Cable dome roof wind pressure partitioning method based on spatial constraint K-means

Abstract

The invention relates to the field of buildings, in particular to a cable dome roof wind pressure partitioning method based on spatial constraint K-means, and solves the problem that spatial position features of wind pressure are not fully considered in the prior art. The method comprises the steps of inputting a data set of measuring point position coordinates and wind pressure coefficients; performing normalization processing on the position coordinate and the wind pressure coefficient of each measuring point; realizing cluster division by utilizing spatial constraint K-means clustering; calculating validity index values of DB and Sil under the cluster k; dB and Sil under different clusters k are compared, the optimal cluster number k is found out, the optimal wind pressure partition corresponding to the classification of the optimal cluster number is used as the result of the cable dome roof wind pressure partition, the wind load shape coefficient of each partition is calculated based on the partition result, the maximum positive pressure area and the maximum negative pressure area are accurately recognized, the partition boundary smoothness is remarkably improved through the method, and the method is suitable for large-scale popularization and application. And safe and reliable technical support is provided for wind resistance design of large-span roofs such as cable domes and the like.

Description

Technical Field

[0001] This application relates to the field of wind-resistant design of building structures, specifically to a wind pressure zoning method for cable dome roofs based on spatially constrained K-means, which is particularly suitable for wind load zoning of large-span roof structures such as cable domes. Background Technology

[0002] When wind flows through complex curved structures like long-span cable domes, the wind pressure distribution is extremely uneven, with significant differences in wind pressure on the windward and leeward sides of the roof. Wind pressure zoning divides the structural surface into different zones, assigning a representative shape coefficient to each zone, thus more realistically simulating the actual effects of wind loads on the structure. The dimensions and strength of the cable dome enclosure structure must be designed based on the maximum wind pressure of its location; the zoning results directly determine the safety and economy of the components. Precise wind pressure zoning avoids the conservative approach of using the maximum wind pressure in a "one-size-fits-all" manner, allowing for targeted optimization of component dimensions and material strength grades based on the actual wind load levels in different zones. Cable dome roofs are often covered with membrane materials. Membrane structures are typical wind-sensitive structures, easily lifted by wind suction or subjected to excessive deformation under pressure. Wind pressure zoning provides crucial basis for the form-finding analysis, cutting design, and connection construction of the membrane surface, ensuring the stability and safety of the roof under various conditions. In summary, the core purpose of wind pressure zoning for cable dome structures is to achieve refined design. By scientifically depicting the true distribution of wind loads on complex curved surfaces, it provides structural engineers with accurate design inputs, thereby ensuring the safety, applicability, and economy of the structure under various wind loads.

[0003] Currently, roof zoning methods mainly include two types: those based on aerodynamic characteristics and those based on clustering data. Aerodynamic characteristic-based methods primarily consider factors such as the roof surface geometry, incoming flow angle, turbulence characteristics, and local wind pressure gradients. These methods are suitable for roof structures with regular geometry and stable wind fields, but their applicability is poor for complex structures and variable wind fields. Clustering data-driven methods, such as K-means and improved GK clustering, with spatially constrained clustering algorithms being one of the most popular fuzzy clustering methods, have wide applications in various research fields, such as classification and system recognition, image processing, pattern recognition, and computer processing. However, existing methods only use the wind pressure coefficient at measurement points to achieve roof wind pressure zoning, without fully considering the spatial location characteristics of wind pressure, ignoring spatial continuity and location constraints.

[0004] Chinese patent CN112487720B discloses a method, system, and storage medium for rapid wind pressure coefficient partitioning based on the K-means three-dimensional clustering algorithm. The method first acquires wind pressure coefficient data from points on building surfaces; establishes a K-means clustering algorithm model and divides it into K clusters; calculates the distance between the centers of each cluster; minimizes the sum of squared errors of each cluster; then calculates the range of cluster numbers K; finally, calculates the values ​​of unified index parameters and determines the optimal K value; and outputs the clustering results. The rapid wind pressure coefficient partitioning method provided by this invention, based on one-dimensional clustering of wind pressure extreme gradient information, proposes assigning certain weights to each parameter in the K-means clustering algorithm, considering the influence of spatial location information to assist in wind pressure partitioning, narrowing the range of k values ​​based on the sum of squared errors and the silhouette coefficient, and then using a series of clustering and engineering indicators to determine the optimal k value. This method can effectively complete the wind pressure coefficient partitioning work.

[0005] However, the drawback of Chinese patent CN112487720B is that although it involves the application of K-means clustering in wind pressure zoning, it adopts fixed weight constraints (which need to satisfy α+β+γ=3 and α=β) and a complex multi-index weighting mechanism (HIP unified index contains 5 engineering parameters), which leads to rigid spatial constraints and computational redundancy, and is particularly difficult to adapt to the wind pressure gradient changes of complex curved surfaces such as cable domes. Summary of the Invention

[0006] The purpose of this invention is to address the problem of zoning extreme positive and negative wind pressure values ​​for cable dome roofs under different operating conditions. It provides a spatially constrained K-means-based wind pressure zoning method for cable dome roofs, which combines the spatial location information of measuring points with the wind pressure coefficient. The optimal number of zoning is determined through the DB and Silhouette dual validity indices, thereby achieving accurate wind pressure zoning for cable dome roofs and providing a reference for the wind-resistant design and wind load shape coefficient of cable dome roofs.

[0007] To achieve the purpose of this invention, the following technical solution is adopted:

[0008] The present invention provides a method for wind pressure zoning of cable dome roofs based on spatially constrained K-means, comprising the following steps:

[0009] (I) Input the dataset containing the coordinates of the measuring points and the wind pressure coefficient.

[0010] Establish a coordinate system with X and Y axes on the top view of the large-span cable dome structure model, where the X and Y axes are tangent to the large-span cable dome structure model. Arrange at least 5 rings of measuring points from the geometric center of the large-span cable dome structure model outwards, with each ring of measuring points evenly distributed, for a total of n measuring points. Obtain the wind pressure at each measuring point using a wind pressure acquisition device. The wind pressure coefficient at each measuring point is calculated using formula (1):

[0011]

[0012] In formula (1), C p,i P represents the wind pressure coefficient at measuring point i; d,i Pi represents the wind pressure at measuring point i; P0 is the reference pressure, selected as the atmospheric pressure at infinite distance from the wind field, with a value of 0; ρ is the air density, with a value of 1.25 kg / m2. 3 V jet To measure the exit wind speed of the downburst, the location coordinates and wind pressure coefficient of each measuring point are recorded to form n datasets;

[0013] (II) Normalize the location coordinates and wind pressure coefficient of each measuring point.

[0014] The location coordinates and wind pressure coefficient of each measuring point are normalized to ensure that the location coordinates and wind pressure coefficient are compared on the same scale. The normalization formula is as follows:

[0015]

[0016] Where: x i 'x' represents the normalized x-coordinate of measurement point i. i Let x be the x-coordinate of the measuring point i. min x is the minimum x-coordinate of the measuring point. max The x-coordinate of the measuring point is the maximum value; y i ' represents the normalized ordinate of measurement point i, y i Let y be the ordinate of measurement point i. min The minimum value of the ordinate of the measuring point, y max C represents the maximum value of the ordinate of the measuring point. pi 'C' represents the normalized wind pressure coefficient at measurement point i. pi Let C be the wind pressure coefficient at measuring point i. pi，min C represents the minimum wind pressure coefficient at the measuring point. pi，max The maximum value of the wind pressure coefficient at each measuring point forms a dataset containing n normalized measuring points;

[0017] in:

[0018] (III) Cluster partitioning using spatially constrained K-means clustering

[0019] (I) Initialize cluster centers

[0020] Set the maximum number of cluster centers Where n is the number of measurement points, and in the above coordinate system, the number of each candidate cluster k∈[2,k] max ], k maxRound to the nearest integer, randomly select k measurement points and their corresponding wind pressure coefficients from the candidate cluster number as the initial cluster centers, and set the number of iterations t = 0;

[0021]

[0022] j (j = 1, 2, ..., k) represents the index of a single cluster center; k (k = 2, 3, ..., k) represents the index of a single cluster center. max ) represents the number of cluster centers in the current test; c j Indicates the initial cluster centers; Represents the initial coordinates of the j-th cluster center. This represents the initial wind pressure coefficient of the j-th cluster center;

[0023] (II) Calculate the weighted distance from each measurement point to the above cluster centers.

[0024] The weighted distance d between all measuring points and all cluster centers j (j=1,2,…,k) is calculated using formula (4). ij ,

[0025]

[0026] In formula (4), j represents the cluster number currently being calculated; d ij v' represents the weighted distance from measurement point i to the j-th cluster center; i =(x' i ,y' i ) represents the spatial coordinates of measuring point i; C' pi This represents the wind pressure coefficient at measuring point i; This represents the center coordinates of the j-th cluster in this iteration; represents the wind pressure coefficient of the j-th cluster center in this iteration; α is the weight parameter, α∈[0,1];

[0027] Calculate the distance from each measurement point to each of the above cluster centers c. j Weighted distance d ij Each measurement point is mapped to each initial cluster center c. j The distances are compared, and the distance from the above cluster center c is... j The measurement points with the shortest distance are grouped into one category, forming k clusters;

[0028] (III) Update the cluster center

[0029] In the clusters formed above, the iteration number t = t + 1, and the center of the new cluster is calculated using formula (5).

[0030]

[0031] In formula (5), the x-coordinate of the new cluster center is the sum of the x-coordinates of all measuring points in the cluster divided by the number of measuring points included in the cluster; the y-coordinate of the new cluster center is the sum of the y-coordinates of all measuring points in the cluster divided by the number of measuring points included in the cluster; and the wind pressure coefficient of the new cluster center is the sum of the wind pressure coefficients of all measuring points in the cluster divided by the number of measuring points included in the cluster. |P j | represents the number of test points in the j-th cluster;

[0032] Replace the original cluster center with the new cluster center, repeat step (II), and re-divide all measurement points into clusters. When the number of iterations t reaches 10000, or when all k cluster centers satisfy formula (6), proceed to step (IV).

[0033]

[0034] In formula (6), c j (t+1) and These are the cluster centers at the (t+1)th and tth iterations, respectively;

[0035] (iv) Calculate the effectiveness index values ​​of DB and Sil under the above k cluster centers.

[0036] (1) DB index

[0037] The DB index represents the ratio of dispersion within each cluster to dispersion between clusters. The smaller the DB value, the better the clustering. The specific expression is as follows:

[0038]

[0039] In formula (7), S r With S j d represents the average intra-cluster distance of the r-th and j-th (r, j = 1, 2, ..., k) clusters, respectively; rj Let r be the inter-cluster center distance between the r-th and j-th clusters, where j (j = 1, 2, ..., k) represents the individual cluster center number; r (r = 1, 2, ..., k) represents the number of an individual cluster center with a different number than j; for each cluster r, calculate the inter-cluster center distance with all other clusters j. And take the maximum value;

[0040] Wherein: the average distance within a class is given by formulas (8) and (9),

[0041]

[0042] In formula (8), m' r v is the spatial coordinate center of the r-th class. i ' represents the spatial coordinates of all measurement points within cluster r, μ'r The mean wind pressure coefficient of the r-th class is the sum of the wind pressure coefficients of all measuring points in cluster r divided by the number of measuring points in that cluster.

[0043] In formula (9), m j ' is the spatial coordinate center of the j-th class, v i ' represents the spatial coordinates of all measurement points within cluster j, μ j ' is the average wind pressure coefficient of the j-th class, which is the sum of the wind pressure coefficients of all measuring points in cluster j divided by the number of measuring points in that cluster;

[0044] Inter-class distance:

[0045] d rj =α||m' r -m' j || 2 +(1-α)(μ' r -μ' j ) 2 (10)

[0046] (2) Silhouette index

[0047] The Silhouette index assesses clustering quality by comparing the similarity of measurement points within the same cluster with the separation of nearest neighbor clusters. A higher Silhouette coefficient (S) closer to 1 indicates better clustering, while a value close to 0 or negative indicates poor clustering. The calculation formula is as follows:

[0048]

[0049] Where: S(i) represents the profile coefficient of measurement point i; a(i) represents the average weighted distance between measurement point i and all other measurement points in the same cluster, reflecting intra-cluster similarity; b(i) represents the average weighted distance between measurement point i and all points in other clusters, reflecting inter-cluster separation.

[0050] Where: the average weighted distance between measuring point i and all other measuring points in the same cluster is given by formula (13).

[0051]

[0052] In formula (13), a(i) represents the average weighted distance from measurement point i to all other points in the same cluster; P j Let |P| represent the set of measurement points contained in the j-th cluster. j | represents cluster P j Total number of measurement points; l represents cluster P j Other measuring points besides measuring point i; v' l =(x' l ,y' l() represents the spatial coordinates of measurement point l in the same cluster; This represents the wind pressure coefficient at measuring point l within the same cluster.

[0053] Where: the average weighted distance between measurement point i and all points in other clusters is given by formula (14).

[0054]

[0055] In formula (14), b(i) represents the distance from measurement point i to other clusters P. r The average weighted distance of all measurement points within the cluster; r (r = 1, 2, ..., k; r ≠ j) represents the cluster number; P r Let |P| be the set of measurement points contained in the r-th cluster. r | represents cluster P r The total number of measurement points in the cluster; h represents any measurement point in the cluster.

[0056] Record the cluster numbers k, DB, and Sil obtained above;

[0057] (v) Compare DB and Sil under different clustering k to find the optimal number of clusters k.

[0058] Repeat steps (3) and (4) to make the following respectively. The cluster classification of the large-span cable dome structure model is determined by identifying the corresponding DB and Sil values. The optimal cluster number k is found to correspond to the maximum difference between DB and Sil. The wind pressure zoning corresponding to the classification with the optimal cluster number is then used as the result of the wind pressure zoning of the large-span cable dome structure model.

[0059] The wind pressure zoning method for cable dome roofs based on spatial constraint K-means of the present invention, wherein: 7 rings of measuring points are arranged from the geometric center of the large-span cable dome structure model to the periphery.

[0060] The wind pressure zoning method for cable dome roofs based on spatially constrained K-means of the present invention, wherein: the outlet wind speed V of the downburst... jet It is known.

[0061] The wind pressure zoning method for cable dome roofs based on spatial constraint K-means of the present invention, wherein the projection of the large-span cable dome structure model on the top view is a circle or an ellipse.

[0062] The wind pressure zoning method for cable dome roofs based on spatially constrained K-means of the present invention, wherein: the weight parameter α depends on the experimental cable dome model, and α=0.2.

[0063] This invention relates to the field of wind-resistant design technology for building structures, specifically disclosing a wind pressure zoning method for cable-stayed dome roofs based on spatially constrained K-means. Addressing the shortcomings of existing wind pressure zoning methods, which neglect spatial continuity and are insufficiently adaptable to complex roofs, this invention innovatively constructs a weighted distance model that integrates the spatial location of measuring points and the wind pressure coefficient, dynamically adjusting the spatial constraint strength through weight parameters. It determines the optimal number of zones by combining a dual-objective optimization mechanism that minimizes the DB exponent and maximizes the Silhouette exponent. Based on the zoning results, it calculates the wind load shape coefficient for each zone, accurately identifying the maximum positive pressure zone and the maximum negative pressure zone. This method significantly improves the smoothness of the zoning boundaries, providing safe and reliable technical support for the wind-resistant design of large-span roofs such as cable domes.

[0064] The wind pressure zoning method for cable dome roofs based on spatially constrained K-means of the present invention has the following advantages:

[0065] 1. By integrating the spatial coordinates of the measuring points with the wind pressure coefficient through weighted distance, the synergistic optimization of wind pressure distribution and spatial continuity can be achieved.

[0066] 2. Introduce a weighting parameter α to flexibly balance location proximity and wind pressure similarity.

[0067] 3. By combining the DB index and the Silhouette index, the optimal number of partitions is adaptively determined, improving the robustness of the partitioning results.

[0068] 4. Provide reference design values ​​for the wind-resistant design of cable domes based on the zoning results. Attached Figure Description

[0069] Figure 1 This is a flowchart of the wind pressure zoning method for cable dome roofs based on spatially constrained K-means according to the present invention;

[0070] Figure 2 The X-axis and Y-axis coordinate systems are established on the top view of the large-span cable dome structure model;

[0071] Figure 3 In order to be in Figure 2 Three cluster centers are randomly selected, and the centers of the clusters are represented by black dots. The three clusters are then divided by calculation.

[0072] Figure 4 In order to be in Figure 3 Based on this, a new cluster center is recalculated, and the cluster center is represented by a black triangle.

[0073] Figure 5 For all cluster centers k = (2, 3, ..., k) max The corresponding DB and Sil;

[0074] Figure 6The output is the wind pressure zoning result corresponding to the best clustering. Detailed Implementation

[0075] like Figure 1 As shown, the wind pressure zoning method for cable dome roofs based on spatially constrained K-means of the present invention includes the following steps:

[0076] (I) Input the dataset containing the coordinates of the measuring points and the wind pressure coefficient.

[0077] like Figure 2 As shown, the projection of the large-span cable-stayed dome structure model on the top view is a circle. A coordinate system with X and Y axes is established on the top view of the large-span cable-stayed dome structure model, where the X and Y axes are tangent to the large-span cable-stayed dome structure model. Seven rings of measuring points are arranged from the geometric center of the large-span cable-stayed dome structure model outwards. The measuring points in each ring are evenly distributed, for a total of 168 measuring points. The wind pressure at each measuring point is obtained through a wind pressure acquisition device, and the wind pressure coefficient at each measuring point is calculated by formula (1):

[0078]

[0079] In formula (1), C p,i P represents the wind pressure coefficient at measuring point i; d,i Pi represents the wind pressure at measuring point i; P0 is the reference pressure, selected as the atmospheric pressure at infinite distance from the wind field, with a value of 0; ρ is the air density, with a value of 1.25 kg / m2. 3 V jet The exit wind speed of the downburst is 10 m / s; the location coordinates and wind pressure coefficient of each measuring point are recorded to form n datasets;

[0080] (II) Normalize the location coordinates and wind pressure coefficient of each measuring point.

[0081] The location coordinates and wind pressure coefficient of each measuring point are normalized to ensure that the location coordinates and wind pressure coefficient are compared on the same scale. The normalization formula is as follows:

[0082]

[0083] Where: x i 'x' represents the normalized x-coordinate of measurement point i. i Let x be the x-coordinate of the measuring point i. min x is the minimum x-coordinate of the measuring point. max The x-coordinate of the measuring point is the maximum value; y i ' represents the normalized ordinate of measurement point i, y i Let y be the ordinate of measurement point i. min The minimum value of the ordinate of the measuring point, y max C represents the maximum value of the ordinate of the measuring point.pi 'C' represents the normalized wind pressure coefficient at measurement point i. pi Let C be the wind pressure coefficient at measuring point i. pi，min C represents the minimum wind pressure coefficient at the measuring point. pi，max The maximum value of the wind pressure coefficient at each measuring point forms a dataset containing n normalized measuring points;

[0084] (III) Cluster partitioning using spatially constrained K-means clustering

[0085] (I) Initialize cluster centers

[0086] Set the maximum number of cluster centers Round to the nearest integer, i.e., k max =13, where n is the number of measurement points, i.e., 168. Let the number of iterations t = 0. In the above coordinate system, the number of each candidate cluster k∈[2,k max (k is an integer), such as Figure 3 As shown, the location coordinates of three measuring points and their corresponding wind pressure coefficients are randomly selected from the candidate cluster number as the initial cluster centers;

[0087]

[0088] j (j = 1, 2, ..., k) represents the number of a single cluster center; k = 3 represents the number of cluster centers being tested; c j Indicates the initial cluster centers, in Figure 3 The center is represented by black dots; This represents the coordinates of the initially selected j-th cluster center before iteration. This represents the wind pressure coefficient of the j-th cluster center initially selected before iteration, where j takes the values ​​1, 2, and 3.

[0089] (II) Calculate the weighted distance from each measurement point to the above cluster centers.

[0090] The weighted distance d between all measuring points and all cluster centers j (j=1,2,…3) is calculated using formula (4). ij ,

[0091]

[0092] In formula (4), j represents the cluster number currently being calculated; d ij v' represents the weighted distance from measurement point i to the j-th cluster center; i =(x' i ,y' i ) represents the spatial coordinates of measuring point i; C' pi This represents the wind pressure coefficient at measuring point i; Represents the center coordinates of the j-th cluster; Let represent the wind pressure coefficient of the j-th cluster center; α is a weighting parameter, α∈[0,1], used to balance the weights of spatial location and wind pressure coefficient in the cluster. The value of α needs to be determined in conjunction with engineering requirements. In this application, α=0.2, which depends on the cable dome model of this experiment; calculate the distance from each measuring point to each of the above-mentioned cluster centers c. j Weighted distance d ij Each measurement point is mapped to each initial cluster center c. j The distances are compared, and the distance from the above cluster center c is... j The measurement points with the shortest distance are grouped into one category, forming three clusters;

[0093] (III) Update the cluster center

[0094] In the clusters formed above, the center of the new cluster is calculated using formula (5).

[0095]

[0096] In formula (5), the x-coordinate of the new cluster center is the sum of the x-coordinates of all measuring points in the cluster divided by the number of measuring points included in the cluster; the y-coordinate of the new cluster center is the sum of the y-coordinates of all measuring points in the cluster divided by the number of measuring points included in the cluster; and the wind pressure coefficient of the new cluster center is the sum of the wind pressure coefficients of all measuring points in the cluster divided by the number of measuring points included in the cluster. |P j | represents the number of data points in the j-th cluster;

[0097] like Figure 4 As shown, the original cluster centers are replaced with new cluster centers, which are represented by black triangles. The iteration number is t = t + 1. Step (II) is repeated to re-divide all measurement points into clusters.

[0098] When the number of iterations t reaches 10000, or when all k cluster centers satisfy formula (6), proceed to step (four);

[0099]

[0100] In formula (6), c j (t+1) and These are the three cluster centers at the (t+1)th and tth iterations, respectively;

[0101] (iv) Calculate the effectiveness index values ​​of DB and Sil under the above three cluster centers.

[0102] (1) DB index

[0103] The DB index represents the ratio of dispersion within each cluster to dispersion between clusters. The smaller the DB value, the better the clustering. The specific expression is as follows:

[0104]

[0105] In formula (7), S r With S j d represents the mean intra-class distance between classes r and j (r, j = 1, 2, ..., k), respectively; rj Let r be the inter-cluster center distance between the r-th and j-th clusters, where j (j = 1, 2, 3) represents the individual cluster center number; r (r = 1, 2, ..., 3) represents the number of an individual cluster center with a different number than j; for each cluster r, calculate the inter-cluster center distance with all other clusters j. And take the maximum value; when there are k=3 clusters, when r=1, j=2, 3, When r = 2, j = 1, 3, When r = 3, j = 1, 2, The definition of the DB metric is: for each cluster r, calculate the worst case (i.e. the maximum value) of the cluster and other clusters respectively, and then take the average of these worst cases of all clusters. In the standard DB metric, the first cluster needs to calculate its ratio with the second cluster, and the second cluster also needs to calculate its ratio with the first cluster, because each cluster must independently evaluate its degree of separation from other clusters.

[0106] Wherein: the average distance within a class is given by formulas (8) and (9),

[0107]

[0108]

[0109] In formula (8), m' r v is the spatial coordinate center of the r-th class. i ' represents the spatial coordinates of all measurement points within cluster r, μ' r The mean wind pressure coefficient of the r-th class is the sum of the wind pressure coefficients of all measuring points in cluster r divided by the number of measuring points in that cluster.

[0110] In formula (9), m j ' is the spatial coordinate center of the j-th class, v i ' represents the spatial coordinates of all measurement points within cluster j, μ j ' is the average wind pressure coefficient of the j-th class, which is the sum of the wind pressure coefficients of all measuring points in cluster j divided by the number of measuring points in that cluster;

[0111] Inter-class distance:

[0112] drj =α||m' r -m' j || 2 +(1-α)(μ' r -μ' j ) 2 (10)

[0113] (2) Silhouette index

[0114] The Silhouette index assesses clustering quality by comparing the similarity of points within the same cluster with the separation of points from their nearest neighbors. A silhouette coefficient closer to 1 indicates better clustering, while a silhouette coefficient close to 0 or a negative value indicates poor clustering. The calculation formula is as follows:

[0115]

[0116]

[0117] S(i) represents the profile coefficient of measurement point i; a(i) represents the average weighted distance between measurement point i and all other measurement points in the same cluster, reflecting the intra-cluster similarity; b(i) represents the average weighted distance between measurement point i and all points in other clusters, reflecting the inter-cluster separation.

[0118] Wherein: the average weighted distance between measuring point i and all other measuring points in the same cluster is calculated using formula (13),

[0119]

[0120] In formula (13), a(i) represents the distance from measurement point i to the same cluster group P. j The average weighted distance of all other points within the range; P j Let |P| represent the set of measurement points contained in the j-th cluster. j | represents cluster P j Total number of measurement points; l represents cluster P j Other measuring points besides measuring point i; v' l =(x' l ,y' l () represents the spatial coordinates of measurement point l in the same cluster; This represents the wind pressure coefficient at measuring point l within the same cluster.

[0121] Wherein: the average weighted distance between measurement point i and all points in other clusters is calculated using formula (14),

[0122]

[0123] In formula (14), b(i) represents the distance from measurement point i to other clusters P. rThe average weighted distance of all measurement points within the cluster; r (r = 1, 2, 3; r ≠ j) represents the cluster number; P r Let |P| be the set of measurement points contained in the r-th cluster. r | represents cluster P r The total number of measurement points in the cluster; h represents any measurement point in the cluster.

[0124] Record the cluster count, DB, and Sil obtained above;

[0125] (v) Compare DB and Sil under different clustering k to find the optimal number of clusters k.

[0126] Repeat steps (iii) and (iv) to classify the clusters of the large-span cable-stayed dome structure models for k = 2, 4, ..., 13, and determine the corresponding DB and Sil values. Find the optimal cluster number k corresponding to the largest difference between DB and Sil. Figure 5 As shown, for the optimal number of clusters k=2, the difference between DB and Sil is the largest. Figure 6 The results show the wind pressure zoning results corresponding to the best clustering. Based on the zoning results, the wind load shape coefficient of each zoning can be calculated (not within the scope of this application), and the maximum positive pressure zone and the maximum negative pressure zone can be accurately identified. This method significantly improves the smoothness of the zoning boundary and provides safe and reliable technical support for the wind-resistant design of large-span roofs such as cable domes.

[0127] The present invention and its embodiments have been described above illustratively. This description is not restrictive, and the figures shown are only one embodiment of the present invention; the actual structure is not limited thereto. Therefore, if those skilled in the art are inspired by this description and design methods and embodiments similar to this technical solution without departing from the spirit of the present invention, such methods and embodiments should fall within the protection scope of this patent.

Claims

1. A spatially constrained K-means-based method for wind pressure zoning of cable dome roofs, comprising: the following step: (I) Input the dataset containing the coordinates of the measuring points and the wind pressure coefficient. Establish a coordinate system with X and Y axes on the top view of the large-span cable dome structure model, where the X and Y axes are tangent to the large-span cable dome structure model. Arrange at least 5 rings of measuring points from the geometric center of the large-span cable dome structure model outwards, with each ring of measuring points evenly distributed, for a total of n measuring points. Obtain the wind pressure at each measuring point using a wind pressure acquisition device. The wind pressure coefficient at each measuring point is calculated using formula (1): In formula (1), C p,i P represents the wind pressure coefficient at measuring point i; d,i Pi represents the wind pressure at measuring point i; P0 is the reference pressure, selected as the atmospheric pressure at infinite distance from the wind field, with a value of 0; ρ is the air density, with a value of 1.25 kg / m2. 3 V jet To measure the exit wind speed of the downburst, the location coordinates and wind pressure coefficient of each measuring point are recorded to form n datasets; (II) Normalize the location coordinates and wind pressure coefficient of each measuring point. The location coordinates and wind pressure coefficient of each measuring point are normalized to ensure that the location coordinates and wind pressure coefficient are compared on the same scale. The normalization formula is as follows: Where: x i 'x' represents the normalized x-coordinate of measurement point i. i Let x be the x-coordinate of the measuring point i. min x is the minimum x-coordinate of the measuring point. max The x-coordinate of the measuring point is the maximum value; y i ' represents the normalized ordinate of measurement point i, y i Let y be the ordinate of measurement point i. min The minimum value of the ordinate of the measuring point, y max C represents the maximum value of the ordinate of the measuring point. pi 'C' represents the normalized wind pressure coefficient at measurement point i. pi Let C be the wind pressure coefficient at measuring point i. pi，min C represents the minimum wind pressure coefficient at the measuring point. pi，max The maximum value of the wind pressure coefficient at each measuring point forms a dataset containing n normalized measuring points; Its features are: (III) Cluster partitioning using spatially constrained K-means clustering (I) Initialize cluster centers Set the maximum number of cluster centers Where n is the number of measurement points, and in the above coordinate system, the number of each candidate cluster k∈[2,k] max ], k max Round to the nearest integer, randomly select the location coordinates of k measuring points and their corresponding wind pressure coefficients from the candidate cluster number as the initial cluster centers, and set the number of iterations t = 0; j (j = 1, 2, ..., k) represents the index of a single cluster center; k (k = 2, 3, ..., k) represents the index of a single cluster center. max ) indicates the number of cluster centers in the current test; c j Indicates the initial cluster centers; Represents the initial coordinates of the j-th cluster center. This represents the initial wind pressure coefficient of the j-th cluster center; (II) Calculate the weighted distance from each measuring point to the above cluster centers. The weighted distance d between all measuring points and all cluster centers j (j=1,2,…,k) is calculated using formula (4). ij , In formula (4), j represents the cluster number currently being calculated; d ij v' represents the weighted distance from measurement point i to the j-th cluster center; i =(x' i ,y' i C' represents the spatial coordinates of measuring point i; pi This represents the wind pressure coefficient at measuring point i; This represents the center coordinates of the j-th cluster in this iteration; α represents the wind pressure coefficient of the j-th cluster center in this iteration; α is the weight parameter, α∈[0,1]; Calculate the distance from each measurement point to each of the above cluster centers c. j Weighted distance d ij Each measurement point is mapped to each initial cluster center c. j The distances are compared, and the distance from the above cluster center c is... j The measurement points with the shortest distance are grouped into one category, forming k clusters; (III) Update the cluster center In the clusters formed above, the iteration number t = t + 1, and the center of the new cluster is calculated using formula (5). In formula (5), the x-coordinate of the new cluster center is the sum of the x-coordinates of all measuring points in the cluster divided by the number of measuring points included in the cluster; the y-coordinate of the new cluster center is the sum of the y-coordinates of all measuring points in the cluster divided by the number of measuring points included in the cluster; and the wind pressure coefficient of the new cluster center is the sum of the wind pressure coefficients of all measuring points in the cluster divided by the number of measuring points included in the cluster. |P j | represents the number of test points in the j-th cluster; Replace the original cluster center with the new cluster center, repeat step (II), and re-divide all measurement points into clusters. When the number of iterations t reaches 10000, or when all k cluster centers satisfy formula (6), proceed to step (IV). In formula (6), c j (t+1) and These are the cluster centers at the (t+1)th and tth iterations, respectively; (iv) Calculate the effectiveness index values ​​of DB and Sil under the above k cluster centers. (1) DB index The DB index represents the ratio of dispersion within each cluster to dispersion between clusters. The smaller the DB value, the better the clustering. The specific expression is as follows: In formula (7), S r With S j d represents the average intra-cluster distance of the r-th and j-th (r, j = 1, 2, ..., k) clusters, respectively; rj Let r be the inter-cluster center distance between the r-th and j-th clusters, where j (j = 1, 2, ..., k) represents the individual cluster center number; r (r = 1, 2, ..., k) represents the number of an individual cluster center with a different number than j; for each cluster r, calculate the inter-cluster center distance with all other clusters j. And take the maximum value; Wherein: the average distance within a class is given by formulas (8) and (9), In formula (8), m' r v is the spatial coordinate center of the r-th class. i ' represents the spatial coordinates of all measurement points within cluster r, μ' r The mean wind pressure coefficient of the r-th class is the sum of the wind pressure coefficients of all measuring points in cluster r divided by the number of measuring points in that cluster. In formula (9), m j ' is the spatial coordinate center of the j-th class, v i ' represents the spatial coordinates of all measurement points within cluster j, μ j ' is the average wind pressure coefficient of the j-th class, which is the sum of the wind pressure coefficients of all measuring points in cluster j divided by the number of measuring points in that cluster; Inter-class distance: d rj =α||m' r -m' j || 2 +(1-a)(m') r -m' j ) 2 (10) (2) Silhouette index The Silhouette index assesses clustering quality by comparing the similarity of measurement points within the same cluster with the separation of nearest neighbor clusters. A higher Silhouette coefficient (S) closer to 1 indicates better clustering, while a value close to 0 or negative indicates poor clustering. The calculation formula is as follows: Where: S(i) represents the profile coefficient of measurement point i; a(i) represents the average weighted distance between measurement point i and all other measurement points in the same cluster, reflecting intra-cluster similarity; b(i) represents the average weighted distance between measurement point i and all points in other clusters, reflecting inter-cluster separation. Where: the average weighted distance between measuring point i and all other measuring points in the same cluster is given by formula (13). In formula (13), a(i) represents the average weighted distance from measurement point i to all other points in the same cluster; P j Let |P| represent the set of measurement points contained in the j-th cluster. j | represents cluster P j Total number of measurement points; l represents cluster P j Other measuring points besides measuring point i; v' l =(x' l ,y' l ) represents the spatial coordinates of measurement point l in the same cluster; C' pl This represents the wind pressure coefficient at measuring point l within the same cluster. Where: the average weighted distance between measurement point i and all points in other clusters is given by formula (14). In formula (14), b(i) represents the distance from measurement point i to other clusters P. r The average weighted distance of all measurement points within the cluster; r (r = 1, 2, ..., k; r ≠ j) represents the cluster number; P r Let |P| be the set of measurement points contained in the r-th cluster. r | represents cluster P r The total number of measurement points in the cluster; h represents any measurement point in the cluster. Record the cluster numbers k, DB, and Sil obtained above; (v) Compare DB and Sil under different clustering k to find the optimal number of clusters k. Repeat steps (iii) and (iv) to calculate k≈2, 3... respectively. The cluster classification of the large-span cable dome structure model is determined by identifying the corresponding DB and Sil values. The optimal cluster number k is found to correspond to the maximum difference between DB and Sil. The wind pressure zoning corresponding to the classification with the optimal cluster number is then used as the result of the wind pressure zoning of the large-span cable dome structure model.

2. The method for wind pressure zoning of cable dome roofs based on spatially constrained K-means as described in claim 1, characterized in that: Seven measuring points were arranged around the geometric center of the large-span cable-stayed dome structure model.

3. The method for wind pressure zoning of cable dome roofs based on spatially constrained K-means as described in claim 2, characterized in that: The exit wind speed V of the downburst jet It is known.

4. The method for wind pressure zoning of cable dome roofs based on spatially constrained K-means as described in claim 3, characterized in that: The projection of the large-span cable-stayed dome structure model on the top view is a circle or an ellipse.

5. The method for wind pressure zoning of cable dome roofs based on spatially constrained K-means as described in claim 4, characterized in that: The weighting parameter α depends on the cable dome model of the experiment, and α = 0.2.

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