CN117195626B - Design method for building free-form surface grid structure division based on generation countermeasure network - Google Patents

Design method for building free-form surface grid structure division based on generation countermeasure network Download PDF

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CN117195626B
CN117195626B CN202311073815.8A CN202311073815A CN117195626B CN 117195626 B CN117195626 B CN 117195626B CN 202311073815 A CN202311073815 A CN 202311073815A CN 117195626 B CN117195626 B CN 117195626B
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陆金钰
侯江军
翟效伟
徐烯铭
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Southeast University
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Abstract

The invention discloses a design method for building free-form surface grid structure division based on a generation countermeasure network, which comprises the following steps: step S1, giving a free-form surface of a building, and obtaining a corresponding grid structure, a curvature cloud picture and an elevation cloud picture of the free-form surface of the building so as to construct a sample database for dividing the grid structure of the free-form surface of the building; s2, constructing a new transformation optimized pix2pixHD to generate an countermeasure network model; s3, generating an countermeasure network model based on the improved optimization in the step S2, and training through the building free-form surface grid structure sample database in the step S1 to generate the countermeasure network model; and S4, testing the trained model by using a plurality of evaluation methods, and putting the model into application after the evaluation is qualified. According to the method, according to the curvature cloud pictures and elevation cloud pictures of the free-form surfaces of the building, the grid structure division result of the free-form surfaces of the building is rapidly output through an artificial intelligence method, so that the design efficiency is higher, and the expansibility is stronger.

Description

Design method for building free-form surface grid structure division based on generation countermeasure network
Technical Field
The invention belongs to the technical field of civil engineering and computer deep learning application, and particularly relates to a design method for dividing a building free-form surface grid structure based on a generated countermeasure network.
Background
With the gradual maturity of space grid technology, people are no longer satisfied with the traditional very regular space grid structure, but expect a structure form with more visual impact force, however, the irregularity of the free-form surface of the building makes the grid structure division design process have a plurality of difficulties. In order to solve the grid structure division of the free-form surface of the building, different design methods are sequentially proposed. However, the existing grid structure dividing technology is either manual dividing or an algorithm is designed only for a specific curved surface, and the defects of low dividing efficiency, limited application range and the like exist. Under the circumstance that building and civil engineering are intelligent and continuously deepened, a high-efficiency and general grid structure dividing method for building free-form surfaces is provided, intelligent building structure design is promoted, and the method has necessity and urgency. With the continuous improvement of the computing capability of a computer, the development of computer vision and deep learning, artificial intelligence and other methods, a new thought and means are provided for solving various technical problems in the field of civil engineering. However, the current artificial intelligence driving and assisting is widely applied only in the field of engineering construction and operation and maintenance, and the combination with structural design is relatively less.
Disclosure of Invention
The invention aims to solve the technical problems of overcoming the defects of the prior grid division technology, and provides a design method for grid structure division of a building free-form surface based on a generated countermeasure network.
The invention provides a design method for dividing a building free-form surface grid structure based on generating an countermeasure network, which comprises the following steps:
S1, obtaining a free-form surface diagram of a building which needs to be subjected to grid division;
s2, generating a corresponding building free-form surface curvature cloud picture and a corresponding building free-form surface elevation cloud picture by utilizing the building free-form surface picture, and constructing a training data set and a testing data set;
S3, inputting the building free-form surface curvature cloud picture and the building free-form surface elevation cloud picture obtained in the step S2 after fusion to generate an countermeasure network model for training, wherein the output of the generated countermeasure network model is a building free-form surface grid structure diagram, training is carried out to obtain a generated countermeasure network model according to the building free-form surface curvature cloud picture and the building free-form surface elevation cloud picture as inputs, and the corresponding building free-form surface grid structure diagram is output;
S4, testing the generated countermeasure network model in the step S3 by using a test set, calculating a comprehensive index average value of a building free-form surface grid structure chart output by the generated countermeasure network model, judging whether the comprehensive index average value is smaller than a preset threshold, if so, generating the countermeasure neural network model to meet the requirements, if not, generating the countermeasure neural network model to not meet the requirements, and retraining again through the steps S1-S3;
And S5, fusing a preset building free-form surface curvature cloud picture and a building free-form surface elevation cloud picture, and inputting the fused building free-form surface curvature cloud picture and the fused building free-form surface elevation cloud picture into the generated countermeasure network model obtained through training in the step S3 to obtain a corresponding building free-form surface grid structure diagram.
Further, in step S2, the steps of obtaining the curvature cloud image and the elevation cloud image of the free-form surface of the building are respectively as follows:
(2.1) the procedure of acquiring a curvature cloud image
(1) Dividing adjacent edges of the free-form surface of the building according to M rows and N columns, dividing the whole free-form surface of the building into M multiplied by N free-form surfaces and representing the M multiplied by N free-form surfaces by S sub, wherein each value in the matrix represents M multiplied by N free-form surfaces obtained by dividing, and M and N are positive integers;
(2) Let S ij be the general formula of M N building freeform surfaces in the matrix of formula (1), representing the freeform surface of the ith row and jth column, where i ε [1: m ], j ε [1: n ], calculating the geometric centers of M multiplied by N building free-form surfaces, and using a general formula P ij to perform representation, namely P ij represents the geometric centers of the free-form surfaces of the ith row and the jth column, and similarly i epsilon [1, M ], j epsilon [1, N ], calculating the main curvature k n of the free-form surfaces S ij along the main direction according to a formula (2), wherein L represents a quadratic term coefficient, M represents a mixed term coefficient, N represents a constant term coefficient, E, F and G are coefficients of the first basic form of the free-form surfaces S ij, solving the formula (2) to obtain two results, wherein the maximum value in the results is the maximum main curvature k ij of the curved surfaces S ij at the P ij, and calculating the maximum main curvature k max of all M multiplied by N building free-form surfaces at the geometric centers, and using the formula (3);
(3) Carrying out maximum and minimum normalization processing on the M multiplied by N maximum principal curvature values k max obtained by calculation, and respectively solving L 1=max{k00,…,kMN},L0=min{k00,…,kMN to obtain a maximum value L 1 and a minimum value L 0 in the maximum principal curvature k max, and substituting the maximum principal curvature values k max of the M multiplied by N into a formula (4) in sequence to obtain a normalized curvature value k 'max, wherein the normalized curvature value is in a range from 0 to 1 as shown in a formula (5), wherein k' ij is an ith row and a jth column of curvature normalized curvature values, i E [1: m ], j ε [1: n ];
(4) Setting a color mapping scheme of a normalized curvature value k max as a gradient color, wherein the gradient color is formed by sequentially arranging five basic colors with the same proportion of red, yellow, green, cyan and blue, and N i(ri,gi,bi) is represented by a general formula of five colors, wherein i=0, 1,2,3,4, (r i,gi,bi) is a numerical code corresponding to the color, N 0 (255, 0) represents red, N 1 (255, 0) represents yellow, N 2 (0, 255, 0) represents green, N 3 (0, 255, 255) represents cyan, and N 4 (0, 255) represents blue;
(5) For any normalized curvature value k ' ij, the calculation using equation (6) yields d n, leaving the fractional part of d n and only the integer d z, then the true value d z of the subscript i of k ' ij left base color N i(ri,gi,bi) is obtained, i.e., the left base color of k ' ij is further expressed as The right base color of k' ij can be expressed as/>
dn=4k′ij (6)
(6) Order theAnd substituting formula (7) to calculate C r, let/> Substituting formula (7) to calculate C g, let/>Substituting the value into the formula (7) to calculate C b, wherein (C r,Cg,Cb) is a numerical code of the color corresponding to the normalized curvature value k ij in the step (5);
C=Cleft+(dn-dz)(Cright-Cleft) (7)
(7) Repeating the steps (5) and (6) one by one for normalized curvature values k 'ij of the MxN building freeform surfaces in the formula (5), and then realizing the visualization of all normalized curvature values k' ij and obtaining a curvature cloud image C sub of the whole building freeform surface, as shown in the formula (8), wherein C ij is a general formula and represents the color endowed by the ith row and jth column of freeform surfaces, i epsilon [1, M ], j epsilon [1, N ];
(2.2) an acquisition step of an elevation cloud picture:
(1) Dividing adjacent edges of the free-form surface of the building according to M rows and N columns, dividing the whole free-form surface of the building into M multiplied by N free-form surfaces and representing the M multiplied by N free-form surfaces by S' sub, wherein each value in the matrix represents M multiplied by N free-form surfaces obtained by dividing, and M and N are positive integers;
(2) Let S 'ij be the general formula of M×N building freeform surfaces in the matrix of formula (9), represent the j th column of freeform surfaces of the i th row, wherein i [1, M ], j [1, N ] calculate the geometric center of M×N building freeform surfaces, and use general formula P' ij(xij,yij,zij) to represent, P 'ij represents the geometric center of the j th column of freeform surfaces of the i th row, (x ij,yij,zij) represents the three-dimensional Cartesian coordinates of the geometric center, and similarly i [1, M ], j [1, N ] extract and separate the Z ij coordinates of P' ij, then the third principal axis component Z sub at the geometric center of all M×N building freeform surfaces is represented by formula (10);
(3) Carrying out maximum and minimum normalization processing on the M multiplied by N third principal axis components Z sub obtained by calculation, and respectively solving L ' 1=max{z00,…,zMN},L′0=min{z00,…,zMN to obtain a maximum value L ' 1 and a minimum value L ' 0 of the third principal axis components Z sub at the geometric center of the M multiplied by N building free-form surfaces, and substituting the maximum value L ' 1 and the minimum value L ' 0 into the M multiplied by N third principal axis components Z ij to a formula (11) in sequence to obtain normalized third principal axis components Z ' sub, wherein the normalized curvature value is in a range from 0 to 1 as shown in a formula (12), and Z ' ij is the third principal axis component normalized by the ith row and the jth column of curved surfaces, i epsilon [1, M ], j epsilon [1, N ];
(4) Setting a normalized color mapping scheme of a third principal axis component Z ' sub as a gradient color, wherein the gradient color is formed by sequentially arranging five basic colors of red, yellow, green, cyan and blue with the same proportion, and N ' i(ri,gi,bi) is represented by a general formula of five colors, wherein i=0, 1,2,3,4, (r i,gi,bi) is a numerical code corresponding to the color, N 0 ' (255, 0) represents red, N 1 ' (255, 0) represents yellow, N 2 ' (0, 255, 0) represents green, N 3 ' (0, 255, 255) represents cyan, and N 4 ' (0, 255) represents blue;
(5) For any normalized third principal axis component z 'ij, d' n can be calculated using equation (13), then the fractional part of d 'n is discarded and only the integer d' z is retained, resulting in the true value d 'z of the subscript i of the left base color N' i(ri,gi,bi) of z 'ij, i.e., the left base color of z' ij is further expressed as The right base color of z' ij can be expressed as
d′n=4z′ij (13)
(6) Order theAnd substituting formula (14) to calculate C' r, let Substituting formula (7) to calculate C' g, and then letting/>Substituting the normalized third principal axis component z 'ij in the formula (5) to calculate C' b, wherein (C 'r,C′g,C′b) is the numerical code of the color corresponding to the normalized third principal axis component z' ij;
C′=C′left+(d′n-d′z)(C′right-C′left) (14)
(7) Repeating steps (5) and (6) one by one for normalized third principal axis components z 'ij of the mxn building freeform surfaces in equation (5), then visualizing all normalized third principal axis components z' ij, and finally obtaining an elevation cloud image C 'sub of the whole building freeform surface, as in equation (15), where C' ij is a general formula representing a color imparted to the freeform surface in the ith row and jth column, i e [1: m ], j ε [1: n ];
Further, in step S2, the view angles of the building free-form surface curvature cloud image and the building free-form surface elevation cloud image are selected as top views, the scaling ratio of the building free-form surface in the two images and the position in the images are kept all the time, the resolution ratio is uniformly set to 1200PPI when the building free-form surface curvature cloud image and the building free-form surface elevation cloud image in PDF files are stored, then the building free-form surface curvature cloud image and the building free-form surface elevation cloud image in PDF are extracted, the stored image size is set to 2048p×1024p in a ". Png" format.
Further, in step S2, the steps of creating the training set and the test set for training and generating the countermeasure network model are sequentially as follows:
(2.1) carrying out grid division on a batch of building free-form surfaces with different forms by utilizing a free-form surface grid division algorithm to obtain a building free-form surface grid diagram; obtaining a curvature cloud picture and an elevation cloud picture corresponding to a free-form surface of a building, selecting a grid division picture, a curvature cloud picture and an elevation cloud picture of the free-form surface of the building as overlooking views, keeping scaling of the free-form surface of the building and positions in the pictures in all the three pictures, uniformly setting resolution to 1200PPI, and exporting in a PDF file format;
(2.2) carrying out data enhancement on the building free-form surface grid graph, the building free-form surface curvature cloud graph and the elevation cloud graph sample library obtained in the step (2.1) so as to increase the training sample data volume of the sample library, wherein the enhancement method is offline enhancement, carrying out rotation, translation and noise increase on the grid division graph, the curvature cloud graph and the elevation cloud graph so as to increase the data volume of the training library, and storing the enhanced picture in a ". Png" format, wherein the stored picture size is set to 2048p multiplied by 1024p;
(2.3) dividing the reinforced building freeform grid division map, the building freeform curvature cloud map and the building freeform elevation cloud map obtained in (2.2) into a training set and a test set in proportion, wherein the training set is used for model training, the test set is used for evaluating model effects, and each element in the training set and the test set is the building freeform curvature cloud map and the building freeform elevation cloud map and a corresponding building freeform structure diagram.
Further, in step S3, when training and learning is performed on the countermeasure network model, the initial learning rate is 1×10 -4, the first 50 training rounds of model learning are counted, and the learning rate is kept unchanged; the learning rate decays linearly for the last 50 training rounds until the learning rate decays to 0.
Further, in step S4, the comprehensive evaluation index is calculated as follows;
(1) The image similarity FID, the index is calculated as follows:
Wherein x represents a real building free-form surface grid picture, y represents a building free-form surface grid division picture generated by generating an countermeasure network model, w and w w are mean vectors of the real free-form surface grid picture x and the free-form surface grid picture y generated by generating the countermeasure network model, tr represents the trace of a matrix, and C w represent covariance matrices of x and y;
(2) The shape quality coefficient, the calculation formula of the index is as follows:
Where m represents the number of basic grid cells constituting the construction free-form surface grid structure, q i represents the shape quality index of the i-th basic grid cell, And s q is the mean value and the mean square error of the shape quality index q of the m grid basic units; the shape quality index calculation methods of the basic units of different grid structures are different, and the shape quality index of the basic unit of a single triangular grid structure is as follows:
Wherein A, B and C represent three vertices of a triangle, S ΔABC represents the area of the triangle, and AB, BC and CA are three side lengths corresponding to the triangle;
The shape quality index of the basic unit of the single quadrilateral grid structure is as follows:
Wherein A, B, C and D represent four vertices of a quadrangle, S ΔABC,SΔADC,SΔADB and S ΔCBD are areas of a triangle formed by any three vertices of the four vertices of the quadrangle, and AB, BC, CD, AD represent four sides of the quadrangle mesh;
(3) The calculation formula of the rod length coefficient is as follows:
Wherein n represents the number of the minimum constituent unit rods in the free-form surface of the building, L i represents the length of the ith rod, And s L is the mean value and the mean square error of the lengths of the n rods;
(4) The calculation formula of the comprehensive evaluation index is as follows:
J=α·FID(x,y)+β·sq+γ·SL
Wherein FID (x, y) is the calculated image similarity in (1), s q and s L are the calculated shape quality coefficients in (2) and (3) and the mean square error of the rod coefficients, and α, β and γ are the corresponding weights respectively;
And adding and averaging all the comprehensive evaluation indexes J of the test set, and selecting the generated countermeasure network model as the final generated countermeasure network model if the average value is smaller than a preset threshold value.
Compared with the prior art, the invention has the following beneficial technical effects by adopting the technical scheme:
(1) The method applies the deep learning method in artificial intelligence to structural design, solves the defects of low manual dividing efficiency and limited code applicability range of automatic grid division when the grid structure division design is carried out on the free curved surface, and can only carry out grid division on the free curved surface of a specific building.
(2) The invention utilizes improved optimized generation countermeasure network model, changes the limitation of the generation algorithm of the grid structure of the building free-form surface which is explicitly written by the existing method, has the defect of difficult wide application, and provides a general structural grid division design method. If a sufficient amount of training data can be provided, the method provided by the invention can be suitable for generating various building free-form surfaces and building free-form surface grids of different types, and has strong practical significance.
Drawings
The foregoing and/or additional aspects and advantages of the application will become apparent and readily appreciated from the following description of the embodiments, taken in conjunction with the accompanying drawings, in which:
Fig. 1 is a flow chart of a design method for building free-form surface grid structure division based on generation of an countermeasure network according to an embodiment of the present invention;
FIG. 2 is a schematic diagram of the generation of a cloud image of curvature of a free-form surface of a building in the method of the invention;
FIG. 3 is a schematic diagram of the creation of an elevation cloud image of a free-form surface of a building in the method of the present invention;
FIG. 4 is a schematic diagram of a sample database of architectural freeform surface grid structure divisions in the method of the present invention;
in fig. 5, a is a schematic diagram of an countermeasure generation network structure according to the present invention; b is a use schematic diagram of the building free-form surface grid structure generated after comprehensive evaluation qualification;
FIG. 6 is a dataset of a typical building freeform grid structure division design in accordance with the present invention;
FIG. 7 is a diagram showing the generation of a free-form surface mesh structure for a building at each stage of training of a neural network model in the present invention.
Detailed Description
In order to make the technical scheme, advantages and final objects of the present invention more clear, the present invention will be further explained and illustrated with reference to the accompanying drawings and detailed description.
The invention provides a design method for building free-form surface grid structure division based on a generation countermeasure network, which comprises the following steps:
S1, obtaining a free-form surface diagram of a building which needs to be subjected to grid division;
S2, generating a corresponding building free-form surface curvature cloud picture and a corresponding building free-form surface elevation cloud picture by utilizing the building free-form surface picture, and constructing a training data set;
S3, inputting the building free-form surface curvature cloud picture and the building free-form surface elevation cloud picture obtained in the step S2 after fusion to generate an countermeasure network model for training, wherein the output of the generated countermeasure network model is a building free-form surface grid structure diagram, training is carried out to obtain a generated countermeasure network model according to the building free-form surface curvature cloud picture and the building free-form surface elevation cloud picture as inputs, and the corresponding building free-form surface grid structure diagram is output;
S4, testing the generated countermeasure network model in the step S3 by using a test set, calculating a comprehensive index average value of a building free-form surface grid structure chart output by the generated countermeasure network model, judging whether the comprehensive index average value is smaller than a preset threshold, if so, generating the countermeasure neural network model to meet the requirements, if not, generating the countermeasure neural network model to not meet the requirements, and retraining again through the steps S1-S3;
And S5, fusing a preset building free-form surface curvature cloud picture and a building free-form surface elevation cloud picture, and inputting the fused building free-form surface curvature cloud picture and the fused building free-form surface elevation cloud picture into the generated countermeasure network model obtained through training in the step S3 to obtain a corresponding building free-form surface grid structure diagram.
Further, in step S2, the steps of obtaining the curvature cloud image and the elevation cloud image of the free-form surface of the building are respectively as follows:
(2.1) the procedure of acquiring a curvature cloud image
(1) Dividing adjacent edges of the free-form surface of the building according to M rows and N columns, dividing the whole free-form surface of the building into M multiplied by N free-form surfaces and representing the M multiplied by N free-form surfaces by S sub, wherein each value in the matrix represents M multiplied by N free-form surfaces obtained by dividing, and M and N are positive integers;
(2) Let S ij be the general formula of M N building freeform surfaces in the matrix of formula (1), representing the freeform surface of the ith row and jth column, where i ε [1: m ], j ε [1: n ], calculating the geometric centers of M multiplied by N building free-form surfaces, and using a general formula P ij to perform representation, namely P ij represents the geometric centers of the free-form surfaces of the ith row and the jth column, and similarly i epsilon [1, M ], j epsilon [1, N ], calculating the main curvature k n of the free-form surfaces S ij along the main direction according to a formula (2), wherein L represents a quadratic term coefficient, M represents a mixed term coefficient, N represents a constant term coefficient, E, F and G are coefficients of the first basic form of the free-form surfaces S ij, solving the formula (2) to obtain two results, wherein the maximum value in the results is the maximum main curvature k ij of the curved surfaces S ij at the P ij, and calculating the maximum main curvature k max of all M multiplied by N building free-form surfaces at the geometric centers, and using the formula (3);
(3) Carrying out maximum and minimum normalization processing on the M multiplied by N maximum principal curvature values k max obtained by calculation, and respectively solving L 1=max{k00,…,kMN},L0=min{k00,…,kMN to obtain a maximum value L 1 and a minimum value L 0 in the maximum principal curvature k max, and substituting the maximum principal curvature values k max of the M multiplied by N into a formula (4) in sequence to obtain a normalized curvature value k max, wherein the normalized curvature value is in a range of 0 to 1, as shown in a formula (5), wherein k' ij is an ith row and a jth column of curvature normalized curvature values, i E [1: m ], j ε [1: n ];
(4) Setting a color mapping scheme of a normalized curvature value k' max as a gradient color, wherein the gradient color is formed by sequentially arranging five basic colors with the same proportion, namely red, yellow, green, cyan and blue, and N i(ri,gi,bi) is represented by a general formula of five colors, wherein i=0, 1,2,3,4, (r i,gi,bi) is a numerical code corresponding to the color, N 0 (255, 0) represents red, N 1 (255, 0) represents yellow, N 2 (0, 255, 0) represents green, N 3 (0, 255, 255) represents cyan, and N 4 (0, 255) represents blue;
(5) For any normalized curvature value k 'ij, the calculation using equation (6) yields d n, leaving the fractional part of d n and only the integer d z, then the true value d z of the subscript i of k' ij left base color N i(ri,gi,bi) is obtained, i.e., the left base color of k ij is further expressed as The right base color of k' ij can be expressed as/>
dn=4k′ij (6)
(6) Order the And substituting formula (7) to calculate C r, let/> Substituting formula (7) to calculate C g, let/>Substituting the value into the formula (7) to calculate C b, wherein (C r,Cg,Cb) is a numerical code of the color corresponding to the normalized curvature value k ij in the step (5);
C=Cleft+(dn-dz)(Cright-Cleft) (7)
(7) Repeating the steps (5) and (6) one by one for normalized curvature values k 'ij of the MxN building freeform surfaces in the formula (5), and then realizing the visualization of all normalized curvature values k' ij and obtaining a curvature cloud image C sub of the whole building freeform surface, as shown in the formula (8), wherein C ij is a general formula and represents the color endowed by the ith row and jth column of freeform surfaces, i epsilon [1, M ], j epsilon [1, N ];
(2.2) an acquisition step of an elevation cloud picture:
(1) Dividing adjacent edges of the free-form surface of the building according to M rows and N columns, dividing the whole free-form surface of the building into M multiplied by N free-form surfaces and representing the M multiplied by N free-form surfaces by S' sub, wherein each value in the matrix represents M multiplied by N free-form surfaces obtained by dividing, and M and N are positive integers;
(2) Let Sv ij be the general formula of m×n building freeform surfaces in the matrix of formula (9), represent the j-th column freeform surfaces of the i-th row, wherein i e [1, M ], j e [1, N ], calculate the geometric center of m×n building freeform surfaces, and use general formula P ' ij(xij,yij,zij) to represent, P ' ij represents the geometric center of the j-th column freeform surfaces of the i-th row, (x ij,yij,zij) represents the three-dimensional cartesian coordinates of the geometric center, and similarly i e [1, M ], j e [1, N ], extract Z ij coordinates separating P ' ij, then the third principal axis component Z sub at the geometric center of all m×n building freeform surfaces is represented by formula (10);
(3) Carrying out maximum and minimum normalization processing on the M multiplied by N third principal axis components Z sub obtained by calculation, and respectively solving L '1=max{z00,…,zMN},L′0=min{z00,…,zMN to obtain a maximum value L' 1 and a minimum value L '0 of the third principal axis components Z' sub at the geometric center of the M multiplied by N building free-form surfaces, and substituting the maximum value L '1 and the minimum value L' 0 into the M multiplied by N third principal axis components Z ij to a formula (11) in sequence to obtain normalized third principal axis components Z 'sub, wherein the normalized curvature value is in a range of 0 to 1, as shown in a formula (12), and Z' ij is the third principal axis component normalized by the ith row and the jth column of curved surfaces, i E [1, M ], j E [1, N ];
(4) Setting a normalized color mapping scheme of a third principal axis component Z ' sub as a gradient color, wherein the gradient color is formed by sequentially arranging five basic colors of red, yellow, green, cyan and blue with the same proportion, and N ' i(ri,gi,bi) is represented by a general formula of five colors, wherein i=0, 1,2,3,4, (r i,gi,bi) is a numerical code corresponding to the color, N 0 ' (255, 0) represents red, N 1 ' (255, 0) represents yellow, N 2 ' (0, 255, 0) represents green, N 3 ' (0, 255, 255) represents cyan, and N 4 ' (0, 255) represents blue;
(5) For any normalized third principal axis component z 'ij, d' n can be calculated using equation (13), then the fractional part of d 'n is discarded and only the integer d' z is retained, resulting in the true value d 'z of the subscript i of the left base color N' i(ri,gi,bi) of z 'ij, i.e., the left base color of z' ij is further expressed as The right base color of z' ij can be expressed as
d′n=4z′ij (13)
(6) Order theAnd substituting formula (14) to calculate C' r, let Substituting formula (7) to calculate C' g, and then letting/>Substituting the normalized third principal axis component z 'ij in the formula (5) to calculate C' b, wherein (C 'r,C′g,C′b) is the numerical code of the color corresponding to the normalized third principal axis component z' ij;
C′=C′left+(d′n-d′z)(C′right-C′left) (14)
(7) Repeating steps (5) and (6) one by one for normalized third principal axis components z 'ij of the mxn building freeform surfaces in equation (5), then visualizing all normalized third principal axis components z' ij, and finally obtaining an elevation cloud image C 'sub of the whole building freeform surface, as in equation (15), where C' ij is a general formula representing a color imparted to the freeform surface in the ith row and jth column, i e [1: m ], j ε [1: n ];
Further, in step S2, the view angles of the building free-form surface curvature cloud image and the building free-form surface elevation cloud image are selected as top views, the scaling ratio of the building free-form surface in the two images and the position in the images are kept all the time, the resolution ratio is uniformly set to 1200PPI when the building free-form surface curvature cloud image and the building free-form surface elevation cloud image in PDF files are stored, then the building free-form surface curvature cloud image and the building free-form surface elevation cloud image in PDF are extracted, the stored image size is set to 2048p×1024p in a ". Png" format.
Further, in step S2, the steps of creating the training set and the test set for training and generating the countermeasure network model are sequentially as follows:
(2.1) carrying out grid division on a batch of building free-form surfaces with different forms by utilizing a free-form surface grid division algorithm to obtain a building free-form surface grid diagram; obtaining a curvature cloud picture and an elevation cloud picture corresponding to a free-form surface of a building, selecting a grid division picture, a curvature cloud picture and an elevation cloud picture of the free-form surface of the building as overlooking views, keeping scaling of the free-form surface of the building and positions in the pictures in all the three pictures, uniformly setting resolution to 1200PPI, and exporting in a PDF file format;
(2.2) carrying out data enhancement on the building free-form surface grid graph, the building free-form surface curvature cloud graph and the elevation cloud graph sample library obtained in the step (2.1) so as to increase the training sample data volume of the sample library, wherein the enhancement method is offline enhancement, carrying out rotation, translation and noise increase on the grid division graph, the curvature cloud graph and the elevation cloud graph so as to increase the data volume of the training library, and storing the enhanced picture in a ". Png" format, wherein the stored picture size is set to 2048p multiplied by 1024p;
(2.3) dividing the reinforced building freeform grid division map, the building freeform curvature cloud map and the building freeform elevation cloud map obtained in (2.2) into a training set and a test set in proportion, wherein the training set is used for model training, the test set is used for evaluating model effects, and each element in the training set and the test set is the building freeform curvature cloud map and the building freeform elevation cloud map and a corresponding building freeform structure diagram.
Further, in step S3, when training and learning is performed on the countermeasure network model, the initial learning rate is 1×10 -4, the first 50 training rounds of model learning are counted, and the learning rate is kept unchanged; the learning rate decays linearly for the last 50 training rounds until the learning rate decays to 0.
Further, in step S4, the comprehensive evaluation index is calculated as follows;
(1) The image similarity FID, the index is calculated as follows:
Wherein x represents a real building free-form surface grid picture, y represents a building free-form surface grid division picture generated by generating an countermeasure network model, w and w w are mean vectors of the real free-form surface grid picture x and the free-form surface grid picture y generated by generating the countermeasure network model, tr represents the trace of a matrix, and C w represent covariance matrices of x and y;
(2) The shape quality coefficient, the calculation formula of the index is as follows:
Where m represents the number of basic grid cells constituting the construction free-form surface grid structure, q i represents the shape quality index of the i-th basic grid cell, And s q is the mean value and the mean square error of the shape quality index q of the m grid basic units; the shape quality index calculation methods of the basic units of different grid structures are different, and the shape quality index of the basic unit of a single triangular grid structure is as follows:
Wherein A, B and C represent three vertices of a triangle, S ΔABC represents the area of the triangle, and AB, BC and CA are three side lengths corresponding to the triangle;
The shape quality index of the basic unit of the single quadrilateral grid structure is as follows:
Wherein A, B, C and D represent four vertices of a quadrangle, S ΔABC,SΔADC,SΔADB and S ΔCBD are areas of a triangle formed by any three vertices of the four vertices of the quadrangle, and AB, BC, CD, AD represent four sides of the quadrangle mesh;
(3) The calculation formula of the rod length coefficient is as follows:
Wherein n represents the number of the minimum constituent unit rods in the free-form surface of the building, L i represents the length of the ith rod, And s L is the mean value and the mean square error of the lengths of the n rods;
(4) The calculation formula of the comprehensive evaluation index is as follows:
J=α·FID(x,y)+β·sq+γ·SL
Wherein FID (x, y) is the calculated image similarity in (1), s q and s L are the calculated shape quality coefficients in (2) and (3) and the mean square error of the rod coefficients, and α, β and γ are the corresponding weights respectively;
And adding and averaging all the comprehensive evaluation indexes J of the test set, and selecting the generated countermeasure network model as the final generated countermeasure network model if the average value is smaller than a preset threshold value.
In order to verify the accuracy of the method, the generation design of the quadrilateral building free-form surface grid structure is developed. Fig. 6 is a data set of the design of the mesh structure division of the typical building free-form surface, and fig. 7 is a diagram of the generation of the mesh structure of the building free-form surface at each stage of training of the neural network model. Table 1 is an evaluation result table of the invention for the construction free-form surface grid structure by using the image similarity FID in the computer vision evaluation; table 2 is a table of the evaluation results of the present invention on the construction free-form surface mesh structure using the structural geometry. In addition, the importance coefficients alpha, beta and gamma of the comprehensive evaluation method are 0.3,0.35 and 0.35 respectively, so that the comprehensive evaluation results of the building free-form surface quadrilateral grid and the triangular grid can be calculated respectively. From tables 1 and 2, it is clear that the comprehensive evaluation index results of the building free-form surface quadrilateral mesh structure and the triangular mesh structure are 7.12 and 2.01, respectively. The figures (fig. 7), the tables (table 1 and table 2) and the comprehensive evaluation respectively illustrate from the qualitative and quantitative angles, and the method is reliable and accurate, thus proving the effectiveness of the design method for building free-form surface grid structure division based on the generation countermeasure network.
Table 1 machine learning evaluation
Table 2 geometric evaluation of the structure
The specific embodiment described above is only one preferred embodiment of the present invention, but it is not intended to limit the present invention. Any alternatives or equivalent modifications, which may be readily apparent to those skilled in the art, are intended to be encompassed within the scope of the present invention as disclosed herein.

Claims (4)

1. A design method for building free-form surface grid structure division based on generation of an countermeasure network, the method comprising the steps of:
s1, acquiring a free-form surface diagram of a building which needs to be subjected to grid division;
s2, generating a corresponding building free-form surface curvature cloud picture and a corresponding building free-form surface elevation cloud picture by utilizing the building free-form surface picture, and constructing a training data set and a testing data set;
S3, inputting the building free-form surface curvature cloud picture and the building free-form surface elevation cloud picture obtained in the step S2 after fusion to generate an countermeasure network model for training, wherein the output of the generated countermeasure network model is a building free-form surface grid structure diagram, training is carried out to obtain a generated countermeasure network model according to the building free-form surface curvature cloud picture and the building free-form surface elevation cloud picture as inputs, and the corresponding building free-form surface grid structure diagram is output;
S4, testing the generated countermeasure network model in the step S3 by using a test set, calculating a comprehensive index average value of a building free-form surface grid structure chart output by the generated countermeasure network model, judging whether the comprehensive index average value is smaller than a preset threshold, if so, generating the countermeasure neural network model to meet the requirements, if not, generating the countermeasure neural network model to not meet the requirements, and retraining again through the steps S1-S3;
S5, fusing a preset building free-form surface curvature cloud picture and a building free-form surface elevation cloud picture, and inputting the fused building free-form surface curvature cloud picture and the fused building free-form surface elevation cloud picture into the generated countermeasure network model obtained through training in the step S3 to obtain a corresponding building free-form surface grid structure diagram;
in step S2, the steps of obtaining the curvature cloud image and the elevation cloud image of the free-form surface of the building are respectively as follows:
(2.1) the procedure of acquiring a curvature cloud image
(1) Dividing adjacent edges of the free-form surface of the building according to M rows and N columns, dividing the whole free-form surface of the building into M multiplied by N free-form surfaces and representing the M multiplied by N free-form surfaces by S sub, wherein each value in the matrix represents M multiplied by N free-form surfaces obtained by dividing, and M and N are positive integers;
(2) Let S ij be the general formula of M x N building freeform surfaces in the matrix of formula (1), represent the j th row of freeform surfaces of the ith row, wherein i epsilon [1, M ], j epsilon [1, N ], calculate the geometric center of M x N building freeform surfaces, and use general formula P ij to represent, namely P ij represent the geometric center of the j th row of freeform surfaces of the ith row, and similarly i epsilon [1, M ], j epsilon [1, N ], calculate the principal curvature k n of the freeform surfaces S ij along the main direction according to formula (2), wherein L represents the quadratic term coefficient, M represents the mixed term coefficient, N represents the constant term coefficient, E, F and G are the coefficients of the first basic form of the freeform surfaces S ij, solve formula (2) to obtain two results, the maximum in the results is the maximum principal curvature k ij of the curved surface S ij at P ij, calculate the maximum principal curvature k max of all M x N building freeform surfaces at the geometric center, and represent by formula (3);
(3) Carrying out maximum and minimum normalization processing on the M multiplied by N maximum principal curvature values k max obtained by calculation, and respectively solving L 1=max{k00,…,kMN},L0=min{k00,…,kMN to obtain a maximum value L 1 and a minimum value L 0 in the maximum principal curvature k max, and substituting the maximum principal curvature values k max of the M multiplied by N into a formula (4) in sequence to obtain a normalized curvature value k 'max, wherein the normalized curvature value is in a range from 0 to 1 as shown in a formula (5), wherein k' ij is the ith row and the jth column of curved surface normalized curvature values, i epsilon [1, M ], j epsilon [1, N ];
(4) Setting a color mapping scheme of a normalized curvature value k' max as a gradient color, wherein the gradient color is formed by sequentially arranging five basic colors with the same proportion of red, yellow, green, cyan and blue, and N i(ri,gi,bi) is represented by a general formula of five colors, wherein i=0, 1,2,3 and 4, (r i,gi,bi) is a numerical code corresponding to the color, N 0 (255, 0) represents red, N 1 (255,255,0) represents yellow, N 2 (0,255,0) represents green, N 3 (0,255,255) represents cyan and N 4 (0,0,255) represents blue;
(5) For any normalized curvature value k ' ij, the calculation using equation (6) yields d n, leaving the fractional part of d n and only the integer d z, then the true value d z of the subscript i of k ' ij left base color N i(ri,gi,bi) is obtained, i.e., the left base color of k ' ij is further expressed as The right base color of k' ij is expressed as/>
dn=4k′ij (6)
(6) Order theAnd substituting formula (7) to calculate C r, let/> Substituting formula (7) to calculate C g, let/>Substituting the normalized curvature value k 'ij in (5) to obtain a numerical code of the color corresponding to C b by substituting the normalized curvature value k' ij in the formula (7);
C=Cleft+(dn-dz)(Cright-Cleft) (7)
(7) Repeating the steps (5) and (6) one by one for normalized curvature values k 'ij of the MxN building freeform surfaces in the formula (5), and then realizing the visualization of all normalized curvature values k' ij and obtaining a curvature cloud image C sub of the whole building freeform surface, as shown in the formula (8), wherein C ij is a general formula and represents the color endowed by the ith row and jth column of freeform surfaces, i epsilon [1, M ], j epsilon [1, N ];
(2.2) an acquisition step of an elevation cloud picture:
(1) Dividing adjacent edges of the free-form surface of the building according to M rows and N columns, dividing the whole free-form surface of the building into M multiplied by N free-form surfaces and representing the M multiplied by N free-form surfaces by S' sub, wherein each value in the matrix represents M multiplied by N free-form surfaces obtained by dividing, and M and N are positive integers;
(2) Let S 'ij be the general formula of M×N building freeform surfaces in the matrix of formula (9), represent the j th column of freeform surfaces of the i th row, wherein i [1, M ], j [1, N ] calculate the geometric center of M×N building freeform surfaces, and use general formula P' ij(xij,yij,zij) to represent, P 'ij represents the geometric center of the j th column of freeform surfaces of the i th row, (x ij,yij,zij) represents the three-dimensional Cartesian coordinates of the geometric center, and similarly i [1, M ], j [1, N ] extract and separate the Z ij coordinates of P' ij, then the third principal axis component Z sub at the geometric center of all M×N building freeform surfaces is represented by formula (10);
(3) Carrying out maximum and minimum normalization processing on the M multiplied by N third principal axis components Z sub obtained by calculation, and respectively solving L ' 1=max{z00,…,zMN},L′0=min{z00,…,zMN to obtain a maximum value L ' 1 and a minimum value L ' 0 of the third principal axis components Z sub at the geometric center of the M multiplied by N building free-form surfaces, and substituting the maximum value L ' 1 and the minimum value L ' 0 into the M multiplied by N third principal axis components Z ij to a formula (11) in sequence to obtain normalized third principal axis components Z ' sub, wherein the normalized curvature value is in a range from 0 to 1 as shown in a formula (12), and Z ' ij is the third principal axis component normalized by the ith row and the jth column of curved surfaces, i epsilon [1, M ], j epsilon [1, N ];
(4) Setting a normalized color mapping scheme of a third principal axis component Z 'sub as a gradient color, wherein the gradient color is formed by sequentially arranging five basic colors with the same proportion, namely red, yellow, green, cyan and blue, and N i′(ri,gi,bi) is represented by a general formula of five colors, wherein i=0, 1,2,3,4, (r i,gi,bi) is a numerical code corresponding to the color, N 0' (255, 0) represents red, N 1 '(255,255,0) represents yellow, N 2' (0,255,0) represents green, N 3 '(0,255,255) represents cyan, and N 4' (0,0,255) represents blue;
(5) For any normalized third principal axis component z ' ij, d ' n can be calculated using equation (13), and then the fractional part of d ' n is discarded and only the integer d ' z is retained, yielding the true value d ' z of the subscript i of z ' ij left base color N i′(ri,gi,bi), i.e., the left base color of z ' ij is further expressed as The right base color of z' ij can be expressed as
d′n=4z′ij (13)
(6) Order theAnd substituting the formula (14) to calculate C' r, let/> Substituting formula (7) to calculate C' g, and then letting/>Substituting the normalized third principal axis component z 'ij in the formula (5) to calculate C' b, wherein (C 'r,C′g,C′b) is the numerical code of the color corresponding to the normalized third principal axis component z' ij;
C′=C′left+(d′n-d′z)(C′right-C′left) (14)
(7) Repeating the steps (5) and (6) one by one for normalized third principal axis components z 'ij of the MxN building freeform surfaces in the formula (5), thereby realizing the visualization of all normalized third principal axis components z' ij and finally obtaining an elevation cloud image C 'sub of the whole building freeform surface, as shown in the formula (15), wherein C' ij is a general formula, and represents the color endowed by the ith row and jth column of freeform surfaces, i epsilon [1:M ], j epsilon [1:N ];
In step S4, the comprehensive evaluation index is calculated as follows;
(1) The image similarity FID, the index is calculated as follows:
Wherein x represents a real building free-form surface grid picture, y represents a building free-form surface grid division picture generated by generating an countermeasure network model, w and w w are mean vectors of the real free-form surface grid picture x and the free-form surface grid picture y generated by generating the countermeasure network model, tr represents the trace of a matrix, and C w represent covariance matrices of x and y;
(2) The shape quality coefficient, the calculation formula of the index is as follows:
Where m represents the number of basic grid cells constituting the construction free-form surface grid structure, q i represents the shape quality index of the i-th basic grid cell, And s q is the mean value and the mean square error of the shape quality index q of the m grid basic units; the shape quality index calculation methods of the basic units of different grid structures are different, and the shape quality index of the basic unit of a single triangular grid structure is as follows:
Wherein A, B and C represent three vertices of a triangle, S ΔABC represents the area of the triangle, and AB, BC and CA are three side lengths corresponding to the triangle;
The shape quality index of the basic unit of the single quadrilateral grid structure is as follows:
Wherein A, B, C and D represent four vertices of a quadrangle, S ΔABC,SΔADC,SΔADB and S ΔCBD are areas of a triangle formed by any three vertices of the four vertices of the quadrangle, and AB, BC, CD, AD represent four sides of the quadrangle mesh;
(3) The calculation formula of the rod length coefficient is as follows:
Wherein n represents the number of the minimum constituent unit rods in the free-form surface of the building, L i represents the length of the ith rod, And s L is the mean value and the mean square error of the lengths of the n rods;
(4) The calculation formula of the comprehensive evaluation index is as follows:
J=α·FID(x,y)+β·sq+γ·SL
Wherein FID (x, y) is the calculated image similarity in (1), s q and s L are the calculated shape quality coefficients in (2) and (3) and the mean square error of the rod coefficients, and α, β and γ are the corresponding weights respectively;
And adding and averaging all the comprehensive evaluation indexes J of the test set, and selecting the generated countermeasure network model as the final generated countermeasure network model if the average value is smaller than a preset threshold value.
2. The method for designing the grid structure division of the building free-form surface based on the generation countermeasure network according to claim 1, wherein in the step S2, the view angles of the building free-form surface curvature cloud picture and the building free-form surface elevation cloud picture are selected as overlooking, the scaling ratio of the building free-form surface in the two pictures and the positions in the pictures are kept consistent, the resolution ratio is uniformly set to 1200PPI when the two pictures are stored in a PDF file, the building free-form surface curvature cloud picture and the building free-form surface elevation cloud picture in the PDF file are extracted, the building free-form surface curvature cloud picture and the building free-form surface elevation cloud picture are stored in a ". Png" format, and the stored picture size is set to 2048p×1024p.
3. The method for designing a grid structure division of a free-form surface of a building based on generation of an countermeasure network according to claim 1 or 2, wherein in step S2, the creating steps of a training set and a test set for training generation of a countermeasure network model are sequentially as follows:
(2.1) carrying out grid division on a batch of building free-form surfaces with different forms by utilizing a free-form surface grid division algorithm to obtain a building free-form surface grid diagram; obtaining a curvature cloud picture and an elevation cloud picture corresponding to a free-form surface of a building, selecting a grid division picture, a curvature cloud picture and an elevation cloud picture of the free-form surface of the building as overlooking views, keeping the scaling of the free-form surface of the building in the three pictures and the positions in the pictures consistent, uniformly setting the resolution to 1200PPI, and exporting the three pictures in a PDF file format;
(2.2) enhancing the sample data of the building freeform surface grid graph, the building freeform surface curvature cloud graph and the elevation cloud graph obtained in the (2.1) so as to increase the training sample data volume of a sample library, wherein the enhancement method is off-line enhancement, rotating, translating and increasing noise points are carried out on the grid division graph, the curvature cloud graph and the elevation cloud graph so as to increase the training data volume, the enhanced picture is stored in a 'png' format, and the size of the stored picture is set to 2048p multiplied by 1024p;
(2.3) dividing the reinforced building freeform grid division map, the building freeform curvature cloud map and the building freeform elevation cloud map obtained in (2.2) into a training set and a test set in proportion, wherein the training set is used for model training, the test set is used for evaluating model effects, and each element in the training set and the test set is the building freeform curvature cloud map and the building freeform elevation cloud map and a corresponding building freeform structure diagram.
4. The method for designing the grid structure division of the building free-form surface based on the generation of the countermeasure network according to claim 1, wherein in the step S3, the initial learning rate is 1×10 -4 when the model of the generation of the countermeasure network is trained and learned, and the learning rate is kept unchanged for the first 50 training rounds of model learning; the learning rate decays linearly for the last 50 training rounds until the learning rate decays to 0.
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