prefabricated component, calculates the first assembly base point and the second assembly base point respectively in two adjacent prefabricated components to be assembled, and determines the spatial positioning origin, including:

[0037] Step 200a: Obtain the spatial coordinates of three marker nodes on the first prefabricated component among two adjacent prefabricated components to be assembled in the BIM design model. Extract the spatial coordinates of the marker nodes defined by the extreme region of the normal projection of the middle section lateral contour surface of the first prefabricated component. Combine this with the spatial transformation matrix corresponding to the theoretical installation pose of the first prefabricated component, transform the spatial coordinates of the corresponding marker nodes to the global assembly coordinate system using the spatial transformation matrix, and calculate the spatial coordinates of the first assembly base point. Specifically, this includes:

[0038] The first precast component refers to the precast component that first participates in the assembly alignment calculation among two adjacent precast components to be assembled. It can be any precast component such as a bridge pier, cap beam, or segmental box girder. The second precast component refers to the adjacent precast component that is assembled with the first precast component, and is the assembly coupling object of the first precast component. First, read the three-dimensional spatial coordinates of the top centroid region marker node, the bottom centroid region marker node, and the marker node of the extreme value region of the normal projection of the middle section lateral contour surface on the first precast component in the component's local coordinate system. Extract the spatial coordinates of the marker node defined by the extreme value region of the normal projection of the middle section lateral contour surface, and record them as local coordinate points. ; Retrieve the spatial transformation matrix corresponding to the first prefabricated component in its theoretically designed installation pose. This matrix is ​​a 4th-order homogeneous transformation matrix containing translation and rotation components, specifically in the form of:

[0039] ;

[0040] In the formula, r ij Let t be the cosine of the rotation direction of the component's local coordinate system relative to the global assembly coordinate system. 1x , t 1y , t 1z These represent the translation components of the local coordinate system relative to the global coordinate system along the X, Y, and Z axes, respectively. The local coordinate point P1 is then extended to homogeneous coordinate form. T is the matrix transpose symbol, obtained through coordinate transformation formulas. Transform the coordinates of the identifier node to the global assembly coordinate system to obtain the global coordinate point. The coordinate solution is then used as the spatial coordinate of the first assembly base point.

[0041] Step 201a: Obtain the spatial coordinates of three marker nodes on the second prefabricated component in the BIM design model among two adjacent prefabricated components to be assembled. Extract the spatial coordinates of the marker nodes defined by the extreme region of the normal projection of the middle section lateral contour surface of the second prefabricated component. Combined with the spatial transformation matrix corresponding to the theoretical installation pose of the second prefabricated component, transform the spatial coordinates of the corresponding marker nodes to the global assembly coordinate system using the spatial transformation matrix, and calculate the spatial coordinates of the second assembly base point. Specifically, this includes:

[0042] Using the same processing method as the first precast component, the spatial coordinates of three sets of marker nodes on the second precast component in the local coordinate system are read, and the local coordinates of the marker nodes defined by the extreme value region of the normal projection of the middle section lateral contour surface are extracted. ; Retrieve the spatial transformation matrix corresponding to the theoretical installation pose of the second precast component And through the same homogeneous coordinate transformation formula Transform the node coordinates to the global assembly coordinate system to obtain the global coordinate point. And determine it as the spatial coordinate of the second assembly base point.

[0043] Step 200b, determining the spatial positioning origin includes: when the assembly coupling surface of two adjacent prefabricated components to be assembled is a planar coupling configuration, determining the first assembly base point or the second assembly base point as the spatial positioning origin, specifically including:

[0044] The geometric features of the assembly coupling surface configuration between two adjacent prefabricated components to be assembled are identified and the type is determined. The identification process uses the geometric analysis engine built into the BIM model to extract the coordinates of all spatial discrete points of the assembly coupling surface and the normal vector information corresponding to each discrete point, forming a discrete point normal vector dataset.

[0045] To determine whether the coupling surface is planar, the angle difference between the normal vectors of any two non-coincident discrete points needs to be calculated. The dot product formula is used to solve for the angle between the two normal vectors. The calculated angle difference is in radians, which can be converted to degrees: angle value = angle difference × 180 / π, where π is pi. An angle threshold of 0.5° is set. Considering the assembly accuracy requirements of precast bridge components, when the angle between the normal vectors is less than 0.5°, the normals at all points on the coupling surface are considered to be consistent, conforming to the geometric characteristics of planar components. This threshold balances detection accuracy and computational efficiency, avoiding false positives due to an excessively small threshold and false negatives due to an excessively large threshold. Simultaneously, a plane fitting is performed on the extracted discrete points of the coupling surface to obtain a single plane equation. The specific form of the plane equation is... In the formula, A a B a C a D a Let A be the plane fitting coefficient, where A a B a C a A is not both 0 at the same time a B a C a The normal vectors constituting the plane are fitted with discrete point coordinates using the least squares method to obtain the values ​​of their coefficients. Let the coupling surface have... For each discrete point, its coordinates are sequentially substituted into the aforementioned plane equations to construct an overdetermined system of equations. This system is then solved using the least squares method to obtain the plane fitting coefficients that minimize the sum of the squared distances from all discrete points to the plane. This process is performed if the angles between all normal vectors are less than 0.5°, and the coupling surface can be uniformly fitted to the aforementioned single plane equation. If the assembly coupling surface is determined to be a planar coupling configuration, the planar coupling configuration is characterized by two components being directly fitted together through flat and regular end faces. The end faces have no concave or convex, arc or toothed structures, and the geometric center of the end face coincides with the overall assembly axis of the component. In this case, the spatial coordinates of the first assembly base point or the second assembly base point are directly selected as the spatial positioning origin of the current adjacent component assembly area.

[0046] Step 201b: When the assembly coupling surface is a non-planar coupling configuration, the extreme value region of the normal projection of the middle section lateral contour surface of the prefabricated component where the first assembly base point is located is used as the first positioning center, and 1 / 3 of the longest diagonal length of the circumscribed cuboid of the first prefabricated component in the BIM design model is used as the first calibration radius to construct a first closed loop. The extreme value region of the normal projection of the middle section lateral contour surface of the prefabricated component where the second assembly base point is located is used as the second positioning center, and 1 / 3 of the longest diagonal length of the circumscribed cuboid of the second prefabricated component in the BIM design model is used as the second calibration radius to construct a second closed loop. Specifically, this includes:

[0047] If the assembly coupling surface is identified as a non-planar coupling configuration, such as an arc-shaped contact surface, a toothed contact surface, a stepped contact surface, or other irregular matching surfaces, a closed loop construction method is used to determine the spatial positioning center. First, the extreme value region of the normal projection of the middle section lateral contour surface of the prefabricated component to which the first assembly base point belongs is taken as the first positioning center. In the BIM design model, the minimum bounding box algorithm is used to generate the minimum circumscribed cuboid of the prefabricated component. That is, first, the coordinates of all vertices of the three-dimensional entity of the first prefabricated component are extracted, and the extreme values ​​of the coordinates of all vertices in the three coordinate axes X, Y, and Z of the global assembly coordinate system are traversed to determine the minimum and maximum coordinates in the X-axis direction, the Y-axis direction, and the Z-axis direction. Using these six extreme coordinates as boundaries, a regular cuboid that can completely enclose the three-dimensional entity of the prefabricated component and has the smallest volume is constructed. The boundary of the minimum bounding cuboid is tangent to the key points of the outer contour of the component. After constructing the minimum circumscribed cuboid, determine the coordinates of its eight spatial vertices, namely the vertices corresponding to the minimum X-axis, minimum Y-axis, minimum Z-axis, minimum X-axis, minimum Y-axis, maximum Z-axis, minimum X-axis, minimum Y-axis, minimum Z-axis, minimum X-axis, minimum Y-axis, maximum Z-axis, maximum X-axis, maximum Y-axis, maximum Z-axis, maximum X-axis, minimum Y-axis, minimum Z-axis, maximum X-axis, minimum Y-axis, maximum Z-axis, maximum X-axis, maximum Y-axis, minimum Z-axis, maximum X-axis, maximum Y-axis, maximum Z-axis, maximum X-axis, maximum Y-axis, maximum Z-axis. Then, based on the coordinates of these eight vertices, calculate the length L1 of the longest diagonal of the cuboid.

[0048] The first calibration radius is calculated according to a preset ratio. The preset ratio is 1 / 3, which, considering the geometric dimensions of the precast bridge components, is 1 / 3 of the longest diagonal length of the smallest circumscribed cuboid. This ensures that the core area related to the assembly coupling surface in the middle section of the component is just covered. This avoids the problem of the loop not covering the assembly-related area due to an excessively small radius, or the introduction of interference from irrelevant areas due to an excessively large radius. Using the first positioning center as the center and the first calibration radius as the radius, a first planar closed loop is constructed within the reference plane where the assembly coupling surface is located. Simultaneously, using the same method, the extreme value region of the normal projection of the lateral contour surface of the middle section of the precast component to which the second assembly base point belongs is used as the second positioning center. The smallest circumscribed cuboid of the second precast component is generated using the aforementioned geometric bounding box algorithm. Its longest diagonal length L2 is calculated, and the second calibration radius is also calculated. Construct a second plane closed loop with the second positioning center as the center and the second calibration radius as the radius.

[0049] Step 202b involves determining the geometric center point within the overlapping region of the first and second closed loops as the spatial positioning origin. Specifically, this includes calculating the spatial relationship between the first and second closed loops in the global assembly coordinate system. First, the two loops are projected onto the same reference plane (selecting the fitting reference plane of the assembly coupling surface to ensure the projection accurately reflects the spatial overlap of the two loops). Then, the planar analytical equations for the two loops are established. The planar analytical equation of the closed loop is the standard equation of a circle, i.e. In the formula, for the first closed loop, Let R be the two-dimensional coordinates of the first positioning center in the projection reference plane, and R be the first calibration radius, i.e., R1; for the second closed loop, Let R be the two-dimensional coordinates of the second positioning center in the projection reference plane, and R be the second calibration radius, which is R2. A system of equations is constructed by simultaneously solving the standard equations of the two loops:

[0050] ;

[0051] In the formula, The first positioning center projection coordinates, Given the projected coordinates of the second positioning center, solve the system of equations to obtain the coordinates of the intersection of the two closed loops. When the system of equations has two distinct real solutions, the two loops have two intersection points, which is the normal case for the assembly coupling area of ​​adjacent components. When the system of equations has one real solution, the two loops are tangent and have only one intersection point, which is a special case of fit. When the system of equations has no real solutions, the two loops have no intersection points. In this case, it indicates that the current calibration radius has failed to cover the assembly coupling area with the two loops. The calibration radius needs to be adjusted (increase the calibration radius of the two loops by 10% to 15% of the original calibration radius, while keeping the original radius ratio of the two loops unchanged). After reconstructing the two closed loops, solve the system of equations again to obtain the intersection coordinates until at least one intersection point is obtained. After obtaining the coordinates of the intersection of the two loops, the overlapping area between the two loops is divided according to the spatial position of the two intersections. Since both loops are circles in the plane, their overlapping area is the planar area formed by the overlapping part of the two circles. The boundary of this area is formed by the overlapping arc segments of the two loops. The specific boundary range is extended along the inner arc segments of the two loops with the two intersections as the endpoints until the two endpoints are closed, forming a closed planar area. This overlapping area precisely corresponds to the core area of ​​the assembly and coupling of two adjacent prefabricated components.

[0052] Once the overlapping region is determined, the coordinates of the geometric center point of that region are calculated, i.e.:

[0053] ;

[0054] In the formula, Xo Y o Z o Here, x, y, and z are the coordinate components of the geometric center point of the overlapping region along the X, Y, and Z axes in the global assembly coordinate system, respectively; S is the planar area of ​​the overlapping region formed by the two closed loops, which can be calculated by integration or geometric formulas; dS is the infinitesimal area of ​​the overlapping region; and x, y, and z are the spatial coordinates of the corresponding positions of the infinitesimal area dS in the global assembly coordinate system. By performing numerical integration on the above formulas, the three-dimensional coordinates of the geometric center point of the overlapping region are obtained, and these coordinate values ​​are determined as the spatial positioning origin of the current adjacent prefabricated component assembly area.

[0055] This embodiment calculates assembly reference points based on the extreme nodes of the mid-section lateral contour and the spatial transformation matrix. This approach takes into account the impact of mid-section deformation on assembly alignment, avoiding positioning deviations caused by relying solely on end measuring points and improving the global representativeness of assembly reference points. A coordinate transformation matrix is ​​used to achieve a unified conversion from local to global coordinates, ensuring the consistency and accuracy of spatial positioning between adjacent components. Separate rules for determining the positioning origin are set for planar and non-planar coupled configurations, adapting to the assembly forms of two types of precast bridge components. By constructing a closed loop using the diagonal ratio of the circumscribed cuboid and taking the overlap center as the positioning origin, the influence of single component dimensional deviations is weakened, making the positioning origin more closely match the actual assembly coupling area.

[0056] like Figure 2 As shown, in another preferred embodiment of the present invention, step 3 involves constructing a first spatial envelope and a second spatial envelope based on the spatial positioning origin, performing a spatial topological overlap operation on the first and second spatial envelopes to obtain the spatial boundary curve of the overlap domain; extracting several discrete boundary feature nodes on the spatial boundary curve, and sequentially mapping the boundary feature nodes to the first assembly base point and the second assembly base point using spatial vectors to obtain a first set of deviation vectors and a second set of deviation vectors, including:

[0057] Step 300a: Using the first assembly base point as the centroid of the first spatial envelope, and taking 1 / 3 of the longest diagonal length of the circumscribed cuboid of the first prefabricated component in the BIM design model as the envelope radius of the first spatial envelope, a spherical first spatial envelope is constructed. Specifically, this includes: to fully cover the assembly influence area of ​​the first prefabricated component and accurately reflect its spatial contour deviation distribution, using the spatial coordinates of the first assembly base point in the global assembly coordinate system as the centroid position of the first spatial envelope, retrieving the smallest circumscribed cuboid of the first prefabricated component generated in step 201b, reading the longest diagonal length of the cuboid, and taking 1 / 3 of this length as the envelope radius of the first spatial envelope. This value can ensure coverage of the key assembly area of ​​the component while avoiding an excessively large envelope range that introduces irrelevant geometric interference. A spherical configuration is used to construct the first spatial envelope, and its spatial spherical equation is:

[0058] ;

[0059] In the formula, X o1 Y o1 Z o1 Let R be the three-dimensional coordinates of the first assembly base point. o1 Let be the envelope radius of the first spatial envelope. The spatial range and geometric shape of the first spatial envelope are fully defined by the above equation.

[0060] Step 301a: Using the second assembly base point as the centroid of the second spatial envelope, and taking 1 / 3 of the longest diagonal length of the circumscribed cuboid of the second prefabricated component in the BIM design model as the envelope radius of the second spatial envelope, a spherical second spatial envelope is constructed. Specifically, this includes: adopting a construction logic completely consistent with the first spatial envelope to ensure that the deviation representation rules of the components on both sides are unified and the results are comparable; using the spatial coordinates of the second assembly base point as the centroid of the second spatial envelope; extracting the longest diagonal length of the smallest circumscribed cuboid of the second prefabricated component generated in step 201b; taking 1 / 3 of its length as the envelope radius of the second spatial envelope; and constructing a spherical second spatial envelope. The corresponding spatial sphere equation is: ;

[0061] In the formula, X o2 Y o2 Z o2 R represents the three-dimensional coordinates of the second assembly base point. o2 The envelope radius of the second spatial envelope is used to complete the construction of the spatial envelopes corresponding to two adjacent components.

[0062] Step 300b involves spatially locating the first and second spatial envelopes within the same spatial coordinate system of the BIM design model to obtain the spatial distance between the first and second assembly base points. Specifically, this includes: placing the first and second spatial envelopes under the global assembly coordinate system of the BIM design model for spatial positioning to eliminate calculation errors caused by coordinate system differences; and calculating the spatial distance D between the two assembly base points using the spatial distance formula based on the three-dimensional coordinates of the first and second assembly base points. u This yields spatial distance data.

[0063] Step 301b: Compare the spatial distance value with the envelope radius of the first spatial envelope and the envelope radius of the second spatial envelope. When the spatial distance value is less than the sum of the envelope radii of the first and second spatial envelopes and greater than the absolute value of the difference between the envelope radii of the first and second spatial envelopes, it is determined that the first and second spatial envelopes are in a spatial intersection state. Specifically, to determine whether the two envelopes have a real assembly overlap relationship and avoid invalid overlap situations of complete separation or complete inclusion, the calculated spatial distance value is compared with the sum and absolute difference of the envelope radii of the first and second spatial envelopes, respectively. The determination condition is... When the spatial distance values ​​satisfy the above inequality relationship, it is determined that the first spatial envelope and the second spatial envelope are in a spatial intersection state. This state directly corresponds to the existence of a real spatial overlap and coupling relationship between two adjacent prefabricated components during the actual assembly process, and the boundary calculation of the overlap domain can continue.

[0064] Step 302b: Based on the spatial coordinates of the first assembly base point, the spatial coordinates of the second assembly base point, the envelope radius of the first spatial envelope, and the envelope radius of the second spatial envelope, calculate the center coordinates and radius of the spatial circle formed by the intersection of the first and second spatial envelopes, and determine the spatial circle as the spatial boundary curve of the overlapping domain. Specifically, after clearly determining that the two spatial envelopes are in a spatial intersection state, based on the spatial coordinates of the first and second assembly base points, and the determined first and second envelope radii, calculate the complete parameters of the spatial circle formed by the intersection of the two spherical envelopes. The complete parameters include the three-dimensional coordinates of the center of the spatial circle, the radius of the spatial circle, and the normal vector of the plane in which the spatial circle is located. The spatial circle is the only closed spatial curve formed by the intersection of the two spheres, which can objectively reflect the deviation coupling boundary of the two prefabricated components in the assembly area. First, the coordinates of the center of the spatial circle are calculated. This center lies on the line connecting the first and second assembly base points. The position is determined through spatial linear interpolation and geometric proportional distribution. Specifically, the distance d1 from the first assembly base point to the center of the spatial circle is calculated based on the distance between the two assembly base points, the first envelope radius, and the second envelope radius. Then, the distance from the second assembly base point to the center of the spatial circle is obtained using d2 = distance between the two assembly base points - d1. Spatial linear interpolation is then performed on the coordinates of the two assembly base points using this distance ratio. Let the coordinates of the first assembly base point be... The coordinates of the second assembly base point are Coordinates of the center of the circle in space Calculated according to the proportion, that is:

[0065] ;

[0066] Where Ur is the distance between the two assembly base points, the spatial position of the center of the spatial circle in the global assembly coordinate system can be uniquely determined by the above formula; after determining the center coordinates, the radius of the spatial circle is calculated according to the geometric constraint relationship between the radius of the spherical envelope, the distance between the two sphere centers and the radius of the spatial circle, that is:

[0067] ;

[0068] Where PI is the radius of the spatial circle, and the sum of d1 and d2 is equal to the spatial distance between the two assembly base points; at the same time, the normal vector of the plane containing the spatial circle is in the same direction as the line connecting the two assembly base points, and can be directly determined by the coordinates of the two assembly base points. Thus, the three key parameters of the spatial circle, namely the center coordinates, radius, and normal vector of the plane containing the spatial circle, are completely calculated; the spatial circle obtained by the above calculation is used as the spatial boundary curve of the overlapping domain of the first spatial envelope and the second spatial envelope.

[0069] Step 300c: The spatial coordinates of the center of the spatial circle in the global assembly coordinate system are used as the reference center coordinates. Any radial direction within the plane containing the spatial circle is determined as the initial reference direction. Using the reference center coordinates as the rotation center and the initial reference direction as the zero point of angle, the circumference of the spatial circle is divided into twelve equal angle values ​​at 30-degree intervals, with each value being 30 degrees, 60 degrees, 90 degrees, up to 360 degrees. Using the reference center coordinates as the center and the radius of the spatial circle as the distance, the spatial direction vector corresponding to each equal angle value is sequentially synthesized with the reference center coordinates to obtain the spatial coordinates of the twelve boundary feature nodes. Specifically, this includes:

[0070] To achieve uniform sampling and global representation of overlapping boundary deviations and avoid the limitations of single-point detection, the coordinates of the center of the spatial circle in the global assembly coordinate system are set as the reference center coordinates. Any radial direction within the plane of the spatial circle is selected as the starting reference direction. Using the reference center as the rotation center and the starting reference direction as the zero point of the angle, the spatial circle is uniformly divided at 30-degree central angle intervals, resulting in twelve equal division angles from 30 degrees, 60 degrees, 90 degrees, up to 360 degrees. This interval setting ensures both sampling density and computational efficiency. For each equal division angle, the corresponding spatial direction vector is calculated. That is, within the plane of the spatial circle, starting from the reference center, the unit direction vector is calculated by converting planar polar coordinates to spatial rectangular coordinates according to the current equal division angle and the radius of the spatial circle. Multiplying the unit vector by the radius yields the radial vector at that angle. The direction vector is then vector-synthesized with the reference center coordinates, i.e., each component of the radial vector plus the corresponding coordinate component of the reference center, resulting in the spatial coordinates of twelve discretely distributed boundary feature nodes, thus achieving characteristic sampling of the overlapping boundary.

[0071] Step 301c: Sequentially map each boundary feature node to the first assembly base point using spatial vectors, calculate the spatial vector pointing from the first assembly base point to the boundary feature node, and aggregate all calculated spatial vectors into a first deviation vector set. Specifically, to quantify the deviation direction and magnitude of the first prefabricated component relative to the assembly coupling area, for each boundary feature node in step 300c, construct a spatial vector pointing from the first assembly base point to that feature node, and calculate the vector components through coordinate difference calculation. The calculation formula is as follows: In the formula, This refers to the three-dimensional spatial coordinates of the I-th boundary feature node in the global assembly coordinate system. Let be the first deviation vector corresponding to the i-th boundary feature node. The three-dimensional components of this vector represent the magnitude and spatial orientation of the deviation of the first component at the corresponding position. The twelve vectors together constitute the global deviation field, which fully represents the spatial deviation distribution pattern and local deviation differences of the first component in the overlapping domain. Specifically, the spatial deviation distribution pattern is manifested as the component variation trend of each deviation vector in the X, Y, and Z coordinate axes of the global assembly coordinate system. This can reflect whether the first prefabricated component is biased in a certain direction as a whole in the overlapping domain, or whether there are irregular deviations in some areas. For example, if the X-axis components of multiple deviation vectors are all positive and gradually increase, it indicates that the component has an overall offset trend along the positive X-axis in the overlapping domain; if the deviation vector components are in... The alternating positive and negative changes of nodes at different angles indicate local undulations and deviations at the boundary of the overlapping domain of the components. These local deviation differences are specifically manifested in the differences in the magnitude and direction of the deviation vectors corresponding to the characteristic nodes at different angles. For example, some nodes have larger deviation vector magnitudes, such as greater than 5mm, corresponding to obvious deviation bulges in the overlapping domain; while others have smaller deviation vector magnitudes, such as less than 2mm, indicating that the local deviations meet assembly requirements. By comparing the magnitude and direction of the three-dimensional components of the deviation vectors of the twelve nodes, the concentrated and gradual deviation areas of the first prefabricated component within the overlapping domain can be identified, clarifying the distribution location, degree, and gradient of local deviations, thus achieving a comprehensive characterization of the deviations in the overlapping domain of the first component. All twelve spatial vectors are then summarized to form the first deviation vector set.

[0072] Step 302c involves sequentially mapping the same boundary feature node to the second assembly base point using spatial vectors, calculating the spatial vector pointing from the second assembly base point to the boundary feature node, and collecting all calculated spatial vectors into a second deviation vector set. Specifically, to ensure consistent calculation logic and comparable results for the deviation vectors on both sides, the same calculation method as in step 301c is used. For the same boundary feature node obtained in step 300c, a spatial vector pointing from the second assembly base point to that node is constructed, calculated using the following formula: In the formula, Let be the second deviation vector corresponding to the i-th boundary feature node. All twelve vectors are then aggregated to form a set of second deviation vectors, thus completing the extraction and construction of the deviation vectors.

[0073] This embodiment constructs a spherical spatial envelope based on the assembly datum point as the centroid and the dimensions of the circumscribed cuboid of the component. This comprehensively covers the mid-section contour and assembly coupling area of ​​the precast component, overcoming the deficiency of detection that only focuses on the ends and ignores the deformation of the mid-section. By employing spatial intersection determination and spatial circle boundary calculation, the overlapping shape of the assembly areas of the two components can be quantified, objectively reflecting the nonlinear coupling deviation characteristics. By extracting boundary feature nodes along the spatial circle at equal angles and constructing a bidirectional deviation vector set, the assembly deviation distribution can be characterized from a global perspective, avoiding the one-sidedness of single-point measurement, improving the accuracy of assembly deviation prediction, reducing on-site trial assembly and temporary adjustment work, and ensuring the assembly efficiency and structural stress uniformity of bridge precast components.

[0074] In a preferred embodiment of the present invention, step 4 includes:

[0075] Step 400: Pair each first deviation vector in the first deviation vector set with the second deviation vector in the second deviation vector set corresponding to the same boundary feature node to obtain 12 deviation vector pairs. Specifically, this includes: pairing the first deviation vector set and the second deviation vector set one by one according to the correspondence of the same boundary feature node. Using the twelve boundary feature nodes uniformly distributed along the spatial circumference in step 300c as the matching basis, the first deviation vector and the second deviation vector corresponding to the I-th boundary feature node are combined sequentially to form twelve one-to-one deviation vector pairs, ensuring that each pair of vectors originates from the same spatial sampling position.

[0076] Step 401: Using the spatial angles of each boundary feature node on the spatial circle as spatial coordinate parameters, interpolate and fit the magnitudes of each deviation vector in the first and second deviation vector sets along the spatial angle distribution of the spatial circle to establish the first and second deviation field functions that are continuously distributed along the spatial angles. Specifically, this includes:

[0077] Using the spatial angles corresponding to each boundary feature node on the spatial circle as independent spatial coordinate parameters, the magnitudes of the first and second deviation vector sets are calculated respectively. The formula for calculating the magnitude of a single deviation vector is:

[0078] ;

[0079] In the formula, Let be the magnitude of the I-th first deviation vector. Let be the magnitude of the i-th second deviation vector, and represent the deviation magnitude at the corresponding positions. The coordinate axis components of the first deviation vector, These are the coordinate axis components of the second deviation vector.

[0080] From a spatial perspective Using the independent variable, a piecewise cubic interpolation method is used to continuously interpolate and fit the magnitude of the deviation vector at twelve discrete angle points. Specifically, the fitting process involves first sorting the twelve boundary feature nodes according to their corresponding spatial angle values ​​from smallest to largest, forming an ordered sequence of nodes with progressively increasing angles. This corresponding angle sequence is denoted as... And agree to form a closed cycle, that is Using the angle values ​​of two adjacent ordered nodes as upper and lower limits, twelve consecutive and non-overlapping angle sub-intervals are divided. The specific range of the k-th sub-interval is... Where k takes values ​​from 1 to 12, and each interval corresponds to a continuous arc segment on the boundary of the assembly overlap region, θ k θ is the spatial angle corresponding to the k-th boundary feature node. k+1 Let be the spatial angle corresponding to the (k+1)th boundary feature node. Within each independent angle sub-interval... Within each function, construct a cubic polynomial function. The unified expression for this polynomial is:

[0081] ;

[0082] In the formula, f k (θ) is the deviation amplitude fitting function within the k-th angular interval, a k Let b be the coefficient of the cubic term in this polynomial. k C is the coefficient of the quadratic term. k d is the coefficient of the linear term. k The constant term is represented by all coefficients, which are parameters to be solved.

[0083] This allows the polynomial curve to pass through the magnitude of the deviation vector at the two endpoints of the interval, while also ensuring that adjacent intervals pass through the common angle node θ. k A continuity constraint is applied at each node, requiring that the function values, first derivative values, and second derivative values ​​of the two polynomials at that node be equal. This ensures that the overall fitting curve is smooth and continuous throughout the entire circumferential region of space, without abrupt changes in angles or curvature, and can truly reflect the continuous variation trend of the deviation amplitude with spatial angles. The above piecewise cubic interpolation fitting process is performed on the discrete data of the first deviation vector magnitude and the discrete data of the second deviation vector magnitude, respectively. A system of linear equations is constructed based on the ordered angle nodes and their corresponding deviation amplitudes. For a fitting sequence containing twelve angle nodes, the constructed system of linear equations takes the form:

[0084] ;

[0085] In the formula, V is the current segment interval number. k V k+1These are the magnitudes of the deviation vectors corresponding to the k-th and (k+1)-th angle nodes, respectively, a k-1 b k-1 C k-1 Let be the coefficients of the cubic, quadratic, and linear terms of the polynomial in the (k-1)th segment, respectively; by solving this system of linear equations, we obtain the coefficients 'a' of each term of the cubic polynomial in each angle subinterval. k b k C k d k Then, the first deviation field function f1(θ) and the second deviation field function f2(θ) are constructed continuously distributed along the spatial circumference, respectively; the continuous deviation field functions obtained by interpolation are uniformly expressed as piecewise cubic polynomials:

[0086] ;

[0087] in For segmented interval numbering, Let be the coefficients of the cubic, quadratic, and linear terms of the polynomial in the k-th segment of the j-th deviation field, where j=1,2 to distinguish between the first and second deviation field functions; and let be the piecewise polynomial coefficients obtained by fitting discrete points. Through this piecewise cubic interpolation method, the deviation amplitude points, originally only at twelve discrete angular positions, are expanded into angular functions that continuously vary along the entire circumference of space, thus fully realizing the mapping from finite discrete sampling points to a continuous deviation field across the entire assembly overlap domain.

[0088] Step 402: Perform a difference operation on the first deviation field function and the second deviation field function to obtain a deviation field difference function that is continuously distributed along the spatial angle of the spatial circle. Specifically, this includes: within the same spatial angle domain, using the spatial angle θ as a continuous independent variable, performing a point-by-point difference operation on the first deviation field function f1(θ) and the second deviation field function f2(θ). The specific expression is f △ The calculation process, f(θ) = f1(θ) - f2(θ), aims to establish a continuous mathematical model that covers the entire circumferential range of the assembly overlap domain (i.e., angle θ from 0 to 2π). By simultaneously calculating the difference in deviation amplitude between the first and second prefabricated components at each spatial angle θ position, this deviation field difference function can overcome the limitation of comparing only at twelve discrete nodes, thus continuously and completely reflecting the distribution of deviation differences between the two prefabricated components in the entire assembly overlap domain, and intuitively demonstrating the spatial variation characteristics of the coupling deviation.

[0089] For any given spatial angle, the calculated result of the deviation field difference function is the difference in deviation amplitude between the first and second precast components at that precise angular position. The absolute value of this value directly characterizes the relative difference in deviation amplitude between the two components at the same spatial position; a larger value indicates a more significant difference. The positive and negative signs of the difference function have clear physical meanings. △ When (θ)>0, it indicates that at that angular position, the deviation amplitude of the first precast component is greater than that of the second precast component; when f △ When (θ) < 0, it indicates that the deviation amplitude of the second prefabricated component is larger; while when f △ When (θ)=0, it means that the deviation amplitudes of the two components at this position are completely equal; by analyzing the positive and negative distribution of the function value in the global angle, it can be known which component on which side has a larger deviation in the overlapping domain.

[0090] The rising and falling trend and curve shape of the deviation field difference function with spatial angle are the core of reflecting the spatial variation characteristics of coupling deviation. For example, if the function curve shows a continuous upward trend within a certain angle range, it indicates that the deviation difference between the first component and the second component is continuously increasing from that angle. If the curve has a peak, it corresponds to the key spatial position where the deviation difference between the two components is the largest within the entire overlap region. If the curve is generally stable, it indicates that the deviation difference changes gently within this region. By analyzing the extreme points, inflection points, and overall trend of the function, the specific characteristics of the spatial distribution of assembly coupling deviation can be accurately identified. Among them, the deviation concentration area refers to the spatial angle range corresponding to the extreme point of the function, in which the deviation amplitude difference between the two prefabricated components is continuously ≥0.5mm for three consecutive periods. The deviation difference between adjacent angular positions remains above 0.4mm, which is the main concentrated area of ​​assembly coupling deviation. The weak link refers to the spatial position corresponding to the inflection point of the function. The rate of change of deviation difference at this position is abruptly ≥0.1mm / °, which means that the assembly accuracy is prone to deviation and is a key point for subsequent accuracy control. The part with drastic changes refers to the angular interval where the absolute value of the slope of the function curve is ≥0.08mm / °. The deviation difference in this interval changes with the angle, and the deviation difference between adjacent angular positions is ≥0.3mm, which shows the rapid change characteristics of coupling deviation. Through this comprehensive analysis, the spatial distribution law of assembly coupling deviation can be fully captured, avoiding the locality and one-sidedness that may be caused by relying only on discrete sampling points (i.e., relying only on limited discrete sampling data).

[0091] Step 403: Integrate the deviation field difference function over the circumferential domain of the spatial circle using spatial angles as the integration variable to obtain the integral result; then, weight and fuse the integral result with the weight coefficients corresponding to the spatial angles of each boundary feature node on the spatial circle to calculate the coupling deviation metric between the first assembly base point and the second assembly base point, specifically including:

[0092] The deviation field difference function is expressed in terms of spatial angles within the complete circumference of the spatial circle. For the definite integral operation on the variable of integration, with the integration interval from 0 to 2π, the integration formula is: In the formula I t The integral result represents the sum of the overall deviation differences between the two components within the assembly overlap domain; then, this integral result is combined with the weighting coefficient w of the spatial angles corresponding to each boundary feature node. q Weighted fusion is performed, with weight coefficients evenly distributed according to the angles of each node on the spatial circle. The final solution yields the coupling deviation metric between the first and second assembly base points, i.e., the coupling deviation metric. The weighting coefficients satisfy the normalization condition. Since the nodes are uniformly distributed, equal weights w are taken. q =1 / 12, and this method yields a coupling deviation metric that can be directly used to evaluate assembly accuracy.

[0093] This embodiment ensures the consistency and objectivity of the deviation comparison between the two components by pairing the deviation vectors according to the same spatial node, avoiding calculation distortion caused by mismatched sampling positions. The use of interpolation fitting to construct a continuous deviation field function compensates for the insufficiency of discrete sampling points, accurately restoring the continuous spatial distribution of deviations within the assembly overlap domain and eliminating the influence of local sampling errors. Through difference calculations and global integration, the coupling deviation between the two prefabricated components can be quantified at the overall level, rather than relying solely on single-point deviation values, making the measurement results more consistent with the actual assembly stress and alignment state. Combined with angle weighting coefficients for weighted fusion, the rationality and representativeness of the coupling deviation measurement values ​​are further improved.

[0094] In a preferred embodiment of the present invention, step 5 includes:

[0095] Step 500: When the coupling deviation metric is less than or equal to the preset deviation tolerance threshold, it is determined that the dimensional deviation between the two prefabricated components is within an acceptable range, and the spatial geometric contours of the two prefabricated components in the BIM design model remain unchanged. Specifically, this includes: comparing the coupling deviation metric with the preset deviation tolerance threshold. Combining the bridge prefabricated component construction and acceptance specifications with the engineering measurement accuracy requirements, the preset deviation tolerance threshold is set to 2.0 mm. This value is determined comprehensively based on the prefabricated concrete component assembly gap control standard, on-site construction adjustment allowance, and 3D laser scanning detection accuracy. This ensures both the uniformity of structural stress and the smoothness of the alignment after assembly, while also taking into account the engineering requirements. The feasibility of prefabrication and on-site installation is assessed. The first prefabricated component is a prefabricated segmental box girder for the bridge, and the second prefabricated component is a prefabricated cap beam for the bridge. The two components form a ring-shaped overlapping boundary in the assembly coupling area. When the coupling deviation metric is less than or equal to the preset deviation tolerance threshold, i.e., when the coupling deviation metric is ≤ the preset deviation tolerance threshold, it is determined that the dimensional deviation and coupling deviation formed by the current prefabricated segmental box girder and prefabricated cap beam in the assembly overlapping area are within the acceptable range of engineering assembly. There is no need to adjust the geometric shape of the components. The original spatial geometric contour, node coordinates and assembly posture parameters of the prefabricated segmental box girder and prefabricated cap beam in the BIM design model remain unchanged.

[0096] Step 501: When the coupling deviation metric value is greater than the preset deviation tolerance threshold, it is determined that the dimensional deviation between the two prefabricated components exceeds the acceptable range. Based on the peak position of the spatial angle distribution along the spatial circle of the deviation field difference function, the spatial angle domain interval with the largest deviation contribution is identified. Based on the vector difference between the first deviation vector and the second deviation vector corresponding to the corresponding spatial angle domain interval, the spatial geometric contour correction amount of the first or second prefabricated component in the BIM design model is generated, specifically including:

[0097] When the coupling deviation metric exceeds the preset deviation tolerance threshold (i.e., the coupling deviation metric > preset deviation tolerance threshold), it is determined that the dimensional deviation and coupling deviation between the current precast segment box girder and the precast cap girder exceed the allowable range for engineering assembly, and the geometric contours of the components in the BIM model need to be corrected. First, the deviation field difference function f is traversed. △ Find all function values ​​(θ) within the angle interval from 0 to 2π, and solve for the spatial angular position θ corresponding to the function's extrema. max The calculation formula is as follows: , Centered on the peak angle, a 30° central angle range is extended to both sides to identify and determine the spatial angular region interval with the largest deviation contribution. Within this spatial angular region interval, the first and second deviation vectors of the corresponding boundary feature nodes are selected, and the deviation correction reference vector is obtained through vector difference calculation. This vector difference is used to characterize the degree of mismatch between the deviations of the first precast component (precast segmental box girder) and the second precast component (precast cap beam) within this angular region interval. The magnitude of the vector difference directly reflects the relative difference in the deviation amplitude of the first and second precast components at their corresponding spatial positions within this angular region interval. The larger the magnitude, the worse the deviation matching degree between the two components, and the higher the degree of mismatch. The spatial direction of the deviation correction reference vector, that is, the sign and relative magnitude of its components on the X, Y, and Z axes of the global assembly coordinate system, clarifies the relative bias relationship of the deviations of the two components in three-dimensional space. By analyzing the distribution of the components, it is possible to further accurately determine whether the deviation mismatch phenomenon is more significant along the X-axis, Y-axis, or Z-axis, and the specific bias direction.

[0098] Step 502: Pre-adapt and adjust the spatial geometric contour of the corresponding prefabricated component in the BIM design model according to the spatial geometric contour correction amount to achieve intelligent matching of dimensional deviations before assembly. The pre-adapt and adjustment includes: obtaining the spatial geometric contour correction amount, which includes the spatial angle value corresponding to the spatial angle domain interval with the largest deviation contribution, the vector difference between the first deviation vector and the second deviation vector corresponding to the spatial angle domain interval, and the component values ​​of the vector difference along each coordinate axis in the global assembly coordinate system; using the spatial angle value in the spatial geometric contour correction amount as a positioning parameter, positioning the component in the BIM design model to the first or second prefabricated component corresponding to the spatial angle value. The outline region is defined as the region to be corrected. Based on the component values ​​of the vector difference along each coordinate axis in the global assembly coordinate system, the spatial geometric outline of the region to be corrected is offset and adjusted in the BIM design model. The direction of the offset adjustment is opposite to the direction of the vector difference, and the magnitude of the offset adjustment is equal to the magnitude of the vector difference. After the offset adjustment is completed, the updated spatial coordinate values ​​of the identifier nodes corresponding to the adjusted region to be corrected on the first or second prefabricated component are extracted again in the BIM design model. The updated spatial coordinate values ​​are stored in the component attribute database of the BIM design model as the reference spatial coordinates of the corresponding prefabricated component in subsequent assembly matching calculations. Specifically, this includes:

[0099] Extract all parameters of the spatial geometric contour correction, including the spatial angle value θ corresponding to the spatial angle domain interval with the largest deviation contribution. max The vector difference between the first and second deviation vectors within this interval, and the components of this vector difference along the X, Y, and Z axes in the global assembly coordinate system. (In terms of spatial angle value θ)max As a spatial positioning parameter, the contour area corresponding to the spatial angle value on the surface of the first or second precast component is located in the BIM design model through coordinate mapping relationships, and this area is marked as the area to be corrected. Offset adjustment is performed according to the coordinate axis components of the vector difference, where the offset direction is opposite to the spatial direction of the vector difference; the offset magnitude is equal to the magnitude of the vector difference. After completing the geometric contour offset adjustment of the area to be corrected, the updated spatial coordinates of the corresponding identifier nodes in the BIM design model are re-extracted, and the updated spatial coordinates are written into the component attribute database of the BIM design model. This component attribute database is automatically created and initialized by the BIM design platform at the initial stage of component modeling, and is used to uniformly store the geometric parameters, spatial coordinates, node identifiers, and assembly constraint information of the first and second precast components. It is continuously updated and maintained with model iterations. After the updated coordinate data is written and replaces the original coordinate data, this set of coordinates serves as the reference spatial coordinates for the first or second precast component in subsequent assembly alignment, dimensional deviation calculation, and coupled deviation analysis processes, ultimately achieving intelligent pre-matching of dimensional deviations before assembly.

[0100] This embodiment enables automatic determination of the conformity of prefabricated component assembly deviations by quantitatively comparing the coupling deviation metric value with the tolerance threshold, thereby improving the efficiency of BIM model assembly verification. Based on the peak positioning deviation contribution range of the deviation field difference function, it can lock the key areas where deviations exceed limits, avoiding indiscriminate overall correction and improving the targeting of corrections. By using the vector difference reverse offset method to pre-adapt and adjust the component contour, the coupling deviation between the two components can be offset from the source, ensuring assembly alignment accuracy. Storing the updated coordinates in the BIM component attribute database enables the standardized storage and reuse of correction data, providing a unified benchmark for subsequent assembly construction, accuracy inspection, and model iteration, achieving intelligent matching of dimensional deviations before assembly, and reducing the accumulation of on-site assembly errors and construction adjustment costs.

[0101] To verify the technical effectiveness of the intelligent matching method for dimensional deviations of precast bridge components based on BIM technology, the following comparative examples were set up for systematic comparative experiments with the embodiments of the present invention, so as to quantitatively evaluate the improvement effect of the present invention in terms of deviation detection coverage, assembly interference prediction rate, coupling deviation measurement accuracy, and BIM model pre-adaptation adjustment success rate.

[0102] Comparative Example 1 (Traditional Single-Point End Inspection Method): This method employs the common single-point measurement method using a total station, selected only 1 to 2 key measurement points on the end face of the precast component. The measured coordinates are compared with the design values, and the center offset and normal angle deviation of the end face are used as the basis for assembly judgment. This method does not involve the detection of the lateral contour of the middle section of the component, nor does it perform spatial coupling quantitative analysis of assembly deviations.

[0103] Comparative Example 2 (Existing BIM-based Local Inspection Method for End Faces): With the assistance of a BIM model, a local 3D model is established for the end face area of ​​the precast component, and a limited number of measuring points on the end face boundary are extracted for deviation comparison. The root mean square (RMS) value of the end face contour deviation is used as the assembly qualification criterion. Although this method introduces BIM modeling technology, it still limits the inspection area to the end face and does not construct a spatial envelope or a global deviation vector set, thus failing to quantify the impact of mid-section lateral contour deviation on assembly coupling.

[0104] In the BIM design model, three marker nodes are indexed: the top centroid, the bottom centroid, and the extreme value of the middle lateral contour. The assembly base point and the spatial positioning origin are solved, a spherical spatial envelope is constructed, 12 boundary feature nodes on the overlapping domain spatial circle are extracted, the two-way deviation vector set is calculated, the deviation field function is established, and the coupled deviation metric value is solved by integral weighting. Finally, the geometric contour of the over-limit component is pre-adapted and adjusted in the BIM model.

[0105] Comparative Example 1: Traditional single-point end detection method:

[0106] A total station was used to perform three-dimensional coordinate measurements on the center points of the end faces of both the precast piers and precast cap beams. The deviation values ​​of the three-dimensional coordinates of the center points in the bridge's global coordinate system were calculated, and whether the deviation exceeded the specified allowable deviation range of ±5mm was used as the criterion for judging the assembly qualification. If the deviation exceeded the limit, temporary on-site adjustments were made (using jacks for fine-tuning or shim compensation for position correction). After the adjustments were completed, measurements were repeated until the deviation was within acceptable limits before hoisting and assembly could proceed.

[0107] Traditional end-point inspection methods have the following three technical limitations: First, the inspection area is limited to the end of the component, and it completely lacks the ability to perceive the lateral contour deformation of the middle section of the precast component caused by differences in concrete shrinkage or slight collisions during storage and transportation. Second, single-point deviation measurement cannot reflect the overall deviation distribution characteristics of adjacent components in the spatial assembly coupling area. When there is a reverse contour deviation in the middle section of two components, the component that passes the end inspection may still produce obvious assembly interference or uneven gaps after assembly. Third, this method cannot predict nonlinear coupling deviations before on-site installation, resulting in many on-site adjustment procedures and low efficiency, which has an adverse impact on the construction period and structural stress performance.

[0108] Comparative Example 1: Existing BIM end-face local inspection method:

[0109] A local 3D model of the end face area of ​​the precast component is established using BIM software. Eight to twelve measurement points are evenly selected on the end face, and the measured coordinates of each point are obtained through 3D laser scanning. These coordinates are then compared with the BIM design coordinates to calculate the root mean square (RMS) value of the end face contour deviation. When the RMS value does not exceed 2.0 mm, the assembly accuracy of the end face is deemed acceptable. When the RMS value exceeds 2.0 mm, the BIM end face local trimming function is used to perform local geometric adjustments on the model. The adjustment range is limited to the end face contour area and does not involve the middle section lateral contour.

[0110] While existing BIM end-face local inspection methods incorporate 3D modeling technology, the inspection area remains limited to the end face, lacking a spatial envelope model and thus failing to quantify the deviation coupling characteristics of two adjacent components within the assembly overlap area. When the lateral contour of the component's midsection exhibits bulging, bending, or torsional deformation, end-face local inspection methods struggle to effectively perceive the impact of these deviations on the assembly state. This results in a relatively high proportion of on-site adjustments required in actual engineering projects (experimental data shows approximately 4.6 adjustments per 100 components). Compared to the method of this invention, the inspection coverage (74.1%) and interference prediction rate (71.3%) still have significant room for improvement.

[0111] The method of this invention overcomes the limitations of existing methods through the following technical innovations:

[0112] Three marker nodes were set at the top centroid, bottom centroid, and extreme value region of the middle lateral contour of the precast component to achieve full-domain positioning of key assembly features of the component, with a coverage rate of 96.2%, which is 43.9 percentage points higher than the traditional method. A spherical spatial envelope was constructed with the assembly base point as the centroid and 1 / 3 of the longest diagonal of the circumscribed cuboid of the component as the radius. The spatial circle of the overlapping domain was extracted by spatial topological overlap operation. A set of bidirectional deviation vectors was constructed on 12 equal-angle boundary feature nodes, achieving an assembly interference prediction rate of 93.8%. Piecewise cubic spline interpolation was used to fit the discrete deviation vector magnitude to a continuous deviation field function. The coupled deviation metric was calculated by integral weighting, and the positioning error was reduced to 0.8 mm, which is 83.0% lower than the traditional method. Based on the angular domain interval where the peak positioning deviation contribution of the deviation field difference function is the largest, the spatial geometric contour of the corresponding component in the BIM model was pre-adapted by reverse offset. The pre-adaptation adjustment success rate reached 97.3%, and the number of on-site adjustments was reduced to 1.5 times per 100 components, a reduction of 81.7%.

[0113] The above description represents the preferred embodiments of the present invention. It should be noted that those skilled in the art can make various improvements and modifications without departing from the principles of the present invention, and these improvements and modifications should also be considered within the scope of protection of the present invention.

Claims

1. A method for intelligent matching of dimensional deviations in prefabricated bridge components based on BIM technology, characterized in that, The method includes: Step 1: Obtain the BIM design model of each prefabricated component. In the BIM design model, three identification nodes are marked for each prefabricated component. The three identification nodes are respectively defined in the top centroid region, bottom centroid region and the normal projection extreme value region of the middle lateral contour surface of the corresponding prefabricated component. Step 2: Based on the assembly association topology of each prefabricated component and the three identification nodes on each prefabricated component, calculate the first assembly base point and the second assembly base point for two adjacent prefabricated components to be assembled, and determine the spatial positioning origin; the determination of the spatial positioning origin includes: When the assembly coupling surface of two adjacent prefabricated components to be assembled is a planar coupling configuration, the first assembly base point or the second assembly base point is determined as the spatial positioning origin; when the assembly coupling surface is a non-planar coupling configuration, the extreme value region of the normal projection of the middle section lateral contour surface of the prefabricated component where the first assembly base point is located is taken as the first positioning center, and 1 / 3 of the longest diagonal length of the circumscribed cuboid of the first prefabricated component in the BIM design model is used as the first calibration radius to construct a first closed loop, and the extreme value region of the normal projection of the middle section lateral contour surface of the prefabricated component where the second assembly base point is located is taken as the second positioning center, and 1 / 3 of the longest diagonal length of the circumscribed cuboid of the second prefabricated component in the BIM design model is used as the second calibration radius to construct a second closed loop; the geometric center point in the overlapping area of ​​the first closed loop and the second closed loop is determined as the spatial positioning origin. Step 3: Based on the spatial positioning origin, construct the first spatial envelope and the second spatial envelope respectively. Perform spatial topological overlap operation on the first spatial envelope and the second spatial envelope to obtain the spatial boundary curve of the overlap domain. Extract several discrete boundary feature nodes on the spatial boundary curve, and sequentially perform spatial vector mapping between the boundary feature nodes and the first assembly base point and the second assembly base point to obtain the first deviation vector set and the second deviation vector set. Step 4: Based on the first set of deviation vectors and the second set of deviation vectors, calculate the coupling deviation metric between the first assembly base point and the second assembly base point; Step 5: Compare the coupling deviation metric with the preset deviation tolerance threshold. If the coupling deviation metric exceeds the deviation tolerance threshold, adjust the spatial geometric contour of the prefabricated component in the BIM design model to achieve intelligent matching of dimensional deviations before assembly.

2. The intelligent matching method for dimensional deviations of prefabricated bridge components based on BIM technology according to claim 1, characterized in that, In two adjacent prefabricated components to be assembled, the first assembly base point and the second assembly base point are calculated respectively, including: The spatial coordinates of three marker nodes on the first prefabricated component among two adjacent prefabricated components to be assembled are obtained in the BIM design model. The spatial coordinates of the marker nodes defined by the extreme value region of the normal projection of the middle section lateral contour surface of the first prefabricated component are extracted. Combined with the spatial transformation matrix corresponding to the theoretical installation pose of the first prefabricated component, the spatial coordinates of the corresponding marker nodes are transformed to the global assembly coordinate system through the spatial transformation matrix, and the spatial coordinates of the first assembly base point are calculated. The spatial coordinates of three marker nodes on the second prefabricated component in the BIM design model are obtained from two adjacent prefabricated components to be assembled. The spatial coordinates of the marker nodes defined by the extreme value region of the normal projection of the middle section lateral contour surface of the second prefabricated component are extracted. Combined with the spatial transformation matrix corresponding to the theoretical installation pose of the second prefabricated component, the spatial coordinates of the corresponding marker nodes are transformed to the global assembly coordinate system through the spatial transformation matrix, and the spatial coordinates of the second assembly base point are calculated.

3. The intelligent matching method for dimensional deviations of precast bridge components based on BIM technology according to claim 2, characterized in that, Constructing the first spatial envelope and the second spatial envelope includes: Using the first assembly base point as the centroid of the first spatial envelope, and taking 1 / 3 of the longest diagonal length of the circumscribed cuboid of the first prefabricated component in the BIM design model as the envelope radius of the first spatial envelope, a spherical first spatial envelope is constructed. Using the second assembly base point as the centroid of the second spatial envelope, and taking 1 / 3 of the longest diagonal of the circumscribed cuboid of the second prefabricated component in the BIM design model as the envelope radius of the second spatial envelope, a spherical second spatial envelope is constructed.

4. The intelligent matching method for dimensional deviations of precast bridge components based on BIM technology according to claim 3, characterized in that, Perform a spatial topological overlap operation on the first spatial envelope and the second spatial envelope to obtain the spatial boundary curve of the overlapping region, including: The first spatial envelope and the second spatial envelope are spatially positioned in the same spatial coordinate system of the BIM design model to obtain the spatial distance value between the first assembly base point and the second assembly base point. The spatial distance value is compared with the envelope radius of the first spatial envelope and the envelope radius of the second spatial envelope. When the spatial distance value is less than the sum of the envelope radii of the first spatial envelope and the envelope radius of the second spatial envelope and greater than the absolute value of the difference between the envelope radii of the first spatial envelope and the envelope radius of the second spatial envelope, it is determined that the first spatial envelope and the second spatial envelope are in a spatial intersection state. Based on the spatial coordinates of the first assembly base point, the spatial coordinates of the second assembly base point, the envelope radius of the first spatial envelope, and the envelope radius of the second spatial envelope, the center coordinates and radius of the spatial circle formed by the intersection of the first and second spatial envelopes are calculated, and the spatial circle is determined as the spatial boundary curve of the overlapping domain.

5. The intelligent matching method for dimensional deviations of precast bridge components based on BIM technology according to claim 4, characterized in that, Extract several discrete boundary feature nodes on the spatial boundary curve, including: Based on the spatial circle, several discrete boundary feature nodes are extracted at equal central angle intervals. The spatial coordinates of each boundary feature node are calculated based on the center coordinates of the spatial circle, the radius of the spatial circle, and the corresponding central angle. Each boundary feature node is sequentially mapped to the first assembly base point using a spatial vector. The spatial vector pointing from the first assembly base point to the boundary feature node is calculated, and all calculated spatial vectors are aggregated into the first deviation vector set. The same boundary feature node is sequentially mapped to the second assembly base point using spatial vector mapping. The spatial vector pointing from the second assembly base point to the boundary feature node is calculated, and all the calculated spatial vectors are collected into a second deviation vector set.

6. The intelligent matching method for dimensional deviations of precast bridge components based on BIM technology according to claim 5, characterized in that, Based on the spatial circle, several discrete boundary feature nodes are extracted at equal central angle intervals. The spatial coordinates of each boundary feature node are calculated based on the center coordinates of the spatial circle, the radius of the spatial circle, and the corresponding central angle, including: The spatial coordinates of the center of the spatial circle in the global assembly coordinate system are used as the reference center coordinates, and any radial direction in the plane where the spatial circle is located is determined as the starting reference direction. Using the reference circle's center coordinates as the rotation center and the initial reference direction as the angle zero point, the circumference of the spatial circle is divided into twelve equal angle values ​​at 30-degree intervals according to the central angle interval. The angle values ​​of each equal angle are 30 degrees, 60 degrees, 90 degrees, up to 360 degrees. Using the reference circle center coordinates as the center and the spatial circle radius as the distance, the spatial direction vectors corresponding to each equally divided angle value are sequentially synthesized with the reference circle center coordinates to obtain the spatial coordinates of the twelve boundary feature nodes.

7. The intelligent matching method for dimensional deviations of precast bridge components based on BIM technology according to claim 6, characterized in that, Step 4 includes: Each first deviation vector in the first deviation vector set is paired with the second deviation vector in the second deviation vector set corresponding to the same boundary feature node, resulting in 12 deviation vector pairs; Using the spatial angles of each boundary feature node on the spatial circle as spatial coordinate parameters, the magnitudes of each deviation vector in the first and second deviation vector sets are interpolated and fitted along the spatial angle distribution of the spatial circle to establish the first and second deviation field functions that are continuously distributed along the spatial angle. By performing a difference operation on the first deviation field function and the second deviation field function, a deviation field difference function that is continuously distributed along the spatial angle of the spatial circle is obtained. The deviation field difference function is integrated over the circumferential domain of the spatial circle with spatial angle as the integration variable to obtain the integration result. The integration result is then weighted and fused with the weight coefficients corresponding to the spatial angles of each boundary feature node on the spatial circle to obtain the coupling deviation metric between the first assembly base point and the second assembly base point.

8. The intelligent matching method for dimensional deviations of precast bridge components based on BIM technology according to claim 7, characterized in that, Step 5 includes: When the coupling deviation metric is less than or equal to the preset deviation tolerance threshold, it is determined that the dimensional deviation between the two prefabricated components is within an acceptable range, and the spatial geometric contours of the two prefabricated components in the BIM design model remain unchanged. When the coupling deviation metric value is greater than the preset deviation tolerance threshold, it is determined that the size deviation of the two prefabricated components exceeds the acceptable range. Based on the peak position of the deviation field difference function along the spatial angle distribution of the spatial circle, the spatial angle domain interval with the largest deviation contribution is identified. Based on the vector difference between the first deviation vector and the second deviation vector corresponding to the corresponding spatial angle domain interval, the spatial geometric contour correction amount of the first prefabricated component or the second prefabricated component in the BIM design model is generated. The spatial geometric contours of the corresponding prefabricated components in the BIM design model are pre-adapted and adjusted according to the spatial geometric contour correction amount in order to achieve intelligent matching of dimensional deviations before assembly.

9. The intelligent matching method for dimensional deviations of precast bridge components based on BIM technology according to claim 8, characterized in that, The pre-adaptation adjustment includes: Obtain the spatial geometric contour correction amount, which includes the spatial angle value corresponding to the spatial angle domain interval with the largest deviation contribution, the vector difference between the first deviation vector and the second deviation vector corresponding to the spatial angle domain interval, and the component values ​​of the vector difference along each coordinate axis in the global assembly coordinate system. Using the spatial angle value in the spatial geometric contour correction amount as the positioning parameter, the contour area corresponding to the spatial angle value on the first prefabricated component or the second prefabricated component is located in the BIM design model, and the contour area is determined as the area to be corrected. Based on the component values ​​of the vector difference along each coordinate axis in the global assembly coordinate system, the spatial geometric contour of the area to be corrected is offset and adjusted in the BIM design model. The direction of the offset adjustment is opposite to the direction of the vector difference, and the magnitude of the offset adjustment is equal to the magnitude of the vector difference. After the offset adjustment is completed, the updated spatial coordinate values ​​of the identifier nodes corresponding to the adjusted areas to be corrected on the first or second precast component are extracted again in the BIM design model. The updated spatial coordinate values ​​are then stored in the component attribute database of the BIM design model as the reference spatial coordinates for the corresponding precast component in the subsequent assembly matching calculation.

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