Modular steel structure building assembly error accumulation prediction method and system

Abstract

The application belongs to the technical field of computer data processing, and particularly discloses a modular steel structure building assembly error accumulation prediction method and system, which comprises the following steps: acquiring a theoretical model and a measured coating thickness, constructing a distribution curved surface, extracting an interference extreme point, taking the extreme point as a fulcrum to calculate a pose change caused by bolt fastening, generating a connection offset matrix, constructing a cantilever beam model to calculate a self-weight deformation, generating a self-weight deformation matrix, multiplying the connection offset matrix, the self-weight deformation matrix and an actual coordinate matrix in sequence, mapping to a global coordinate system to obtain a terminal node real three-dimensional coordinate prediction value, comparing the prediction value with a theoretical coordinate to calculate a deviation vector, and generating a gasket layout drawing. The application couples physical effects such as coating unevenness, bolt fastening and self-weight deformation, and realizes error prediction and active correction.

Description

Technical Field

[0001] This invention belongs to the field of computer data processing technology and relates to a method and system for predicting the cumulative assembly error of modular steel structure buildings. Background Technology

[0002] Modular steel structure construction, as a modern construction method, revolves around breaking down the building into independent modular units, prefabricating them in a factory, and then transporting them to the site for hoisting and assembly. The efficiency and final building quality of this construction model highly depend on the assembly precision of the interfaces between the modules. In this process, utilizing computer-aided design and simulation technology—that is, predicting and controlling the assembly process through data processing—has become a key technology for improving project quality.

[0003] In existing technologies, the prediction of assembly errors in modular steel structures typically employs computer simulation methods based on ideal theoretical geometric model data. These methods create idealized digital modules in a computer and simulate their docking process, using geometric interference analysis to predict potential assembly problems. Alternatively, on the construction site, measuring equipment such as laser trackers is used to measure the attitude of installed modules, and then manual experience or simple geometric calculations are used to guide the installation of the next module. This approach also involves basic data acquisition and processing.

[0004] However, the aforementioned existing technical solutions have significant technical shortcomings in practical applications. Simulation methods that rely entirely on ideal theoretical geometric models for data processing ignore various physical influencing factors that inevitably exist during manufacturing and construction. For example, the thickness of the anti-corrosion coating on the module surface is not uniform; this unevenness alters the initial contact state between modules. During bolt tightening to eliminate initial coating gaps, the tightening sequence causes slight spatial orientation deflections of the connecting plates, and traditional nonlinear contact mechanics calculations are too complex to meet the rapid calculation needs of construction sites. Furthermore, when only one end of the module is fixed, its own weight causes sag and rotation at the cantilever end. Existing data processing methods fail to integrate these real and interrelated physical effects into the prediction model, resulting in discrepancies between simulation results and actual assembly conditions, leading to insufficient prediction accuracy. In addition, existing prediction methods often only provide error values, lacking a data processing mechanism to convert prediction deviations into quantitative compensation schemes. This means that on-site construction still relies on manual trial and error, making proactive error correction difficult. Summary of the Invention

[0005] In order to overcome the above-mentioned defects of the prior art and to achieve the above objectives, the present invention proposes the following technical solution: a method for predicting the cumulative assembly error of modular steel structure buildings, comprising: S1, acquiring theoretical geometric model data of the module to be assembled and the installed module, and receiving the thickness of the anti-corrosion coating at discrete measurement points collected on the nodal contact surface of the module, spatially aligning the thickness of the anti-corrosion coating at discrete measurement points with the theoretical geometric model data, and generating multi-point measured data of the anti-corrosion coating thickness with coordinate labels.

[0006] S2. Based on the measured data of multi-point anti-corrosion coating thickness with coordinate labels, construct a continuous coating thickness distribution surface of the module to be assembled and the installed module. By superimposing two continuous coating thickness distribution surfaces, extract the coordinates of the position with the maximum total thickness as the coordinates of the interference extreme point.

[0007] S3. Obtain the bolt tightening sequence. Using the coordinates of the interference extreme point as the initial rotation fulcrum, calculate the pose change of the node connection plate caused by the bolt tightening process according to the bolt tightening sequence. Accumulate the pose changes to generate a homogeneous matrix of node connection offset.

[0008] S4. Based on the module structure parameters in the theoretical geometric model data, construct a cantilever beam stress model with the already fastened nodes as fixed ends, calculate the terminal deformation of the module to be assembled under its own weight, and convert the terminal deformation into a homogeneous matrix of self-weight deformation in the local coordinate system.

[0009] S5. Obtain the actual three-dimensional coordinate matrix of the installed module's terminal, multiply the actual three-dimensional coordinate matrix of the terminal by the homogeneous matrix of the node connection offset to generate the offset spatial reference matrix, and then multiply it by the homogeneous matrix of the self-weight deformation to obtain the global pose result matrix. Then extract the translation component from it to obtain the predicted value of the actual three-dimensional coordinates of the terminal node of the module to be assembled.

[0010] S6. Obtain the theoretical access coordinates of the next module to be assembled. By comparing the predicted real three-dimensional coordinates of the terminal node with the theoretical access coordinates, calculate the three-dimensional deviation vector, and then calculate the non-negative shim thickness value required for each bolt hole position. Generate and output the shim layout diagram.

[0011] The second aspect of the present invention provides a modular steel structure building assembly error cumulative prediction system, comprising: a data acquisition and alignment module, used to acquire theoretical geometric model data of the module to be assembled and the installed module, and to receive the thickness of the anti-corrosion coating at discrete measurement points collected on the nodal contact surface of the module, spatially aligning the thickness of the anti-corrosion coating at discrete measurement points with the theoretical geometric model data, and generating multi-point measured data of the anti-corrosion coating thickness with coordinate labels.

[0012] The coating surface overlay module is used to construct a continuous coating thickness distribution surface of the module to be assembled and the installed module based on the measured data of the thickness of the multi-point anti-corrosion coating with coordinate labels. By overlaying two continuous coating thickness distribution surfaces, the coordinates of the position with the maximum total thickness are extracted as the coordinates of the interference extreme point.

[0013] The fastening offset accumulation module is used to obtain the bolt fastening sequence. Using the coordinates of the interference extreme point as the initial rotation fulcrum, it calculates the pose change of the node connection plate caused by the bolt fastening process according to the bolt fastening sequence, accumulates the pose change, and generates a homogeneous node connection offset matrix.

[0014] The self-weight deformation calculation module is used to construct a cantilever beam stress model with the already fastened nodes as fixed ends based on the module structural parameters in the theoretical geometric model data, calculate the terminal deformation of the module to be assembled under its own weight, and convert the terminal deformation into a homogeneous matrix of self-weight deformation in the local coordinate system.

[0015] The pose mapping prediction module is used to obtain the actual three-dimensional coordinate matrix of the terminal of the installed module, multiply the actual three-dimensional coordinate matrix of the terminal by the node connection offset homogeneous matrix to generate the offset spatial reference matrix, and then multiply it by the self-weight deformation homogeneous matrix to obtain the global pose result matrix. Then, the translation component is extracted from it to obtain the true three-dimensional coordinate prediction value of the terminal node of the module to be assembled.

[0016] The gasket thickness layout module is used to obtain the theoretical access coordinates of the next module to be assembled. By comparing the predicted real three-dimensional coordinates of the terminal node with the theoretical access coordinates, the three-dimensional deviation vector is calculated, and then the non-negative gasket thickness value required for each bolt hole position is calculated, generating a gasket layout diagram and outputting it.

[0017] Compared with the prior art, the beneficial effects of the present invention are as follows: (1) The present invention obtains the thickness of the anti-corrosion coating at discrete measurement points and aligns it spatially with the theoretical geometric model, thereby constructing a continuous coating thickness distribution surface to extract the coordinates of the interference extreme points, overcoming the defect that traditional simulation relies solely on the ideal theoretical geometric model. This process introduces the real coating non-uniformity into the prediction data stream, restores the initial physical contact state during module assembly, and ensures the objectivity and accuracy of the error prediction results from the data input source.

[0018] (2) This invention uses the coordinates of the interference extreme point as the initial rotation fulcrum, and iteratively calculates the minute rotation angle and translation of the node connection plate in combination with the bolt tightening sequence, and accumulates to generate a homogeneous matrix of node connection offset. The algorithm logic reduces the nonlinear contact mechanics problem of multi-point contact to a serialized spatial kinematic transformation, effectively reducing the computational complexity of the system and meeting the engineering needs of rapid assessment and real-time calculation of assembly errors at the construction site.

[0019] (3) This invention calculates the terminal deformation of the module to be assembled under its own weight based on the cantilever beam stress model, and transforms it into a homogeneous matrix of self-weight deformation in the local coordinate system. Then, the homogeneous matrix of connection offset and the homogeneous matrix of self-weight deformation are sequentially multiplied with the actual three-dimensional coordinate matrix of the terminal. This operation mechanism systematically couples various physical effects such as microscopic coating interference, fastening deflection and macroscopic self-weight sagging, realizes the accurate mapping of local physical deformation to the global coordinate system, and constructs a digital model of the entire error accumulation process.

[0020] (4) Based on the comparison between the predicted real three-dimensional coordinates of the terminal node and the theoretical access coordinates, the present invention generates a three-dimensional deviation vector. By decomposing the normal deviation component and the tangential deviation component, the foundation thickness and thickness adjustment amount are calculated for each bolt hole position, and finally a gasket layout diagram is generated. This mechanism opens up the data link from error prediction to error compensation, provides direct and quantitative guidance for gasket layout for modular splicing on site, and realizes active correction of assembly errors. Attached Figure Description

[0021] To more clearly illustrate the technical solutions of 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.

[0022] Figure 1 This is a schematic diagram of the implementation steps of the method of the present invention.

[0023] Figure 2 This is a schematic diagram of the superposition of the coating thickness distribution cross sections and the extraction of interference extremum points according to the present invention.

[0024] Figure 3 This is a schematic diagram illustrating the generation of a gasket layout diagram based on coating interference and three-dimensional deviation vector, and the subsequent physical compensation according to the present invention.

[0025] Figure 4 This is a schematic diagram of the system module connections of the present invention. Detailed Implementation

[0026] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0027] Please see Figure 1As shown, the present invention proposes a method for predicting the cumulative assembly error of modular steel structure buildings, including: S1, acquiring theoretical geometric model data of the module to be assembled and the installed module, and receiving the thickness of the anti-corrosion coating at discrete measurement points collected on the nodal contact surface of the module, spatially aligning the thickness of the anti-corrosion coating at discrete measurement points with the theoretical geometric model data, and generating multi-point measured data of the anti-corrosion coating thickness with coordinate labels.

[0028] In a preferred embodiment, before spatially aligning the discrete measurement point anti-corrosion coating thickness with the theoretical geometric model data, the method includes: setting statistical criteria for judging the degree of data dispersion; performing outlier identification on the discrete measurement point anti-corrosion coating thickness based on the statistical criteria; removing the measurement point data identified as outliers; and generating multi-point measured anti-corrosion coating thickness data with coordinate labels using the remaining valid measurement point data.

[0029] In a specific embodiment, two basic data points are first acquired: the theoretical geometric model data of the module to be assembled and the installed module, and the thickness of the anti-corrosion coating at discrete measurement points on the nodal contact surfaces of the modules. The theoretical geometric model data refers to the three-dimensional digital model of the module created using computer-aided design software, which defines all geometric dimensions, shapes, and spatial positions of the module in an ideal state, including specific areas to be connected, namely the nodal contact surfaces. The nodal contact surfaces are flat or curved areas where two modules are designed to fit together and be connected by fasteners such as bolts. The discrete measurement point anti-corrosion coating thickness is a series of coating thickness readings measured on the nodal contact surfaces of the actual modules using tools such as thickness gauges. Initially, these readings are only numerical lists, lacking spatial coordinate references.

[0030] To ensure the accuracy of the data source, outlier identification and removal are performed on the anti-corrosion coating thickness at discrete measurement points before spatial alignment. This process first establishes statistical criteria for judging the degree of data dispersion. A statistical criterion is a clear mathematical criterion used to define whether a data point significantly deviates from the overall distribution of the dataset, thus being judged as an outlier. In this embodiment, the 3-sigma criterion based on standard deviation is used. This criterion is based on the fact that under a normal distribution, approximately 99.7% of the data points will fall within three standard deviations from the mean; data points outside this range are considered low-probability events, i.e., outliers. (A measurement point data...) The criteria for identifying a value as an outlier are expressed by the following formula:

[0031]

[0032] In the formula, Represents the number of collected samples The thickness value of the anti-corrosion coating at each discrete measuring point. The mean value representing the thickness of the anti-corrosion coating is the stable process value obtained by statistical analysis of a large amount of historical production data (e.g., the expected thickness after actual measurement of the same coating on 200 groups of steel structure modules of the same type under standard process). This is to avoid the interference of small sample data fluctuations on the mean and standard deviation and to ensure the stability of the criterion. The stable process standard deviation representing the thickness of the anti-corrosion coating production process, and its acquisition method is similar to... The same value reflects the normal fluctuation range of coating thickness under stable process control. It is a dimensionless coefficient used to define the strictness of outlier detection. In this embodiment, Setting it to 3 is a widely accepted setting in the field of industrial quality control, as it strikes a balance between effectively identifying the vast majority of outliers and avoiding misjudging normal fluctuations as abnormal.

[0033] Based on the aforementioned statistical criteria, the system iterates through all collected discrete measurement points of the anti-corrosion coating thickness and removes any measurement point data that does not meet the criteria, i.e., the measurement point data identified as outliers. Outliers are usually caused by accidental factors such as momentary malfunction of the measuring instrument, presence of oil or impurities on the contact surface, or human error.

[0034] After removing outliers, the remaining valid measurement point data are used to generate the final multi-point measured thickness data of the anti-corrosion coating with coordinate labels through spatial alignment. Spatial alignment refers to aligning each valid thickness measurement value... Its three-dimensional coordinates in theoretical geometric model data The binding process involves several steps. Since actual measurements typically use the physical coordinate system of a coordinate measuring machine (CMM) or total station, while the theoretical geometric model uses a global design coordinate system, the process includes: First, while measuring the thickness, simultaneously recording the initial spatial position of the measuring points in the physical coordinate system using a CMM or total station; second, selecting at least three non-collinear reference feature points on the module to be assembled, such as module corner points or preset targets, and obtaining their measured coordinates in the physical coordinate system and their theoretical coordinates in the theoretical geometric model; then, based on the two sets of coordinates of the aforementioned reference feature points, using Singular Value Decomposition (SVD) or Iterative Closest Point (ICP) algorithms to calculate the rigid body transformation matrix from the physical coordinate system to the global coordinate system of the theoretical geometric model, including rotation matrices and translation vectors; finally, using this rigid body transformation matrix, mapping the initial spatial positions of all measuring points to the global coordinate system of the theoretical geometric model data, thus achieving coordinate alignment. The final generated multi-point anti-corrosion coating thickness measurement data with coordinate labels is a structured point set. Its form is as follows:

[0035]

[0036] In the formula, Representing the The three-dimensional coordinates of each effective measuring point in the global coordinate system are derived from theoretical geometric model data and obtained through rigid body transformation matrix mapping. Representative and coordinates Correspondingly, the effective anti-corrosion coating thickness values ​​are retained after outlier filtering. This represents the total number of valid measurement points remaining after outlier removal. This dataset describes the spatial distribution of the actual coating thickness on the nodal contact surface and serves as the direct input for all subsequent calculations.

[0037] An exemplary implementation scenario is as follows: Suppose we are processing node contact surface data of a module to be assembled. First, we acquire theoretical geometric model data (the contact surface is located on the Z=0 plane), and receive a set of discrete measurement points on the physical surface showing the thickness of the anti-corrosion coating. .

[0038] Outlier identification is performed before spatial alignment. This is based on known process stability averages. and standard deviation The 3-sigma criterion is adopted. The calculated normal data threshold range is as follows: After system comparison, the thickness is... The number of measurement points significantly exceeded the upper limit and was identified as outliers and removed. The remaining valid measurement points are: .

[0039] Finally, the effective measurement points are mapped to the global coordinate system of the theoretical geometric model data using a coordinate transformation matrix, generating a set of multi-point measured anti-corrosion coating thickness data with coordinate labels. ={(100.1,150.5,0.0,312),(899.5,149.8,0.0,307),(101.3,400.7,0.0,315),(901.0,401.2,0.0,309)}, this dataset accurately reflects the true coating thickness distribution.

[0040] S2. Based on the measured data of multi-point anti-corrosion coating thickness with coordinate labels, construct a continuous coating thickness distribution surface of the module to be assembled and the installed module. By superimposing two continuous coating thickness distribution surfaces, extract the coordinates of the position with the maximum total thickness as the coordinates of the interference extreme point.

[0041] In a preferred embodiment, constructing the continuous coating thickness distribution surface of the module to be assembled and the installed module includes: performing gridding processing on the measured data of the multi-point anti-corrosion coating thickness with coordinate labels to generate a coating thickness data grid; using a bilinear interpolation algorithm to calculate the coating thickness at any point within the grid based on the coating thickness data grid; and fitting and generating a continuous coating thickness distribution surface based on the calculated coating thickness at any point within the grid.

[0042] In a specific embodiment, the input multi-point measured data of anti-corrosion coating thickness with coordinate labels is first processed into a grid. This is based on the three-dimensional coordinates that have been uniformly mapped to the global coordinate system of the theoretical geometric model in step S1. First, the spatial plane equation of the nodal contact surface is extracted based on the theoretical geometric model, and the three-dimensional coordinates are projected onto the contact plane to obtain the corresponding two-dimensional plane coordinates (x, y). Then, a regular rectangular grid is divided within the domain of this two-dimensional plane, and a meshing process is performed. Meshing is the process of mapping irregularly distributed measurement points onto a two-dimensional regular grid defined on the nodal contact surface, generating a coating thickness data grid. This data grid can be viewed as a two-dimensional array, where the node positions correspond to specific coordinates on the contact surface, and the node value is the coating thickness at that position. For grid nodes that coincide with measured points, the thickness value is directly taken from the measured value; for grid nodes without measured data, data from surrounding known discrete measurement points is used for assignment. In this embodiment, the inverse distance weighted (IDW) interpolation method or the nearest neighbor method is used to calculate the initial thickness value of the grid node, thereby ensuring that each intersection of the grid contains definite thickness data, providing a complete data foundation for subsequent continuous interpolation.

[0043] Furthermore, a bilinear interpolation algorithm is employed to calculate the coating thickness at any point within the coating thickness data grid. Bilinear interpolation is a numerical calculation method that performs interpolation on a two-dimensional grid, estimating the value at any point by performing linear interpolation in two directions. For a corner point located within the coating thickness data grid with four known thickness values... , , , Any point within the enclosed rectangular area Its coating thickness Calculated using the following formula:

[0044]

[0045] In the formula, Represents coordinates The coating thickness to be calculated. Represents the coordinates of the point to be interpolated. The coordinates of the four corner points of the rectangular grid cell surrounding the point to be interpolated are represented. Representing the four corner points respectively The known coating thickness values ​​are derived from the coating thickness data grid. The calculated result has the same dimensions as the input thickness values, both being in units of length.

[0046] By repeatedly applying the bilinear interpolation algorithm to all points within the domain of the node contact surface, a continuous function surface is generated based on the calculated coating thickness at any point within the mesh. This surface is the continuous coating thickness distribution surface. This process is performed on the data of the module awaiting assembly and the installed module respectively, resulting in two independent surfaces, denoted as... and .

[0047] After obtaining the continuous coating thickness distribution surfaces of the two modules, the total coating thickness distribution under ideally aligned contact is simulated by superimposing the two continuous coating thickness distribution surfaces. Since the measured data of the module to be assembled and the installed module in step S1 have been accurately mapped to the same theoretical geometric model global coordinate system through rigid body transformation matrices, these two surfaces have completely aligned identical domains under this reference, allowing for direct point-to-point thickness accumulation. Total thickness function This can be expressed as the sum of the thicknesses of the two surfaces at corresponding locations:

[0048]

[0049] From the total thickness distribution, the coordinates of the location with the maximum total thickness are extracted as the coordinates of the interference extremum point. The interference extremum point is the point where two modules first come into contact, solely due to coating unevenness, without any external force; this point corresponds to the maximum assembly interference. Its coordinates... This is obtained by solving the following optimization problem:

[0050]

[0051] In the formula, Represents the coordinates of the extreme points of interference. For mathematical operators, it means finding the function that makes the function The independent variable that achieves its maximum value The value of . It is the calculated two-dimensional coordinate of the interference extremum point within the contact surface. These are the coordinates of the interference extremum points in the direction perpendicular to the contact surface, and are usually determined by the position of the contact surface in the theoretical geometric model data.

[0052] An exemplary implementation scenario is as follows: This step is based on the module data to be assembled generated in step S1, and assumes that the corresponding alignment data of the installed module has been obtained in the same way. First, the data is meshed. A bilinear interpolation algorithm is used. For example, assuming the coordinates of the four grid corner points surrounding the interpolation point (500, 275) are (400, 200), (600, 200), (400, 400), and (600, 400), and their known coating thicknesses are 305 μm, 310 μm, 315 μm, and 320 μm respectively, substituting the grid corner point coordinates and thicknesses into the aforementioned interpolation formula, the coating thickness at any point within the grid (e.g., at coordinates (500, 275)) can be calculated to be 311.25 μm. This process is repeated iteratively to fit and generate continuous surfaces of the installed modules. Continuous surface of the module to be assembled Subsequently, the total thickness distribution function is obtained by superimposing the two surfaces. Through numerical optimization, the total thickness was determined to reach a maximum of 629.3 μm near the coordinate point (101.2, 400.8). The coordinates of this point were then extracted to generate the interferometric extreme point coordinates. mm, serving as the physical reference for the spatial fulcrum in subsequent simulations of the bolt tightening process. Please refer to... Figure 2 As shown, this invention extracts and draws the continuous coating distribution cross-sections of the installed module and the module to be assembled, and obtains the total thickness interference cross-section through mathematical superposition. This allows for intuitive and accurate optimization of the local thickness maximum position as the interference extreme point, providing a highly realistic initial physical support for subsequent three-dimensional kinematic modeling.

[0053] S3. Obtain the bolt tightening sequence. Using the coordinates of the interference extreme point as the initial rotation fulcrum, calculate the pose change of the node connection plate caused by the bolt tightening process according to the bolt tightening sequence. Accumulate the pose changes to generate a homogeneous matrix of node connection offset.

[0054] In a preferred embodiment, the calculation of the pose change of the node connection plate caused by the bolt tightening process includes: obtaining the local coating gap at each bolt position based on the continuous coating thickness distribution surface; converting the local coating gap into a small rotation angle and translation amount around the initial rotation pivot point based on the small angle approximation principle; and combining the small rotation angle and translation amount into a single-step pose change matrix as the pose change of the node connection plate caused by the bolt tightening process.

[0055] In a further preferred embodiment, the step of accumulating pose changes to generate a homogeneous node connection offset matrix includes: initializing an identity matrix as an initial accumulated pose change matrix; iteratively calculating the single-step pose change matrix generated by tightening each bolt according to the bolt tightening order; generating a new accumulated pose change matrix by multiplying the single-step pose change matrix of the current step with the accumulated pose change matrix updated in the previous step, until all bolts have been traversed, to obtain the final homogeneous node connection offset matrix.

[0056] In a specific embodiment, this step aims to transform the bolt tightening process caused by uneven coating surfaces into a series of spatial kinematic transformations, ultimately quantified as the overall pose deflection of the module to be assembled relative to the installed module. The core of this process is to simplify a complex, multi-point contact mechanical problem into a continuous accumulation of rotations around a fixed fulcrum.

[0057] First, the bolt tightening sequence is determined, specifically by a pre-defined operating procedure that specifies the order in which multiple bolts on the node connection plate are tightened. Simultaneously, the coordinates of the interference extremum point determined in step S2 are used as the initial rotation fulcrum for the entire tightening process. This fulcrum... This is the point where the two modules first come into contact due to the thickest coating, simulating the initial physical state of the assembly, without external force. It should be noted that all coordinate points involved in this step have been uniformly mapped to the global coordinate system of the theoretical geometric model in step S1.

[0058] Based on the bolt tightening sequence, the pose change of the node connection plate caused by each bolt tightening action is calculated iteratively. For the first bolt in the sequence... For each bolt, the first step is to calculate its corresponding single-step pose change. The first step in this calculation is to obtain the local coating gap at the bolt location based on the continuous coating thickness distribution surface constructed in step S2. (Local coating gap) This refers to the current bolt position. Total coating thickness at the location With the initial pivot point Total coating thickness at the location The difference between them, i.e. Its dimension is length. Because... This is the point of maximum total thickness; this gap represents the vertical distance that needs to be compressed or eliminated when tightening the bolt.

[0059] After obtaining the local coating gap, based on the principle of small-angle approximation, it is converted into a small rotation angle and translation around the initial rotation fulcrum. When the bolt... When fastened, the module to be assembled will rotate around the initial pivot point. A minute rotation occurs until the gap at the bolt location is eliminated. This rotation is decomposed into two minute angles about the X and Y axes. and The size of the corner and the gap between local coatings. and the distance from the bolt to the fulcrum Related.

[0060]

[0061]

[0062] In the formula, It is the total minute angle, measured in radians. It is the first The planar distance from the center of each bolt to the initial pivot point. and These are the two-dimensional coordinates of the bolt and the fulcrum, respectively. This rotation... This occurs on an axis perpendicular to the vector connecting the pivot point and the bolt. Specifically, it is defined from the initial pivot point... Pointing to the current bolt The plane direction vector is Based on the perpendicularity relationship in plane geometry, the unit vector of the axis of rotation around which this minute rotation revolves is... The calculation formula is Based on this unit vector of rotation axis, the angular components about the X and Y axes can be precisely obtained by projecting the total rotation angle onto each axis, i.e. , .

[0063] To represent this as a homogeneous transformation matrix, we need to transform it around any point... The rotation is decomposed into a combination of three fundamental transformations: first, the coordinate system is translated to... Then, a rotation is performed, and finally, the position is translated back to the origin. This process is encapsulated as a 4x4 single-step pose transformation matrix. Describes the fastening of the first The small rotation and translation caused by each bolt. The mathematical expression for this single-step pose change matrix is: ,in The translation vector is A 4x4 translation matrix, It is its inverse matrix. For small-angle rotations, the rotation matrix is... Approximately:

[0064]

[0065] in, These are the angular components about each axis. For planar contact problems, These components are usually 0. It is determined by the direction of the rotation axis.

[0066] The pose changes of all bolts are accumulated to generate the final homogeneous matrix of node connection offsets. This process first initializes a 4x4 identity matrix as the initial accumulated pose change matrix. Next, following the bolt tightening sequence, tighten each bolt... Calculate its single-step pose change matrix Subsequently, through matrix multiplication, the single-step pose change matrix of the current step is multiplied by the cumulative pose change matrix updated in the previous step to generate a new cumulative pose change matrix. The expression for this iterative process is:

[0067]

[0068] In the formula, It is the first to be tightened The cumulative pose change matrix after each bolt. It is to fasten the first The single-step pose change matrix generated by each bolt. Before tightening The cumulative pose change matrix after each bolt.

[0069] After all bolts have been traversed in sequence, the final cumulative matrix is ​​obtained. ( The total number of bolts is the homogeneous offset matrix of the node connection. This matrix contains the total spatial attitude deflection information caused by the sequential tightening of all bolts.

[0070] An exemplary implementation scenario is as follows: Continuing from the example result of step S2, the coordinates of the interference extreme point are... mm, assuming the connecting plate has two theoretical coordinates respectively mm and mm, and the obtained bolt tightening sequence is: tighten bolt 1 first, then tighten bolt 2.

[0071] The local coating gap at bolt 1 is obtained based on the continuous coating thickness distribution surface, assumed to be... Based on the principle of small-angle approximation and the distance from bolt 1 to the fulcrum, the minute rotation angle around the fulcrum is calculated. By combining the rotation axis unit vector, it is decomposed into rotational angular components about each axis in space, generating a single-step pose transformation matrix. .

[0072] After initializing the identity matrix, perform the first accumulation. Similarly, calculate the single-step pose change matrix caused by fastening bolt 2. This is then multiplied together with the matrix from the previous step. Through iterative calculations, a homogeneous node connection offset matrix is ​​finally generated, containing the cumulative amounts of all tiny rotations and translations. The initial spatial attitude shift caused by bolt tightening was quantified.

[0073] S4. Based on the module structure parameters in the theoretical geometric model data, construct a cantilever beam stress model with the already fastened nodes as fixed ends, calculate the terminal deformation of the module to be assembled under its own weight, and convert the terminal deformation into a homogeneous matrix of self-weight deformation in the local coordinate system.

[0074] In a preferred embodiment, calculating the terminal deformation of the module to be assembled under its own weight includes: obtaining the uniformly distributed self-weight load, elastic modulus, and moment of inertia of the module to be assembled from theoretical geometric model data; substituting the uniformly distributed self-weight load, elastic modulus, and moment of inertia into the structural mechanics analytical equations; and calculating the terminal vertical sag displacement and end face rotation of the cantilever beam stress model by solving the structural mechanics analytical equations, which together are used as the terminal deformation.

[0075] In a specific embodiment, based on the module structural parameters in the theoretical geometric model data, a cantilever beam force model is constructed with the already tightened nodes as the fixed ends. The cantilever beam force model is a simplified model widely used in structural mechanics, specifically considering a long strip-shaped structure with one end firmly fixed and the other end freely extending as a cantilever beam. In this scenario, the node connection plate of the module to be assembled, which is tightened by bolts in step S3, is considered the fixed end of the cantilever beam, while the remaining part of the module constitutes the beam body of the cantilever beam, with its distal end being the free end.

[0076] To calculate the final deformation of the module to be assembled under its own weight, a series of key physical and geometric parameters are first obtained from the theoretical geometric model data. These parameters include the uniformly distributed load of the module's self-weight, the elastic modulus and moment of inertia of the section, and the effective length of the cantilever beam.

[0077] The uniformly distributed self-weight load This refers to the force per unit length of a module when its weight is evenly distributed along its length. It is obtained by dividing the module's total weight by its length; the formula is as follows: ,in For the total mass of the module, The gravitational acceleration constant is used, while the total weight is calculated from the volume and material density provided by the physical property analysis module of the CAD model or BIM (Building Information Modeling) software, in units of Newtons per meter (N / m).

[0078] The elastic modulus It is a measure of a material’s ability to resist elastic deformation. It is a physical quantity that characterizes the stiffness of a material. For a specific material (such as Q345 steel), it is a known constant, and its unit is Pascal (Pa) or Newton per square meter (N / m²).

[0079] The moment of inertia of the cross section This is a geometric property of the beam's cross-section, reflecting the cross-sectional shape's resistance to bending deformation. Its value is determined by the module's cross-sectional dimensions and shape. In the case of a solid rectangular cross-section in this embodiment, the calculation formula is as follows: ,in For the cross-sectional width, The height of the cross section is expressed in meters to the fourth power. ).

[0080] The effective length of the cantilever beam The coordinates are obtained by extracting the centroid coordinates of the fixed end section and the centroid coordinates of the free end section in the global coordinate system of the theoretical geometric model, and calculating the spatial Euclidean distance between the two points, with the unit being meters (m).

[0081] After obtaining these parameters, the self-weight is uniformly distributed as a load. Elastic modulus and moment of inertia of cross section Substitute into the structural mechanics analytical equations. Structural mechanics analytical equations are classic mathematical formulas describing the deformation behavior of a beam under load. For a beam of length... A cantilever beam under a uniformly distributed load Under the action, the deformation of its free end is calculated by the following formula.

[0082] By solving the analytical equations of structural mechanics, the vertical downward displacement at the end of the cantilever beam stress model was calculated. and end face corner These two together constitute the terminal deformation.

[0083] Terminal vertical downward displacement The calculation formula is:

[0084]

[0085] End face corner The calculation formula is:

[0086]

[0087] The calculated terminal deformation is converted into a homogeneous matrix of self-weight deformation in the local coordinate system. This 4x4 matrix describes the pose transformation of a rigid body in three-dimensional space. Here, it represents the translation and rotation of the free end due to its own weight. To ensure spatial consistency with the global coordinate system in the preceding steps and the subsequent matrix multiplication pose, we define the following assumptions for the module's local coordinate system: the X-axis points from the fixed end to the free end along its length, the Z-axis points vertically upward, and the Y-axis is determined by the right-hand rule. Under this coordinate system definition, the drooping of the module's free end mainly manifests as a positive rotation about the Y-axis, a negative translation along the Z-axis, and an extension of the module's effective length along the X-axis. Geometric translation. Homogeneous matrix of self-weight deformation. Its structure is as follows:

[0088]

[0089] This matrix transforms the coordinates of a point from the fixed end node before deformation to the position of the free end node of the cantilever after deformation, encapsulating the geometric effects caused by its own weight.

[0090] An exemplary implementation scenario is as follows: Based on a theoretical geometric model, the key structural parameters of the module to be assembled (such as a solid steel box girder) are obtained: elastic modulus. Pa, effective length m, cross-sectional width m, height m, total mass is 9420 kg, gravitational acceleration constant is taken as .

[0091] Substituting the above parameters into the structural mechanics analytical equations, the vertical downward displacement at the end of the cantilever beam force model is calculated: End face corner .

[0092] The above deformation is converted into a homogeneous matrix of self-weight deformation in the local coordinate system. The matrix is... and Construct rotational components with effective length and sagging displacement The translation component is constructed to describe the pose change of the module's free end under its own weight.

[0093] S5. Obtain the actual three-dimensional coordinate matrix of the installed module's terminal, multiply the actual three-dimensional coordinate matrix of the terminal by the homogeneous matrix of the node connection offset to generate the offset spatial reference matrix, and then multiply it by the homogeneous matrix of the self-weight deformation to obtain the global pose result matrix. Then extract the translation component from it to obtain the predicted value of the actual three-dimensional coordinates of the terminal node of the module to be assembled.

[0094] In a preferred embodiment, the step of multiplying the actual three-dimensional coordinate matrix of the terminal with the homogeneous matrix of node connection offset to generate an offset spatial reference matrix, and then multiplying it with the homogeneous matrix of self-weight deformation to obtain a global pose result matrix, includes: multiplying the actual three-dimensional coordinate matrix of the terminal with the homogeneous matrix of node connection offset to generate an offset spatial reference matrix that includes the bolt fastening effect; multiplying the offset spatial reference matrix with the homogeneous matrix of self-weight deformation; obtaining the final global pose result matrix through the above ordered multiplication, and extracting the predicted values ​​of the actual three-dimensional coordinates of the terminal nodes from it.

[0095] In a specific embodiment, the actual three-dimensional coordinate matrix of the terminal with the installed module is first obtained, and this matrix is ​​denoted as... The transformation matrix is ​​a 4x4 homogeneous transformation matrix that not only contains the three-dimensional coordinates of the installed module terminal node in the global coordinate system, but also defines the spatial orientation (i.e., direction) of the node. This matrix is ​​typically obtained by field measurement of the installed structure using high-precision measuring equipment (such as a laser tracker or total station). To ensure the consistency of the entire coordinate transfer chain, the initial physical coordinate matrix obtained by the field measurement must be mapped through the rigid body transformation matrix in step S1 to uniformly transform it to the global coordinate system of the theoretical geometric model, serving as the unified benchmark and starting point for subsequent matrix operations.

[0096] Furthermore, the node connection offset homogeneous matrix generated in step S3 is used. The homogeneous matrix of self-weight deformation generated in step S4 sequentially compared with the actual three-dimensional coordinate matrix of the terminal Perform matrix multiplication. This order of operations ensures the correct simulation of the physical processes.

[0097] The first step in the calculation is to multiply the actual three-dimensional coordinate matrix of the terminal with the homogeneous offset matrix of the node connection to generate an offset spatial reference matrix that includes the bolt fastening effect. .

[0098]

[0099] In the formula, This represents an intermediate result matrix that describes the new spatial position and orientation of the connection end of the module to be assembled after it has been fastened to the installed module. It is the actual three-dimensional coordinate matrix of the terminal with the installed module, which serves as the reference for transformation. It is a node connection offset homogeneous matrix, representing a relative... Local transformation of the defined coordinate system. Matrix multiplication here achieves the coordinate system transformation, superimposing the local deflections caused by coating unevenness and bolt tightening onto the global reference coordinates.

[0100] The second step of the calculation is to multiply the offset spatial reference matrix generated in the previous step with the homogeneous matrix of self-weight deformation. This step ensures that the self-weight deformation is calculated relative to the actual attitude of the module after offset. If the module to be assembled has tilted due to bolt tightening, then the direction of its self-weight drooping will also be deflected accordingly, rather than simply being perpendicular to the geodetic coordinate system.

[0101]

[0102] In the formula, It is the final global pose result matrix, which describes the final spatial position and orientation of the free end of the module to be assembled after considering all offset and deformation factors. This is the homogeneous deformation matrix based on self-weight, representing a local deformation relative to the coordinate system of the module to be assembled. Through post-multiplication, this deformation is correctly applied to the already assembled module. The transformed module posture.

[0103] The final global pose result matrix is ​​obtained through the ordered matrix multiplication described above. It is a 4x4 homogeneous matrix, and its general form is:

[0104]

[0105] Extract the translation component from the resulting matrix, which is the first three elements of the last column of the matrix. The predicted true three-dimensional coordinates of the terminal nodes of the module to be assembled are obtained. , .

[0106] An exemplary implementation scenario is: obtaining the actual three-dimensional coordinate matrix of the terminal with the installed module. Assuming that after measurement and mapping, its terminal node is located in global coordinates At position mm, and with no initial spatial orientation deviation, meaning the rotation is a 3×3 identity matrix, the assigned node connection offset homogeneous matrix obtained in step S3 is called. and the homogeneous matrix of self-weight deformation obtained in step S4 Perform ordered matrix chain multiplication: This matrix multiplication process maps physical effects such as deviations caused by local bolt tightening, beam geometric extension, and self-weight sagging to the global reference coordinate system. Finally, the pose result matrix... Extracting the translation component yields the predicted true 3D coordinates of the terminal node of the module to be assembled. for mm.

[0107] S6. Obtain the theoretical access coordinates of the next module to be assembled. By comparing the predicted real three-dimensional coordinates of the terminal node with the theoretical access coordinates, calculate the three-dimensional deviation vector, and then calculate the non-negative shim thickness value required for each bolt hole position. Generate and output the shim layout diagram.

[0108] In a preferred embodiment, the step of calculating the three-dimensional deviation vector and then calculating the required non-negative shim thickness for each bolt hole includes: decomposing the three-dimensional deviation vector into a normal deviation component perpendicular to the node contact surface and a tangential deviation component along the node contact surface; determining the base thickness for shim compensation at all bolt holes based on the value of the normal deviation component: when the normal deviation component is negative, its absolute value is taken as the base thickness; when the normal deviation component is positive, a preset process reference thickness is used as the base thickness; calculating the shim thickness adjustment amount for compensating the tangential deviation at each bolt hole based on the magnitude and direction of the tangential deviation component, wherein the adjustment amount is expressed as a positive or negative value representing an increase or decrease in shim thickness, and is superimposed on the base thickness; when the superimposed thickness value is less than a preset non-negative thickness threshold, the shim thickness at all bolt holes is compensated by an equal upward translation to obtain the final required shim thickness for each bolt hole.

[0109] In a specific embodiment, the theoretical access coordinates of the next module to be assembled are first obtained. The theoretical access coordinates refer to the spatial position that the connection endpoint of the next module should occupy under ideal design conditions. These coordinates are directly derived from the initial theoretical geometric model data. Subsequently, the predicted true three-dimensional coordinates of the terminal nodes of the modules to be assembled, obtained in step S5, are used... With theoretical access coordinates The comparison is performed, and the spatial difference between the two is calculated as a three-dimensional deviation vector. Represented in the form of .

[0110]

[0111] In the formula, This represents a three-dimensional deviation vector, with three components. These represent the deviation values ​​in the X, Y, and Z directions in the global coordinate system, respectively, with the dimension being length. These are the predicted values ​​of the actual three-dimensional coordinates of the terminal nodes of the module to be assembled. These are the theoretical access coordinates for the next module to be assembled.

[0112] After obtaining the three-dimensional deviation vector, the required non-negative shim thickness for each bolt hole is calculated based on this vector. This calculation does not simply apply the deviation value directly; instead, it decomposes it into components with different physical meanings for assembly. The system decomposes the three-dimensional deviation vector into a normal deviation component perpendicular to the node contact surface and a tangential deviation component along the direction of the node contact surface. Here, the node contact surface refers to the connection interface of the next module to be assembled. The normal direction vector of this interface... It can be obtained from theoretical geometric model data.

[0113] Normal deviation component It is the projection length of the three-dimensional deviation vector in the normal direction, which directly reflects the average gap or interference between the two contact surfaces.

[0114]

[0115] Tangential deviation component It is the remaining part of the three-dimensional deviation vector after removing the normal component, representing the in-plane misalignment between the contact surfaces.

[0116]

[0117] In the formula, It represents the normal deviation component and is a scalar with the dimension of length. This represents the unit normal vector of the next node's contact surface; it is dimensionless. It represents the tangential deviation component, which is a vector with the dimension of length. This represents the dot product operation of vectors.

[0118] After calculating these two components, the system will calculate the normal deviation component. The base thickness for shim compensation at all bolt hole locations In this embodiment, the unit normal vector is defined. The direction is the extension from the installed module to the next module to be assembled. This is due to the three-dimensional deviation vector. It is the predicted coordinates minus the theoretical coordinates, therefore, if A negative value means that the predicted node has not reached the theoretical position in the normal direction, i.e., there is a gap, and shims need to be added. In this case, the foundation thickness is taken as its absolute value, i.e. ;if A positive value indicates that the predicted position exceeds the theoretical position, meaning there is an interference, which theoretically requires reduction. However, in practice, this is usually resolved by adjusting other components, or by setting the base thickness to a preset process reference thickness and considering only tangential adjustments. To ensure the feasibility of the gaskets in physical manufacturing and assembly, when the calculated gasket thickness for each bolt hole position is less than zero, the gasket thickness for all holes is equally superimposed with an upward shift amount to ensure that the final gasket thickness value at each bolt hole position is a non-negative value.

[0119] Furthermore, based on the magnitude and direction of the tangential deviation component, the shim thickness adjustment amount for compensating for the tangential deviation at each bolt hole position is calculated. This adjustment amount is expressed as a positive or negative value, representing an increase or decrease in shim thickness, respectively. Tangential deviation can cause the module to tilt during assembly. To correct this tilt, the system calculates and assigns shims of varying thicknesses for different bolt hole locations, thus creating a compensating tilt plane opposite to the direction of the deviation. Shim thickness adjustment value. In the The value at each bolt hole location, and the position vector of that bolt hole location. (Relative to the center of the contact surface) and tangential deviation vector Related. Its distribution pattern can be modeled as a linear plane, whose gradient is in the opposite direction to the tangential deviation vector. A simplified calculation model is as follows:

[0120]

[0121] In the formula, It is the first Adjustment value for the shim thickness of each bolt hole. This is a geometric transformation coefficient used to convert the result of a vector dot product (in units of length squared) to shim thickness (in units of length). To ensure the far end of the next module to be assembled is aligned with theoretical coordinates, a small inverted tilt angle needs to be generated on the current contact surface. Based on the principle of geometric similarity, this coefficient... The calculation formula is clearly defined as follows: ,in The effective length of the next module to be assembled is obtained in the same way as in step S4, and its dimension is the reciprocal of the length, eliminating the arbitrariness of empirical estimation. From the geometric center of the nodal contact surface to the first The vector of the center of each bolt hole.

[0122] Finally, the base thickness and the thickness adjustment value are added together to obtain the final shim thickness required for each bolt hole. .

[0123]

[0124] Please see Figure 3 As shown, after calculating the gasket thickness for all bolt hole positions, the system integrates this data with the corresponding bolt hole position information to generate and output a gasket layout diagram. The gasket layout diagram is an intuitive engineering drawing or data table that clearly indicates the appropriate gasket thickness for each bolt hole position, providing direct operational guidance for on-site construction personnel.

[0125] An exemplary implementation scenario is: obtaining the theoretical access coordinates of the next module to be assembled. mm. The three-dimensional deviation vector is calculated by comparing it with the predicted value from step S5. Assuming the unit normal vector of the nodal contact surface is (1,0,0), decompose the three-dimensional deviation vector to obtain the normal deviation components. mm, tangential deviation component mm. The absolute value of the normal deviation is taken as the base gasket thickness for all bolt holes. mm.

[0126] Assuming there are four bolt holes on the contact surface, obtain their local coordinates relative to the center of the contact surface. to Bolt 1: mm; Bolt 2: mm; Bolt 3: mm; Bolt 4: mm.

[0127] Set conversion factor Taking bolt hole 1 as an example, the adjustment amount for compensating for its tangential deviation is calculated according to the dot product formula: mm, the required thickness is obtained by adding the base thickness. mm. Similarly, the computer program iterates through and calculates the remaining bolt hole positions, finally generating and outputting the gasket layout diagram (thickness values ​​have been rounded to standard precision), as shown in the table below:

[0128]

[0129] Please see Figure 4 As shown, the second aspect of the present invention provides a modular steel structure building assembly error cumulative prediction system, comprising: a data acquisition and alignment module, a coating surface superposition module, a fastening offset cumulative module, a self-weight deformation calculation module, a pose mapping prediction module, and a shim thickness layout module.

[0130] The data acquisition and alignment module is used to acquire the theoretical geometric model data of the module to be assembled and the installed module, and to receive the thickness of the anti-corrosion coating at discrete measurement points collected on the nodal contact surface of the module. The module spatially aligns the thickness of the anti-corrosion coating at discrete measurement points with the theoretical geometric model data to generate multi-point measured data of the anti-corrosion coating thickness with coordinate labels.

[0131] The coating surface overlay module is used to construct a continuous coating thickness distribution surface of the module to be assembled and the installed module based on the measured data of the thickness of the multi-point anti-corrosion coating with coordinate labels. By overlaying two continuous coating thickness distribution surfaces, the coordinates of the position with the maximum total thickness are extracted as the coordinates of the interference extreme point.

[0132] The fastening offset accumulation module is used to obtain the bolt fastening sequence, take the coordinates of the interference extreme point as the initial rotation fulcrum, calculate the pose change of the node connection plate caused by the bolt fastening process according to the bolt fastening sequence, accumulate the pose change, and generate a homogeneous matrix of node connection offset.

[0133] The self-weight deformation calculation module is used to construct a cantilever beam stress model with the already fastened nodes as fixed ends based on the module structure parameters in the theoretical geometric model data, calculate the terminal deformation of the module to be assembled under its own weight, and convert the terminal deformation into a homogeneous matrix of self-weight deformation in the local coordinate system.

[0134] The pose mapping prediction module is used to obtain the actual three-dimensional coordinate matrix of the terminal of the installed module, multiply the actual three-dimensional coordinate matrix of the terminal by the node connection offset homogeneous matrix to generate the offset spatial reference matrix, and then multiply it by the self-weight deformation homogeneous matrix to obtain the global pose result matrix. Then, the translation component is extracted from it to obtain the true three-dimensional coordinate prediction value of the terminal node of the module to be assembled.

[0135] The gasket thickness layout module is used to obtain the theoretical access coordinates of the next module to be assembled. By comparing the predicted real three-dimensional coordinates of the terminal node with the theoretical access coordinates, the three-dimensional deviation vector is calculated, and then the non-negative gasket thickness value required for each bolt hole position is calculated, generating a gasket layout diagram and outputting it.

[0136] Each of the modules can be implemented in whole or in part through software, hardware, or a combination thereof. It supports hardware embedded in or independent of the processor in the computer device, and also supports software stored in the memory of the computer device, so that the processor can call and execute the operations corresponding to each of the above modules.

[0137] The above embodiments are only used to illustrate the technical solutions of the present invention, and are not intended to limit it. Although the present invention has been described in detail with reference to the foregoing embodiments, those skilled in the art should understand that modifications can still be made to the technical solutions described in the foregoing embodiments, or equivalent substitutions can be made to some of the technical features. Such modifications or substitutions do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention, and should all be included within the protection scope of the present invention.

Claims

1. A method for predicting the cumulative assembly error of modular steel structure buildings, characterized in that, include: S1. Obtain the theoretical geometric model data of the module to be assembled and the installed module, and receive the thickness of the anti-corrosion coating at discrete measurement points collected on the nodal contact surface of the module. Align the thickness of the anti-corrosion coating at discrete measurement points with the theoretical geometric model data in space to generate multi-point measured data of the anti-corrosion coating thickness with coordinate labels. S2. Based on the measured data of multi-point anti-corrosion coating thickness with coordinate labels, construct a continuous coating thickness distribution surface of the module to be assembled and the installed module. By superimposing two continuous coating thickness distribution surfaces, extract the coordinates of the position with the maximum total thickness as the coordinates of the interference extreme point. S3. Obtain the bolt tightening sequence. Using the coordinates of the interference extreme point as the initial rotation fulcrum, calculate the pose change of the node connection plate caused by the bolt tightening process according to the bolt tightening sequence. Accumulate the pose changes to generate a homogeneous matrix of node connection offset. S4. Based on the module structure parameters in the theoretical geometric model data, construct a cantilever beam force model with the already fastened nodes as fixed ends, calculate the terminal deformation of the module to be assembled under its own weight, and convert the terminal deformation into a homogeneous matrix of self-weight deformation in the local coordinate system. S5. Obtain the actual three-dimensional coordinate matrix of the terminal of the installed module, multiply the actual three-dimensional coordinate matrix of the terminal by the homogeneous matrix of node connection offset to generate the offset spatial reference matrix, and then multiply it by the homogeneous matrix of self-weight deformation to obtain the global pose result matrix. Then extract the translation component from it to obtain the predicted value of the actual three-dimensional coordinates of the terminal node of the module to be assembled. S6. Obtain the theoretical access coordinates of the next module to be assembled. By comparing the predicted real three-dimensional coordinates of the terminal node with the theoretical access coordinates, calculate the three-dimensional deviation vector, and then calculate the non-negative shim thickness value required for each bolt hole position. Generate and output the shim layout diagram.

2. The method for predicting the cumulative assembly error of modular steel structure buildings according to claim 1, characterized in that, Before spatially aligning the thickness of the anti-corrosion coating at discrete measurement points with the theoretical geometric model data, the following steps are included: Establish statistical criteria for judging the degree of dispersion of data; Based on statistical criteria, outlier identification is performed on the thickness of the anti-corrosion coating at discrete measurement points. Data points identified as outliers are removed, and the remaining valid data points are used to generate multi-point measured data of anti-corrosion coating thickness with coordinate labels.

3. The method for predicting the cumulative assembly error of modular steel structure buildings according to claim 1, characterized in that, The construction of the continuous coating thickness distribution surface for the module to be assembled and the installed module includes: The measured data of multi-point anti-corrosion coating thickness with coordinate labels are processed into a grid to generate a coating thickness data grid. The bilinear interpolation algorithm is used to calculate the coating thickness at any point within the coating thickness data grid. Based on the calculated coating thickness at any point within the grid, a continuous coating thickness distribution surface is generated by fitting.

4. The method for predicting the cumulative assembly error of modular steel structure buildings according to claim 1, characterized in that, The calculation of the positional change of the node connection plate caused by the bolt tightening process includes: Based on the continuous coating thickness distribution surface, the local coating gap at each bolt location is obtained; Based on the principle of small angle approximation, the local coating gap is converted into a small rotation angle and translation around the initial rotation pivot point; The small rotation angle and translation amount are combined into a single-step pose change matrix, which is used as the pose change of the node connection plate caused by the bolt tightening process.

5. The method for predicting the cumulative assembly error of modular steel structure buildings according to claim 4, characterized in that, The step of accumulating pose changes to generate a homogeneous node connection offset matrix includes: Initialize an identity matrix as the initial cumulative pose change matrix; According to the bolt tightening sequence, iteratively calculate the single-step pose change matrix generated by each bolt tightening; A new cumulative pose change matrix is ​​generated by multiplying the single-step pose change matrix of the current step with the cumulative pose change matrix updated in the previous step. This process continues until all bolts have been traversed, resulting in the final homogeneous matrix of node connection offsets.

6. The method for predicting the cumulative assembly error of modular steel structure buildings according to claim 1, characterized in that, The calculation of the final deformation of the module to be assembled under its own weight includes: Obtain the uniformly distributed self-weight load, elastic modulus, and moment of inertia of the module to be assembled from the theoretical geometric model data; Substitute the self-weight uniformly distributed load, elastic modulus, and moment of inertia of the cross section into the analytical equations of structural mechanics; By solving the analytical equations of structural mechanics, the vertical sag displacement and end face rotation of the cantilever beam stress model are calculated and used together as the end deformation.

7. The method for predicting the cumulative assembly error of modular steel structure buildings according to claim 1, characterized in that, The process of multiplying the actual three-dimensional coordinate matrix of the terminal with the homogeneous matrix of node connection offset to generate the offset spatial reference matrix, and then multiplying it with the homogeneous matrix of self-weight deformation to obtain the global pose result matrix, includes: Multiply the actual three-dimensional coordinate matrix of the terminal with the homogeneous matrix of the node connection offset to generate the offset spatial reference matrix that includes the bolt fastening effect. Multiply the offset spatial reference matrix by the homogeneous matrix of self-weight deformation; The final global pose result matrix is ​​obtained through the above ordered multiplication, and the predicted values ​​of the actual 3D coordinates of the terminal nodes are extracted from it.

8. The method for predicting the cumulative assembly error of modular steel structure buildings according to claim 1, characterized in that, The calculation of the three-dimensional deviation vector, and then the calculation of the required non-negative shim thickness for each bolt hole, includes: The three-dimensional deviation vector is decomposed into a normal deviation component perpendicular to the node contact surface and a tangential deviation component along the direction of the node contact surface. The base thickness for shim compensation at all bolt hole locations is determined based on the value of the normal deviation component: when the normal deviation component is negative, its absolute value is taken as the base thickness; when the normal deviation component is positive, the preset process reference thickness is used as the base thickness. Based on the magnitude and direction of the tangential deviation component, the shim thickness adjustment amount for compensating the tangential deviation at each bolt hole position is calculated. The adjustment amount is expressed as a positive or negative value, representing an increase or decrease in shim thickness, and is superimposed on the base thickness. When the superimposed thickness value is less than a preset non-negative thickness threshold, the shim thickness of all bolt holes is compensated by an equal upward translation to obtain the final shim thickness value required for each bolt hole position.

9. A modular steel structure building assembly error cumulative prediction system, characterized in that, include: The data acquisition and alignment module is used to acquire the theoretical geometric model data of the module to be assembled and the installed module, and to receive the thickness of the anti-corrosion coating at discrete measurement points collected on the nodal contact surface of the module. The module spatially aligns the thickness of the anti-corrosion coating at discrete measurement points with the theoretical geometric model data to generate multi-point measured data of the anti-corrosion coating thickness with coordinate labels. The coating surface overlay module is used to construct a continuous coating thickness distribution surface of the module to be assembled and the installed module based on the measured data of the thickness of the multi-point anti-corrosion coating with coordinate labels. By overlaying two continuous coating thickness distribution surfaces, the coordinates of the position with the maximum total thickness are extracted as the coordinates of the interference extreme point. The fastening offset accumulation module is used to obtain the bolt fastening sequence. Using the coordinates of the interference extreme point as the initial rotation fulcrum, it calculates the pose change of the node connection plate caused by the bolt fastening process according to the bolt fastening sequence, accumulates the pose change, and generates a homogeneous node connection offset matrix. The self-weight deformation calculation module is used to construct a cantilever beam stress model with the fixed ends of the already fastened nodes based on the module structure parameters in the theoretical geometric model data, calculate the terminal deformation of the module to be assembled under its own weight, and convert the terminal deformation into a homogeneous matrix of self-weight deformation in the local coordinate system. The pose mapping prediction module is used to obtain the actual three-dimensional coordinate matrix of the terminal of the installed module, multiply the actual three-dimensional coordinate matrix of the terminal by the node connection offset homogeneous matrix to generate the offset spatial reference matrix, and then multiply it by the self-weight deformation homogeneous matrix to obtain the global pose result matrix. Then, the translation component is extracted from it to obtain the predicted value of the actual three-dimensional coordinates of the terminal node of the module to be assembled. The gasket thickness layout module is used to obtain the theoretical access coordinates of the next module to be assembled. By comparing the predicted real three-dimensional coordinates of the terminal node with the theoretical access coordinates, the three-dimensional deviation vector is calculated, and then the non-negative gasket thickness value required for each bolt hole position is calculated, generating a gasket layout diagram and outputting it.

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