Automated Structural Design of Shear Wall Residential Buildings Using GAN-Based Machine Learning Algorithm

3 Artificial intelligence is transforming many industries and reshaping building design processes to be smarter 4 and automated. While a large number of studies on automated building design have been carried out recently, they 5 focused on architectural aspects, leaving a gap in its application to structural design. Considering the increasingly 6 wide application of shear wall systems in high-rise buildings and envisioning the massive benefit of automated 7 structural design, this paper proposes a shear-wall design automation model based on a generative adversarial 8 network (GAN). Its goal is to learn from existing shear wall design documents and then perform structural design 9 intelligently and swiftly. To this end, a database of representative architectural and structural design documents was 10 developed. Then, datasets were prepared via abstraction, semanticization, classification, and parameterization in 11 terms of building height and seismic design category. The GAN model improved its shear wall design proficiency 12 through adversarial training supported by data and hyper-parametric analytics. The performance of the trained GAN 13 model was appraised against the metrics based on the confusion matrix and the intersection-over-union approach. 14 Finally, case studies were conducted to evaluate the applicability, effectiveness, and appropriateness of the innovative 15 GAN-based structural design method. 16


Introduction
Intelligent design offers advantages in its ability to minimize manual design work, promote diversity in the 22 design space, and ultimately provide optimal design performance [1-4]. As a result of rapid global urbanization, the 23 demand for high-rise residential buildings is continuously increasing [5][6][7]. Reinforced concrete shear wall systems 24 have been widely used in high-rise designs. The transfer of architectural proposals to construction documents 25 involves arranging structural layouts, defining the position and orientation of structural systems, and controlling the 26 dimensions of structural components [8]. These steps are fundamental to the design process. However, because of 27 their iterative nature, they are also very time consuming, even when conducted by competent engineers. An 28 innovative design approach with greater efficiency is needed, and the intelligent structural design is an emerging 29

approach. 30
Existing approaches are primarily based on generative design. The commonly used options are as follows: (1) 31 design exploration using topology optimization, genetic algorithms, and cellular automata; (2) design synthesis using 32 generative grammars; and (3) design by analogy [1][2][3][4]. These approaches are particularly favorable for geometric 33 modeling and are less suitable for engineering calculations. Hence, they are mainly applied to architecture and have 34 found very few applications in structural design. In addition, the considerable computational expense of the 35 underlying algorithms forfeits their use in the scheme design stage. 36 Deep learning methods offer a new option to overcome these challenges. They have been used efficiently for 37 various purposes via pre-training [9][10][11][12][13]. The generative adversarial network (GAN) is one of the most widely used 38 frameworks [14] for automated architectural design [15][16][17]. In this study, we extend the application of GAN to shear 39 IoU metric can properly gauge the overall similarity of the design under evaluation against the reference design and 65 provide valuable guidance and feedback to the training direction. These innovations provide a solid foundation for 66 the design performance that StructGAN delivers consistently to all types of building structures. 67 The components of StructGAN are summarized in Figure 1a: interpreter, designer, and modeler. The interpreter 68 digests and semanticizes the architectural sketches. Then, the designer analyzes the semantic drawings, performs the 69 inference, and devises the structural design. Finally, the modeler proposes the design and presents the structural 70 model. Figure 1b compares the performances of StructGAN and the conventional design process. StructGAN offers 71 a promising increase in speed by a factor of 10, which is equivalent to saving billions of US dollars per annum in the 72 industry. As it learns and evolves continuously, StructGAN will undoubtedly obtain much higher savings. 73  the study of Chakrabarti [21]. The potential seismic losses are analyzed by the widely adopted FEMA P58 method 81 [22], and the values are the mean losses of two typical high-rise shear wall residential buildings. Adopting StructGAN, this study developed two structural designs following the guide in Figure 1a, and then 130 compared their safety and economic properties with those of the designs by competent engineers. The two buildings 131 are shown in Figures 3a and 3b. 132 First, structural safety is primarily evaluated by the seismic story drift ratio because excessive story deformation 133 under an earthquake can induce damage to structural components and facilities and even cause a large number of 134 casualties. Hence, ensuring that the seismic deformation of buildings satisfies the specifications is essential in the 135 overall structural design. The comparisons of seismic story drift ratios for two buildings are shown in Figures 3d and  136 3e. As depicted in the figures, the maximum seismic deformation of the StructGAN design is only 11% larger than 137 that of the design by engineers, which is perfectly acceptable in the preliminary design and meets the safety 138 requirements. Subsequently, this work compared the StructGAN designs and designs by engineers with respect to 139 material consumption, and the results are shown in Figure 3c. The maximum difference is within 5% in the two cases, 140 indicating that the automated designs consume almost the same amount of materials as manual designs and fully 141 meet the economic requirements. Additionally, the seismic repair costs of the StructGAN designs and designs by 142 engineers are comparable, as illustrated in Figure 3c. Consequently, the economic and safety differences in the 143 structural designs by StructGAN and experienced engineers are relatively slight, and the StructGAN design meets 144 the requirements of high efficiency and high quality in the preliminary structural design. 145   with pix2pix, pix2pixHD is an improved algorithm that can generate high-resolution photo-realistic images with 162 significantly higher computational demands [26]. In the above two algorithms, the characteristic "structures loss" 163 can effectively reflect the physical position relationship of pixels in an image [25]. Thus, deduced from the "structures 164 loss," pix2pix and pix2pixHD can capture the potential spatial position distribution of structural layouts. The 165 structural distribution correlation can contribute to establishing a direct map relationship for StructGAN to convert 166 the crucial architectural elements into the corresponding structural layouts. Furthermore, their significant 167 performance in generative architectural design has proved the applicability of pix2pix and pix2pixHD [15,16]. 168 Consequently, this work adopted them as core algorithms for StructGAN. consistency between the designs by StructGAN and engineers, and the difference in SWratio estimates the discrepancy of the total structural layout area between two designs. As these metrics show, a high PA , WIoU, and 180 SIoU and low difference in SWratio indicate that the designs by StructGAN and engineers are highly consistent. 181 Subsequently, this study discussed the influence of (GAN / L1) and FM based on the proposed evaluations, where GAN was fixed as 1, and the Group7-H2 dataset of shear wall residential buildings was adopted.   designs and design quality closely related to the datasets; hence, this study discussed the influence induced by datasets 212 under different design conditions. Building heights and seismic design intensities were adopted as the classification 213 criteria of the datasets because they are the critical factors that determine the mechanical performance of building 214 structures. Higher heights and seismic design intensities correspond to increased requirements for structural 215 components [8]. Notably, utilizing mixed design datasets with different heights and seismic design intensities for 216 training, the final probability distributions of the automated designs were consistent with the average probability 217 distribution of the mixed data, which cannot satisfy the demand for different design conditions. Therefore, datasets 218 were divided into Group7-H1 (seismic design intensity = 7-degree, and height ≤ 50 m), Group7-H2 (seismic design 219 intensity = 7-degree, and height > 50 m), and Group8 (seismic design intensity = 8-degree). In addition, for contrast, 220 Group Mix (mixed dataset) was composed of various data.     enhances the generation quality based on the feedback from the discriminator until the discriminator fails to judge. 286 Simultaneously, the discriminator consistently elevates the skill at detecting synthetic outputs by the generator. 287 Adversarial training is applied to both networks so that the generator and discriminator can master the generation and  This study adopted the semantic process by extracting essential architectural and structural elements in design 305 images and coding them by color patterns, so that critical design elements and the corresponding structural layout 306 information are maintained. Semantic designs can effectively reduce the dimension of probability distributions and 307 enhance training performance. In this study, the red (i.e., RGB = (255, 0, 0)), gray (i.e., RGB = (132, 132, 132)), 308 green (i.e., RGB = (0, 255, 0)), and blue ( RGB = (0, 0, 255)) colors denote the structural shear wall, nonstructural 309 infill wall, indoor window, and outdoor gate, respectively. 310 In addition, the structural design for shear wall residential buildings is directly related to the design conditions to 320. Furthermore, the complexity of local features is significantly reduced owing to the semantic architectural-331 structural designs; hence, the generator architecture can be simplified to generate more confined and precise image 332 elements. The numbers of global down-sample layers (n_downsample_global) and residual blocks in the global 333 generator network (n_blocks_global) were reduced from 4 to 2 (or 1) and from 9 to 6, respectively. Consequently, 334 the StructGAN design performance was improved, with more integrated auto-designed structural shear walls and 335 higher ScoreIoU, as shown in Extended Data Fig. 3. For the Group8 dataset, the performance was not enhanced because the normal method was sufficiently good. Simultaneously, the performance of StructGAN using Group7-H1 and 337 Group7-H2 for training was obviously enhanced. Consequently, the improved StructGAN is recommended for 338 automated structural design. "AI" or "Engineer" judgment, which involves inviting engineers to distinguish designs produced by StructGAN or 352 competent engineers, and (2) rationality score for designs, which comprises asking for scores given by engineers 353 based on their experience and perception. Similar to the AMT method, the engineer perception-based evaluation was 354 conducted on the Questionnaire Star (https://www.wjx.cn/) platform for blind tests, and typical parts of the 355 questionnaire are illustrated in Extended Data Fig. 5. This study invited 11 senior experts (work experience > 15 356 years), 12 practicing engineers, and graduate students to participate in the judgment and assessment tasks, and the 357 corresponding metrics were proposed based on the evaluation results. SEP-1 is the metric for the "AI" or "Engineer" 358 judgment, expressed in Equation (1), and which equally counts the judgment of experts and ordinary engineers. SEP-359 2 is the metric for rationality evaluation, expressed in Equation (2), and which adopts the coefficient of the variation 360 to weight the scores by experts and ordinary engineers (Equation (3) (1) where Nex and Nnonex denote the number of experts and non-experts, respectively, and NFP and NTN indicate the number 363 of misjudgments and correct judgments of StructGAN designs, respectively. Nimg is the number of assessed images, 364 Sj is the score of image j, and  and ex and nonex are the weight coefficients of the scores of experts and non-experts, respectively. ex and nonex are the standard deviations of the scores of experts and non-experts, respectively, and ex Step 1 subdivision Step 2 contour detection Step  Figs. 6a and 6b). The extracted elements of 385 the StructGAN design are compared with those of engineers pixel-by-pixel, and then the comparison results are used 386 to create a confusion matrix (Figure 6a). Subsequently, based on the confusion matrix, PA , WIoU, and SWratio are 387 proposed and used, where PA (Equation (4)) measures the image clarity, WIoU (Equation (5) In the structural IoU-based evaluation, the core superiority is the consistency measurement of the structural 400 layouts designed by StructGAN and experienced engineers. Detailed steps for the structural IoU-based evaluation 401 are illustrated in Figure 6b, and the corresponding metric is named SIoU (structural intersection over union). First, 402 the images are subdivided into multiple sub-images to reduce the number of structural shear walls in each image and 403 elevate the edge capture precision of the contour detection algorithm. Subsequently, the shear wall elements of each 404 sub-image are extracted based on the HSV color mode, and their contour coordinates are identified by the contour 405 detection API "OpenCV.findContours (image)." Then, the total intersection area of the shear walls in the StructGAN 406 design and design by engineers are obtained using the Shapely API "shapely.geometry.Polygon (coordinates)" and 407 SIoU is calculated using Equation (7). 408 where Ainter is the intersection area of the walls in the GAN-synthetic and target designs, Aunion is the union area of the walls, which is unfavorable for the evaluation. Hence, the difference in the total shear wall area between the synthetic 428 image and target image is adopted as the correction coefficient, and a smaller diversity corresponds to a larger SWratio.                   Evaluation results of the optimal StructGAN. a, Typical structural designs by StructGAN (red, gray, blue, and green denote structural shear wall, nonstructural in ll wall, indoor windows, and outdoor gates, respectively). b, Computer vision-based evaluation results (ScoreIoU = ηSWratio × (ηSIoU × SIoU + ηWIoU × WIoU); ηSWratio = 1 − |SWratioGAN − SWratiotarget| / SWratioGAN; ηSIoU = ηWIoU = 0.5). c, Engineer perception-based evaluation results, including "AI" or "Engineer" judgment and rationality quanti cation.

Figure 3
Comparisons between the StructGAN designs and designs by engineers. The two cases are named Case-7degree and Case-8degree, with heights of approximately 100 m and seismic design intensities of 7degree and 8-degree, respectively. a, 3D view of Case-7degree. b, 3D view of Case-8degree. c, Comparisons of overall performance in Case-7degree and Case-8degree. d, Comparisons of story drift ratios in Case-7degree. e, Comparisons of story drift ratios in Case-8degree.

Figure 4
Analyses of the hyperparameters and quanti cation of testing results for different GAN algorithms with various parameters. a, Comparison of the pix2pix-generated images with different parameters. b, Comparison of the pix2pixHD-generated images with different parameters. c-f, Comparisons of SIoU, WIoU, PA, and the difference in SWratio between pix2pix and pix2pixHD with various parameters. The evaluation results show that the designs by StructGAN equipped with pix2pixHD coincide well with those by engineers, with high stability. However, the performance of pix2pix needs further enhancement in future studies.

Figure 6
Computer vision-based evaluation. a, Confusion matrix used to obtain PA, WIoU, and SWratio. b, Detailed steps to get SIoU. c, Typical cases of SIoU.

Supplementary Files
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