A three-dimensional point cloud-based foamed ceramic insulation board layout optimization method

Abstract

The application belongs to the technical field of data processing, and discloses a foamed ceramic heat preservation plate layout optimization method based on three-dimensional point clouds, which comprises the following steps: carrying out grid division on a wall surface according to the nominal size of the plate material, and distinguishing complete installation units from cutting installation units; collecting edge top line point clouds and edge surface point clouds of each edge of each plate material, and respectively extracting edge height curves and concave-convex amount curves along the edge direction; for any plate material pair under each installation orientation combination, screening out illegal combinations based on the edge height curves and the concave-convex amount curves; calculating pairing costs for legal combinations, and forming a pairing cost matrix; and taking the minimum sum of the height difference of the plate joint as the optimization target, and solving an optimal layout scheme under the constraint of the pairing cost matrix. The application realizes quantitative prediction of the plate joint misalignment distribution before installation, and overcomes the problems that the existing manual layout method cannot predict the misalignment condition before installation, and can only rely on polishing and rework after the misalignment exceeds the limit.

Description

Technical Field

[0001] This invention relates to the field of data processing technology, and more specifically, to a method for optimizing the layout of foamed ceramic insulation boards based on three-dimensional point clouds. Background Technology

[0002] Foamed ceramic insulation board is a lightweight insulation material with ceramic as the base material and containing a large number of closed pores. It is widely used in building exterior wall insulation systems. During wall installation, multiple boards are spliced ​​together, leaving gaps between adjacent boards. These gaps are usually filled with materials such as expanding foam, sealant, or crack-resistant mortar.

[0003] During the high-temperature sintering process of foamed ceramic panels, uneven temperature distribution within the kiln leads to varying degrees of shrinkage in different parts of the panel, resulting in warping deformation in the finished product. This warping deformation causes a non-uniform distribution of the top surface height along the edge direction of the panel. After installation, adjacent panels will have a height difference at the joint, known as misalignment. Current construction specifications have clear limits on the amount of misalignment at the joint. Excessive misalignment not only affects the flatness of the wall surface but also creates stress concentration at the misalignment point after the filler material has cured, leading to cracking of the filler layer and subsequent durability problems such as water seepage. Currently, on-site layout usually relies on visual judgment by construction workers, who determine the installation position and orientation of each panel based on experience. Due to the lack of quantitative description of the actual geometric shape of the panel edges, it is impossible to predict the misalignment situation after adjacent panels are installed during the layout stage. Whether the misalignment exceeds the limit can only be discovered after the panels are fixed to the wall. For fixed boards, excessive misalignment usually requires grinding and leveling the joints or disassembling and reinstalling the boards, which not only increases construction costs but also affects the construction period. Summary of the Invention

[0004] To overcome the aforementioned problems in the prior art, this invention proposes a layout optimization method for foamed ceramic insulation boards based on three-dimensional point clouds, which is used to solve the above problems.

[0005] This invention provides the following technical solution: A method for optimizing the layout of foamed ceramic insulation boards based on 3D point clouds, comprising: The wall surface is divided into grids according to the nominal size of the board material. The residual areas at the edges and corners are identified. The residual areas at the edges and corners are defined as cutting installation units and their effective filling size is recorded. The remaining areas are defined as complete installation units, which together constitute the installation unit grid. Collect edge top line point cloud and edge surface point cloud of each side of each board; extract the edge height curve of each side of each board along the edge direction from the edge top line point cloud; extract the concavity and convexity curve of each side of each board along the edge direction from the edge surface point cloud. For any pair of boards under various installation orientation combinations, valid combinations are obtained by filtering out those based on the edge height curve and the concavity / convexity curve. Calculate the pairing cost for each legal combination of board pairs to form a pairing cost matrix; The optimal layout scheme is solved under the constraint of the pairing cost matrix, with the goal of minimizing the total sum of global board seam height differences.

[0006] Preferably, the method for extracting the edge height curve includes: The edge top line point cloud is divided into several equally spaced arc length compartments according to its position along the edge direction; Extract representative height values ​​from the height coordinates of all points within each arc-length compartment; Linear fitting is performed on the height representative value sequence of all arc length chambers to separate the overall tilt trend component. The edge height curve is obtained by subtracting the overall tilt trend component from the height representative value sequence.

[0007] Preferably, the extraction of representative height values ​​from the height coordinates of all points within each arc-length compartment includes: Calculate the preset quantiles of the height coordinates of all points within each arc-length compartment to obtain the quantile height value of each compartment; Calculate the median and median absolute deviation of the quantile height values ​​of all arc length warehouses. Determine the arc length warehouses whose quantile height values ​​deviate from the median by more than a preset multiple of the median absolute deviation as outliers. Replace the quantile height values ​​of the outliers with the linear interpolation of the adjacent warehouses. The height values ​​of each compartment quantile after replacement are used as the representative height values.

[0008] Preferably, the method for extracting the concavity / convexity curve includes: The edge point cloud is divided into several equally spaced arc length compartments according to their position along the edge direction. The spacing between the arc length compartments is the same as the spacing used when extracting the edge height curve. Take the maximum value of the coordinates of all points in each arc-length compartment in the normal direction of the edge surface, and use the difference between the maximum value and the nominal edge position of the edge as the concavity / convexity representative value of the compartment. The concavity and convexity representative value sequences of all arc length chambers are filtered and smoothed to obtain the concavity and convexity curves.

[0009] Preferably, the step of filtering out valid combinations based on the edge height curve and the concavity / convexity curve includes: For each pair of plates, each adjacent direction, and each installation orientation combination, apply direction reversal and edge number substitution transformation to the edge height curve and the concavity / convexity curve according to the installation orientation; The difference between the edge height curves after transformation on both sides is used to obtain the misalignment function; the sum of the concavity and convexity curves after transformation on both sides is used to obtain the trend superposition function. The absolute value of each point of the misalignment function exceeding the misalignment limit is considered a misalignment constraint, and the value of each point of the trend superposition function exceeding the seam tolerance range is considered a seam width constraint. Any installation orientation combination that violates either constraint is determined to be an illegal combination, and the rest are determined to be legal combinations.

[0010] Preferably, the calculation of pairing costs for each legal combination of plate pairs, forming a pairing cost matrix, includes: For each pair of boards and each legal mounting orientation combination under adjacent directions, calculate the cost of that combination; For each reserved side selection of each board, the edge height curve and concavity / convexity curve of the corresponding side are intercepted with the effective filling size of the corresponding cutting and installation unit. The concavity / convexity and misalignment contribution of the cut edge are set to zero to obtain the equivalent edge parameters of the board under each reserved side and calculate the corresponding cost. Using the combinations of plate pairs, adjacent directions, and installation orientations as indexes, the cost value of each legal combination and the cost value of each reserved side of each plate are uniformly stored in the pairing cost matrix, which can be used for subsequent global optimization to look up the table according to the current decision to obtain the pairing cost matrix.

[0011] Preferably, the cost of calculating the combination includes: The mean square value of each sampling point of the misalignment function is used as the principal term; the square of the mean value of the misalignment function along the edge direction is used as the soft constraint penalty term; the principal term and the soft constraint penalty term are weighted and summed to obtain the combined cost.

[0012] Preferably, the method for finding the optimal typesetting scheme includes: Each board material is screened for warpage magnitude and included in either the complete installation candidate pool or the cutting candidate pool. The allocation of installation positions and orientation of the plates in the complete installation candidate pool, as well as the selection and retention of each cutting installation unit by the plates in the cutting candidate pool, are used as synchronous decision variables. The sum of the pairing costs of all adjacent installation units in the installation unit grid to the corresponding plate seams is used as the objective function. The cost of each pair of adjacent plates under the current decision is obtained by looking up a table in the pairing cost matrix and then accumulated. An initial layout scheme is constructed using a greedy algorithm. Then, a simulated annealing algorithm is used to iteratively search under three types of neighborhood operations: swapping the positions of complete boards, changing the orientation, and selecting and replacing cut boards. After each neighborhood operation, the objective function value is updated incrementally using the pairing cost matrix to obtain the optimal layout scheme.

[0013] Preferably, the step of screening each board for warpage and including them in either the complete installation candidate pool or the cutting candidate pool includes: The range of edge height curves on each side of each board is used as the warping amplitude; Boards whose warpage does not exceed a preset threshold are included in the complete installation candidate pool and participate in the location allocation and orientation optimization of complete installation units; Boards with warping exceeding a preset threshold are downgraded and included in the cutting candidate pool to participate in the board selection and retention optimization of the cutting and installation unit.

[0014] This invention provides a method for optimizing the layout of foamed ceramic insulation boards based on three-dimensional point clouds, which has the following beneficial effects: This invention collects edge top line point clouds and edge surface point clouds of each board, and extracts edge height curves and concavity / convexity curves from them respectively. It expresses the warping shape of the board edge in a quantifiable data form, and obtains the measured geometric characteristics of each board edge before layout decision-making. This enables quantitative prediction of the misalignment distribution of board seams after installation, overcoming the problem that existing manual layout methods cannot predict misalignment before installation and can only rely on sanding and rework after misalignment exceeds the limit.

[0015] This invention calculates the misalignment function and trend superposition function for any pair of boards under various installation orientation combinations, and uses misalignment constraints and joint width constraints to filter out illegal combinations. For legal combinations, it calculates the pairing cost to form a pairing cost matrix. Then, with the goal of minimizing the total sum of global board joint height differences, it uses the installation position, installation orientation, and the selection and retention of boards for cutting installation units as synchronous decision variables for global optimization. This enables the final layout scheme to minimize the total misalignment of the entire wall surface while meeting the specification constraints. Compared with layout methods that rely on manual experience, the layout quality is no longer affected by the personal experience of construction personnel, and it has determinism and repeatability. Attached Figure Description

[0016] Figure 1 This is a flowchart illustrating a method for optimizing the layout of foamed ceramic insulation boards based on three-dimensional point clouds, according to the present invention. Detailed Implementation

[0017] 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. Example

[0018] Please see Figure 1 In this embodiment, a method for optimizing the layout of foamed ceramic insulation boards based on three-dimensional point clouds includes: S1. Divide the wall surface into grids according to the nominal size of the board, identify the residual areas at the edges and corners, define the residual areas at the edges and corners as cutting installation units and record their effective filling size, and define the remaining areas as complete installation units, which together constitute the installation unit grid. It should be noted that this embodiment uses a 4200mm×3600mm building exterior wall, with a nominal panel size of 300mm×600mm, and the standard specifies a panel joint width of 5mm, an allowable deviation range of ±2mm, and a panel joint misalignment limit of no more than 2mm as an example for illustration.

[0019] In this embodiment, the grid division process is illustrated using the horizontal direction as an example. The wall is 3600mm long horizontally, the nominal width of the panels is 600mm, and the joint width is 5mm. There are joints between the panels, but no joints are found at the edges near the wall. If n columns of complete panels are arranged horizontally, n-1 horizontal joints will be generated, occupying a total width of n×600+(n-1)×5. When n=5, the area occupied is 3025mm, leaving 575mm, which is insufficient to accommodate a complete panel. Therefore, the remaining area on the right is a corner residual area, which is 575mm wide. A 5mm joint is reserved between this area and the adjacent complete panel on the left. The actual width of the panel to be cut is 570mm. The same applies to the vertical direction. The wall is 4200mm high, the nominal height of the panels is 300mm, and a total of 13 rows occupy 3955mm. The remaining 245mm is insufficient to accommodate a complete panel. The top is a corner residual area, which is 245mm high. A 5mm joint is reserved between this area and the adjacent complete panel below. The actual height of the panel to be cut is 240mm.

[0020] The horizontal direction consists of 5 columns of complete installation units plus 1 column of cut installation units, and the vertical direction consists of 13 rows of complete installation units plus 1 row of cut installation units. The actual size of the cut plate material in the upper right corner unit is 570mm × 240mm. The aforementioned residual area at the corner is defined as a cut installation unit, and the remaining 5 × 13 = 65 positions are defined as complete installation units, together forming the installation unit grid.

[0021] S2. Collect edge top line point cloud and edge surface point cloud of each side of each board; extract the edge height curve of each side of each board along the edge direction from the edge top line point cloud; extract the concavity and convexity curve of each side of each board along the edge direction from the edge surface point cloud. In this embodiment, the plate is placed flat on the inspection table with the top surface facing upwards. A line laser profilometer is used to scan at a constant speed along each edge direction to collect two types of point clouds.

[0022] The edge top line point cloud acquisition area is a narrow band along the edge direction on the top surface of the board, with a width of 15mm (extending from the edge towards the inside of the board). The scanning step interval along the edge direction is 1mm, and approximately 15 points are acquired in the width direction for each cross-section, which are used for subsequent extraction of the edge height curve. For a 600mm long edge, approximately 9000 points are acquired per side; for a 300mm long edge, approximately 4500 points are acquired per side.

[0023] The edge point cloud acquisition area covers the four sides of the material, with a scanning step interval of 1mm. The height direction covers the entire thickness of the material, used for subsequent extraction of the convexity / concave curve. Before use, the testing platform must be calibrated, and the platform plane equation recorded. This is used for subsequent tilt compensation of the height coordinates of each point, eliminating systematic errors introduced by the platform's non-horizontal nature. The compensation method is as follows: subtract the calculated value of the platform plane equation at the horizontal position of each point from the measured height coordinates to obtain the net height relative to the ideal horizontal plane.

[0024] The method for extracting the edge height curve includes: The edge top line point cloud is divided into several equally spaced arc length compartments according to its position along the edge direction; Extract representative height values ​​from the height coordinates of all points within each arc-length compartment; Linear fitting is performed on the height representative value sequence of all arc length chambers to separate the overall tilt trend component. The edge height curve is obtained by subtracting the overall tilt trend component from the height representative value sequence.

[0025] The extraction of representative height values ​​from the height coordinates of all points within each arc-length compartment includes: Calculate the preset quantiles of the height coordinates of all points within each arc-length compartment to obtain the quantile height value of each compartment; Calculate the median and median absolute deviation of the quantile height values ​​of all arc length warehouses. Determine the arc length warehouses whose quantile height values ​​deviate from the median by more than a preset multiple of the median absolute deviation as outliers. Replace the quantile height values ​​of the outliers with the linear interpolation of the adjacent warehouses. The height values ​​of each compartment quantile after replacement are used as the representative height values.

[0026] In this embodiment, the interval between the arc length compartments is 2mm, and the 600mm long side is divided into 300 arc length compartments. Each arc length compartment contains approximately 15 points (derived from the overlap of 1mm step × 15 cross-sectional points during data acquisition). The extraction of the height representative value will be explained in the next layer.

[0027] The preset quantile is the 90th percentile. The 90th percentile, rather than the mean or maximum value, is chosen because: the top surface of the foamed ceramic panel has pores, and the height coordinates of the point cloud at these pores are significantly lower than the actual top surface. Taking the mean would systematically underestimate the top surface height; taking the maximum value would be sensitive to occasional burrs or noise points. The 90th percentile is equivalent to the robust top surface height after removing the lowest 10% of pore points and the highest few noise points. It represents the representative contact height of the actual top surface of the panel at that cross-section, i.e., the effective height that determines the height difference between the panel seams after installation.

[0028] The threshold for identifying outliers is set at 5 times the median absolute deviation. Taking the 300 arc-length cells in this example, if a cell happens to be located at the edge of the plate where it is chipped, the quantile height value of that cell will be significantly lower, and the difference from other cells will be far beyond the range of height changes caused by normal warping. This cell will be identified as an outlier and replaced with linear interpolation of adjacent cells, which can avoid interference from individual outliers in subsequent analysis.

[0029] After extracting the representative height values, a linear least-squares fit was performed on the height representative value sequence of 300 arc-length sections to obtain a trend line along the arc length direction. The trend line reflects the overall tilt of the board. Subtracting the corresponding value of the trend line from the height representative value sequence yields the residual sequence after removing the overall tilt, i.e., the edge height curve. The mean of the edge height curve is approximately zero, and its value reflects the local height deviation of each arc-length position relative to the average level of the board itself. A positive value indicates that the top surface is too high at that point, and a negative value indicates that it is too low.

[0030] The method for extracting the concavity / convexity curve includes: The edge point cloud is divided into several equally spaced arc length compartments according to their position along the edge direction. The spacing between the arc length compartments is the same as the spacing used when extracting the edge height curve. Take the maximum value of the coordinates of all points in each arc-length compartment in the normal direction of the edge surface, and use the difference between the maximum value and the nominal edge position of the edge as the concavity / convexity representative value of the compartment. The concavity and convexity representative value sequences of all arc length chambers are filtered and smoothed to obtain the concavity and convexity curves.

[0031] In this embodiment, the arc length compartment spacing is also set to 2mm to ensure that the concave and convex curves correspond to the edge height curves point by point in the arc length direction, providing a consistent data basis for the subsequent calculation of the trend superposition function.

[0032] The meaning of taking the maximum normal coordinate value within each arc length compartment is: at that cross-section, the point on the edge surface farthest from the outer edge of the board represents the outermost convex position of the edge surface at that cross-section. The difference between this maximum value and the nominal edge position is used as the representative value of concavity / convexity—the nominal edge position is determined by the nominal dimensions of the board and corresponds to the normal coordinate of the ideal flat edge surface. A positive difference indicates that the edge surface of the cross-section convexes outward relative to the ideal position, and a negative difference indicates that it is concave inward. The maximum value is chosen instead of the average value because the impact of the concavity / convexity of the edge surface on the width of the board gap is determined by the most prominent position—if the average value were taken, local concavities such as pores would lower the average value, underestimate the amount of outward convexity, and thus underestimate the degree to which the gap narrows at that point.

[0033] The filtering and smoothing process uses median filtering with a length of 5 arc lengths to remove spikes in individual compartments caused by pore exposure or measurement noise. Then, mean filtering with a length of 5 arc lengths is used for further smoothing, preserving the macroscopic concavity and convexity trend along the edge direction to obtain the concavity and convexity curve.

[0034] S3. For any pair of plates under various installation orientation combinations, legal combinations are obtained by filtering out those based on the edge height curve and the concavity / convexity curve. The process of filtering out valid combinations based on the edge height curve and the concavity / convexity curve includes: For each pair of plates, each adjacent direction, and each installation orientation combination, apply direction reversal and edge number substitution transformation to the edge height curve and the concavity / convexity curve according to the installation orientation; The difference between the edge height curves after transformation on both sides is used to obtain the misalignment function; the sum of the concavity and convexity curves after transformation on both sides is used to obtain the trend superposition function. The absolute value of each point of the misalignment function exceeding the misalignment limit is considered a misalignment constraint, and the value of each point of the trend superposition function exceeding the seam tolerance range is considered a seam width constraint. Any installation orientation combination that violates either constraint is determined to be an illegal combination, and the rest are determined to be legal combinations.

[0035] In this embodiment, the rectangular plate has four installation orientations: upright, left-right mirror flip, top-bottom mirror flip, and 180° rotation. The corresponding transformation rules are as follows: When left-right mirror flip, the edge numbers of the left and right sides are swapped, and the arc length directions of the curves on both sides are reversed (i.e., the beginning and end of the sequence are interchanged); when top-bottom mirror flip, the edge numbers of the top and bottom sides are swapped, and the arc length directions of the curves are also reversed; when rotating 180°, the top and bottom sides are swapped, the left and right sides are swapped, and the arc length directions of the curves are reversed. The reason for reversing the arc length direction is that after flipping, the starting point of the arc length of that side of the plate becomes the original ending point. If it is not reversed, the physical positions of the two sides at the corresponding arc length positions will no longer correspond, and the difference will lose its meaning.

[0036] Taking board A installed facing forward, with its right side adjacent to the left side of board B installed facing forward, as an example. Both adjacent edges of the boards are 300mm long. Divided into 2mm arc length gaps, 150 sampling points are obtained for each. The misalignment function is defined as the point-by-point difference between the two curves: for each sampling point, the misalignment value at that location is obtained by subtracting the value of the edge height curve of board A at that location from the value of the edge height curve of board B at that location. A positive misalignment value indicates that the top surface of board A is higher than that of board B at that point, and a negative value indicates that board A is lower than board B. The absolute value is the height difference of the board joint at that location.

[0037] The misalignment constraint requires that the absolute value of each of the 150 sampling points of the misalignment function does not exceed 2mm. If the absolute value of any sampling point exceeds 2mm, the orientation combination is deemed invalid.

[0038] The trend superposition function is defined as the point-by-point sum of the concavity and convexity curves on both sides: for each sampling point, the value of the concavity and convexity curve on the side of board A at that position is added to the value of the concavity and convexity curve on the side of board B at the corresponding position to obtain the trend superposition value at that position. This represents the combined effect of the concavity and convexity of both edge surfaces at that arc length position on the board seam. Outward convexity is positive, narrowing the gap; inward concavity is negative, widening the gap. The superposition value reflects the deviation of the actual gap width from the nominal 5mm. The gap width constraint requires that the point-by-point value of the trend superposition function be within the allowable range. According to the specification, the allowable deviation of the board seam width is ±2mm, and the limit range of the trend superposition function is [-2mm, +2mm]. That is, the concavity and convexity superposition of both edge surfaces must not cause the actual gap width to exceed the allowable range of 3mm to 7mm. For example, when the superposition value is +2mm, the actual gap narrows to 3mm, just reaching the lower limit of the specification; if the superposition value further exceeds +2mm, the actual gap is less than 3mm, and is judged as illegal. Similarly, when the superposition value is -2mm, the actual gap widening to 7mm is the upper limit threshold; a superposition value below -2mm is considered invalid. Orientation combinations that violate the gap width constraint are also considered invalid.

[0039] Perform the above screening process for all board pairs, all adjacent directions (horizontal and vertical seams), and all orientation combinations, retaining the legal combinations that pass both constraints.

[0040] S4. Calculate the pairing cost for each legal combination of board pairs and construct a pairing cost matrix; The calculation of pairing costs for each legal combination of plate pairs, forming a pairing cost matrix, includes: For each pair of boards and each legal mounting orientation combination under adjacent directions, calculate the cost of that combination; For each reserved side selection of each board, the edge height curve and concavity / convexity curve of the corresponding side are intercepted with the effective filling size of the corresponding cutting and installation unit. The concavity / convexity and misalignment contribution of the cut edge are set to zero to obtain the equivalent edge parameters of the board under each reserved side and calculate the corresponding cost. Using the combinations of plate pairs, adjacent directions, and installation orientations as indexes, the cost value of each legal combination and the cost value of each reserved side of each plate are uniformly stored in the pairing cost matrix, which can be used for subsequent global optimization to look up the table according to the current decision to obtain the pairing cost matrix.

[0041] The cost of calculating this combination includes: The mean square value of each sampling point of the misalignment function is used as the principal term; the square of the mean value of the misalignment function along the edge direction is used as the soft constraint penalty term; the principal term and the soft constraint penalty term are weighted and summed to obtain the combined cost.

[0042] In this embodiment, the main term is the mean square value of 150 sampling points of the misalignment function, which is the average of the squares of each of the 150 misalignment values, expressed in mm². A smaller mean square value indicates a smaller overall misalignment along the entire seam for that pairing under that orientation combination. The soft constraint penalty term is the square of the mean of the 150 sampling points of the misalignment function. The mean reflects whether there is a systematic unidirectional deviation in the misalignment—if one side of the entire seam is consistently higher than the other, the mean is not zero. The square of the mean, as a penalty term, makes the optimization tend to select pairs with alternating high and low sides rather than a unidirectional bias. When the two terms are weighted and summed, the main term has a weight of 0.7, and the soft constraint penalty term has a weight of 0.3, reflecting that uniformity control has a higher priority than systematic deviation control.

[0043] The calculation method for the equivalent edge parameters of the cut board is as follows: For the board to be cut, the cutting operation divides the board into a retained part and a discarded part. Which side to retain (i.e., from which end of the board to cut the effective filling size) is called the retained side selection. Taking the actual width of the board to be cut, 570mm, as the cutting length, 285 sampling points are taken from the corresponding edge height curve and concavity / convexity curve of the corresponding edge as the equivalent curve under the retained side. The concavity / convexity curve of the cutting edge (i.e., the new edge generated by the cutting) is set to a sequence of all zeros, and the misalignment contribution is also set to zero. The reason is that the cutting surface is generated by the sawing process, and the flatness is guaranteed by the cutting accuracy. It does not have random concavity / convexity caused by sintering warping. Its influence on the board seam can be regarded as an ideal plane.

[0044] The pairing cost matrix is ​​stored using a three-level index: plate pair number, adjacent direction (horizontal or vertical), and installation orientation combination. Each valid combination corresponds to a cost value. The matrix is ​​calculated once before the optimization solution begins, and subsequent optimization iterations directly look up the table without recalculating the misalignment function.

[0045] S5. With the goal of minimizing the total sum of global board seam height differences, solve for the optimal layout scheme under the constraints of the pairing cost matrix.

[0046] The method for finding the optimal typesetting scheme includes: Each board material is screened for warpage magnitude and included in either the complete installation candidate pool or the cutting candidate pool. The allocation of installation positions and orientation of the plates in the complete installation candidate pool, as well as the selection and retention of each cutting installation unit by the plates in the cutting candidate pool, are used as synchronous decision variables. The sum of the pairing costs of all adjacent installation units in the installation unit grid to the corresponding plate seams is used as the objective function. The cost of each pair of adjacent plates under the current decision is obtained by looking up a table in the pairing cost matrix and then accumulated. An initial layout scheme is constructed using a greedy algorithm. Then, a simulated annealing algorithm is used to iteratively search under three types of neighborhood operations: swapping the positions of complete boards, changing the orientation, and selecting and replacing cut boards. After each neighborhood operation, the objective function value is updated incrementally using the pairing cost matrix to obtain the optimal layout scheme.

[0047] The step of screening each board for warpage magnitude and including it in either the complete installation candidate pool or the cutting candidate pool includes: The range of edge height curves on each side of each board is used as the warping amplitude; Boards whose warpage does not exceed a preset threshold are included in the complete installation candidate pool and participate in the location allocation and orientation optimization of complete installation units; Boards with warping exceeding a preset threshold are downgraded and included in the cutting candidate pool to participate in the board selection and retention optimization of the cutting and installation unit.

[0048] In this embodiment, the range (maximum minus minimum) of the height curves of each edge is used as the warp amplitude. The preset threshold is selected based on the following: after detrending, the mean of the edge height curves is approximately zero. If the warp amplitude (i.e., the range) of a single edge is 4mm, then the highest point of the curve is approximately +2mm, the lowest point is approximately -2mm, and the maximum absolute value is approximately 2mm, which just touches the specification limit. When this edge is paired with the opposite straight edge (where all height curves are zero), the misalignment function is equal to the height curve of that edge, and the maximum misalignment value is close to the specification limit of 2mm. If there is also warping on the opposite side, the superposition of the two is very likely to exceed the limit. Therefore, 4mm is used as the pooling threshold. Boards with a warp amplitude exceeding 4mm are downgraded and included in the cutting candidate pool—after cutting, the retained side is shorter, and the warp amplitude is reduced accordingly, so that the board that originally exceeded the limit still has utilization value. Boards with a warp amplitude not exceeding 4mm are included in the complete installation candidate pool, and boards with a warp amplitude exceeding 4mm are downgraded and included in the cutting candidate pool—after cutting, the retained side is shorter, and the warp amplitude is reduced accordingly, so that the board that originally exceeded the limit still has utilization value.

[0049] The objective function is the sum of the pairing costs of all adjacent installation units in the installation unit grid for their corresponding seams. In this embodiment, there are 52 horizontal seams between complete installation units and 60 vertical seams on the wall surface. Adding several seams between cutting installation units and adjacent complete installation units, there are approximately 120 seams in total. The cost of each seam is obtained from the pairing cost matrix according to the current decision (position allocation, orientation selection, and reserved side selection). The sum of the costs of the 120 seams is the objective function value of the current layout scheme.

[0050] The greedy initial solution is constructed as follows: The materials for each installation unit are determined sequentially, expanding outwards from the center of the wall. Once the positional order is fixed, for each unfilled position, the materials are enumerated one by one from the unassigned materials. The material and its orientation that minimize the cost increment of the currently determined seam are selected and filled into that position. This serves as the greedy decision for that position. The reason for starting from the center is that the central installation unit has adjacent seams on all four sides, and each decision affects a large number of seams. Prioritizing a better pairing decision here has a more significant effect on improving the overall objective function. After filling all complete installation units in this order, the installation unit is cut, and the material that minimizes the cost of the corresponding seam and the reserved side are selected from the cutting candidate pool to fill the cut, resulting in the greedy initial layout scheme.

[0051] During the simulated annealing iteration, one of three neighborhood operations is randomly selected at each step: 1) Complete Plate Position Swap: Two complete installation units are randomly selected, their plates are swapped, and their orientations are updated to the orientation with the minimum cost in the new position (by looking up the pairing cost matrix and comparing 16 combinations to find the minimum); 2) Orientation Switch: A complete installation unit is randomly selected, and its plate orientation is switched from one of four options to another, updating the cost of adjacent plate seams by looking up the matrix; 3) Cutting Plate Selection and Replacement: A cutting installation unit is randomly selected, and another plate is added from the cutting candidate pool or the retained side is changed, updating the cost by looking up the matrix. After each operation, the update of the objective function value only involves the directly adjacent plate seams of the operated installation unit (at most four), which can be accumulated by looking up the matrix, without recalculating the global value. After the operation is completed, it is determined whether to accept the result: if the objective function value decreases, it is accepted directly; if the objective function value increases, the operation is accepted with a probability that increases with the current temperature and decreases with a large increase in the objective function value.

[0052] It should be noted that the initial temperature setting ensures an initial acceptance probability of approximately 50%, meaning the initial temperature is approximately equal to the initial objective function value divided by the natural logarithm 2. A cooling coefficient of 0.995 is used, and 20N neighborhood operations (N being the total number of boards) are performed at each temperature step. The process terminates when the temperature drops to one-thousandth of the initial temperature or when the objective function value shows no improvement after 200 consecutive temperature steps. Annealing is repeated 5 times with different random seeds, and the scheme with the smallest objective function value and no invalid pairings is output as the final layout scheme.

[0053] The final layout scheme includes the board number, installation orientation, and reserved side of each installation unit, allowing construction personnel to match the boards according to the diagram. This allows them to predict the misalignment of each board joint before installation, thereby reducing the need for sanding rework due to excessive misalignment after installation.

[0054] In the several embodiments provided by this invention, it should be understood that the disclosed systems, apparatuses, and methods can be implemented in other ways. For example, the apparatus embodiments described above are merely illustrative; for instance, the division of units is only one method, and in actual implementation, there may be other division methods. For example, multiple units or components may be combined or integrated into another system, or some features may be ignored or not executed. Furthermore, the coupling or direct coupling or communication connection shown or discussed may be through some interfaces; the indirect coupling or communication connection between apparatuses or units may be electrical, mechanical, or other forms.

[0055] The above description is merely a specific embodiment of the present invention, but the scope of protection of the present invention is not limited thereto. Any changes or substitutions that can be easily conceived by those skilled in the art within the scope of the technology disclosed in the present invention should be included within the scope of protection of the present invention.

[0056] In conclusion, the above description is only a preferred embodiment of the present invention and is not intended to limit the present invention. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for optimizing the layout of foamed ceramic insulation boards based on three-dimensional point clouds, characterized in that, include: The wall surface is divided into grids according to the nominal size of the board material. The residual areas at the edges and corners are identified. The residual areas at the edges and corners are defined as cutting installation units and their effective filling size is recorded. The remaining areas are defined as complete installation units, which together constitute the installation unit grid. Collect edge top line point cloud and edge surface point cloud of each side of each board; extract the edge height curve of each side of each board along the edge direction from the edge top line point cloud; extract the concavity and convexity curve of each side of each board along the edge direction from the edge surface point cloud. The edge top line point cloud is the point cloud within a narrow band along the edge direction on the top surface of the board, and the edge surface point cloud is the point cloud within the four sides of the board. The edge height curve corresponds to the local height deviation of the top surface of the board along the edge, and is used to characterize the subsequent board seam. The concavity and convexity curve reflects the outward and inward convexity of the side of the board edge along the normal direction of the board edge, and is used to evaluate the change in the width of the board gap; For any pair of boards under various installation orientation combinations, valid combinations are obtained by filtering based on the edge height curve and the concavity / convexity curve; the valid combination is a combination that simultaneously satisfies the misalignment constraint and the joint width constraint. For each legal combination of board pairs, the pairing cost is calculated to form a pairing cost matrix; the pairing cost is used to quantitatively characterize the severity of misalignment of the board seams under a set of board-orientation pairing combinations; The optimal layout scheme is solved under the constraint of the pairing cost matrix, with the goal of minimizing the total sum of global board seam height differences.

2. The method for optimizing the layout of foamed ceramic insulation boards based on three-dimensional point clouds according to claim 1, characterized in that, The method for extracting the edge height curve includes: The edge top line point cloud is divided into several equally spaced arc length compartments according to its position along the edge direction; Extract representative height values ​​from the height coordinates of all points within each arc-length compartment; Linear fitting is performed on the height representative value sequence of all arc length chambers to separate the overall tilt trend component. The edge height curve is obtained by subtracting the overall tilt trend component from the height representative value sequence.

3. The method for optimizing the layout of foamed ceramic insulation boards based on three-dimensional point clouds according to claim 2, characterized in that, The extraction of representative height values ​​from the height coordinates of all points within each arc-length compartment includes: Calculate the preset quantiles of the height coordinates of all points within each arc-length compartment to obtain the quantile height value of each compartment; Calculate the median and median absolute deviation of the quantile height values ​​of all arc length warehouses. Determine the arc length warehouses whose quantile height values ​​deviate from the median by more than a preset multiple of the median absolute deviation as outliers. Replace the quantile height values ​​of the outliers with the linear interpolation of the adjacent warehouses. The height values ​​of each compartment quantile after replacement are used as the representative height values.

4. The method for optimizing the layout of foamed ceramic insulation boards based on three-dimensional point clouds according to claim 3, characterized in that, The method for extracting the concavity / convexity curve includes: The edge point cloud is divided into several equally spaced arc length compartments according to their position along the edge direction. The spacing between the arc length compartments is the same as the spacing used when extracting the edge height curve. Take the maximum value of the coordinates of all points in each arc-length compartment in the normal direction of the edge surface, and use the difference between the maximum value and the nominal edge position of the edge as the concavity / convexity representative value of the compartment. The concavity and convexity representative value sequences of all arc length chambers are filtered and smoothed to obtain the concavity and convexity curves.

5. The method for optimizing the layout of foamed ceramic insulation boards based on three-dimensional point clouds according to claim 4, characterized in that, The process of filtering out valid combinations based on the edge height curve and the concavity / convexity curve includes: For each pair of plates, each adjacent direction, and each installation orientation combination, apply direction reversal and edge number substitution transformation to the edge height curve and the concavity / convexity curve according to the installation orientation; The difference between the edge height curves after transformation on both sides is used to obtain the misalignment function; the sum of the concavity and convexity curves after transformation on both sides is used to obtain the trend superposition function. The absolute value of each point of the misalignment function exceeding the misalignment limit is considered a misalignment constraint, and the value of each point of the trend superposition function exceeding the seam tolerance range is considered a seam width constraint. Any installation orientation combination that violates either constraint is determined to be an illegal combination, and the rest are determined to be legal combinations.

6. The method for optimizing the layout of foamed ceramic insulation boards based on three-dimensional point clouds according to claim 5, characterized in that, The calculation of pairing costs for each legal combination of plate pairs, forming a pairing cost matrix, includes: For each pair of boards and each legal mounting orientation combination under adjacent directions, calculate the cost of that combination; For each reserved side selection of each board, the edge height curve and concavity / convexity curve of the corresponding side are intercepted with the effective filling size of the corresponding cutting and installation unit. The concavity / convexity and misalignment contribution of the cut edge are set to zero to obtain the equivalent edge parameters of the board under each reserved side and calculate the corresponding cost. Using the combinations of plate pairs, adjacent directions, and installation orientations as indexes, the cost value of each legal combination and the cost value of each reserved side of each plate are uniformly stored in the pairing cost matrix, which can be used for subsequent global optimization to look up the table according to the current decision to obtain the pairing cost matrix.

7. The method for optimizing the layout of foamed ceramic insulation boards based on three-dimensional point clouds according to claim 6, characterized in that, The cost of calculating this combination includes: The mean square value of each sampling point of the misalignment function is used as the principal term; the square of the mean value of the misalignment function along the edge direction is used as the soft constraint penalty term; the principal term and the soft constraint penalty term are weighted and summed to obtain the combined cost.

8. The method for optimizing the layout of foamed ceramic insulation boards based on three-dimensional point clouds according to claim 7, characterized in that, The method for finding the optimal typesetting scheme includes: Each board material is screened for warpage magnitude and included in either the complete installation candidate pool or the cutting candidate pool. The allocation of installation positions and orientation of the plates in the complete installation candidate pool, as well as the selection and retention of each cutting installation unit by the plates in the cutting candidate pool, are used as synchronous decision variables. The sum of the pairing costs of all adjacent installation units in the installation unit grid to the corresponding plate seams is used as the objective function. The cost of each pair of adjacent plates under the current decision is obtained by looking up a table in the pairing cost matrix and then accumulated. An initial layout scheme is constructed using a greedy algorithm. Then, a simulated annealing algorithm is used to iteratively search under three types of neighborhood operations: swapping the positions of complete boards, changing the orientation, and selecting and replacing cut boards. After each neighborhood operation, the objective function value is updated incrementally using the pairing cost matrix to obtain the optimal layout scheme.

9. The method for optimizing the layout of foamed ceramic insulation boards based on three-dimensional point clouds according to claim 8, characterized in that, The step of screening each board for warpage magnitude and including it in either the complete installation candidate pool or the cutting candidate pool includes: The range of edge height curves on each side of each board is used as the warping amplitude; Boards whose warpage does not exceed a preset threshold are included in the complete installation candidate pool and participate in the location allocation and orientation optimization of complete installation units; Boards with warping exceeding a preset threshold are downgraded and included in the cutting candidate pool to participate in the board selection and retention optimization of the cutting and installation unit.

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