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Aggregate Point Cloud Geometric Features for Processing
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作者 Yinghao Li Renbo Xia +4 位作者 Jibin Zhao Yueling Chen Liming Tao Hangbo Zou Tao Zhang 《Computer Modeling in Engineering & Sciences》 SCIE EI 2023年第7期555-571,共17页
As 3D acquisition technology develops and 3D sensors become increasingly affordable,large quantities of 3D point cloud data are emerging.How to effectively learn and extract the geometric features from these point clo... As 3D acquisition technology develops and 3D sensors become increasingly affordable,large quantities of 3D point cloud data are emerging.How to effectively learn and extract the geometric features from these point clouds has become an urgent problem to be solved.The point cloud geometric information is hidden in disordered,unstructured points,making point cloud analysis a very challenging problem.To address this problem,we propose a novel network framework,called Tree Graph Network(TGNet),which can sample,group,and aggregate local geometric features.Specifically,we construct a Tree Graph by explicit rules,which consists of curves extending in all directions in point cloud feature space,and then aggregate the features of the graph through a cross-attention mechanism.In this way,we incorporate more point cloud geometric structure information into the representation of local geometric features,which makes our network perform better.Our model performs well on several basic point clouds processing tasks such as classification,segmentation,and normal estimation,demonstrating the effectiveness and superiority of our network.Furthermore,we provide ablation experiments and visualizations to better understand our network. 展开更多
关键词 Deep learning point-based models point cloud analysis 3D shape analysis point cloud processing
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Point Cloud Processing Methods for 3D Point Cloud Detection Tasks
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作者 WANG Chongchong LI Yao +2 位作者 WANG Beibei CAO Hong ZHANG Yanyong 《ZTE Communications》 2023年第4期38-46,共9页
Light detection and ranging(LiDAR)sensors play a vital role in acquiring 3D point cloud data and extracting valuable information about objects for tasks such as autonomous driving,robotics,and virtual reality(VR).Howe... Light detection and ranging(LiDAR)sensors play a vital role in acquiring 3D point cloud data and extracting valuable information about objects for tasks such as autonomous driving,robotics,and virtual reality(VR).However,the sparse and disordered nature of the 3D point cloud poses significant challenges to feature extraction.Overcoming limitations is critical for 3D point cloud processing.3D point cloud object detection is a very challenging and crucial task,in which point cloud processing and feature extraction methods play a crucial role and have a significant impact on subsequent object detection performance.In this overview of outstanding work in object detection from the 3D point cloud,we specifically focus on summarizing methods employed in 3D point cloud processing.We introduce the way point clouds are processed in classical 3D object detection algorithms,and their improvements to solve the problems existing in point cloud processing.Different voxelization methods and point cloud sampling strategies will influence the extracted features,thereby impacting the final detection performance. 展开更多
关键词 point cloud processing 3D object detection point cloud voxelization bird's eye view deep learning
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Modeling and Performance Analysis of UAV-Aided Millimeter Wave Cellular Networks with Stochastic Geometry
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作者 Li Junruo Wang Yuanjie +2 位作者 Cui Qimei Hou Yanzhao Tao Xiaofeng 《China Communications》 SCIE CSCD 2024年第6期146-162,共17页
UAV-aided cellular networks,millimeter wave(mm-wave) communications and multi-antenna techniques are viewed as promising components of the solution for beyond-5G(B5G) and even 6G communications.By leveraging the power... UAV-aided cellular networks,millimeter wave(mm-wave) communications and multi-antenna techniques are viewed as promising components of the solution for beyond-5G(B5G) and even 6G communications.By leveraging the power of stochastic geometry,this paper aims at providing an effective framework for modeling and analyzing a UAV-aided heterogeneous cellular network,where the terrestrial base stations(TBSs) and the UAV base stations(UBSs) coexist,and the UBSs are provided with mm-wave and multi-antenna techniques.By modeling the TBSs as a PPP and the UBSs as a Matern hard-core point process of type Ⅱ(MPH-Ⅱ),approximated but accurate analytical results for the average rate of the typical user of both tiers are derived through an approximation method based on the mean interference-to-signal ratio(MISR) gain.The influence of some relevant parameters is discussed in detail,and some insights into the network deployment and optimization are revealed.Numerical results show that some trade-offs are worthy of being considered,such as the antenna array size,the altitude of the UAVs and the power control factor of the UBSs. 展开更多
关键词 average rate DOWNLINK millimeter wave point process theory SIR stochastic geometry UAVaided cellular networks
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Existence and numerical approximation of a solution to frictional contact problem for electro-elastic materials
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作者 Othman Baiz EL-Hassan Benkhira Rachid Fakhar 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2024年第2期201-219,共19页
In this paper,a frictional contact problem between an electro-elastic body and an electrically conductive foundation is studied.The contact is modeled by normal compliance with finite penetration and a version of Coul... In this paper,a frictional contact problem between an electro-elastic body and an electrically conductive foundation is studied.The contact is modeled by normal compliance with finite penetration and a version of Coulomb’s law of dry friction in which the coefficient of friction depends on the slip.In addition,the effects of the electrical conductivity of the foundation are taken into account.This model leads to a coupled system of the quasi-variational inequality of the elliptic type for the displacement and the nonlinear variational equation for the electric potential.The existence of a weak solution is proved by using an abstract result for elliptic variational inequalities and a fixed point argument.Then,a finite element approximation of the problem is presented.Under some regularity conditions,an optimal order error estimate of the approximate solution is derived.Finally,a successive iteration technique is used to solve the problem numerically and a convergence result is established. 展开更多
关键词 piezoelectric material frictional contact variational Inequality fixed point process finite element method error estimation iteration method
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Regression Method for Rail Fastener Tightness Based on Center-Line Projection Distance Feature and Neural Network
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作者 Yuanhang Wang Duxin Liu +4 位作者 Sheng Guo Yifan Wu Jing Liu Wei Li Hongjie Wang 《Chinese Journal of Mechanical Engineering》 SCIE EI CAS CSCD 2024年第2期356-371,共16页
In the railway system,fasteners have the functions of damping,maintaining the track distance,and adjusting the track level.Therefore,routine maintenance and inspection of fasteners are important to ensure the safe ope... In the railway system,fasteners have the functions of damping,maintaining the track distance,and adjusting the track level.Therefore,routine maintenance and inspection of fasteners are important to ensure the safe operation of track lines.Currently,assessment methods for fastener tightness include manual observation,acoustic wave detection,and image detection.There are limitations such as low accuracy and efficiency,easy interference and misjudgment,and a lack of accurate,stable,and fast detection methods.Aiming at the small deformation characteristics and large elastic change of fasteners from full loosening to full tightening,this study proposes high-precision surface-structured light technology for fastener detection and fastener deformation feature extraction based on the center-line projection distance and a fastener tightness regression method based on neural networks.First,the method uses a 3D camera to obtain a fastener point cloud and then segments the elastic rod area based on the iterative closest point algorithm registration.Principal component analysis is used to calculate the normal vector of the segmented elastic rod surface and extract the point on the centerline of the elastic rod.The point is projected onto the upper surface of the bolt to calculate the projection distance.Subsequently,the mapping relationship between the projection distance sequence and fastener tightness is established,and the influence of each parameter on the fastener tightness prediction is analyzed.Finally,by setting up a fastener detection scene in the track experimental base,collecting data,and completing the algorithm verification,the results showed that the deviation between the fastener tightness regression value obtained after the algorithm processing and the actual measured value RMSE was 0.2196 mm,which significantly improved the effect compared with other tightness detection methods,and realized an effective fastener tightness regression. 展开更多
关键词 Railway system Fasteners Tightness inspection Neural network regression 3D point cloud processing
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Building Facade Point Clouds Segmentation Based on Optimal Dual-Scale Feature Descriptors
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作者 Zijian Zhang Jicang Wu 《Journal of Computer and Communications》 2024年第6期226-245,共20页
To address the current issues of inaccurate segmentation and the limited applicability of segmentation methods for building facades in point clouds, we propose a facade segmentation algorithm based on optimal dual-sca... To address the current issues of inaccurate segmentation and the limited applicability of segmentation methods for building facades in point clouds, we propose a facade segmentation algorithm based on optimal dual-scale feature descriptors. First, we select the optimal dual-scale descriptors from a range of feature descriptors. Next, we segment the facade according to the threshold value of the chosen optimal dual-scale descriptors. Finally, we use RANSAC (Random Sample Consensus) to fit the segmented surface and optimize the fitting result. Experimental results show that, compared to commonly used facade segmentation algorithms, the proposed method yields more accurate segmentation results, providing a robust data foundation for subsequent 3D model reconstruction of buildings. 展开更多
关键词 3D Laser Scanning Point Clouds Building Facade Segmentation Point Cloud processing Feature Descriptors
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Energy Efficiency Optimization for Heterogeneous Cellular Networks Modeled by Matérn Hard-Core Point Process 被引量:4
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作者 Yonghong Chen Jie Yang +1 位作者 Xuehong Cao Shibing Zhang 《China Communications》 SCIE CSCD 2020年第8期70-80,共11页
The Poisson point process(PPP) has been widely used in wireless network modeling and performance analysis due to the independence between its nodes. Therefore, it may not be a suitable model for many of the exclusive ... The Poisson point process(PPP) has been widely used in wireless network modeling and performance analysis due to the independence between its nodes. Therefore, it may not be a suitable model for many of the exclusive networks between the nodes. This paper analyzes the energy efficiency(EE) and optimizes the two-tier heterogeneous cellular networks(Het Nets). Considering the mutual exclusion between macro base stations(MBSs) distribution, the deployment of MBSs is modeled by the Matérn hard-core point process(MHCPP), and the deployment of pico base stations(PBSs) is modeled by the PPP. We adopt a simple approximation method to study the signal to interference ratio(SIR) distribution in two-tier MHCPP-PPP networks and then derive the coverage probabilities, the average data rates and the energy efficiency of Het Nets. Finally, an optimization algorithm is proposed to improve the EE of Het Nets by controlling the transmit power of PBSs. The simulation results show that the EE of a system can be effectively improved by selecting the appropriate transmit power for the PBSs. In addition, two-tier MHCPP-PPP Het Nets have higher energy efficiency than two-tier PPP-PPP Het Nets. 展开更多
关键词 energy efficiency heterogeneous cellular networks coverage probability matérn hard-core point process
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Joint asymptotic distribution of exceedances point process and partial sum of stationary Gaussian sequence 被引量:3
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作者 TAN Zhong-quan PENG Zuo-xiang 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2011年第3期319-326,共8页
Let {Xi}i=1^∞ be a standardized stationary Gaussian sequence with covariance function τ(n) =EX1Xn+1, Sn =∑i=1^nXi,and X^-n=Sn/n.And let Nn be the point process formed by the exceedances of random level (x/√2 l... Let {Xi}i=1^∞ be a standardized stationary Gaussian sequence with covariance function τ(n) =EX1Xn+1, Sn =∑i=1^nXi,and X^-n=Sn/n.And let Nn be the point process formed by the exceedances of random level (x/√2 log n+√2 log n-log(4π log n)/2√log n) √1-τ(n) + X^-n by X1,X2,…, Xn. Under some mild conditions, Nn and Sn are asymptotically independent, and Nn converges weakly to a Poisson process on (0,1]. 展开更多
关键词 stationary Gaussian sequence exceedances point process partial sum.
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Reliability Analysis of Repairable Systems Using Stochastic Point Processes 被引量:1
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作者 谭芙蓉 江志斌 白同朔 《Journal of Shanghai Jiaotong university(Science)》 EI 2008年第3期366-369,共4页
In order to analyze the failure data from repairable systems, the homogeneous Poisson process (HPP) is usually used. In general, HPP cannot be applied to analyze the entire life cycle of a complex, re-pairable system ... In order to analyze the failure data from repairable systems, the homogeneous Poisson process (HPP) is usually used. In general, HPP cannot be applied to analyze the entire life cycle of a complex, re-pairable system because the rate of occurrence of failures (ROCOF) of the system changes over time rather than remains stable. However, from a practical point of view, it is always preferred to apply the simplest method to address problems and to obtain useful practical results. Therefore, we attempted to use the HPP model to analyze the failure data from real repairable systems. A graphic method and the Laplace test were also used in the analysis. Results of numerical applications show that the HPP model may be a useful tool for the entire life cycle of repairable systems. 展开更多
关键词 repairable systems reliability analysis homogeneous Poisson process (HPP) rate of occurrence of failures (ROCOF) stochastic point process Laplace test
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Study on mixing and segregation behaviors in particulate fluidized bed system for mineral processing 被引量:2
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作者 Sahu S.N. Sahu A.K. Biswal S.K. 《International Journal of Mining Science and Technology》 SCIE EI CSCD 2015年第3期459-464,共6页
In order to identify the mixing and segregation behaviors in a mineral processing operation, present study aimed on the hydrodynamics of solid–liquid fluidization. The study was carried out in a fluidization column w... In order to identify the mixing and segregation behaviors in a mineral processing operation, present study aimed on the hydrodynamics of solid–liquid fluidization. The study was carried out in a fluidization column with tapings at different height of the bed to collect the sample. The binary particles considered in this study are hematite(4800 kg/m3) and quartz(2600 kg/m3) at different size fractions in the range of average size 87×10^(-6)m to 400×10^(-6)m. It is observed that for various binary mixtures, both quartz and hematite particles share the equal composition by mass(50%) at a particular height of fluidized bed, referred as ‘‘locus point'' of mixing. Study indicates that the mixing zone volume will increase for a continuous fluidized bed plant operation. It is observed that the number of locus points varies from 1 to 3 signifying their dependency on the size ratios of binary mixture. Whenever, the difference in terminal velocity between quartz and hematite particles approaches to zero, mixing is enhanced.Further, the present study is extended to find the segregation index for the different size ratios of quartz and hematite particles. It is evident that depending on the size ratios, various regions such as complete segregation, partial mixing and complete mixing can be observed. 展开更多
关键词 Liquid-solid fluidization Mixing Segregation Locus point Mineral processing
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Model for Failure Point Process of a Repairable System and Application 被引量:1
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作者 JIANG Renyan CHEN Hao 《International Journal of Plant Engineering and Management》 2018年第2期89-96,共8页
A engineering system is usually repairable, and failure process of a repairable by a failure point process. The power law model is a commonly used approach to model syst the em is often described failure point process... A engineering system is usually repairable, and failure process of a repairable by a failure point process. The power law model is a commonly used approach to model syst the em is often described failure point process. This paper introduces the concept and model for the failure process of repairable system. The method of parameter estimation is developed, and failure observations are fitted into a power-law model by using the least square method. Two applications of the pressent model are discussed according to the practical failure data of the central cooling system of a nuclear power plant. One application is determining the optimal overhaul time, and the other is evaluating the quality of maintenance. This paper provides references for the overhaul decision making and maintenance quality evaluation in reality. 展开更多
关键词 repairable system failure point process overhaul decision maintenance quality
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RATE OF CONVERGENCE FOR MULTIPLE CHANGEPOINTS ESTIMATION OF MOVING-AVERAGE PROCESSES
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作者 Li Yunxia Zhang Lixin 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2005年第4期416-422,共7页
In this paper, the least square estimator in the problem of multiple change points estimation is studied. Here, the moving-average processes of ALNQD sequence in the mean shifts are discussed. When the number of chang... In this paper, the least square estimator in the problem of multiple change points estimation is studied. Here, the moving-average processes of ALNQD sequence in the mean shifts are discussed. When the number of change points is known, the rate of convergence of change-points estimation is derived. The result is also true for p-mixing, φ-mixing, a-mixing, associated and negatively associated sequences under suitable conditions. 展开更多
关键词 mean shift multiple change points moving-average process ALNQD least square.
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Standby Redundancy Allocation for a Coherent System under Its Signature Point Process Representation
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作者 Vanderlei da Costa Bueno 《American Journal of Operations Research》 2016年第6期489-501,共13页
Willing to work in reliability theory in a general set up, under stochastically dependence conditions, we intend to characterize a not identically spare standby redundancy operation through compensator transform under... Willing to work in reliability theory in a general set up, under stochastically dependence conditions, we intend to characterize a not identically spare standby redundancy operation through compensator transform under a complete information level, the physic approach, that is, observing its component lifetime. We intend to optimize system reliability under standby redundancy allocation of its components, particularly, under minimal standby redundancy. To get results, we will use a coherent system representation through a signature point process. 展开更多
关键词 RELIABILITY Martingale Methods in Reliability Theory Signature Point process Standby Redundancy Coherent System
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Research on 3D Laser Scanning Reconstruction of Ancient Buildings Combined with BIM Technology
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作者 Ensheng Liu Chunyong Luo +1 位作者 Chunbaixue Yang Yuhua Huang 《Journal of Computer and Communications》 2023年第7期233-240,共8页
After more than 30 years of scientific and social development, surveying and mapping technology by leaps and bounds, engineering surveying technology has undergone tremendous changes. In the process of protecting anci... After more than 30 years of scientific and social development, surveying and mapping technology by leaps and bounds, engineering surveying technology has undergone tremendous changes. In the process of protecting ancient buildings, it is necessary to obtain the precise dimensions of architectural details. In this study, the path of 3D laser scanning combined with BIM technology is explored. Taking the observation and protection of the ancestral hall of the Liu family as an example, this study aims to draw drawings that reflect the relevant information about the ancient buildings, the accurate three-dimensional model of ancient buildings is established with BIM technology, which provides new methods and ideas for the research and protection of ancient buildings. . 展开更多
关键词 Liu Ancestral Hall 3D Laser Scanning Technology BIM Technology Point Cloud processing
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Load-Aware Offloading Strategy in Two-Tier Heterogeneous Network 被引量:5
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作者 Jianyuan Feng Zhiyong Feng Zhiqing Wei 《China Communications》 SCIE CSCD 2016年第8期148-158,共11页
Although small cell offloading technology can alleviate the congestion in macrocell, aggressively offloading data traffic from macrocell to small cell can also degrade the performance of small cell due to the heavy lo... Although small cell offloading technology can alleviate the congestion in macrocell, aggressively offloading data traffic from macrocell to small cell can also degrade the performance of small cell due to the heavy load. Because of collision and backoff, the degradation is significant especially in network with contention-based channel access, and finally decreases throughput of the whole network. To find an optimal fraction of traffic to be offloaded in heterogeneous network, we combine Markov chain with the Poisson point process model to analyze contention-based throughput in irregularly deployment networks. Then we derive the close-form solution of the throughput and find that it is a function of the transmit power and density of base stations.Based on this, we propose the load-aware offloading strategies via power control and base station density adjustment. The numerical results verify our analysis and show a great performance gain compared with non-load-aware offloading. 展开更多
关键词 heterogeneous networks offloading strategies load-aware Poisson point process Markov chain throughput maximization CSMA
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Modeling forest fires in Mazandaran Province, Iran 被引量:2
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作者 Amir T.Payandeh Najafabadi Fatemeh Gorgani Maryam Omidi Najafabadi 《Journal of Forestry Research》 SCIE CAS CSCD 2015年第4期851-858,共8页
We used a spafio-temporal shot-noise Cox process to study the distribution of forest fires reported between 2006 and 2010 in the Mazandaran Province's forests. The fitted model shows that daily temperature, altitude,... We used a spafio-temporal shot-noise Cox process to study the distribution of forest fires reported between 2006 and 2010 in the Mazandaran Province's forests. The fitted model shows that daily temperature, altitude, and slope-exposure impacted fire occurrence. Forest fire occurred in the region had an aggregated behavior, which increased in radius below 1-km away from fired areas; a periodic pattern of fire occurrence in the region was verified. The risk of forest fire is significantly higher for areas with southern exposure and slope between 30° and 50°, northern exposure and slope between 0° and 50°, and eastern exposure and slope between 0° and 30°. The risk of fire was also significantly higher at altitudes between 1350 and 3000 m asl. Human causes were the main ignition source for forest fires in the region. The fire occurrence rate stayed above average during the drought period from September 2008 to September 2009. Our findings could lead to the development of fire-response and fire-suppression strategies appropriate to specific regions. 展开更多
关键词 Forest fire Spatio-temporal shot-noise Coxprocesses Spatial point process
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Characterizing the Seasonal and Directional Varying Properties in A Marine Environment 被引量:1
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作者 张熠 程涛 《China Ocean Engineering》 SCIE EI CSCD 2016年第4期549-564,共16页
With noticing an increasing number of failure events for offshore structures in the present days, it is now realized that modeling the marine environment especially for exceptional environmental conditions is quite im... With noticing an increasing number of failure events for offshore structures in the present days, it is now realized that modeling the marine environment especially for exceptional environmental conditions is quite important. It is recognized that a possible improvement in the traditional modeling of environmental characteristics, which are the basis for the load models for structural analysis and design, may be needed. In this paper, the seasonal and directional varying properties in modeling the ocean parameter, the wave height, are studied. The peak over threshold(POT) method is selected to model the extreme wave height by utilizing a non-stationary discrete statistical extreme model. The varying parameters are taken into account with a changing pattern to reflect the seasonal and directional dependent behavior. Both the magnitude and the occurrence rate of the extreme values are investigated. Detailed discussion on the continuity of the established model is also given. The importance of the proposed model is demonstrated in reliability analysis for a jacket structure. The sensitivity to the changing marine environment in reliability analyses is investigated. 展开更多
关键词 peak over threshold method climate change reliability analysis offshore structures point process extreme value distribution significant wave height
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Existence results for unilateral contact problem with friction of thermo-electro-elasticity 被引量:1
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作者 H.BENAISSA EL-H.ESSOUFI R.FAKHAR 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2015年第7期911-926,共16页
This work studies a mathematical model describing the static process of contact between a piezoelectric body and a thermally-electrically conductive foundation. The behavior of the material is modeled with a thermo-el... This work studies a mathematical model describing the static process of contact between a piezoelectric body and a thermally-electrically conductive foundation. The behavior of the material is modeled with a thermo-electro-elastic constitutive law. The contact is described by Signorini's conditions and Tresca's friction law including the electrical and thermal conductivity conditions. A variational formulation of the model in the form of a coupled system for displacements, electric potential, and temperature is de- rived. Existence and uniqueness of the solution are proved using the results of variational inequalities and a fixed point theorem. 展开更多
关键词 static frictional contozt thermo-piezoelectric material Signorini's condi-tion Tresca's friction frictional heat generation variational inequality fixed point process
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Dynamic A^*path finding algorithm and 3D lidar based obstacle avoidance strategy for autonomous vehicles 被引量:2
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作者 Wang Xiaohua Ma Pin +1 位作者 Wang Hua Li Li 《High Technology Letters》 EI CAS 2020年第4期383-389,共7页
This paper presents a novel dynamic A^*path finding algorithm and 3D lidar based local obstacle avoidance strategy for an autonomous vehicle.3D point cloud data is collected and analyzed in real time.Local obstacles a... This paper presents a novel dynamic A^*path finding algorithm and 3D lidar based local obstacle avoidance strategy for an autonomous vehicle.3D point cloud data is collected and analyzed in real time.Local obstacles are detected online and a 2D local obstacle grid map is constructed at 10 Hz/s.The A^*path finding algorithm is employed to generate a local path in this local obstacle grid map by considering both the target position and obstacles.The vehicle avoids obstacles under the guidance of the generated local path.Experiment results have shown the effectiveness of the obstacle avoidance navigation algorithm proposed. 展开更多
关键词 autonomous navigation local obstacle avoidance dynamic A*path finding algorithm point cloud processing local obstacle map
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EQUI-ATTRACTION AND BACKWARD COMPACTNESS OF PULLBACK ATTRACTORS FOR POINT-DISSIPATIVE GINZBURG-LANDAU EQUATIONS 被引量:1
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作者 李扬荣 佘连兵 尹金艳 《Acta Mathematica Scientia》 SCIE CSCD 2018年第2期591-609,共19页
A new concept of an equi-attractor is introduced, and defined by the minimal compact set that attracts bounded sets uniformly in the past, for a non-autonomous dynam- ical system. It is shown that the compact equi-att... A new concept of an equi-attractor is introduced, and defined by the minimal compact set that attracts bounded sets uniformly in the past, for a non-autonomous dynam- ical system. It is shown that the compact equi-attraction implies the backward compactness of a pullback attractor. Also, an eventually equi-continuous and strongly bounded process has an equi-attractor if and only if it is strongly point dissipative and strongly asymptotically compact. Those results primely strengthen the known existence result of a backward bounded pullback attractor in the literature. Finally, the theoretical criteria are applied to prove the existence of both equi-attractor and backward compact attractor for a Ginzburg-Landau equation with some varying coefficients and a backward tempered external force. 展开更多
关键词 Non-autonomous systems point dissipative processes pullback attractors backward compact attractors equi-attractors Ginzburg-Landau equations
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