Method for solving virtual pre-assembly deviation of steel structure based on point cloud constraint assembly chain

Abstract

The application discloses a steel structure virtual pre-assembly deviation solving method based on a point cloud constraint assembly chain, relates to the field of steel structure digitization technology, and comprises the following steps: a steel structure design model is acquired, and component theoretical assembly features are extracted; an assembly chain skeleton is established according to component connection relations and installation sequences; three-dimensional scanning is performed on solid steel components, and measured assembly features are extracted; the measured assembly features are matched with the theoretical assembly features, and body deviation results of each component are obtained; a point cloud constraint assembly chain is constructed, and rigid constraints and releasable constraints are divided; virtual pre-assembly is performed according to the installation sequences, node residual occupation amounts are recorded and transmitted; when mismatching occurs at the end of the assembly chain, residual occupation contributions of each connection node are traced back reversely, and deviation solving results are output. Through comprehensive identification of assembly deviations, assembly chain transmission analysis, leading deviation node and coupling deviation section determination, the accuracy of the virtual pre-assembly of the steel structure and the deviation source determination capability are improved.

Description

Technical Field

[0001] This invention relates to the field of steel structure digitization technology, specifically to a method for solving virtual pre-assembly deviations of steel structures based on point cloud-constrained assembly chains. Background Technology

[0002] Steel structures are widely used in industrial plants, large-span public buildings, bridge structures, and prefabricated buildings due to their advantages such as light weight, high strength, fast construction speed, and suitability for industrial manufacturing and prefabricated construction. Steel structure projects typically employ a combination of factory prefabrication and on-site installation. Various steel columns, beams, supports, node plates, and connecting plates are transported to the construction site after processing and then hoisted and connected according to a predetermined installation sequence. Because on-site installation of steel structures usually involves the continuous splicing of multiple components, multi-node coordination, and multi-directional positioning control, problems such as component processing errors, connection hole deviations, connection surface deformation, local warping, and installation posture deviations can easily accumulate during the actual assembly process, ultimately manifesting as assembly mismatches such as misaligned holes, incomplete connection surface closure, excessive edge misalignment, or abnormal installation posture.

[0003] To reduce on-site installation risks, minimize rework, and ensure installation accuracy, pre-assembly or pre-assembly is typically performed in existing projects before formal hoisting. Traditional pre-assembly methods mainly involve trial assembly of physical components in a factory or construction site to identify compatibility issues between components in advance. While this method can identify problems such as connection mismatch, hole misalignment, and component interference to some extent, it generally suffers from drawbacks such as large site requirements, high labor input, high hoisting and turnaround costs, long organization cycles, and low implementation efficiency. The cost and implementation difficulty of physical pre-assembly are particularly prominent for large steel structures, irregular nodes, or complex assembly paths.

[0004] With the development of 3D laser scanning, point cloud modeling, and BIM technologies, digital comparative analysis using steel structure design models and measured point cloud models has gradually become an important technical means to replace or assist in physical pre-assembly. Existing digital analysis methods typically acquire point cloud data of physical steel components and register them with theoretical design models to identify deviations in component dimensions, hole positions, or connection surfaces. Some technologies can also simulate component assembly in a virtual environment to help determine whether components meet assembly requirements. However, most existing methods still focus on identifying geometric deviations of single components or only perform static matching judgments on local connection nodes, making it difficult to fully reflect the actual characteristics of steel structure on-site installation, such as the sequential installation of multiple components, the occupation of assembly margins by preceding nodes, the restricted assembly of subsequent nodes, and the step-by-step transmission of assembly deviations along connection relationships.

[0005] Specifically, during the continuous assembly of steel structures, the translation, rotation, or partial relocation of preceding components to meet local installation requirements consumes the adjustment space available for subsequent nodes. When multiple nodes have small deviations, a single node may not yet be out of tolerance. However, under the influence of the installation sequence, these deviations will gradually accumulate along the component connection relationship, and at the end of the assembly chain, they will manifest as holes not aligning, difficulty in closing connection surfaces, or insufficient remaining adjustment margin. Existing methods based on static model comparison or ordinary virtual assembly can usually only provide the deviation results for a single component or a single connection node. It is difficult to further determine whether the mismatch at the end is caused by the current node itself or by the deviation transmission and margin occupation of multiple upstream nodes. It is also difficult to effectively distinguish between the dominant deviation node and the coupled deviation section.

[0006] Furthermore, the constraint attributes of different nodes during steel structure assembly are not the same. Some constraints belong to the main control benchmark conditions during installation, such as key elevations, column base positioning, and main hole position benchmarks. These constraints cannot usually be released arbitrarily during assembly. Other constraints correspond to installation alignment allowances, local fitting allowances, or shim compensation space, and can be adjusted within a certain range. Existing technologies generally do not distinguish between rigid and releasable constraints at assembly nodes, nor do they chain-record and transmit the occupancy of available adjustment allowances at each node during assembly, resulting in shortcomings in deviation calculation and mismatch attribution. Summary of the Invention

[0007] Based on the shortcomings of the prior art described above, the purpose of this invention is to provide a method for solving the deviation of virtual pre-assembly of steel structures based on point cloud constraint assembly chain, so as to solve the above-mentioned technical problems.

[0008] To achieve the above objectives, the present invention provides the following technical solution: a method for solving virtual pre-assembly deviations of steel structures based on point cloud-constrained assembly chains, comprising: Obtain the steel structure design model and extract the theoretical assembly features of the components. Establish the assembly chain skeleton based on the component connection relationship and installation sequence. Three-dimensional scanning of solid steel components is performed to obtain the measured point cloud model of each component, and the measured assembly features corresponding to the main axis or baseline, end face, connection surface, hole group and boundary line of the component are extracted. The measured assembly features are registered with the corresponding theoretical assembly features to obtain the body deviation results of each component; The measured assembly features of each component are mapped to the assembly chain skeleton to construct a point cloud constrained assembly chain, and the constraints of the connecting nodes are divided into rigid constraints and releasable constraints. Virtual pre-assembly is performed according to the installation sequence of the point cloud constraint assembly chain. Under the premise of satisfying rigid constraints, the pose of the components to be assembled is adjusted based on the releasable constraints. The adaptive pose of each component to be assembled is solved, and the hole displacement, inter-surface gap, edge misalignment and attitude offset of the connection nodes are calculated. Record the node residual occupancy based on the adjustment results of each connected node within the releasable constraint range, and pass the node residual occupancy downstream along the point cloud constraint assembly chain. When the end of the assembly chain fails to close the hole, the connection surface fails to close, or the remaining adjustment margin corresponding to the release constraint is insufficient, the residual occupancy contribution of each connection node is traced back along the point cloud constraint assembly chain to determine the dominant deviation node or coupled deviation section. The solution results for the virtual pre-assembly deviation of the steel structure are output based on the body deviation results of each component, the residual occupancy of nodes, and the reverse backtracking results.

[0009] The present invention is further configured to obtain a steel structure design model, including: obtaining steel structure construction drawings, detailed drawings, component list and installation sequence information, and establishing a three-dimensional steel structure design model based on the steel structure construction drawings, detailed drawings and component list; Alternatively, a pre-built BIM model of the steel structure can be read as the steel structure design model.

[0010] The present invention is further configured to extract the theoretical assembly features of the components, including: extracting the theoretical installation posture, main axis or reference line, end face, connection surface, hole group center, hole axis, boundary line, installation reference point, installation reference edge and theoretical connection relationship between adjacent components from the steel structure design model, and extracting at least one of the flange surface, web surface and node plate surface.

[0011] The present invention is further configured to include: performing noise point removal, background point separation, point cloud segmentation, occlusion and missing area marking, point density equalization and coordinate unification processing on the original point cloud data obtained by 3D scanning, and binding the processed point cloud data with the component number of the corresponding physical steel component to form a measured point cloud model corresponding to the physical steel component.

[0012] The present invention is further configured to extract the measured assembly features corresponding to the main axis or baseline of the component, end face, connecting surface, hole group and boundary line, including: performing geometric fitting on the measured point cloud model to obtain at least one of the component main axis or baseline, end face fitting plane, connecting surface fitting plane, flange fitting plane, web fitting plane and node plate fitting plane; identifying the holes in the connecting area to obtain the hole center coordinates, hole axis direction, hole group centroid position and hole group distribution relationship; and performing edge analysis on the outer contour of the component to obtain the boundary line and local warped area.

[0013] The present invention is further configured to register the measured assembly features with the corresponding theoretical assembly features, including: coarse registration based on the main axis or reference line of the component, and fine registration based on the end face, connecting surface, hole group and boundary line; the body deviation results include the component's external dimension deviation, the main axis or reference line direction deviation, the cross section posture deviation, the end face tilt deviation, the overall offset deviation of the hole group, the local distortion deviation of the hole group and the local warping deviation.

[0014] The present invention is further configured to map the measured assembly features of each component to the assembly chain skeleton to construct a point cloud constrained assembly chain, including: using each physical steel component as an assembly node and the connection relationship between components as an assembly edge; wherein, each assembly node records at least the component number, theoretical pose, measured pose, body deviation result, measured assembly features and current adjustable degrees of freedom, and the assembly edges in the assembly chain are sorted according to the installation order, and each assembly edge records at least the connection type, theoretical connection interface and allowable deviation range.

[0015] The present invention is further configured such that the rigid constraints include the position constraints of the main control reference plane, the key elevation constraints, the main hole position reference constraints, the column base positioning constraints, and the direction constraints of the main axis or reference line; the releasable constraints include the installation alignment allowance, the local fitting allowance of the connection surface, the temporary positioning release space, the shim compensation space, and the local alignment allowance of the non-main control hole position.

[0016] The present invention is further configured to perform virtual pre-assembly according to the installation sequence of the point cloud constraint assembly chain, including: setting the upstream reference component of the assembly chain as the anchor component, and fixing the pose of the anchor component in the theoretical installation coordinate system; installing the subsequent components to be installed step by step according to the installation sequence, and adjusting the pose of the components to be installed within the range of translation and rotation allowed by the release constraints without destroying the rigid constraints, to obtain the adapted pose; calculating the hole displacement, average gap between surfaces, local maximum gap, edge misalignment, elevation difference, principal axis or reference line offset, and attitude offset at each connection node; recording the node residual occupancy based on the adjustment amount of each connection node within the range of the release constraints, and transmitting the node residual occupancy downstream along the point cloud constraint assembly chain in the plane direction, elevation direction, and attitude direction.

[0017] The present invention is further configured to backtrack the residual occupancy contribution of each connection node along the point cloud constraint assembly chain, including: when the end of the assembly chain cannot close the hole, the connection surface cannot be closed, or the remaining adjustment margin corresponding to the release constraint is insufficient, the end node is backtracked step by step to the upstream node, the solution is resolved, and the end response is observed; when the end mismatch decreases by more than a preset proportion after the backtracking of an upstream node, the upstream node is identified as the dominant deviation node; when the cumulative decrease of the end mismatch exceeds a preset cumulative proportion after the backtracking of multiple adjacent nodes, and the decrease of the end mismatch of each adjacent node exceeds the corresponding minimum contribution proportion, the corresponding section is identified as the coupling deviation section; the solution result of the deviation of the virtual pre-assembly of the steel structure includes a single component deviation list, a connection node deviation list, a dominant deviation node, a coupling deviation section, and an assembly feasibility judgment result, wherein the end mismatch is at least one of the hole displacement, inter-surface gap, edge misalignment, and attitude offset of the connection node at the end of the assembly chain, or a comprehensive mismatch characterization quantity composed of at least one of them.

[0018] This invention provides a method for solving deviations in virtual pre-assembly of steel structures based on point cloud-constrained assembly chains. The method involves acquiring a steel structure design model and extracting theoretical assembly features of components. An assembly chain skeleton is established based on component connection relationships and installation sequence. The solid steel components are 3D scanned to obtain measured point cloud models of each component. Measured assembly features corresponding to the component's main axis or baseline, end faces, connection surfaces, hole groups, and boundary lines are extracted. These measured assembly features are registered with their corresponding theoretical assembly features to obtain the body deviation results for each component. The measured assembly features of each component are mapped to the assembly chain skeleton to construct a point cloud-constrained assembly chain. Connection node constraints are divided into rigid constraints and releasable constraints. Virtual pre-assembly is performed according to the installation sequence of the point cloud-constrained assembly chain, prioritizing the fulfillment of rigid constraints. The method involves adjusting the pose of components to be assembled based on releasable constraints, solving for the adapted pose of each component, and calculating the hole displacement, inter-surface gap, edge misalignment, and attitude offset of the connecting nodes. Based on the adjustment results of each connecting node within the releasable constraint range, the node residual occupancy is recorded and propagated downstream along the point cloud constraint assembly chain. When the assembly chain ends and holes cannot be closed, connecting surfaces cannot be closed, or the remaining adjustment margin corresponding to the releasable constraints is insufficient, the residual occupancy contribution of each connecting node is traced back along the point cloud constraint assembly chain to determine the dominant deviation node or coupled deviation section. Based on the body deviation results of each component, the node residual occupancy, and the backtracking results, the solution results for the virtual pre-assembly deviation of the steel structure are output. The beneficial effects include: 1. More comprehensive and accurate assembly deviation identification: By extracting theoretical assembly features from the steel structure design model and registering them with the measured assembly features corresponding to the main axis or baseline, end face, connection surface, hole group and boundary line in the actual measured point cloud model of the solid steel component, it can comprehensively identify deviations in component shape dimensions, deviations in the direction of the main axis or baseline, deviations in the tilt of the end face, deviations in the overall offset of the hole group, deviations in the local distortion of the hole group and deviations in the local warping. This avoids the one-sided problem of deviation judgment caused by relying only on a single dimension or local hole position detection, thereby improving the completeness and accuracy of deviation identification before steel structure component assembly and providing a reliable foundation for subsequent virtual pre-assembly. 2. Quantifiable analysis of assembly chain transmission relationship: By constructing a point cloud constrained assembly chain and dividing the connection node constraints into rigid constraints and releasable constraints, the adjustment results of each connection node during the virtual pre-assembly process are recorded as the node residual occupancy amount. The node residual occupancy amount is then transmitted downstream along the assembly chain, which can reflect the impact of the adjustment of the preceding node on the remaining assembly allowance of the subsequent node. This reveals the process of deviations being transmitted, accumulated and amplified step by step along the connection relationship and installation sequence during the steel structure assembly process. This reduces the problem in the existing technology of only statically analyzing a single node and making it difficult to identify the source of chain coupling deviation, and improves the pertinence and credibility of assembly mismatch analysis. 3. Clearer attribution of end-of-assembly mismatches and more targeted assembly decisions: When the end of the assembly chain cannot align holes, the connection surface cannot be closed, or the remaining adjustment margin is insufficient, the residual occupancy contribution of each connection node can be traced back along the point cloud constraint assembly chain. This can identify the dominant deviation node or coupled deviation section and output a single component deviation list, a connection node deviation list, and assembly feasibility judgment results. This allows for the early identification of key issues affecting assembly closure before formal installation, reducing blind rework and repeated adjustments on site, and improving the guiding role of the virtual pre-assembly analysis results of steel structures in construction organization, deviation rectification, and installation implementation.

[0019] The above description is only an overview of the technical solution of this application. In order to better understand the technical means of this application and to implement it in accordance with the contents of the specification, and to make the above and other objects, features and advantages of this application more obvious and understandable, the following are specific embodiments of this application. Attached Figure Description

[0020] To more clearly illustrate the technical solutions in the embodiments of the present invention, the accompanying drawings used in the description of the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of the present invention. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort. In the drawings: Figure 1The flowchart illustrates a method for solving the deviation of virtual pre-assembly of steel structures based on point cloud constraint assembly chain, which is an exemplary embodiment of the present invention. Detailed Implementation

[0021] The embodiments of the present invention will be described below with reference to the accompanying drawings and preferred embodiments. Those skilled in the art can easily understand other advantages and effects of the present invention from the content disclosed in this specification. The present invention can also be implemented or applied through other different specific embodiments, and various details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of the present invention. It should be understood that the preferred embodiments are only for illustrating the present invention and not for limiting the scope of protection of the present invention.

[0022] It should be noted that the illustrations provided in the following embodiments are only schematic representations of the basic concept of the present invention. Therefore, the drawings only show the components related to the present invention and are not drawn according to the actual number, shape and size of the components in the actual implementation. In the actual implementation, the form, quantity and proportion of each component can be arbitrarily changed, and the layout of the components may also be more complex.

[0023] In the following description, numerous details are explored to provide a more thorough explanation of embodiments of the invention. However, it will be apparent to those skilled in the art that embodiments of the invention may be practiced without these specific details. In other embodiments, well-known structures and devices are shown in block diagram form rather than in detail to avoid obscuring embodiments of the invention.

[0024] A method for solving virtual pre-assembly deviations of steel structures based on point cloud-constrained assembly chains, such as... Figure 1 As shown, it includes: Obtain the steel structure design model and extract the theoretical assembly features of the components. Establish the assembly chain skeleton based on the component connection relationship and installation sequence. Three-dimensional scanning of solid steel components is performed to obtain the measured point cloud model of each component, and the measured assembly features corresponding to the main axis or baseline, end face, connection surface, hole group and boundary line of the component are extracted. The measured assembly features are registered with the corresponding theoretical assembly features to obtain the body deviation results of each component; The measured assembly features of each component are mapped to the assembly chain skeleton to construct a point cloud constrained assembly chain, and the constraints of the connecting nodes are divided into rigid constraints and releasable constraints. Virtual pre-assembly is performed according to the installation sequence of the point cloud constraint assembly chain. Under the premise of satisfying rigid constraints, the pose of the components to be assembled is adjusted based on the releasable constraints. The adaptive pose of each component to be assembled is solved, and the hole displacement, inter-surface gap, edge misalignment and attitude offset of the connection nodes are calculated. Record the node residual occupancy based on the adjustment results of each connected node within the releasable constraint range, and pass the node residual occupancy downstream along the point cloud constraint assembly chain. When the end of the assembly chain fails to close the hole, the connection surface fails to close, or the remaining adjustment margin corresponding to the release constraint is insufficient, the residual occupancy contribution of each connection node is traced back along the point cloud constraint assembly chain to determine the dominant deviation node or coupled deviation section. The solution results for the virtual pre-assembly deviation of the steel structure are output based on the body deviation results of each component, the residual occupancy of nodes, and the reverse backtracking results.

[0025] Specifically, acquiring a steel structure design model is not simply a matter of importing a 3D file; rather, it involves establishing a theoretical assembly reference space required for subsequent virtual pre-assembly analysis. Virtual pre-assembly of steel structures essentially involves comparing the measured state of physical components with their design state and further analyzing the transmission process of assembly deviations in connection relationships. Therefore, it is essential to first construct a unified model that accurately represents the theoretical geometric shape of the components, their theoretical assembly pose, theoretical connection relationships, and theoretical installation sequence. Only by establishing this unified model can subsequent point cloud feature attachment, registration, deviation calculation, and assembly chain analysis have a consistent reference basis.

[0026] There are two approaches to obtaining a steel structure design model. The first approach uses steel structure construction drawings, detailed drawings, component lists, and installation sequence information as input data to create a 3D steel structure design model. The second approach directly reads a pre-existing steel structure BIM model as the design model. This dual-path input method is compatible with different engineering scenarios. For projects with existing BIM models, the pre-defined component geometry and connection relationships can be directly utilized. For projects without a BIM model, a 3D design model is reconstructed from 2D drawings and component lists.

[0027] When using construction drawings, detailed drawings, and component lists to establish a three-dimensional design model of a steel structure, first read the section type, external dimensions, plate thickness parameters, hole position parameters, node connection methods, and component number information of steel columns, steel beams, supports, connecting plates, node plates, and other steel components. Then, based on the relative positional and installation relationships given in the detailed drawings, reconstruct the three-dimensional geometric entities of each component in a unified coordinate system.

[0028] When using a pre-established steel structure BIM model as the steel structure design model, the three-dimensional entity information, component family attributes, node relationship information, and installation stage information of each component in the BIM model are read, and the component number, component category, node location, and connection interface are standardized and organized.

[0029] After the steel structure design model is established or retrieved, theoretical assembly features are extracted from each component in the model. Theoretical assembly features refer to design-side feature information that can directly participate in subsequent assembly registration, node constraint expression, and deviation judgment. The theoretical installation posture, main axis or datum line, end face, connection surface, hole group center, hole axis, boundary line, installation datum point, installation datum edge, and theoretical connection relationship between adjacent components are extracted from the steel structure design model. Based on the component type, at least one of the flange surface, web surface, and node plate surface is further extracted.

[0030] The theoretical installation pose characterizes the spatial position and attitude of a component relative to the global coordinate system in its design state, serving as the starting reference for subsequently judging the degree of assembly deviation of the physical component. The principal axis or reference line characterizes the dominant direction or installation control direction of the component. For rod-shaped components such as steel columns, beams, and supports, the principal axis typically reflects the overall direction, while for plate-shaped components such as node plates and connecting plates, the reference line is more suitable for reflecting the installation reference. Therefore, using a dual-mode feature expression of principal axis or reference line is compatible with different component types. End faces, connecting faces, flange faces, web faces, and node plate faces are used to express surface features directly related to assembly fit, bolted connections, and attitude correction. Their function is to convert the geometric shape into a theoretical surface object that can be used for subsequent constraint calculations.

[0031] Extracting the center of the hole group, the hole axis, and the boundary lines has more direct significance for assembly judgment. The center of the hole group and the hole axis are used to represent the theoretical alignment relationship and theoretical insertion direction of the bolt connection area. In steel structure assembly, many mismatch problems ultimately manifest as misalignment of holes, difficulty in bolt insertion, or misalignment of connecting plates. Therefore, hole system features are one of the most important assembly-sensitive features. Boundary lines are used to represent the component outline, mating boundary, and installation control edge. Their function is to assist in judging edge misalignment, component interference, and local offset. Installation datum points and installation datum edges are used to characterize the positioning datums that play a controlling role in the design, so that when constructing rigid constraints and releasable constraints, it is clear which features must remain stable as the main control objects.

[0032] After extracting the theoretical assembly features of each component, an assembly chain skeleton is established based on the connection relationships and installation sequence between the components. This assembly chain skeleton is not a simple connection diagram, but a directed assembly relationship framework that can simultaneously express "who connects to whom," "who depends on whom for installation," and "the path along which deviations are propagated." Steel structure installation is not a process of simultaneous free assembly of all components, but rather a sequential process of installation and closure. The installation state of preceding components directly affects the assemblability of subsequent components. Therefore, simply knowing that there are connection relationships between components is insufficient; these relationships must also be incorporated into the installation sequence to provide the correct structural skeleton for the subsequent point cloud-constrained assembly chain construction.

[0033] The assembly chain skeleton is established as follows: each theoretical component is used as a skeleton node, and the theoretical connection relationship between adjacent components is used as a skeleton edge. The skeleton edges are then ordered according to the installation sequence information. Components that are installed first and play a role in overall positioning, such as the bottom steel column, the first main beam, or the main control node, are set as upstream nodes in the assembly chain. Components that are installed by attaching to preceding components are set as downstream nodes in the assembly chain according to the construction sequence. The resulting assembly chain skeleton is essentially a theoretical assembly topology with sequential dependencies, used to characterize the transmission path of component installation and the direction of residual transmission to subsequent nodes.

[0034] Furthermore, in the assembly chain skeleton, each skeleton node corresponds to a theoretical component unit, and each skeleton edge corresponds to a theoretical assembly interface unit. The theoretical component unit records at least the component number, theoretical installation pose, and theoretical assembly feature set; the theoretical assembly interface unit records at least the connection type, theoretical connection interface, and upstream and downstream dependencies. When the measured point cloud features are subsequently mapped to the assembly chain skeleton, the entity state is essentially attached to the theoretical assembly topology. Therefore, the skeleton stage needs to pre-define what information each node and edge carries. In this way, the design model is no longer just a static geometric model, but is transformed into a theoretical assembly data foundation for subsequent registration, constraint partitioning, residual recording, and reverse attribution.

[0035] Three-dimensional scanning of solid steel components begins with scanning the actual, completed steel columns, beams, supports, connecting plates, gusset plates, and other steel components awaiting assembly. Using 3D laser scanning equipment, structured light scanning equipment, or other scanning devices capable of acquiring the spatial coordinates of the component surface, the entire surface or assembly-sensitive areas of each solid steel component are scanned to obtain the corresponding raw point cloud data. During the scanning process, priority is given to ensuring the sampling integrity and density of the component's end connection areas, bolt hole areas, connection surface areas, flange-web transition areas, gusset plate areas, and outer contour edge areas. This ensures that the subsequently extracted measured assembly features can fully reflect the component's geometry, connection status, and spatial distribution of assembly-sensitive parts in its actual processing state. Through this scanning method, the actual spatial state of the solid steel component can be digitized into a raw point cloud set composed of a large number of discrete coordinate points.

[0036] When processing the raw point cloud data obtained from 3D scanning, noise point removal is performed first to remove discrete floating points and outliers caused by environmental reflections, equipment vibration, missampling of scan occlusion boundaries, and background interference, reducing the interference of invalid points on subsequent geometric fitting results. Then, background point separation is performed to remove point clouds corresponding to the ground, supports, hoisting fixtures, surrounding equipment, or other environmental objects that do not belong to the target steel component, retaining only the point cloud data of the target component area. After noise point removal and background point separation, the purity of the component's point cloud is significantly improved, making the point cloud data closer to the actual surface morphology of the solid steel component.

[0037] After initial purification, point cloud segmentation is performed on the raw point cloud data to separate the point clouds corresponding to different physical steel components from the overall scanning scene, or to divide the point clouds corresponding to different assembly functional areas within the same component into regions. For multi-component joint scanning scenarios, the raw point cloud can be divided into several independent component point cloud subsets based on the spatial interval between components, the position of component number labels, the outer contour boundary of the component, or manually preset partition information. For single-component scanning scenarios, functional regions can be further divided according to end connection areas, hole group areas, boundary areas, and main structure areas, so that differentiated geometric fitting and feature extraction strategies can be adopted for different regions in the future. Through point cloud segmentation, subsequent feature recognition is no longer based on the mixed overall point set, but is instead based on point cloud units with clear component affiliation and regional semantics.

[0038] After point cloud segmentation, occluded and missing regions in the point cloud are marked. Occluded and missing regions refer to areas where certain local areas are not fully covered by the point cloud due to factors such as limited scanning viewpoint, component stacking obstruction, large hole depth, or surface reflection. The purpose of explicitly marking these regions is to distinguish between "true geometric boundaries" and "sampling missing boundaries" during subsequent geometric fitting and assembly feature extraction, avoiding misjudging incomplete sampling as local component deformation or contour anomalies. For marked occluded and missing regions, subsequent processing can be aided by considering the geometric continuity of adjacent complete regions, corresponding features of the component design model, or multi-view rescan results, thereby improving the stability of measured assembly feature extraction.

[0039] After marking the occluded and missing areas, point cloud data undergoes point density equalization and coordinate unification processing. Point density equalization reduces point density differences caused by variations in scanning distance, scanning angle, or device sampling strategies, ensuring a relatively balanced point cloud distribution across the component. This prevents high-density areas from over-dominantly affecting the fitting calculations, or low-density areas from under-sampling and impacting the analytical accuracy of surface and hole features. Coordinate unification transforms point cloud data acquired from different scanning stations, times, or devices into a unified reference coordinate system. This allows for accurate stitching of point clouds from different perspectives of the same component, and enables comparison, mapping, and assembly analysis between point clouds of different components within a unified coordinate space. After these processing steps, a structurally complete, noise-controlled, and spatially consistent point cloud is obtained.

[0040] To ensure a one-to-one correspondence between the theoretical model, measured point cloud, and physical components in subsequent virtual pre-assembly analysis, the processed point cloud data is bound to the component number of the corresponding physical steel component. The component number can be derived from a unique number in the component list, a component QR code label, RFID tag, inkjet marking, or a pre-set identification label. After binding, each set of processed point cloud data corresponds to a unique physical steel component, forming a measured point cloud model corresponding to the physical steel component. This measured point cloud model not only preserves the geometric shape and connection area information of the component in its actual processing state but also possesses clear component identity attributes, facilitating the subsequent mapping of measured assembly features to the corresponding theoretical component nodes and assembly chain skeleton.

[0041] After forming the measured point cloud model, it is geometrically fitted to extract measured assembly features that can directly participate in assembly registration and deviation solving. Specifically, the measured point cloud model is first truncated according to the theoretical assembly features to form candidate point sets for end connection areas, connection surfaces, hole groups, and boundary areas. The candidate point set for end connection areas is obtained by truncating a preset thickness window on both sides of the theoretical end face along its normal direction. The candidate point set for connection surfaces is obtained by truncating a preset thickness window on both sides of the theoretical connection surface along its normal direction. The candidate point set for hole groups is obtained by expanding a preset boundary width outward from the center of the theoretical hole group according to the circumscribed rectangle of the hole group. The candidate point set for boundary areas is obtained by expanding a preset neighborhood width inward and outward from the theoretical boundary line according to the boundary normal direction.

[0042] For the candidate point sets of the end face and the connecting face, the initial plane screening is performed using a random sampling consensus method. Specifically, three points P1(x1,y1,z1), P2(x2,y2,z2), and P3(x3,y3,z3) are randomly selected from the candidate point set. The vectors u=P2-P1 and v=P3-P1 are calculated. The cross product n=u×v=(a,b,c) is taken as the normal vector of the candidate plane, and the candidate plane equation aX+bY+cZ+d=0 is obtained from d=-(ax1+by1+cz1).

[0043] For any point Pi(xi,yi,zi) in the candidate point set, calculate its distance to the candidate plane: di = |axi + byi + cji + d| / √(a² + b² + c²). Points satisfying di ≤ Td1 are designated as interior points of the candidate plane, where Td1 is the first distance threshold. Repeat the above random sampling process, selecting the candidate plane with the largest number of interior points as the initial plane. Then, perform least-squares plane fitting on all interior points of this initial plane. Specifically, construct a covariance matrix with the geometric center C of all interior points as the origin, and take the eigenvector corresponding to the smallest eigenvalue of the covariance matrix as the normal vector n* = (a*, b*, c*) of the fitting plane. Then, obtain the fitted plane equation a*X + b*Y + c*Z + d* = 0 using d* = -(a*xC + b*yC + c*zC).

[0044] Project all interior points onto the plane and obtain the two-dimensional convex hull or α-shaped boundary of the projected point set as the boundary parameters of the end face fitting plane or the connecting surface fitting plane.

[0045] For rod-shaped or long strip-shaped steel components, the main direction is first estimated from the main point cloud of the component. Specifically, the covariance matrix of the main point cloud is calculated, and the eigenvector corresponding to the largest eigenvalue is taken as the initial main direction e1 of the component. Then, the main point cloud is sliced ​​along the e1 direction at a preset slice spacing Δl to obtain m slice point sets. For the k-th slice point set, its cross-sectional center point Ck(xk,yk,zk) is calculated. All cross-sectional center points are combined into a center point sequence, and the least squares linear fitting is performed again on the center point sequence to obtain the main axis L(t) = C0 + t·v, where C0 is the reference point of the main axis and v is the direction vector of the main axis. For the baseline extraction of plate-shaped components, the edge point set corresponding to the long side or installation control side of the component is first identified in the candidate point set of the boundary area, and then the least squares linear fitting is performed on the edge point set to obtain the baseline Lb(t) = Cb + t·vb, where Cb is the reference point of the baseline and vb is the direction vector of the baseline. Use the direction vector v or vb as the direction parameter of the principal axis or baseline, and use the reference point C0 or Cb as the reference point of the line feature.

[0046] For hole feature extraction, the candidate point set of the hole group area is first projected onto the fitting plane of the corresponding connecting surface to establish a local two-dimensional coordinate system (u,v), resulting in a two-dimensional projected point set. The two-dimensional projected region is then discretized into a grid to construct an occupancy raster map. After performing a closing operation on the occupancy raster map to fill local gaps, the raster hole boundaries are extracted to obtain the closed hole boundary point set. For a single hole boundary point set, least squares circle fitting or ellipse fitting is performed. If the fitting residual is less than the second distance threshold Td2, the center of the fitted circle or ellipse is taken as the hole center coordinates. For the hole axis direction, when the hole wall point cloud is complete, the hole wall point set is extracted and cylindrical surface fitting is performed, with the direction of the central axis of the cylinder taken as the hole axis direction; when the hole wall point cloud is incomplete, the normal vector of the fitting plane of the corresponding connecting surface is taken as the approximate direction of the hole axis. For the hole group region, after determining the center of each individual hole, let Cg=(1 / n)ΣCi be the centroid position of the hole group, where Ci is the coordinate of the i-th hole center and n is the number of holes; then, form the hole distance matrix D=[dij] using the Euclidean distance between any two hole centers, and form the direction set V={vij} using the directions of the lines connecting the hole centers, which together represent the hole group distribution relationship. Thus, the hole center coordinates, hole axis directions, the centroid position of the hole group, and the hole group distribution relationship are obtained.

[0047] For component boundary line extraction, a k-neighborhood is first constructed for each point in the candidate point set of the boundary region. The local normal vector ni and local curvature κi = λ3 / (λ1+λ2+λ3) are obtained using the covariance matrix of the neighboring points, where λ1≥λ2≥λ3 are the eigenvalues ​​of the covariance matrix. For the current point Pi, if the maximum angle between its normal vector and the normal vector of its neighboring points satisfies maxarccos(ni·nj)>Tn1 or its local curvature satisfies κi>Tc1, then the point is recorded as an edge candidate point, where Tn1 is the first normal threshold and Tc1 is the first curvature threshold. All edge candidate points are clustered into connected components according to their spatial adjacency. The points in each connected component are sorted in order of arc length, and polyline transformation or spline curve fitting is performed to obtain the component boundary line.

[0048] For the identification of locally warped regions, the theoretical connecting surface or the plane fitted to the connecting surface is used as the reference surface. For each point Pi in the connecting region and the boundary region, the signed distance si to the reference surface is calculated as si = (a*xi + b*yi + c*zi + d*) / √(a*² + b*² + c*²).

[0049] Points satisfying |si|>Td3 are selected as warping candidate points, where Td3 is the third distance threshold. All warping candidate points are divided into connected components according to spatial adjacency, resulting in several continuous regions Qq. For each continuous region, the number of points Nq is counted, and the region is projected onto the reference plane to calculate the projected area Sq. When a continuous region simultaneously satisfies Nq>Tq1 and Sq>Ts1, the continuous region is determined to be a locally warped region, where Tq1 is the first quantity threshold and Ts1 is the first area threshold. The maximum |si| within this region is taken as the local warping amount.

[0050] Specifically, the first distance threshold Td1 is taken as 1.0 to 1.5 times the larger of the root mean square error of the scanned point cloud and the allowable deviation of the corresponding design plane; the second distance threshold Td2 is taken as the larger of the allowable deviation of the hole diameter processing and the projection error of the scanned plane; and the third distance threshold Td3 is taken as the upper limit of the allowable fitting deviation of the connection interface. The first normal threshold Tn1 is preset based on the theoretical included angle between adjacent surfaces and the upper limit of the scanning normal disturbance; the first curvature threshold Tc1 is preset based on the statistical value of the curvature distribution of the edge and non-edge regions of the component; the first quantity threshold Tq1 is calculated based on the point cloud sampling density and the minimum identifiable warped area size; and the first area threshold Ts1 is preset based on the minimum effective fitting area requirement of the connection interface. All of the above thresholds are derived from the point cloud sampling accuracy, component type, and design allowable deviation range, thereby ensuring that the fitting of the end face and connection surface, hole boundary identification, and local warping determination all have repeatable judgment criteria.

[0051] The present invention is further configured to register the measured assembly features with the corresponding theoretical assembly features, including: coarse registration based on the main axis or reference line of the component, and fine registration based on the end face, connecting surface, hole group and boundary line; the body deviation results include the component's external dimension deviation, the main axis or reference line direction deviation, the cross section posture deviation, the end face tilt deviation, the overall offset deviation of the hole group, the local distortion deviation of the hole group and the local warping deviation.

[0052] The purpose of registering the measured assembly features with their corresponding theoretical assembly features is to map the spatial geometric information of the actual steel component in its actual processing state to the theoretical assembly reference system in its design state, thereby providing a unified comparison benchmark between the measured and theoretical components. During the processing, transportation, stacking, and scanning of steel structure components, the measured point cloud model is usually located in an independent coordinate system or a local scanning coordinate system, while the theoretical assembly features are located in the theoretical installation coordinate system corresponding to the design model. These two systems typically have initial differences in position, orientation, and attitude, making direct deviation calculation impossible. Through registration, the effects of overall translation and rotation caused by coordinate system inconsistencies can be eliminated first, while retaining the true differences caused by actual processing errors, local deformations, and connection feature offsets. This ensures that the subsequently obtained deviation results accurately reflect the degree of deviation between the component body and its design state.

[0053] During registration, coarse registration is first performed based on the main axis or baseline of the component. For rod-shaped components with significant length direction, such as beams, columns, and supports, the main axis is preferentially used as the directional reference for coarse registration; for plate-shaped components such as connecting plates, node plates, and stiffening plates, the baseline is used as the directional reference for coarse registration. In the coarse registration process, the main axis or baseline in the measured assembly feature is first aligned with the corresponding main axis or baseline in the theoretical assembly feature to ensure that the overall orientation of the measured component is consistent with the design orientation of the theoretical component. Then, based on the reference points, end reference points, or center of gravity position of the component on the main axis or baseline, an overall translation adjustment is performed to bring the measured component close to the initial position of the theoretical component in a unified reference coordinate system. Through this step, the initial unification of the overall orientation and position of the component can be achieved, reducing the search range and computational complexity of subsequent fine registration of local features.

[0054] The underlying logic of using a principal axis or baseline for coarse registration is that the dominant directional features of steel structural members are usually the most stable and best represent the overall posture of the member. If local end faces, hole groups, or boundary lines are used for matching without achieving overall directional unification, the matching results are easily disturbed due to the large number of local features, the existence of local deformation, or residual noise at the hole edges. First, using the principal axis or baseline to achieve overall alignment is equivalent to eliminating large-scale spatial differences at the member level, ensuring that the theoretical member and the measured member are in the same approximate assembly direction. Then, fine correction is performed using assembly-sensitive features, making the registration process more stable and more in line with the actual logic of step-by-step correction of steel structural members from the whole to the parts.

[0055] After coarse registration, fine registration is performed based on end faces, connecting surfaces, hole groups, and boundary lines. During fine registration, firstly, the correspondence between the end face fitting plane and the theoretical end face is used to correct the positional deviation and end posture deviation of the component ends in the normal direction, making the relative spatial relationship between the component ends and the theoretical ends more consistent. Then, the correspondence between the connecting surface fitting plane and the theoretical connecting surface is used to further correct the contact direction and connection posture of the actual connection interface, ensuring that the interface state related to the subsequent assembly of adjacent components can be accurately represented. Next, the hole group center, hole axis, and hole group distribution relationship are used to locally refine and align the bolt connection area, maximizing the geometric correspondence between the theoretical hole system and the measured hole system at the connection function level. Finally, the relative relationship between the boundary line and the theoretical boundary is used to correct the local contour direction and edge control position of the component, suppressing the accumulation of registration residuals caused by local contour offsets. Through the above multi-feature hierarchical constraints, the registration results are not only reasonable in the overall direction but also have higher consistency in the actual assembly-sensitive areas.

[0056] The underlying logic of using end faces, connection surfaces, hole groups, and boundary lines for precise registration lies in the fact that these features directly correspond to the most critical functional parts of steel structure components during assembly. End faces determine the butt joint state of the components, connection surfaces determine the interface fit quality, hole groups determine bolt insertion and node closure capabilities, and boundary lines affect misalignment, interference, and local contour offsets. Therefore, precise registration does not pursue absolute overlap of the entire component surface, but prioritizes ensuring accurate mapping between the design and measured states of functional features directly related to assembly closure. This registration strategy, centered on assembly-sensitive features, avoids the problem of local connection mismatches being masked by overall shape fitting, making subsequent deviation calculation results closer to actual assembly conditions.

[0057] After registering the measured assembly features with the theoretical assembly features, the body deviation results for each component are further calculated. The body deviation results refer to the true geometric deviations retained by the measured component relative to the theoretical component after eliminating overall coordinate differences and overall installation direction differences. These deviation results do not directly reflect the transmission deviations caused by the mutual influence of preceding and following nodes in the assembly chain, but are specifically used to characterize the deviation of a single component's own processing, forming, and local deformation state from its design state, providing component-level basic deviation information for subsequent assembly chain analysis. Body deviation results include component dimensional deviations, main axis or baseline direction deviations, cross-sectional orientation deviations, end face tilt deviations, overall hole group offset deviations, local hole group distortion deviations, and local warping deviations. The deviations in the external dimensions of components are obtained by comparing the key external dimensions of the measured components with the corresponding design dimensions of the theoretical components; the deviations in the direction of the main axis or baseline are obtained by comparing the directional angle, projection offset, or spatial deviation between the measured main axis or baseline and the theoretical main axis or baseline; the deviations in the attitude of the cross sections are obtained by comparing the rotation angle, plane normal relationship, or local cross-sectional direction relationship of the measured component cross sections relative to the theoretical cross sections; the deviations in the tilt of the end face are obtained by comparing the normal angle between the fitted plane of the measured end face and the theoretical end face, the end normal offset, or the edge height difference; the overall offset deviation of the hole group is obtained by comparing the overall deviation between the centroid position of the measured hole group and the centroid position of the theoretical hole group; the deviations in the local distortion of the hole group are obtained by comparing the measured hole spacing, hole group arrangement direction, hole axis consistency, and relative geometric relationship between holes with the corresponding relationship of the theoretical hole group; the deviations in the local warping deviation are obtained by comparing the degree of deviation of the local area of ​​the measured component surface relative to the theoretical plane, theoretical boundary surface, or theoretical connection surface.

[0058] Dimensional deviations of structural members are obtained by comparing the measured key dimensions of the member with the corresponding theoretical design dimensions. For rod-shaped members, the length, cross-sectional width, thickness, and boundary range can be compared; for plate-shaped members, parameters such as outer contour length, width, and thickness projection boundary range can be compared. This deviation characterizes the manufacturing error of the member in terms of overall dimensions and is an important basis for judging whether the member is over-lengthened, under-lengthened, or has local expansion or contraction. Dimensional deviations of steel structure members directly affect the space occupied by nodes, the overlap range between members, and the assembly clearance conditions, and are one of the most basic types of structural deviations.

[0059] The deviation of the main axis or baseline direction is obtained by comparing the directional angle, projection offset, or spatial deviation between the measured main axis or baseline and the theoretical main axis or baseline. This deviation is used to reflect whether the overall direction of the component has been skewed, twisted, or axially offset. For members such as beams and columns, this deviation can reveal whether the component has been bent, laterally tilted, or twisted due to processing or hoisting. For plates, it can reflect whether its reference edge has drifted overall. Once the overall direction of the component deviates from the theoretical reference, it will be amplified in the subsequent assembly process as misalignment of node interfaces, misalignment of hole systems, or abnormal installation posture. Therefore, this deviation is a critical directional deviation that must be identified before assembly.

[0060] Cross-sectional attitude deviation is obtained by comparing the angular relationship, planar normal relationship, or local cross-sectional direction relationship of the measured component cross-section relative to the theoretical cross-section. It is used to reflect whether the component cross-section has rotated, flipped, or twisted. For components with clear cross-sectional direction characteristics, such as H-beams and box columns, this deviation can reveal the attitude differences between the flange direction, web direction, and the design state. For plate-shaped components, it can characterize the attitude deviation of its surface normal direction relative to the theoretical direction. Incorrect cross-sectional attitude will directly change the spatial orientation of the connection surface and the interface matching method of adjacent components, thus affecting the inter-surface fit and hole position correspondence. Therefore, cross-sectional attitude deviation is another important type of component body deviation besides the overall direction deviation.

[0061] End face tilt deviation is obtained by comparing the normal angle between the measured end face fitting plane and the theoretical end face, the end normal offset, or the edge height difference. It is used to characterize whether there is end face distortion caused by cutting tilt, uneven processing, or local warping at the end of the component. End face tilt deviation directly affects the fitting effect when the end of the component is mated with adjacent components, and may manifest as increased gaps between surfaces, uneven contact, or local stress concentration after assembly. Steel structure connections often use the ends as the main installation interface, and the end face condition is an important geometric condition affecting the assembly closure quality. Therefore, extracting end face tilt as a separate type of body deviation helps to accurately reveal the potential sources of mismatch at the assembly interface.

[0062] The overall offset deviation of the hole group is obtained by comparing the overall deviation between the measured centroid position of the hole group and the theoretical centroid position. It is used to characterize the translational offset of the hole group as an integral connecting unit relative to the design position. This deviation usually reflects problems such as drilling positioning errors, node plate machining offsets, or overall installation reference deviations of the connecting plate. The local distortion deviation of the hole group is obtained by comparing the measured hole spacing, hole group arrangement direction, hole axis consistency, and relative geometric relationship between holes with the correspondence of the theoretical hole group. It is used to characterize local deformation within the hole group, local hole position anomalies, or geometric distortion of the multi-hole connection area. The underlying logic of the two is different: the overall offset of the hole group emphasizes "overall relocation," while the local distortion of the hole group emphasizes "instability of internal relationships." Distinguishing between these two types of deviations is helpful for subsequent determination of whether the connection mismatch originates from the overall positioning deviation of the hole group or from local hole position machining anomalies.

[0063] Local warpage deviation is obtained by comparing the degree of deviation of a local area on the surface of a measured component from the theoretical plane, theoretical boundary surface, or theoretical connection surface. It is used to characterize whether there are non-ideal flat conditions on the component surface, such as local bulges, depressions, thermal deformation, or post-weld deformation. Local warpage deviation can occur in assembly-sensitive areas such as ends, near connection surfaces, flange edges, and gusset plate areas, and may manifest as uneven fit, excessive local gaps, or abnormal stress on nodes in subsequent assembly. Not all errors in steel structure components manifest as changes in overall size and direction; many actual assembly problems originate from non-uniform deformation in local areas. Therefore, extracting local warpage as an independent deviation type can improve the fineness and accuracy of subsequent node mismatch analysis.

[0064] After registering the measured assembly features of each component with the theoretical assembly features and obtaining the corresponding component's body deviation results, the measured assembly features of each component are mapped to the aforementioned assembly chain skeleton to construct a point cloud-constrained assembly chain. When constructing the point cloud-constrained assembly chain, each solid steel component is used as an assembly node, and the connection relationships between components are used as assembly edges. Assembly nodes are used to represent the structural identity, geometric state, and adjustability of a single component, while assembly edges are used to represent the connection methods, connection interfaces, and assembly constraint relationships between adjacent components. This node-edge chain organization allows for the separate expression of the "component body" and the "relationships between components" in the steel structure system: nodes describe "what this component is, its current state, and whether it can be adjusted," while edges describe "how this component connects to the preceding and following components, the assembly order, and the allowable assembly deviation." In this way, the steel structure assembly process is transformed from a static geometric model into a dynamic assembly relationship model, facilitating the expression of the transmission of deviations along the connection paths.

[0065] Each assembly node records at least the component number, theoretical pose, measured pose, body deviation results, measured assembly features, and currently adjustable degrees of freedom. The component number ensures a one-to-one correspondence between the assembly node and the design model, fabrication list, and on-site entity; the theoretical pose represents the target position and orientation of the component in the designed assembly state; the measured pose represents the actual spatial state of the component after point cloud registration; the body deviation results record information such as dimensional deviations, orientation deviations, hole group deviations, and local warping deviations relative to the design state; the measured assembly features preserve key feature objects such as the main axis or baseline, end faces, connecting surfaces, hole groups, and boundary lines of the component in the actual fabrication state; and the currently adjustable degrees of freedom characterize the translational and rotational directions in which the component can participate in pose correction during subsequent virtual pre-assembly. The above node information ensures that each assembly node is not merely an abstract component identifier, but an assembly unit simultaneously possessing theoretical targets, actual states, deviation bases, and adjustable attributes.

[0066] In the assembly chain, each assembly edge is ordered according to the installation sequence. Each assembly edge records at least the connection type, theoretical connection interface, and allowable deviation range. The connection type distinguishes between beam-column connections, beam-beam connections, column-column connections, bracing connections, plate connections, and other node interface forms, facilitating the selection of the corresponding constraint expression method later. The theoretical connection interface represents the functional area where adjacent components should contact, fit, align, or interlock under design conditions, including end-face connection interfaces, plate-face connection interfaces, hole group connection interfaces, and edge butt joint interfaces. The allowable deviation range indicates the permissible range of hole misalignment, inter-face gap, edge misalignment, or directional deviation during assembly. The reason for ordering the assembly edges according to the installation sequence is that in steel structure assembly, not all nodes act simultaneously; rather, preceding edges close first, and subsequent edges are constrained step by step. Therefore, the order of the assembly edges on the chain directly determines the transmission direction of residual occupancy in subsequent nodes and the cumulative path of end-point mismatch.

[0067] When mapping the measured assembly features of each component to the assembly chain skeleton, the measured component nodes are first matched with the corresponding skeleton nodes in the theoretical assembly chain based on the component number. Then, the theoretical pose, measured pose, body deviation results, and measured assembly features of the component are written into the matched assembly nodes. Next, based on the theoretical connection relationships between adjacent components in the design model, their corresponding connection types, theoretical connection interfaces, and allowable deviation ranges are written into the corresponding assembly edges. Through this mapping process, the original assembly chain skeleton, which only had theoretical connection relationships, is instantiated into a point cloud constrained assembly chain with solid geometric states and connection constraint states. In other words, each node and each edge in the chain no longer remains at the theoretical description level but possesses point cloud features and deviation information corresponding to the actual processing state of the solid steel component, thus enabling subsequent assembly solutions to be directly oriented towards the real component state.

[0068] After the point cloud-constrained assembly chain is constructed, the constraints of the connection nodes are further divided into rigid constraints and releasable constraints. This division aims to reflect the actual control logic during steel structure assembly, meaning that not all assembly conditions have the same adjustability: some conditions are mandatory control conditions that cannot be arbitrarily released during virtual pre-assembly; others are non-mandatory control conditions that can be yielded, adjusted, or compensated within a certain range. Without distinguishing between these two types of constraints, subsequent pose adjustments will lack boundaries, easily leading to situations where key positioning conditions are sacrificed for local interface closure, resulting in solutions that do not match actual construction constraints. Therefore, by dividing the connection node constraints into rigid and releasable constraints, clear adjustment boundaries can be established for subsequent component adaptation pose solutions.

[0069] Rigid constraints include primary control datum plane position constraints, critical elevation constraints, primary hole position datum constraints, column base positioning constraints, and primary axis or datum line direction constraints. Primary control datum plane position constraints restrict critical components or critical connection interfaces from being kept near their designed spatial positions, preventing excessive displacement during virtual assembly from disrupting the overall assembly datum. Critical elevation constraints ensure that beam top elevations, node elevations, or other important elevation control conditions remain stable within allowable error ranges, preventing overall structural elevation loss of control due to localized adjustments. Primary hole position datum constraints limit the holes responsible for positioning main bolts to prioritize design alignment, preventing the accuracy of primary positioning holes from being sacrificed during localized hole matching. Column base positioning constraints ensure that the support and installation starting points of foundation-related components are not disrupted by subsequent assembly adjustments. Primary axis or datum line direction constraints control the overall orientation of components to prevent deviation from the designed assembly direction, avoiding subsequent multi-node chain misalignment caused by directional drift. The common characteristic of these rigid constraints is that they correspond to primary control conditions that should not be skewed or only allow minimal skew during assembly, forming the basis for the stability and traceability of the entire assembly chain.

[0070] Releasable constraints include installation alignment allowance, local fit allowance of connection surfaces, temporary positioning release space, shim compensation space, and local alignment allowance of non-master control holes. Installation alignment allowance represents the small range of translational or rotational adjustments allowed before formal locking of components to accommodate machining and on-site assembly errors. Local fit allowance of connection surfaces represents the allowable small gaps and local fit deviations in the connection area without disrupting the master control interface conditions. Temporary positioning release space represents the constraints originally provided by temporary tooling or positioning measures during virtual pre-assembly, which can be appropriately released in the analysis to observe their impact on subsequent node assembly conditions. Shim compensation space represents the adjustable range between components that can be compensated for by shims, backing plates, or small-range shimming. Local alignment allowance of non-master control holes represents the acceptable small offsets of auxiliary holes other than the master control holes within a certain range. The common feature of these releasable constraints is that they do not directly disrupt the overall assembly master datum but provide assembly adjustment capabilities within a certain range, serving as an important buffer to absorb component body deviations and local mismatches.

[0071] The distinction between rigid and releasable constraints essentially introduces a two-tiered control structure of "non-yielding conditions" and "acceptable conditions" into the assembly chain. The goal of virtual pre-assembly of steel structures is not simply to achieve the minimum residual at all interfaces mathematically, but rather to absorb local errors by rationally utilizing adjustable space while maintaining key installation datums as much as possible, thereby obtaining an assembly result that better reflects actual construction conditions. By setting rigid constraints, the solution results are guaranteed not to deviate from the design control conditions; by setting releasable constraints, the solution process can accommodate body deviations and local assembly errors. Together, these two mechanisms enhance the engineering realism of subsequent pose adjustments, residual recording, and mismatch attribution.

[0072] Based on the aforementioned constraint partitioning, the point cloud constraint assembly chain is not only a chain-like data structure recording the state of components, but also an assembly analysis model capable of supporting constraint-driven solutions. The theoretical pose, measured pose, and ontological deviation results in the assembly nodes provide the foundation for subsequent judgment of single-component deviations; the connection type, theoretical connection interface, and allowable deviation range in the assembly edges provide boundaries for subsequent construction of node residuals and judgment of connection closure conditions; the parallel setting of rigid constraints and releasable constraints provides a rule framework for subsequent adaptive pose solving and residual occupancy propagation. Through this structured expression, the steel structure can be transformed from a "collection of several components" into an "assembly chain system with state, sequence, boundaries, and adjustable mechanisms," providing direct support for subsequent virtual pre-assembly according to the installation sequence, recording node residual occupancy, and reverse tracing of dominant deviation nodes and coupled deviation sections.

[0073] Therefore, by constructing a point cloud-constrained assembly chain and dividing the connection node constraints, the entire steel structure assembly analysis process has been transformed from static design comparison to dynamic assembly solution: the former focuses on "how much the component differs from the design," while the latter further focuses on "how the component can be adjusted under the current chain assembly conditions, which conditions cannot be changed, which errors can be absorbed, and along which path the errors will propagate backward." This transformation enables subsequent virtual pre-assembly analysis to more realistically reflect the process of steel structure assembly, constraint, and deviation accumulation at each level on site, thereby improving the hierarchy, interpretability, and engineering guidance value of the deviation solution results.

[0074] When performing virtual pre-assembly according to the installation sequence of the point cloud constrained assembly chain, the upstream reference component of the assembly chain is first set as an anchor component, and the pose of the anchor component is fixed in the theoretical installation coordinate system. Anchor components are typically selected as those that bear the overall positioning role and are prioritized for placement during actual installation, such as column base sections, bottom steel columns, first main beam sections, or other key control node components. Fixing the pose of the anchor component is equivalent to establishing a stable initial assembly reference for the entire point cloud constrained assembly chain, ensuring that the loading, adjustment, and error propagation of all subsequent components are based on a unified spatial reference. This method avoids drift of the overall coordinate reference during subsequent solving and allows the residual changes of each connection node to be accurately attributed to specific assembly behaviors and specific connection interfaces.

[0075] After the anchoring components are fixed, subsequent components are loaded level by level according to the assembly edge sorting results in the point cloud constraint assembly chain. During the loading process, the components to be loaded are not directly and rigidly placed at their theoretical poses. Instead, the theoretical pose of the component is used as the initial reference, and the measured pose, body deviation results, and theoretical connection interfaces, allowable deviation ranges, and constraint types recorded by the assembly edges are used as inputs. Combined with the current actual pose of the preceding components, the pose adaptation solution of the components to be loaded under constrained conditions is performed. This level-by-level loading essentially simulates the connection between the subsequent components and the preceding components in the current assembly chain state. This means that the subsequent components are no longer assembled under ideal independent conditions, but participate in the solution under the condition that the preceding nodes have occupied part of the assembly margin and formed an actual assembly state. This more realistically reflects the constrained assembly characteristics of steel structure components during continuous installation.

[0076] When adjusting the pose of the component to be assembled, the rigid constraints must always be preserved. This means that conditions such as the position of the main control datum plane, key elevations, main hole references, column base positioning, and the direction of the main axis or datum line are prioritized during the solution process. Only minimal corrections are allowed within their respective allowable error ranges, and it is not permitted to achieve local interface closure by disrupting the main control positioning conditions. Simultaneously, within the allowable translation and rotation range of the release constraints, limited pose corrections are made to the component to be assembled, bringing it as close as possible to the assembled closed state within the adjustable space. The translation range can include planar translation and elevation fine-tuning, and the rotation range can include small rotations around the main axis, datum line, or the normal direction of the connecting interface. Specifically, when adjusting the pose of the component to be assembled, a rigid feasible region for the component is first established based on the rigid constraints. The rigid feasible region satisfies the following: the position deviation of the main control datum plane does not exceed the allowable deviation value of the main control datum plane; the deviation of the critical elevation does not exceed the allowable deviation value of the critical elevation; the deviation of the main hole position datum does not exceed the allowable deviation value of the main hole position; the column base positioning deviation does not exceed the allowable deviation value of the column base positioning; and the deviation of the main axis or datum line direction does not exceed the allowable deviation value of the direction. The allowable deviation values ​​of the main control datum plane, critical elevation, main hole, column base positioning, and direction are obtained from the corresponding tolerance values ​​in the design drawings, detailed drawings, installation acceptance standards, or installation process cards to form an allowable deviation range table. If the current measured pose of the component to be installed does not satisfy the rigid feasible region, rigid constraint correction is only allowed within the range not exceeding the corresponding allowable deviation value; if the rigid feasible region is still not satisfied after correction, the current component to be installed is determined not to be able to directly enter the pose adaptation solution stage; under the premise of satisfying the rigid feasible region, a local adjustment window for the component to be installed is established based on the releasable constraints. The local adjustment windows include a planar translation window, an elevation translation window, and a posture rotation window. The planar translation window is determined by the installation alignment allowance and the local alignment allowance for non-master control holes. The elevation translation window is determined by the remaining allowance for key elevations and the shim compensation space. The posture rotation window is determined by the local fitting allowance of the connecting surface and the temporary positioning release space. The initial adjustable windows of the component to be installed in the three directions are denoted as Wp,j, Wz,j, and Wθ,j, respectively. Each adjustment window is discretized into a sequence of candidate adjustment values ​​according to a preset step size. The planar adjustment step size is 1 / 10 to 1 / 20 of Wp,j, the elevation adjustment step size is 1 / 10 to 1 / 20 of Wz,j, and the posture adjustment step size is 1 / 10 to 1 / 20 of Wθ,j. The pose adjustment is performed using a staged constrained search method.First, using the theoretical assembly pose as the initial pose and combining it with the current poses of previously assembled components, a first set of candidate poses in the planar direction is generated. For each candidate pose in the planar direction, the corresponding hole displacement is calculated, and candidate poses with hole displacement less than the current value and without violating rigid constraints are selected. If multiple candidate poses satisfy the conditions, the candidate pose that minimizes the hole displacement is retained as the current updated pose in the planar direction. Subsequently, a set of candidate poses in the elevation direction is generated based on the updated pose in the current planar direction. For each candidate pose in the elevation direction, the average inter-face gap and the local maximum gap are calculated, and candidate poses that simultaneously reduce the average inter-face gap and the local maximum gap without violating the main hole reference constraints and key elevation constraints are selected. If multiple candidate poses satisfy the conditions, the candidate pose that minimizes the local maximum gap is retained as the current updated pose in the elevation direction. Finally, based on the updated pose in the current elevation direction, a set of candidate poses for the attitude direction is generated. For each candidate pose, the edge misalignment and attitude offset are calculated, and the candidate poses that reduce edge misalignment and attitude offset without violating the main axis or baseline direction constraints are selected. If multiple candidate poses meet the conditions, the one that minimizes edge misalignment is retained as the current updated pose for the attitude direction. After completing one round of adjustments in the planar direction, elevation direction, and attitude direction, the hole displacement, average inter-surface gap, local maximum gap, edge misalignment, elevation difference, main axis or baseline offset, and attitude offset between the current component to be installed and the previously installed components are recalculated. When at least one of the above residual indices continues to decrease compared to the previous round, and all rigid constraints still meet the corresponding allowable deviation range, the current updated pose is used as the new starting pose, and the next round of search begins. When all residual indices no longer decrease, or further adjustment would cause any rigid constraint to deteriorate, the search continues. When the constraint exceeds the corresponding allowable deviation range, or when all candidate adjustment amounts in each direction have been exhausted, the pose adjustment process is terminated, and the current pose is determined as the suitable pose of the component to be installed. For allowable error ranges, installation alignment allowances, shim compensation space, temporary positioning release space, and local alignment allowances for non-master control holes, the following methods are used: Allowable values ​​for master control datum plane position deviation, key elevation deviation, master hole datum deviation, column base positioning deviation, and main axis or datum line direction deviation are directly read from the corresponding tolerances in the design drawings, detailed drawings, and installation acceptance standards; Installation alignment allowances are determined based on the structural dimensions of the connection node, the length of the oblong hole, the installation process card, and the on-site construction allowance; Shim compensation space is determined based on the shim thickness grade and the allowable number of superimposed layers; Temporary positioning release space is determined based on the temporary tooling positioning stroke or the release amount of the temporary clamping mechanism; Local alignment allowances for non-master control holes are determined based on the difference between the hole diameter and the nominal bolt diameter, the hole wall safety allowance, and the allowable insertion allowance.

[0077] The process of obtaining the adaptive pose is essentially a constrained pose search and matching process. Specifically, a local adjustment space for the component to be assembled can be established first, centered on the theoretical assembly pose. Then, within this adjustment space, the relative position and attitude between the component to be assembled and the preceding component are gradually corrected, so that the hole correspondence, interface fit, and boundary docking state at the connection nodes are gradually improved. If the residual in a certain direction continues to decrease after adjustment without breaking the rigid constraint, the adjustment amount in that direction is retained; if an adjustment direction is beneficial to local closure but will cause the main control datum to deviate or the key elevation to exceed the boundary, then further adjustment in that direction is restricted. Through the above iterative method, the optimal adaptive pose within the current rigid constraint boundary and the range of releasable constraints can be obtained. This adaptive pose does not mean absolutely error-free, but rather that, under the current assembly chain state, the component to be assembled has reached an installation state that can maximally meet the connection requirements and is consistent with the actual construction adjustment logic.

[0078] At each connection node, based on the relative relationship between the adapted pose of the component to be assembled and the current pose of the preceding component, the assembly residual of the connection node is further calculated. Specifically, the hole displacement, average inter-surface gap, local maximum gap, edge misalignment, elevation difference, principal axis or baseline offset, and attitude offset of the current connection node are organized into a node residual vector Rj=(Δh,j, Gav,j, Gmax,j, Δe,j, Δz,j, Δa,j, Δθ,j), where Rj is the node residual vector of the j-th connection node, Δh,j is the hole displacement of the j-th connection node, Gav,j is the average inter-surface gap of the j-th connection node, Gmax,j is the local maximum gap of the j-th connection node, Δe,j is the edge misalignment of the j-th connection node, Δz,j is the elevation difference of the j-th connection node, Δa,j is the principal axis or baseline offset of the j-th connection node, and Δθ,j is the attitude offset of the j-th connection node.

[0079] The hole displacement Δh,j is obtained by comparing the two-dimensional projection offset between the center of each hole in the hole group of the component to be installed and the center of the corresponding hole in the preceding component. When the corresponding hole centers are denoted as Cj,m=(xj,m,yj,m) and C'j,m=(x'j,m,y'j,m) respectively, the hole displacement of the m-th pair of corresponding holes is denoted as δh,j,m=√[(xj,m-x'j,m)^2+(yj,m-y'j,m)^2], and the maximum value among all corresponding hole offsets is taken as the hole displacement Δh,j of the connecting node. The average inter-surface gap Gaav,j is obtained by calculating the average distance along the normal direction from the sampling point of the connecting surface of the component to be installed to the corresponding connecting surface of the preceding component; the local maximum gap Gmax,j is taken as the maximum value of the normal distances; the edge misalignment Δe,j is obtained by comparing the offset of the corresponding boundary points on the docking boundary line of the two components in the normal direction of the boundary, and the maximum boundary offset value is taken as the edge misalignment; the elevation difference Δz,j is obtained by comparing the difference in the vertical coordinate direction of the control points of the connecting node of the two components; the main axis or baseline offset Δa,j is obtained by comparing the minimum distance between the main axis or baseline of the component to be installed and the corresponding control line of the preceding component; the attitude offset Δθ,j is obtained by comparing the relative angle between the current attitude matrix of the component to be installed and the theoretical installation attitude matrix.

[0080] Each component of the node residual vector is compared item by item with its corresponding allowable deviation value to form the assembly status judgment result of the connection node. When Δh,j is not greater than the allowable hole position misalignment value, Gav,j is not greater than the allowable average gap value, Gmax,j is not greater than the allowable maximum gap value, Δe,j is not greater than the allowable edge misalignment value, Δz,j is not greater than the allowable elevation deviation, Δa,j is not greater than the allowable offset value of the main axis or baseline, and Δθ,j is not greater than the allowable attitude deviation, the j-th connection node is determined to meet the assembly requirements; otherwise, the j-th connection node is determined to have an assembly mismatch. Through the above definition, the assembly status of the connection node is transformed from the abstract "whether it can be installed" into a quantifiable and comparable node residual vector.

[0081] After obtaining the assembly residuals of each connection node, the node residual occupancy is further recorded based on the actual adjustment amount of each connection node within the releasable constraint range. Specifically, the node residual occupancy is defined as a three-directional occupancy vector Oj=(Op,j, Oz,j, Oθ,j), where Oj is the node residual occupancy vector of the j-th assembly node, Op,j is the adjustment amount already occupied in the planar direction of the j-th assembly node, Oz,j is the adjustment amount already occupied in the elevation direction of the j-th assembly node, and Oθ,j is the adjustment amount already occupied in the attitude direction of the j-th assembly node. The actual planar translation, elevation translation, and attitude rotation amounts used by the component to be assembled during the adaptation process of the current connection node are recorded as Lp,j, Lz,j, and Lθ,j, respectively, and are used as the local increment sources of Op,j, Oz,j, and Oθ,j, respectively.

[0082] Wherein, the planar translation Lp,j is the displacement modulus of the component to be installed relative to the previous wheel's pose in the installation plane during the current wheel adaptation solution; the elevation translation Lz,j is the absolute value of the vertical displacement of the component to be installed; and the attitude rotation Lθ,j is the absolute value of the actual angular change of the component to be installed around the principal axis, datum line, or normal direction of the connecting interface. Therefore, the node residual occupancy is no longer a qualitative definition, but is directly formed by the actual three-directional adjustment consumed by the current node to achieve the adaptation state.

[0083] When propagating the node residual occupancy downstream along the point cloud constraint assembly chain, the point cloud constraint assembly chain is first represented as a directed graph G=(V,E), where V is the set of assembly nodes and E is the set of assembly edges. For any assembly node vj, its entire set of upstream predecessor nodes is denoted as Pred(j). For the assembly edge eij between the upstream predecessor node vi and the current node vj, the planar direction transfer coefficient βij,p, the elevation direction transfer coefficient βij,z, and the attitude direction transfer coefficient βij,θ are preset respectively. Each transfer coefficient takes a value in [0,1] and is pre-written into the assembly edge attribute table according to the connection type, the rigidity level of the connection interface, and the installation order. When the connection type is a rigid connection, the transfer coefficient in the corresponding direction takes a higher value; when the connection type is a connection that allows local yielding, the transfer coefficient in the corresponding direction takes a lower value.

[0084] The upstream residual occupancy inputs received by the current node vj in the three directions are defined as follows: Ij,p=max(βij,p×Op,i), where i∈Pred(j); Ij,z=max(βij,z×Oz,i), where i∈Pred(j); Ij,θ=max(βij,θ×Oθ,i), where i∈Pred(j).

[0085] Where Ij,p represents the upstream residual occupancy input received by node vj in the planar direction, Ij,z represents the upstream residual occupancy input received by node vj in the elevation direction, and Ij,θ represents the upstream residual occupancy input received by node vj in the attitude direction. The maximum value method is used for input aggregation for multiple predecessor nodes because, in the same direction, the upstream dominant path with the strongest constraint on the current node determines the minimum remaining adjustable space of the current node.

[0086] Let the initial adjustable space of node vj without upstream influence be M0j = (M0p,j, M0z,j, M0θ,j), where M0p,j is the initial adjustable space of node vj in the planar direction, M0z,j is the initial adjustable space of node vj in the elevation direction, and M0θ,j is the initial adjustable space of node vj in the attitude direction. The initial adjustable spaces are calculated from the installation alignment allowance, shim compensation space, temporary positioning release space, and local alignment allowance of non-master hole positions, respectively. Then, the remaining adjustable space of node vj after considering the influence of upstream nodes is: Mj,p = max(0, M0p,j - Ij,p); Mj,z = max(0, M0z,j - Ij,z); Mj,θ = max(0, M0θ,j - Ij,θ). Where Mj,p, Mj,z, and Mj,θ represent the remaining adjustable space of node vj in the planar, elevation, and attitude directions, respectively. When the remaining adjustable space in a certain direction is zero, it means that there is no further release margin in that direction.

[0087] When node vj actually adopts local adjustment amounts Lp,j, Lz,j and Lθ,j in the current round of adaptation, the cumulative residual occupancy amount output downstream is updated as follows: Op,j=min(M0p,j,Ij,p+Lp,j); Oz,j=min(M0z,j,Ij,z+Lz,j); Oθ,j=min(M0θ,j,Ij,θ+Lθ,j).

[0088] Through the aforementioned update rules, the output residual occupancy of node vj includes both the constraint occupancy input inherited from upstream nodes and the additional local adjustments consumed to achieve the current node's assembly closure, and is limited by the node's own initial adjustable space limit. Therefore, any node in a tree-like or network-like assembly chain can simultaneously receive residual occupancy transfers from multiple upstream nodes, and on this basis, form its own new three-directional residual occupancy, thereby realizing residual transfer and margin accumulation analysis in nonlinear, non-single-chain assembly structures.

[0089] After completing the residual calculation and residual occupancy update for the current connected node, the node residual vector Rj, the node residual occupancy vector Oj, and the remaining adjustable space Mj are written into the current assembly node state table. When subsequent downstream nodes perform adaptive pose solving, they directly read the node state tables of all their predecessor nodes, using Ij,p, Ij,z, and Ij,θ as upstream constraint inputs for the current node's local adjustment window. This ensures that each subsequent node in the entire assembly chain is solved under the actual remaining assembly conditions after the preceding nodes have consumed the resources, rather than repeatedly solving under ideal independent adjustment conditions.

[0090] After the aforementioned process of hierarchical loading, pose adaptation, node residual calculation, and residual occupancy transfer is executed sequentially along the entire point cloud constraint assembly chain, a set of assembly process data is obtained, containing both the current residual state of the nodes and the path of surplus consumption on the chain. This data not only reflects "how much difference each node currently has," but also "how much adjustment capacity has been consumed to reach the current state, and how this consumption will affect subsequent nodes." Thus, the virtual pre-assembly of steel structures no longer remains at the level of static component splicing simulation, but is transformed into a dynamic assembly solution process capable of hierarchical loading, correction, recording, and transfer of constraint consumption. This lays a direct foundation for subsequently identifying the sources of mismatch at the end of the assembly chain, determining the dominant deviation nodes, and identifying coupled deviation sections.

[0091] When the end of the assembly chain fails to close holes, connection surfaces, or has insufficient remaining adjustment margin corresponding to releasable constraints, it indicates that the current point cloud constrained assembly chain, under the given installation sequence and constraint boundaries, can no longer achieve complete assembly closure through continued local adjustments. In this case, judging the source of the problem solely based on the current mismatch status of the end node can easily lead to misinterpreting the end phenomenon as a problem with the end component itself, failing to identify the transitive mismatch caused by the gradual accumulation of residual occupancy from preceding nodes. Therefore, after obtaining the deviation results of each component and the residual occupancy of each connecting node, it is further necessary to trace back along the point cloud constrained assembly chain to identify the nodes or sections in the assembly chain that truly play a dominant role in the end-of-line mismatch. This method transforms the analysis of end-of-line assembly failure from a single-point phenomenon to a chain-like source analysis, extending the deviation solution from "where it can't be assembled" to "why it can't be assembled, who is in charge, and whether it involves multiple nodes in a coupled manner."

[0092] End-point mismatch is used to characterize the current degree of mismatch at the end-connection node of the assembly chain. It can be taken as at least one of the following: hole misalignment, inter-face gap, edge misalignment, and attitude offset, or a comprehensive mismatch characterization quantity composed of at least one of the above. When the end mainly manifests as bolted connections that cannot be inserted, hole misalignment can be used as the main characterization of end-point mismatch; when the end mainly manifests as poor fit of the connection interface, inter-face gap or local maximum gap can be used as the main characterization; when the end mainly manifests as edge misalignment or abnormal interface attitude, edge misalignment or attitude offset can be used as the main characterization; when multiple types of mismatch phenomena exist at the end, multiple indicators can be uniformly transformed or normalized to form a comprehensive mismatch characterization quantity. Through the above definition method, the end-point mismatch quantity can not only adapt to the main mismatch patterns of different connection nodes, but also provide a unified comparison object for subsequent backtracking analysis.

[0093] When tracing back along the point cloud constraint assembly chain to determine the residual occupancy contribution of each connected node, local rollback, resolving, and end-point response observation are performed step-by-step from the end node to the upstream nodes. Local rollback refers to releasing some or all of the releasable constraint adjustments already occupied by the currently observed node during the virtual pre-assembly process, while keeping the current states of upstream and unrelated nodes unchanged. This allows the node to temporarily return to a reference state without consuming the corresponding assembly margin, or to its pose solution state from the previous stage. The purpose of local rollback is not to rebuild the entire assembly chain, but to observe the extent to which the assembly margin already occupied by a node contributes to the formation of end-point mismatch. By performing node-by-node local rollback, the influence of each node on end-point mismatch in the assembly chain can be gradually decoupled from the overall coupled state.

[0094] After each local rollback, the current assembly chain is re-solved. During the re-solve, the currently rolled-back node is used as the new local state boundary. Without changing the fixed rigid constraints upstream, the adaptation pose solution, node residual calculation, and residual occupancy transfer are performed downstream according to the assembly chain sequence until the new mismatch state of the end node under the rollback condition is obtained again. Since this re-solve process still follows the original rigid constraint boundary and releasable constraint boundary, the difference before and after the rollback can be regarded as "the net contribution of the residual occupied by the examined node to the end mismatch". In this way, it is possible to avoid presuming node responsibility based solely on static differences or empirical judgments, and instead establish the actual correspondence between node contribution and end response through controlled release and re-solve.

[0095] After obtaining the end-point mismatch status after rollback, further end-point response observation is performed, i.e., comparing the change in end-point mismatch amount under the current rollback conditions with the end-point mismatch amount before rollback. When the end-point mismatch amount decreases by more than a preset proportion after a certain upstream node rolls back, that upstream node is identified as the dominant deviation node. If the end-point mismatch status significantly decreases after releasing the existing residual occupancy of a certain node, it indicates that the node consumed adjustable space that plays a key role in end-point closure in the assembly chain, or its own deviation caused a major constraint on the downstream through residual transmission. Therefore, this node should be identified as the dominant deviation node, i.e., the main driving node in the end-point mismatch formation process. The preset proportion can be set based on the initial end-point mismatch amount, connection node level, component category, or historical sample experience, and is used to distinguish between "ordinary influencing nodes" and "dominant influencing nodes".

[0096] When multiple adjacent nodes retract, and the cumulative decrease in end-point mismatch exceeds a preset cumulative proportion, and the decrease in end-point mismatch for each adjacent node exceeds its corresponding minimum contribution proportion, the corresponding segment is identified as a coupling deviation segment. Many mismatches in continuous steel structure assembly are not caused by a single node independently, but rather by several adjacent nodes each occupying a portion of the assembly allowance and transmitting a portion of the deviation, ultimately accumulating at the end to form assembly failure. If only a single node retracts, the decrease in end-point mismatch is insufficient to reach the dominant judgment threshold, but a significant cumulative decrease in end-point mismatch occurs after multiple consecutive nodes retract together, it indicates a coupling relationship in deviation transmission between these nodes, and their contributions cannot be decomposed into independent single-node effects. By setting preset cumulative proportions and minimum contribution proportions, the situation where "multiple nodes contribute relatively little individually but have a significant cumulative effect" can be identified from ordinary node fluctuations, thus classifying the continuous segment as a coupling deviation segment.

[0097] The process of step-by-step backtracking, resolving, and observing the end-point response is essentially a reverse sensitivity analysis oriented towards the assembly chain. The forward virtual pre-assembly stage records "how nodes progressively occupy assembly margins and pass them downstream," while the reverse backtracking stage analyzes "how much the end-point mismatch will decrease if the assembly margins already occupied by a node are released." These two stages complement each other, forming a complete closed loop for solving the source of deviations. This combination of forward recording and reverse verification avoids misjudgments caused by inferring upstream causes solely from end-point appearances, and also avoids simply attributing multiple small deviations to the end-point components themselves. Thus, the residual occupancy path in the assembly chain is transformed into an interpretable and verifiable responsibility contribution path, enabling the formation mechanism of end-point mismatches to be clearly characterized at the node and segment levels.

[0098] After completing the reverse backtracking analysis of all candidate nodes and candidate segments, the virtual pre-assembly deviation solution results of the steel structure are output based on the body deviation results of each component, the residual occupancy of nodes, and the reverse backtracking results. Specifically, a component-level result set Rc, a node-level result set Rn, a chain segment-level result set Rs, and an assembly feasibility result set Rf are first established. Among them, Rc is used to record the body deviation results of a single component, Rn is used to record the assembly residual results of the connection nodes, Rs is used to record the results of the dominant deviation nodes and coupled deviation segments, and Rf is used to record the assembly feasibility judgment results.

[0099] For any component vk, read its body deviation result Bk=(Δs,k, Δd,k, Δp,k, Δt,k, Δg,k, Δm,k, Δw,k), where Bk is the body deviation result vector of the k-th component, Δs,k is the external dimension deviation of the k-th component, Δd,k is the main axis or baseline direction deviation of the k-th component, Δp,k is the cross-sectional attitude deviation of the k-th component, Δt,k is the end face tilt deviation of the k-th component, Δg,k is the overall offset deviation of the hole group of the k-th component, Δm,k is the local distortion deviation of the hole group of the k-th component, and Δw,k is the local warping deviation of the k-th component. Each component in the body deviation result vector Bk is compared with the corresponding component allowable deviation value. When any component exceeds the corresponding allowable deviation value, the component number, body deviation type, deviation value and corresponding allowable deviation value are written into the component-level result set Rc to form a single component deviation list. When all components do not exceed the corresponding allowable deviation value, the component number and "body deviation not exceeded" mark are written into the component-level result set Rc.

[0100] For any connected node vj, read its node residual vector Rj=(Δh,j, Gav,j, Gmax,j, Δe,j, Δz,j, Δa,j, Δθ,j), node residual occupancy vector Oj=(Op,j, Oz,j, Oθ,j), and remaining adjustable space Mj=(Mp,j, Mz,j, Mθ,j).

[0101] Each component of the node residual vector Rj is compared with its corresponding node allowable deviation value to obtain a node out-of-tolerance judgment mark. Then, the node residual occupancy vector Oj is compared with the remaining adjustable space Mj to obtain a node margin status judgment mark. When all components of the node residual vector Rj do not exceed their corresponding allowable deviation values, the connection node is marked as "directly assembleable," and the node number, corresponding residual value, and occupancy vector are written into the node-level result set Rn. When there are components in the node residual vector Rj that exceed their corresponding allowable deviation values, but the excess portion can be covered by the remaining adjustable space Mj, the connection node is marked as "adjustable for assembly," and the node number, out-of-tolerance item, occupancy vector, and remaining adjustable space are written into the node-level result set Rn. When there are components in the node residual vector Rj that exceed their corresponding allowable deviation values, and the excess portion cannot be covered by the remaining adjustable space Mj, the connection node is marked as "unassembleable," and the node number, out-of-tolerance item, occupancy vector, and remaining adjustable space are written into the node-level result set Rn.

[0102] For chain segment-level results, the dominant deviation node set Sd and the coupled deviation segment set Sc obtained from the reverse backtracking analysis are read. Specifically, if the decrease in end-point mismatch after backtracking of an upstream node vi is greater than or equal to the dominant judgment threshold T1, then the upstream node vi is written into the dominant deviation node set Sd. If the cumulative decrease in end-point mismatch after backtracking of each node in a continuous segment Pq={vi,…,vj} is greater than or equal to the cumulative judgment threshold T2, and the decrease in end-point mismatch corresponding to each node within the segment is greater than or equal to the minimum contribution threshold T3, then the continuous segment Pq is written into the coupled deviation segment set Sc. The node number, the corresponding decrease in end-point mismatch after backtracking, and the component number to which each node belongs in the dominant deviation node set Sd are written into the chain segment-level result set Rs. The starting node number, ending node number, cumulative contribution value of the segment, and minimum contribution value of each node within the segment of each continuous segment in the coupled deviation segment set Sc are written into the chain segment-level result set Rs.

[0103] The assembly feasibility result set Rf is generated based on the joint judgment results of the component-level result set Rc, the node-level result set Rn, and the chain segment-level result set Rs. Specifically, when there are no components with excessive body deviation in the component-level result set Rc, and all connected nodes in the node-level result set Rn are marked as "can be directly assembled" or "can be assembled after adjustment", and there are no coupling deviation sections in the chain segment-level result set Rs, the entire point cloud constraint assembly chain is marked as "can be closed for assembly". When there are "unassembleable" nodes in the node-level result set Rn, but no coupling deviation sections are identified in the chain segment-level result set Rs, the entire point cloud constraint assembly chain is marked as "can be re-verified after local adjustment", and the corresponding unassembleable nodes are written into the assembly feasibility result set Rf. When there are coupling deviation sections in the chain segment-level result set Rs, or when there are key components with excessive body deviation in the component-level result set Rc and there are unassembleable nodes in the corresponding node-level result set, the entire point cloud constraint assembly chain is marked as "needs to be re-measured or repaired before assembly", and the corresponding dominant deviation nodes, coupling deviation sections, and related component numbers are written into the assembly feasibility result set Rf.

[0104] When finally outputting the solution results for the virtual pre-assembly deviation of the steel structure, the component-level result set Rc, node-level result set Rn, chain segment-level result set Rs, and assembly feasibility result set Rf are uniformly sorted according to the assembly chain installation sequence, and a result output table is formed. The result output table includes at least the component number, node number, deviation type, deviation value, allowable deviation value, residual occupancy, remaining adjustable space, dominant deviation marker, coupling segment marker, and assembly feasibility marker. Through the above result organization method, the body deviation results, node residual occupancy, and reverse backtracking results are uniformly converted into virtual pre-assembly deviation solution results for the steel structure that can be directly used for assembly judgment, re-measurement positioning, and rework decisions.

[0105] When outputting the deviation solution results, they can be further organized into three levels: component level, node level, and chain segment level. Component-level results reflect whether the problem mainly originates from the deviation of a single component; node-level results reflect whether the problem is mainly concentrated at a specific interface or local assembly relationship; and chain segment-level results reflect whether the problem has evolved from a local deviation to a multi-node cumulative transmission problem. This hierarchical output method makes the results of the virtual pre-assembly analysis of steel structures both locally operable and globally interpretable. For on-site assembly organization, if the dominant deviation node is clear, corrective measures can be prioritized for the corresponding component or interface; if the coupled deviation segment is clear, overall optimization can be prioritized from the perspectives of adjusting the installation sequence, reconstructing local relocation strategies, or verifying continuous segment components.

[0106] It should be noted that the allowable deviation range, adjustable interval, moderate release range, small offset range, dominant judgment threshold, preset cumulative ratio, and corresponding minimum contribution ratio mentioned in this article are all obtained in the following general manner: For the allowable deviation range corresponding to rigid constraints, including the deviation of the main control reference plane position, the deviation of the key elevation, the deviation of the main hole position reference, the deviation of the column base positioning, and the deviation of the main axis or reference line direction, the corresponding tolerance values ​​in the design drawings, detailed drawings, component lists, installation process cards, or steel structure installation acceptance standards are directly read and a table of allowable deviation ranges is formed. For the allowable deviation range corresponding to the residuals of connection nodes, including the allowable misalignment value of the hole position, the allowable value of the average gap between surfaces, the allowable value of the local maximum gap, the allowable value of the edge misalignment, the allowable deviation value of the elevation, the allowable offset value of the main axis or reference line, and the allowable deviation value of the attitude, the values ​​are retrieved from the table of allowable deviation ranges according to the connection type, node level, and component category.

[0107] For the adjustable range, it is determined separately according to the direction. The adjustable range in the planar direction is jointly limited by the installation alignment allowance and the local centering allowance of non-master hole positions; the adjustable range in the elevation direction is jointly limited by the remaining allowance of the key elevation and the shim compensation space; the adjustable range in the attitude direction is jointly limited by the local fitting allowance of the connection surface and the temporary positioning release space. Let the initial adjustable spaces of node vj in the planar direction, elevation direction and attitude direction be M0p,j, M0z,j and M0θ,j respectively, then M0p,j, M0z,j and M0θ,j are obtained by conversion from the installation process card, the structural dimensions of the connector, the difference between the hole diameter and the nominal diameter of the bolt, the length of the oblong hole, the shim thickness grade, the positioning stroke of the temporary tooling and the construction allowance.

[0108] The term "allowable deviation" in the text refers to the corresponding residual amount not exceeding the upper limit of the corresponding item in the allowable deviation range table; "moderate release" refers to the release amount not exceeding a preset proportion of the remaining adjustable space in the current direction without violating rigid constraints; and "small offset" refers to the single adjustment step size not exceeding a preset proportion of the adjustable range in the current direction. Let the remaining adjustable space in the current direction be Mj,*, then the single adjustment step size ΔLj,* satisfies ΔLj,*=α4×Mj,*, where α4 is the step size proportionality coefficient, and its value satisfies 0<α4≤0.2.

[0109] For the dominant judgment threshold, preset cumulative ratio, and corresponding minimum contribution ratio in reverse backtracking, the initial end mismatch amount E0 of the end node before backtracking is first recorded. When the end mismatch amount is a single index, E0 is the corresponding item among hole position displacement, inter-surface gap, edge misalignment, or attitude offset; when the end mismatch amount is a comprehensive mismatch characterization quantity, the selected mismatch index is first normalized according to the corresponding allowable deviation value, and then the maximum value among the normalized indexes is taken as E0. The dominant judgment threshold is taken as T1=α1×E0, the cumulative judgment threshold is taken as T2=α2×E0, and the minimum contribution threshold of a single node is taken as T3=α3×E0, where α1, α2, and α3 satisfy 0<α3<α1<α2<1, and are preset according to the connection node level, component category, connection type, or historical assembly samples.

[0110] The point cloud processing thresholds, such as the first distance threshold, the second distance threshold, the first normal threshold, the first curvature threshold, the first quantity threshold, and the first area threshold, are all set based on the point cloud sampling accuracy, component type, and design allowable deviation range. For end face and connection surface fitting, the threshold range that is not greater than the corresponding design allowable plane deviation is preferred. For hole boundary recognition, the threshold range that is not greater than the hole diameter processing allowable deviation is preferred. For local warping determination, the threshold range that is not greater than the connection interface allowable fitting deviation is preferred.

[0111] Therefore, based on the reverse backtracking mechanism triggered by mismatch at the end of the assembly chain, a complete solution process is achieved, from component deviation identification and node residual occupancy recording to the determination of dominant deviation nodes and coupled deviation sections. Its core lies not in judging whether a single component "exceeds tolerance," but in revealing the contribution method and degree of each node in the assembly chain to the end-of-chain mismatch, enabling the deviation solution results to truly reflect the objective laws of error propagation, margin consumption, and problem amplification in continuous steel structure assembly. Through this process, the virtual pre-assembly analysis of steel structures is further upgraded from static matching judgment to dynamic solution oriented towards source identification and chain-based attribution, providing a more targeted basis for subsequent assembly decisions, component correction, and construction organization optimization.

[0112] The above description is merely a specific embodiment of this application, but the scope of protection of this application is not limited thereto. Any variations or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in this application should be included within the scope of protection of this application. Therefore, the scope of protection of this application should be determined by the scope of the claims.

Claims

1. A method for solving virtual pre-assembly deviations of steel structures based on point cloud-constrained assembly chains, characterized in that, include: Obtain the steel structure design model and extract the theoretical assembly features of the components. Establish the assembly chain skeleton based on the component connection relationship and installation sequence. Three-dimensional scanning of solid steel components is performed to obtain the measured point cloud model of each component, and the measured assembly features corresponding to the main axis or baseline, end face, connection surface, hole group and boundary line of the component are extracted. The measured assembly features are registered with the corresponding theoretical assembly features to obtain the body deviation results of each component; The measured assembly features of each component are mapped to the assembly chain skeleton to construct a point cloud constrained assembly chain, and the constraints of the connecting nodes are divided into rigid constraints and releasable constraints. Virtual pre-assembly is performed according to the installation sequence of the point cloud constraint assembly chain. Under the premise of satisfying rigid constraints, the pose of the components to be assembled is adjusted based on the releasable constraints. The adaptive pose of each component to be assembled is solved, and the hole displacement, inter-surface gap, edge misalignment and attitude offset of the connection nodes are calculated. Record the node residual occupancy based on the adjustment results of each connected node within the releasable constraint range, and pass the node residual occupancy downstream along the point cloud constraint assembly chain. When the end of the assembly chain fails to close the hole, the connection surface fails to close, or the remaining adjustment margin corresponding to the release constraint is insufficient, the residual occupancy contribution of each connection node is traced back along the point cloud constraint assembly chain to determine the dominant deviation node or coupled deviation section. The solution results for the virtual pre-assembly deviation of the steel structure are output based on the body deviation results of each component, the residual occupancy of nodes, and the reverse backtracking results.

2. The method for solving the virtual pre-assembly deviation of steel structures based on point cloud constraint assembly chain according to claim 1, characterized in that, Obtaining the steel structure design model includes: obtaining steel structure construction drawings, detailed drawings, component list and installation sequence information, and establishing a three-dimensional steel structure design model based on the steel structure construction drawings, detailed drawings and component list; Alternatively, a pre-built BIM model of the steel structure can be read as the steel structure design model.

3. The method for solving the virtual pre-assembly deviation of steel structures based on point cloud constraint assembly chain according to claim 2, characterized in that, Extracting theoretical assembly features of components includes: extracting the theoretical installation pose, main axis or datum line, end face, connection surface, hole group center, hole axis, boundary line, installation datum point, installation datum edge and theoretical connection relationship between adjacent components from the steel structure design model, and extracting at least one of the flange surface, web surface and node plate surface.

4. The method for solving the virtual pre-assembly deviation of steel structures based on point cloud constraint assembly chain according to claim 1, characterized in that, Also includes: The original point cloud data obtained from 3D scanning is processed by noise point removal, background point separation, point cloud segmentation, marking of occluded and missing areas, point density equalization, and coordinate unification. The processed point cloud data is then bound to the component number of the corresponding physical steel component to form a measured point cloud model corresponding to the physical steel component.

5. The method for solving the virtual pre-assembly deviation of steel structures based on point cloud constraint assembly chain according to claim 4, characterized in that, Extracting the measured assembly features corresponding to the main axis or baseline of the component, end face, connecting surface, hole group and boundary line, including: performing geometric fitting on the measured point cloud model to obtain at least one of the component's main axis or baseline, end face fitting plane, connecting surface fitting plane, flange fitting plane, web fitting plane and node plate fitting plane; identifying holes in the connecting area to obtain the hole center coordinates, hole axis direction, hole group centroid position and hole group distribution relationship; performing edge analysis on the component's outer contour to obtain the boundary line and local warped areas.

6. The method for solving the virtual pre-assembly deviation of steel structures based on point cloud constraint assembly chain according to claim 1, characterized in that, The measured assembly features are registered with the corresponding theoretical assembly features, including: coarse registration based on the main axis or datum line of the component, and fine registration based on the end face, connecting surface, hole group and boundary line; the body deviation results include the component's external dimension deviation, main axis or datum line direction deviation, cross section posture deviation, end face tilt deviation, overall hole group offset deviation, hole group local distortion deviation and local warping deviation.

7. The method for solving the virtual pre-assembly deviation of steel structures based on point cloud constraint assembly chain according to claim 1, characterized in that, The measured assembly features of each component are mapped to the assembly chain skeleton to construct a point cloud constrained assembly chain, including: using each solid steel component as an assembly node and the connection relationship between components as an assembly edge; wherein, each assembly node records at least the component number, theoretical pose, measured pose, body deviation result, measured assembly features and current adjustable degrees of freedom, and the assembly edges in the assembly chain are sorted according to the installation order, and each assembly edge records at least the connection type, theoretical connection interface and allowable deviation range.

8. The method for solving the virtual pre-assembly deviation of steel structures based on point cloud constraint assembly chain according to claim 7, characterized in that, Rigid constraints include main control datum plane position constraints, key elevation constraints, main hole position datum constraints, column base positioning constraints, and main axis or datum line direction constraints; releasable constraints include installation alignment allowance, local fitting allowance of connection surfaces, temporary positioning release space, shim compensation space, and local centering allowance of non-main control holes.

9. The method for solving the virtual pre-assembly deviation of steel structures based on point cloud constraint assembly chain according to claim 8, characterized in that, Virtual pre-assembly is performed according to the installation sequence of the point cloud constraint assembly chain, including: setting the upstream reference component of the assembly chain as the anchor component, and fixing the pose of the anchor component in the theoretical installation coordinate system; installing the subsequent components to be installed step by step according to the installation sequence, and adjusting the pose of the components to be installed within the range of translation and rotation allowed by the release constraints without destroying the rigid constraints, to obtain the adapted pose; calculating the hole displacement, average gap between surfaces, local maximum gap, edge misalignment, elevation difference, principal axis or reference line offset, and attitude offset at each connection node; recording the node residual occupancy based on the adjustment amount of each connection node within the range of the release constraints, and transferring the node residual occupancy downstream along the point cloud constraint assembly chain in the plane direction, elevation direction, and attitude direction.

10. The method for solving the virtual pre-assembly deviation of steel structures based on point cloud constraint assembly chain according to claim 9, characterized in that, The residual occupancy contribution of each connection node is traced back in reverse along the point cloud constraint assembly chain, including: when the end of the assembly chain cannot close the hole, the connection surface cannot be closed, or the remaining adjustment margin corresponding to the release constraint is insufficient, the end node is backed up step by step to the upstream node, the solution is resolved, and the end response is observed; when the end mismatch decreases by more than a preset proportion after the backing up of an upstream node, the upstream node is identified as the dominant deviation node; when the cumulative decrease of the end mismatch exceeds a preset cumulative proportion after the backing up of multiple adjacent nodes, and the decrease of the end mismatch of each adjacent node exceeds the corresponding minimum contribution proportion, the corresponding section is identified as the coupling deviation section; the solution results of the deviation of the virtual pre-assembly of steel structure include a single component deviation list, a connection node deviation list, a dominant deviation node, a coupling deviation section, and an assembly feasibility judgment result. Among them, the end mismatch is at least one of the hole displacement, inter-surface gap, edge misalignment, and attitude offset of the connection node at the end of the assembly chain, or a comprehensive mismatch characterization quantity composed of at least one of them.

Images