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31 August 2020, Volume 41 Issue 4 Previous Issue    Next Issue

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A review of natural language processing application in construction engineering WANG Yu1, DENG Hui1, LI Xiao-yao1, DENG Yi-chuan1,2 2020, 41(4): 501-511.  DOI: 10.11996/JG.j.2095-302X.2020040501 Abstract ( 231 )   PDF (463KB) ( 204 )   Natural language processing (NLP) can transform unstructured documents in the construction field into structured information, which is convenient for relevant practitioners to carry out daily management of construction projects. In recent years, NLP-related algorithms have been widely developed, but pertinent research in the construction field is still in its infancy. Through examining the past-decade literature on NLP in construction, the past research conducted on the technical level and application level at home and abroad was sorted out. The development, common methods and the open source tools of NLP were outlined. More importantly, the application of NLP in various stages of construction was summarized from the perspectives of statistical analysis tools, application systems and three other aspects. In addition, the extant problems of NLP in the construction field were discussed and future prospects were proposed from the three aspects of technology, construction industry and government. Related Articles | Metrics

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Feature extraction of video data based on trigonometric function iteration YU Wan-bo, FAN Qing-tao 2020, 41(4): 512-519.  DOI: 10.11996/JG.j.2095-302X.2020040512 Abstract ( 187 )   PDF (3142KB) ( 208 )   In the research of computer vision, the recognition of image objects based on video data is on an increasing trend. Focusing on the feature extraction of video data, a method based on trigonometric function iteration was proposed to extract 3D iterative trajectory features of the video. Considering the time and space dimensions of video data, this paper constructed a three-dimensional dynamic system by using a trigonometric function, obtained the features of video segment data as a whole in one extraction, and extracted a set of three-dimensional feature points similar to chaotic attractors. This iterative feature of video data is an iterative set of track points. Face recognition experiments using VidTIMIT datasets of face videos show that increasing the number of initial iterations and reducing the number of iterations could lead to a better effect of the extracted feature points set. After 43 groups of 559 videos of VidTIMIT were all experimented with, the recognition rate could reach 88.16%. Compared with other methods recorded in the existing literature, the method proposed in this paper is characterized by high recognition rate and short computing time. It is proved that this 3D video iterative trajectory feature is of great practical significance and requires further research, analysis and verification. Related Articles | Metrics

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The method of image enhancement under extremely low-light conditions YANG Yong, LIU Hui-yi 2020, 41(4): 520-528.  DOI: 10.11996/JG.j.2095-302X.2020040520 Abstract ( 126 )   PDF (5087KB) ( 172 )   The process of obtaining the image with normal exposure time from the image with short exposure time photographed in extreme low-light conditions is defined as the image enhancement under extreme low-light conditions. In this paper, we proposed a method for the enhancement of the extreme low-light image based on the encoding-and-decoding network architecture and residual block. We designed an end-to-end fully convolutional network as the translation model, which consists of two parts: the encoding-and-decoding network and refinement network. The input data of the translation model is the extreme low-light raw data captured with short exposure time in extreme low-light conditions, and the output data is the image in RGB format. Firstly, the low-frequency information of the image was reconstructed via U-net and then was input into the residual network to reconstruct the high-frequency information of the image. Through the experiments carried out on the SID data set and comparisons with previous research results, it is proved that the method described in this paper can effectively enhance the visual effect of the images captured under extreme low-light conditions and improved with low-light enhancement, and increase the expression of the image details. Related Articles | Metrics

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A prior-image-based metal artifact reduction method for cone beam CT LIU Yang-chuan1, GAO Peng1,2, ZHU Ye-chen1, GAO Xin1 2020, 41(4): 529-538.  DOI: 10.11996/JG.j.2095-302X.2020040529 Abstract ( 218 )   PDF (1342KB) ( 161 )   To effectively suppress the artifacts caused by metal implants in the reconstruction process of cone beam CT (CBCT) image, a prior-image-based metal artifact reduction method was proposed. Firstly, the reconstructed image with metal artifacts was preprocessed by bilateral filtering, metal threshold segmentation and tissue clustering to produce the metal image and the prior image without metal information. Secondly, the metal image and prior image were respectively forward-projected to produce the metal projection region and prior projection data. Then, the metal projection region was interpolated by the prior projection data and the metal neighborhood projection data to produce the restored projection data. Finally, the CT image was reconstructed by the FDK algorithm and was fused with the metal image to produce the final corrected image. To verify the performance of the proposed algorithm, the metal artifact reduction experiments were carried out on the 3D Shepp-Logan head phantom and clinical head CT data. The experimental results show that compared with the commonly used linear-interpolation-based method and image-inpainting-based method, the corrected image of the proposed method can keep the root-mean-square error to the minimum and the peak signal-to-noise ratio to the maximum. This indicates that the proposed method can effectively suppress metal artifacts while preserving image edge information. Related Articles | Metrics

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Pose-guided scene-preserving person video generation algorithm LI Gui, LI Teng 2020, 41(4): 539-547.  DOI: 10.11996/JG.j.2095-302X.2020040539 Abstract ( 127 )   PDF (6387KB) ( 162 )   The person video generation technology learns the feature representation of human body structure and motion, so as to realize the spatial generation mapping from the feature representation to the character video frame. In view of the existing person video generation algorithm lacking in the transformation of background environment and the low accuracy of human pose estimation, a pose-guided scene-preserving person video generation algorithm was proposed. First, the appropriate source video and target video were selected, and the video frame with the appearance of the segmented character served as the network input instead of the source video frame. Then, based on GAN, a motion transformation model was employed to replace characters in source videos with target characters and maintain the consistency of motion. Finally, the Poisson image editing was used to fuse the character appearance with the source background, enabling the flowed advantages: (a) removing border anomaly pixels; (b) realizing character blending naturally into the source scene; and  (c) avoiding changing the background environment and overall image style. The proposed algorithm used the segmented foreground person image instead of the source video frame to reduce background interference and improve the accuracy of pose estimation, thus naturally realizing scene-preserving during the motion transfer process and producing artistic and authentic person videos. Related Articles | Metrics

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Image feature points extraction and matching method based on improved ORB algorithm YANG Hong-fan, LI Hang, CHEN Kai-yang, LI Jia-qi, WANG Xiao-fei 2020, 41(4): 548-555.  DOI: 10.11996/JG.j.2095-302X.2020040548 Abstract ( 316 )   PDF (3889KB) ( 194 )   The fixed threshold selection of traditional ORB algorithm results in many false extractions and mismatches, which cannot meet the requirements of accurate extraction and matching of different image feature points. To solve this problem, an improved ORB feature point extraction and matching method was proposed. Firstly, the local adaptive threshold was set up. Then, an adaptive threshold selection criterion was designed by classifying the pixels, and thus the precise extraction of ORB feature points was achieved. Finally, the PROSAC algorithm was used to complete the matching of feature points based on the improved ORB feature points. The experimental results indicate that the improved method has a high adaptability to variations in brightness, and both the calculation speed and extraction accuracy are greatly improved. The total matching time is reduced, the number of mismatches is less, and the accurate matching rate is increased, which indicates that this improved method is characterized with accuracy and real-time performance. In addition, the RMSE error obtained by tracking the feature points acquired at the matching stage is small, which demonstrates a significant improvement in matching accuracy. Compared with other existing methods, this method has better environmental adaptive capacity and application value. Related Articles | Metrics

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Research on path planning of teeth movement in invisible orthodontic LI Zhan-li, LIU Tong-xin, LI Hong-an, SUN Zhi-hao 2020, 41(4): 556-566.  DOI: 10.11996/JG.j.2095-302X.2020040556 Abstract ( 89 )   PDF (6624KB) ( 88 )   Aimed at solving low efficiency and accuracy of path planning of teeth movement in invisible orthodontic schedule, a new method was proposed. First, a new objective function was proposed based on the evaluation parameters of teeth and jaws. Based on the traditional artificial bee colony algorithm (ABC), Pareto solution sets were stored through external storage, and then the Pareto solution set was updated by the improved Harmonic distance, thus diversifying the population. Then, the Slerp spherical linear interpolation and linear interpolation were used to obtain the initial value of the tooth movement path, which was combined with the initial food source generation method in the artificial colony algorithm to generate a better food source. Finally, the new objective function was optimized by the priority scheme of the optimized ABC, leading to the collision-free path for the teeth movement. The experiment showed the effect of the proposed method and compared it with the traditional objective function. The results show that the proposed objective function can generate a more suitable schedule for clinical orthodontic. The improved algorithm can result in a better path and reduce the number of orthodontic stages, and is of practical value. Related Articles | Metrics

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Improved 3D-NDT point cloud registration algorithm based on 3D-Harris and FPFH FAN Qiang1, LIU Peng1, YANG Jun2, ZHOU Pei-xi1 2020, 41(4): 567-575.  DOI: 10.11996/JG.j.2095-302X.2020040567 Abstract ( 292 )   PDF (3490KB) ( 164 )   Aimed at addressing the shortcomings of the traditional point cloud registration normal distribution transform (3D-NDT) and iterative closure points (ICP) algorithms, such as poor registration effect, long registration time and serious errors, a precise and relatively efficient point cloud matching algorithm was proposed. First, the 3D-Harris algorithm was used to identify the key points of each point cloud, and the key points were adopted to establish a local reference frame for the basic points and calculate the fast point feature histograms (fpfh) descriptor. Then, the corresponding estimation algorithm of the least median of squares (LMeds) minimum median method was utilized to eliminate the inaccurate point correspondence and obtain the feature point pairs with corresponding 3D feature relationships. The transformation matrix required for coarse registration was calculated to complete the preliminary registration. Subsequently, according to the 3D-NDT algorithm, the point cloud data space was voxelized, and the probability distribution function was employed to complete the final point cloud for accurate registration. Finally, we used this method to match three groups of point cloud files, which were downloaded from the network with less noise and large-scale overlapped with more noise collected by Kinect V2.0 to the same spatial reference frame, and compared the classical 3D-NDT, ICP and other algorithms through accuracy analysis. The experimental results show that the proposed algorithm can achieve the high accuracy registration of point cloud data in indoor scenes with low iteration times and is less affected by noise. However, how to reduce the complexity of the algorithm appropriately and shorten the registration time needs further research. Related Articles | Metrics

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Polynomial reparameterization detection of Bézier curves SHEN Wan-qiang, WANG Hong-kai 2020, 41(4): 576-582.  DOI: 10.11996/JG.j.2095-302X.2020040576 Abstract ( 63 )   PDF (439KB) ( 91 )   An algorithm is presented to determine whether the degree of Bézier curve can be reduced by polynomial reparameterization. In the algorithm, for any Bézier curve, the relation between the basis functions before and after reparameterization is expressed as a system of equations. Instead of solving the equations, the polynomial for reparameterization and the control points of the lower degree Bézier curve can be calculated directly by a pyramid algorithm of coefficient reparameterization. In addition, the polynomial for reparameterization is unique to within a scale factor and a constant. Compared with the previous algorithm by examples, this algorithm possesses shorter computational time. Related Articles | Metrics

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Construction method of overpass structure based on directed acyclic graph WANG Yu-kun1,2, CAO Li1,2, ZHAO Yang1,2, LI Lin1,2 2020, 41(4): 583-592.  DOI: 10.11996/JG.j.2095-302X.2020040583 Abstract ( 88 )   PDF (1800KB) ( 77 )   Road information is an important element for a digital city. Modeling the overpass structure is of great significance to many areas, such as the simulation of urban traffic, traffic optimization, and urban planning. Although a great amount of research was conducted on the modeling of urban road networks, a targeted solution for the treatment of overpass structures remained to be put forward. Through the analysis of the overpass structure, a method for constructing overpass structures is proposed based on the directed acyclic graph, with the purpose of realizing efficient and high-quality modeling. Firstly, the two-dimensional raster data was preprocessed to extract effective road information. Secondly, a directed acyclic graphs (DAG) was constructed to express the topological relationship of overpass structure. Then, the height of each control point was calculated using the proposed height calculation method designed according to the structural characteristics, functional characteristics and related prior knowledge of the road. Finally, the overpass structure was constructed, based on the calculated road height and topological information with component units. The experiments selected three typical overpass structures in East China for testing. The results prove that the proposed method is advantageous in data acquisition and calculation accuracy and can help simplify the modeling process of overpass structures. Related Articles | Metrics

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Investigation of parameters significance and predicted model on surface roughness on fused deposition modeling PAN Li-juan, SHANG Zheng, JIA Gui-hong, CHU Kai-yu, WANG Jin-feng 2020, 41(4): 593-598.  DOI: 10.11996/JG.j.2095-302X.2020040593 Abstract ( 108 )   PDF (2445KB) ( 62 )   Nine orthogonal experiments consisting of temperature, printing speed, layer thickness were designed to investigate the factors and rules influencing fused deposition modeling (FDM) precision. Surface roughness was measured using portable surface roughness apparatus. The significant factor influencing surface roughness was determined by calculating the signal-to-noise ratio and conducting the variance analysis. By means of the Taguchi method, the multiple regression equation and exponential equation were employed to predict the surface roughness and to determine the parameter combination of minimum surface roughness of FDM printouts. Results of the analysis reveal the following factors in order of the extent of their influence on surface roughness: layer thickness > temperature > printing speed. Validation experiments were undertaken regarding different printing models and FDM printers to verify the validity and adaptability of the analysis results. Experiment results show that the prediction result of the multiple regression equation outperformed that of the exponential equation and Taguchi method. Furthermore, the above conclusions exhibit broad adaptability to different printing models and FDM printers. Related Articles | Metrics

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Dimensional completeness check and analytical technology of 3D MBD model ZHANG Sheng-wen1,2, YOU Yan-yan1, LI Bin-cheng1,2, CHENG De-jun1,2 2020, 41(4): 599-605.  DOI: 10.11996/JG.j.2095-302X.2020040599 Abstract ( 89 )   PDF (595KB) ( 75 )   A technology for checking the completeness of dimensioning and analyzing the dimensional chain was proposed to solve problems, such as complicated structure of the 3D model based definition (MBD) model, error-prone dimensioning and the difficulty of manual check. The spatial dimensions were converted into a series of matrices to ensure the completeness of the dimensions at 3D level, based on which the sizes of each member of the dimensional chain were calculated to verify the rationality of the design. Matrix was used to express and store the dimensions on the 3D model and the redundancy and deletion of the dimensions was judged by the position and quantity of dimension nodes. Then the to-be-judged dimensional chain was extracted from the model for analysis and verification to ensure the accuracy of product manufacturing information transmission and an inspection report was produced. The feasibility of the method was verified by using the connecting rod of a certain type of marine diesel engine, which greatly reduced the inspection time and the design error rate and improved the design efficiency of the staff. Related Articles | Metrics

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Innovative method of ethnic pattern based on neural style transfer network HOU Yu-kang, LV Jian, LIU Xiang, HU Tao, ZHAO Ze-yu 2020, 41(4): 606-613.  DOI: 10.11996/JG.j.2095-302X.2020040606 Abstract ( 125 )   PDF (11873KB) ( 102 )   Aiming at the problems of low manual extraction efficiency of traditional ethnic pattern symbols as well as the difficulty of designing creative graphic combination, this paper proposed an innovative model of traditional ethnic pattern style by taking the batik and cross-stitch work of the Miao nationality as an example. This model combined the improved shape grammar with neural style transfer network based on deep learning, to extract e and encode ethnic pattern configuration frames. Then, a large number of innovative ethnic patterns was generated through shape grammars, and the basic features of ethnic patterns was extracted quickly using the style-transfer network, so as to transfer and generate innovative ethnic pattern designs based on this framework. The experimental results show that the model can generate brand-new ethnic ornament patterns on the basis of the specified frame, which are more orderly than those generated directly by means of the neural network transfer. The generated pattern will finally be applied to the design of the Miao fabric patterns, which verifies the feasibility of this method and design process. Related Articles | Metrics

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Problems with and reflections on BIM forward design TAO Gui-lin1, MA Wen-yu1, TANG Ke-qiang2, DU Yi-cheng3 2020, 41(4): 614-623.  DOI: 10.11996/JG.j.2095-302X.2020040614 Abstract ( 242 )   PDF (1327KB) ( 262 )   The BIM forward design has become widely recognized due to its advantages of simplifying the modelling process and reducing costs of labor and information exchange. As the BIM technology has been increasingly popularized in the architecture industry in China for many years, the current BIM consulting model cannot satisfy the highly demanding application. Many challenges still remain when the BIM forward design was applied in the practical projects. This study performed a critical survey based on the practical experience from many projects and the literature investigation, so as to summarize the existing questions as follows: ① the lack of adaptive standards; ② domestic constraints; ③ underdeveloped related technical and industrial chains. Based on the analysis of the mentioned questions, several conclusions can be drawn such as: The drawing-oriented application is a transitional strategy. The effective solutions for developing the BIM forward design should be based on the adaptive standard. The domestic BIM software and cloud platforms should be developed, and the integration of design and construction management should be reinforced. Not only is the strong support of technical required, but the innovation of management mode is needed to guarantee the application and development of BIM. Related Articles | Metrics

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Similarity calculation method of BIM model WANG Jia1,2, SU Ding-ding1, ZHOU Xiao-ping1,2, LU Yi-xin3 2020, 41(4): 624-631.  DOI: 10.11996/JG.j.2095-302X.2020040624 Abstract ( 257 )   PDF (2544KB) ( 123 )   At present, whether in a local BIM model library or on an online BIM model sharing website, practitioners can only obtain the required BIM models by searching and reading them one by one manually. With the increasing number of models, it takes much time and labor to obtain models that meet the requirements. In this light, a component-level BIM model similarity calculation method was proposed. Based on the components of the model, this method used the industry foundation classes (IFC) files in the BIM universal interactive format as the data source and the universal data standard IFC 2×3 as the data foundation. First, the geometric information and semantic information of the components in the model were extracted, and the improved oriented bounding box (OBB) collision detection algorithm was used to find connected components. Then the BIM model was built as an adjacency graph model with the components as vertexes and the connection relationship among components as edges, and he graph editing distance algorithm was used to calculate the edit distance of the adjacency graphs. Finally, the similarity between different BIM models was calculated. Based on the similarity of component-level BIM models, the retrieval speed and accuracy of BIM models can be greatly improved. Related Articles | Metrics

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Method for cultural feature extraction based on rank correlation and entropy weight SHANG Zhong-an, CHEN Xiang 2020, 41(4): 632-639.  DOI: 10.11996/JG.j.2095-302X.2020040632 Abstract ( 80 )   PDF (2075KB) ( 91 )   In the process of developing cultural and creative products of museums, there is no objective and robust method to evaluate and extract design elements. In this context, this paper proposed a design method for the extraction and application of cultural features from museum artifacts based on rank correlation and entropy weight method. First, select the artifacts to disassemble their explicit and implicit features, and then establish a cultural feature interpretation table. At the same time, analyze the users and collect pairs of sensible words about user experience, so as to perform cluster analysis. Next, the sensible word pairs and the factors of extensibility and discernibility in explicit features were taken as indicators for evaluation. The rank correlation method was used to implement weight analysis and comprehensive evaluation, and the ranking of cultural feature goodness was obtained. Then the entropy weight method was used to figure out the key feature category. Finally, based on the key features and feature goodness rank, the optimal design was generated through the intersection, reorganization and metaphor of the elements. In conclusion, through an example of a smart reading pen design for children, it is proved that this method can improve the efficiency in cultural feature extraction and the usefulness of design, and provides an implication for the development of cultural and creative product of the museum. Related Articles | Metrics

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Research on influencing factors of satisfaction with commercial complex guidance system based on grounded theory HU Shan1, LIU Jing1, SUN En-mei1, WANG Neng1, LUO Yi-ming2 2020, 41(4): 640-648.  DOI: 10.11996/JG.j.2095-302X.2020040640 Abstract ( 89 )   PDF (800KB) ( 64 )   A guidance system is an important means to convey information and guide disoriented users, effectively displaying the urban culture. An excellent guidance system can quickly and easily lead users to their destinations. How to improve the guidance system to better serve the users is of great significance to boosting the quality of the guidance system service and enhancing user satisfaction. Semi-structured interviews were conducted with 35 users. Based on a large amount of interview data, the grounded theory, a qualitative research method, was employed to analyze and summarize the interview data to extract the influencing factors of users’ satisfaction with the commercial complex guidance system. Finally, five main categories were summarized, namely, readability, accessibility, security, interactivity and friendliness. Based on this, the theoretical models of influencing factors and action paths were constructed, and the structural equation model was further utilized to verify and analyze them. The rationality and scientificity of the model were thus verified. The research results are of practical value for improving the users’ satisfaction with the guidance system, helping designers deepen the future prospects of constructing the guidance system service from the user perspective, and providing experience for real estate operators in resource organization and service updates. Related Articles | Metrics

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Research on the product demands configuration method based on user satisfaction ZHANG Di-jing, HOU Zeng-xuan, HUANG Lei, ZHAO You-hang 2020, 41(4): 649-657.  DOI: 10.11996/JG.j.2095-302X.2020040649 Abstract ( 82 )   PDF (460KB) ( 82 )   In order to reasonably determine the preferences and priorities of user demands to adapt to the mass customization production mode and maximize user satisfaction, an improved product user demands configuration method is proposed. The fuzzy clustering analysis method was integrated into the Kano model to classify user demands, the screening was conducted according to their contribution to the improvement of satisfaction, then the evaluation factors of customer satisfaction and importance were calculated and a hierarchical structure model of product user demands was established. On this basis, in the fuzzy analytic hierarchy process (FAHP), a fuzzy best-worst method (FBWM) was employed to construct a consistent triangular fuzzy number complementary judgment matrix, the probability concept was introduced to achieve defuzzification and obtain the initial weights of user demands, and the demands evaluation factors served as the correction factors of the initial weights. Then the modified weights were normalized to obtain the comprehensive weights of user demands, thus realizing the configuration of product demands. Taking an enterprise’s eyewear product design and development as an example, the effectiveness of this method was verified, and a user demand configuration strategy was provided for the design and development of eyewear and other products. Related Articles | Metrics

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Proactive interaction design of conversational agent for smart homes WANG Er-zhuo1, YUAN Xiang1, LI Shi-yan2 2020, 41(4): 658-666.  DOI: 10.11996/JG.j.2095-302X.2020040658 Abstract ( 166 )   PDF (1237KB) ( 181 )   Aimed at the proactive interaction design strategies of conversational agents (CAs) in the smart home, the proactivity was discussed in this article based on decision right and communication style. In this light, four proactive styles (straight forward decision-maker and adviser, euphemistic decision-maker and adviser) were designed for smart home CAs. A Wizard-of-OZ experiment was conducted to investigate the effects of users’ gender, age, experience and living status on their preferences for proactive styles. The results reveal that: ① Users having had experience with smart home products are more satisfied with the “adviser” style; family users feel more comfortable with the “adviser” style. ② Users generally feel more satisfied and comfortable when the CA communicates with them in an explicit manner. And the experiment verifies that: ① Users’ prior experience with smart home products and their living states have an impact on users’ preferences for proactive styles of smart home CAs. ② In the smart home scenario, it is found that the communication efficiency of CAs is more important than politeness. Related Articles | Metrics

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On axonometric projection HE Yuan-jun 2020, 41(4): 667-676.  DOI: 10.11996/JG.j.2095-302X.2020040667 Abstract ( 135 )   PDF (2742KB) ( 145 )   The definition of axonometric projection was re-examined. Axonometric projection is a method by means of parallel projection, projecting the spatial coordinate system to the projection plane along the projection direction to obtain the axonometric coordinate system and express the spatial shape under this coordinate system. The resulting drawing is designated as axonometric drawing. Three views represent three directions of a body respectively, and the axonometric drawing represents three straight and three face angles with one view. The essence is to express the spatial body on the plane. This paper further discussed some fundamental problems in axonometric projection, such as the parallel projection system, axonometric triangle, axonometric projection system, the basic elements and formulas of axonometric projection, analyzed the similarities and differences between normal axonometric projection and oblique axonometric projection, and gave their schematic diagrams. Related Articles | Metrics

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Research on simulation analysis and optimization method of ball head hanging ring based on contact model LIU Xiao-hui1,2, HUANG Fei2, ZHENG Jia-yan2, CAI Meng-qi3, ZHOU Xiao-hui2 2020, 41(4): 677-686.  DOI: 10.11996/JG.j.2095-302X.2020040677 Abstract ( 79 )   PDF (2678KB) ( 70 )   As a key component of the transmission line, the ball head hanging ring has great effects on the safety of transmission. In order to optimize the ball head hanging ring, under the action of the horizontal force along the wind direction, the nonlinear static simulation analysis of the ball head hanging ring was simulated through the finite element analysis, using the commercial software Abaqus. Two contact models for ball head hanging rings of different sizes, different grid densities, and different contact surface widths were established, with the contact type being face-to-face. The rules of influences of ring size, grid density and contact surface width on the maximum stress were discussed. According to the results, in the cases of different grid densities, the contact width and maximum stress of the two types of ball head hanging rings are almost the same. As the contact width increases, the maximum stress tends to decrease, which can be roughly divided into the rapid descent area, slow descent area, and stable area. In the stable area, the maximum stress and fluctuation range are small, which can be used as the ideal contact width of the ball head hanging ring, thus providing theoretical guidance for the optimal design of ball head hanging rings in the future. Related Articles | Metrics