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Atomic-scale understanding of martensitic transformation and transition-induced twinning in deformed Fe-Mn alloys
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作者 ZHANG Hong-bo LI Hong-kui +2 位作者 OU Xiao-qin SHEN Jie SONG Min 《Journal of Central South University》 2025年第4期1211-1222,共12页
In the present study,molecular dynamic simulation(MD)was used to investigate the plastic deformation process of the Fe-Mn alloys with different Mn contents.The influences of Mn contents ranging from 10%to 30%(at%)on t... In the present study,molecular dynamic simulation(MD)was used to investigate the plastic deformation process of the Fe-Mn alloys with different Mn contents.The influences of Mn contents ranging from 10%to 30%(at%)on the deformation behavior and the controlling mechanism of the Fe-base alloys were analyzed.The results show that phase transformations and{112}<111>_(BCC)deformation twinning occur in all Fe-Mn alloys but follow different deformation paths.In the Fe-10%Mn alloy the deformation twinning mechanism obeys the FCC-related path,the Fe-20%Mn alloy involves both the FCC-and HCP-related paths,and the deformation of the Fe-30%Mn alloy is dominated by the HCP-related twinning path.The addition of Mn can increase the stacking fault energy and retard the activation of slip systems as well as the formation of stacking faults.Thus,a higher content of Mn can delay the FCC®ε-martensite and the subsequentε-martensite®BCC phase transition at the intersection of twoε-martensitic bands.Therefore,the addition of Mn alloying element increases the yield strength and reduces the elastic modulus of the Fe-Mn alloys.The formation of deformation twins will contribute to the work-hardening effect and delay the necking and fracture of alloys.It is expected that the results in the present study will provide theoretical reference for the design and optimization of high-performance steels. 展开更多
关键词 Fe-Mn steel tensile deformation molecular dynamics simulation phase transformation
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Coverage of communication-based sensor nodes deployed location and energy efficient clustering algorithm in WSN 被引量:6
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作者 Xiang Gao Yintang Yang Duan Zhou 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2010年第4期698-704,共7页
An effective algorithm based on signal coverage of effective communication and local energy-consumption saving strategy is proposed for the application in wireless sensor networks.This algorithm consists of two sub-al... An effective algorithm based on signal coverage of effective communication and local energy-consumption saving strategy is proposed for the application in wireless sensor networks.This algorithm consists of two sub-algorithms.One is the multi-hop partition subspaces clustering algorithm for ensuring local energybalanced consumption ascribed to the deployment from another algorithm of distributed locating deployment based on efficient communication coverage probability(DLD-ECCP).DLD-ECCP makes use of the characteristics of Markov chain and probabilistic optimization to obtain the optimum topology and number of sensor nodes.Through simulation,the relative data demonstrate the advantages of the proposed approaches on saving hardware resources and energy consumption of networks. 展开更多
关键词 wireless sensor network probability distribution function Markov chain received signal strength indicator Gaussian distribution.
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Seepage law and permeability calculation of coal gas based on Klinkenberg effect 被引量:6
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作者 王登科 魏建平 +2 位作者 付启超 刘勇 夏玉玲 《Journal of Central South University》 SCIE EI CAS CSCD 2015年第5期1973-1978,共6页
Focused on the Klinkenberg effect on gas seepage, the independently developed triaxial experimental system of gas seepage was applied to conduct research on the seepage characteristics of coal seam gas. By means of ex... Focused on the Klinkenberg effect on gas seepage, the independently developed triaxial experimental system of gas seepage was applied to conduct research on the seepage characteristics of coal seam gas. By means of experimental data analysis and theoretical derivation, a calculation method of coal seam gas permeability was proposed, which synthesized the respective influences of gas dynamic viscosity, compressibility factor and Klinkenberg effect. The study results show that the Klinkenberg effect has a significant influence on the coal seam gas seepage, the permeability estimated with the method considering the Klinkenberg effect is correct, and this permeability can fully reflect the true seepage state of the gas. For the gas around the standard conditions, the influences of dynamic viscosity and compressibility factor on the permeability may be ignored. For the gas deviating far away from the standard conditions, the influences of dynamic viscosity and compressibility factor on the permeability must be considered. The research results have certain guiding significance in forming a correct understanding of the Klinkenberg effect and selecting a more accurate calculation method for the permeability of coal containing gas. 展开更多
关键词 coalbed gas seepage law Klinkenberg effect gas adsorption-desorption PERMEABILITY
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Vehicle kinematics modeling and design of vehicle trajectory generator system 被引量:3
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作者 李昭 蔡自兴 +2 位作者 任孝平 陈爱斌 薛志超 《Journal of Central South University》 SCIE EI CAS 2012年第10期2860-2865,共6页
A trajectory generator based on vehicle kinematics model was presented and an integrated navigation simulation system was designed.Considering that the tight relation between vehicle motion and topography,a new trajec... A trajectory generator based on vehicle kinematics model was presented and an integrated navigation simulation system was designed.Considering that the tight relation between vehicle motion and topography,a new trajectory generator for vehicle was proposed for more actual simulation.Firstly,a vehicle kinematics model was built based on conversion of attitude vector in different coordinate systems.Then,the principle of common trajectory generators was analyzed.Besides,combining the vehicle kinematics model with the principle of dead reckoning,a new vehicle trajectory generator was presented,which can provide process parameters of carrier anytime and achieve simulation of typical actions of running vehicle.Moreover,IMU(inertial measurement unit) elements were simulated,including accelerometer and gyroscope.After setting up the simulation conditions,the integrated navigation simulation system was verified by final performance test.The result proves the validity and flexibility of this design. 展开更多
关键词 vehicle kinematics model integrated navigation system track generator IMU element system simulation
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Reliability analysis of monotone coherent multi-state systems based on Bayesian networks 被引量:2
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作者 Binghua Song Zhongbao Zhou +2 位作者 Chaoqun Ma Jinglun Zhou Shaofeng Geng 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2016年第6期1326-1335,共10页
The Bayesian networks (BNs) provide a robust probabilistic method of reasoning under uncertainty and have been successfully applied to a variety of real-world tasks. Aiming to explore the capabilities of the BN formal... The Bayesian networks (BNs) provide a robust probabilistic method of reasoning under uncertainty and have been successfully applied to a variety of real-world tasks. Aiming to explore the capabilities of the BN formalism in reliability analysis of monotone coherent multi-state systems, the BNs are compared with a popular tool for reliability analysis of monotone coherent multi-state systems, namely the multi-state fault trees (MFTs). It is shown that any MFT can be directly mapped into BN and the basic inference techniques on the latter may be used to obtain classical parameters computed from the former (i.e. probability distribution of top variable, minimal upper vectors and maximum lower vectors for any performance level, importance measures of components). Furthermore, some additional information can be obtained by using BN, both at the modeling and analysis level. At the modeling level, several restrictive assumptions implicit in the MFT methodology can be removed and various kinds of dependencies among components can be accommodated. At the analysis level, a general diagnostic analysis can be performed. The comparison of these methods is illustrated by an example of the water supply system. © 2016 Beijing Institute of Aerospace Information. 展开更多
关键词 Bayesian networks Probability distributions RELIABILITY Reliability theory VECTORS Water supply Water supply systems
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Analysis of system trustworthiness based on information flow noninterference theory 被引量:1
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作者 Xiangying Kong Yanhui Chen Yi Zhuang 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2015年第2期367-380,共14页
The trustworthiness analysis and evaluation are the bases of the trust chain transfer. In this paper the formal method of trustworthiness analysis of a system based on the noninterfer- ence (NI) theory of the inform... The trustworthiness analysis and evaluation are the bases of the trust chain transfer. In this paper the formal method of trustworthiness analysis of a system based on the noninterfer- ence (NI) theory of the information flow is studied. Firstly, existing methods cannot analyze the impact of the system states on the trustworthiness of software during the process of trust chain trans- fer. To solve this problem, the impact of the system state on trust- worthiness of software is investigated, the run-time mutual interfer- ence behavior of software entitles is described and an interference model of the access control automaton of a system is established. Secondly, based on the intransitive noninterference (INI) theory, a formal analytic method of trustworthiness for trust chain transfer is proposed, providing a theoretical basis for the analysis of dynamic trustworthiness of software during the trust chain transfer process. Thirdly, a prototype system with dynamic trustworthiness on a plat- form with dual core architecture is constructed and a verification algorithm of the system trustworthiness is provided. Finally, the monitor hypothesis is extended to the dynamic monitor hypothe- sis, a theorem of static judgment rule of system trustworthiness is provided, which is useful to prove dynamic trustworthiness of a system at the beginning of system construction. Compared with previous work in this field, this research proposes not only a formal analytic method for the determination of system trustworthiness, but also a modeling method and an analysis algorithm that are feasible for practical implementation. 展开更多
关键词 trusted computing trust chain intransitive noninterference(INI) dynamic trustworthiness access control
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Web software reliability modeling with random impulsive shocks 被引量:1
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作者 Jianfeng Yang Ming Zhao Wensheng Hu 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2014年第2期349-356,共8页
As the web-server based business is rapidly developed and popularized, how to evaluate and improve the reliability of web-servers has been extremely important. Although a large num- ber of software reliability growth ... As the web-server based business is rapidly developed and popularized, how to evaluate and improve the reliability of web-servers has been extremely important. Although a large num- ber of software reliability growth models (SRGMs), including those combined with multiple change-points (CPs), have been available, these conventional SRGMs cannot be directly applied to web soft- ware reliability analysis because of the complex web operational profile. To characterize the web operational profile precisely, it should be realized that the workload of a web server is normally non-homogeneous and often observed with the pattern of random impulsive shocks. A web software reliability model with random im- pulsive shocks and its statistical analysis method are developed. In the proposed model, the web server workload is characterized by a geometric Brownian motion process. Based on a real data set from IIS server logs of ICRMS website (www.icrms.cn), the proposed model is demonstrated to be powerful for estimating impulsive shocks and web software reliability. 展开更多
关键词 web software software reliability growth model(SRGM) change-point (CP) impulsive shocks geometric Brown-ian motion.
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Developing Objective SensitivityAnalysis of Periodic Systems: Case Studies of Biological Oscillators 被引量:1
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作者 LU Bao-Yun YUE Hong 《自动化学报》 EI CSCD 北大核心 2012年第7期1065-1073,共9页
关键词 周期系统 生物系统 振荡器 敏感性分析 灵敏度指标 案例 开发 信号转导通路
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Optimization of ultrasonic elastography by coded excitation and transmit-side multi-frequency compounding
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作者 张志宏 刘昊霖 +1 位作者 何颖妮 刘东权 《Journal of Central South University》 SCIE EI CAS 2014年第3期1003-1010,共8页
To improve the quality of ultrasonic elastography, by taking the advantage of code excitation and frequency compounding, a transmitting-side multi-frequency with coded excitation for elastography (TFCCE) was propose... To improve the quality of ultrasonic elastography, by taking the advantage of code excitation and frequency compounding, a transmitting-side multi-frequency with coded excitation for elastography (TFCCE) was proposed. TFCCE adopts the chirp signal excitation scheme and strikes a balance in the selection of sub-signal bandwidth, the bandwidth overlap and the number of sub-strain image based on theoretical derivation, so as to further improve the quality of elastic image. Experiments have proved that, compared with the other optimizing methods, the elastographyic signal-to-noise ratio(Re-SN) and contrast-to-noise ratio(Re-CN) are improved significantly with different echo signal-to-noise ratios (ReSN) and attenuation coefficients. When ReSN is 50 dB, compared with short pulse, Rc-SN and Re-CN obtained by TFCCE increase by 53% and 143%, respectively. Moreover, in a deeper investigation (85-95 mm), the image has lower strain noise and clear details. When the attenuation coefficient is in the range of 0-1 dB/(cm.MHz), Re-SN and Re-CN obtained by TFCCE can be kept in moderate ranges of 5〈Re-SN〈6.8 and 11.4〈Re-CN〈15.2, respectively. In particular, for higher tissue attenuation, the basic image quality cannot be ensured with short pulse excitation, while mediocre quality strain figure can be obtained by TFCCE. Therefore, the TFCCE technology can effectively improve the elastography quality and can be applied to ultrasonic clinical trials. 展开更多
关键词 ultrasonic elastography coded excitation transmit-side multi-frequency compounding elastographyic signal-to-noise ratio echo signal-to-noise ratio contrast-to-noise ratio
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Relevance-based content extraction of HTML documents
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作者 吴麒 陈兴蜀 +1 位作者 朱锴 王春晖 《Journal of Central South University》 SCIE EI CAS 2012年第7期1921-1926,共6页
Content extraction of HTML pages is the basis of the web page clustering and information retrieval,so it is necessary to eliminate cluttered information and very important to extract content of pages accurately.A nove... Content extraction of HTML pages is the basis of the web page clustering and information retrieval,so it is necessary to eliminate cluttered information and very important to extract content of pages accurately.A novel and accurate solution for extracting content of HTML pages was proposed.First of all,the HTML page is parsed into DOM object and the IDs of all leaf nodes are generated.Secondly,the score of each leaf node is calculated and the score is adjusted according to the relationship with neighbors.Finally,the information blocks are found according to the definition,and a universal classification algorithm is used to identify the content blocks.The experimental results show that the algorithm can extract content effectively and accurately,and the recall rate and precision are 96.5% and 93.8%,respectively. 展开更多
关键词 content extraction DOM NODE RELEVANCE information block
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Evaluating accuracy of Hessian-based predictor-corrector integrators
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作者 LU Shao-fei WU Heng LIU Xu-chong 《Journal of Central South University》 SCIE EI CAS CSCD 2017年第7期1696-1702,共7页
Direct dynamics simulations are a useful and general approach for studying the atomistic properties of complex chemical systems because they do not require fitting an analytic potential energy function.Hessian-based p... Direct dynamics simulations are a useful and general approach for studying the atomistic properties of complex chemical systems because they do not require fitting an analytic potential energy function.Hessian-based predictor-corrector integrators are a widely used approach for calculating the trajectories of moving atoms in direct dynamics simulations.We employ a monodromy matrix to propose a tool for evaluating the accuracy of integrators in the trajectory calculation.We choose a general velocity Verlet as a different object.We also simulate molecular with hydrogen(CO_2) and molecular with hydrogen(H_2O) motions.Comparing the eigenvalues of monodromy matrix,many simulations show that Hessian-based predictor-corrector integrators perform well for Hessian updates and non-Hessian updates.Hessian-based predictor-corrector integrator with Hessian update has a strong performance in the H_2O simulations.Hessian-based predictor-corrector integrator with Hessian update has a strong performance when the integrating step of the velocity Verlet approach is tripled for the predicting step.In the CO_2 simulations,a strong performance occurs when the integrating step is a multiple of five. 展开更多
关键词 MONODROMY matrix eigenvalue Hessian-based PREDICTOR-CORRECTOR velocity Verlet
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A user-oriented resource scheduling method for improving agile software pattern in cloud environment
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作者 龙飞 杨昌 +1 位作者 荣辉桂 李建方 《Journal of Central South University》 SCIE EI CAS CSCD 2016年第11期2906-2916,共11页
The crowdsourcing, as a service pattern in cloud environment, usually aims at the cross-disciplinary cooperation and creating value together with customers and becomes increasingly prevalent. Software process, as a ki... The crowdsourcing, as a service pattern in cloud environment, usually aims at the cross-disciplinary cooperation and creating value together with customers and becomes increasingly prevalent. Software process, as a kind of software development and management strategy, is defined as a series of activities implemented by software life cycle and provides a set of rules for various phases of the software engineering to achieve the desired objectives. With the current software development cycle getting shorter, facing more frequent needs change and fierce competition, a new resource management pattern is proposed to respond to these issues agilely by introducing the crowdsourcing service to agile software development for pushing the agility of software process. Then, a user-oriented resource scheduling method is proposed for rational use of various resources in the process and maximizing the benefits of all parties. From the experimental results, the proposed pattern and resources scheduling method reduces greatly the resource of project resource manager and increases the team resource utilization rate, which greatly improves the agility of software process and delivers software products quickly in crowdsourcing pattern. 展开更多
关键词 resource scheduling agile software development project resource manager(PRM) individual resource provider(IRP)-
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Bug localization based on syntactical and semantic information of source code
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作者 YAN Xuefeng CHENG Shasha GUO Liqin 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2023年第1期236-246,共11页
The existing software bug localization models treat the source file as natural language, which leads to the loss of syntactical and structure information of the source file. A bug localization model based on syntactic... The existing software bug localization models treat the source file as natural language, which leads to the loss of syntactical and structure information of the source file. A bug localization model based on syntactical and semantic information of source code is proposed. Firstly, abstract syntax tree(AST) is divided based on node category to obtain statement sequence. The statement tree is encoded into vectors to capture lexical and syntactical knowledge at the statement level.Secondly, the source code is transformed into vector representation by the sequence naturalness of the statement. Therefore,the problem of gradient vanishing and explosion caused by a large AST size is obviated when using AST to the represent source code. Finally, the correlation between bug reports and source files are comprehensively analyzed from three aspects of syntax, semantics and text to locate the buggy code. Experiments show that compared with other standard models, the proposed model improves the performance of bug localization, and it has good advantages in mean reciprocal rank(MRR), mean average precision(MAP) and Top N Rank. 展开更多
关键词 bug report abstract syntax tree code representation software bug localization
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Analysis of Distributed and Adaptive Genetic Algorithm for Mining Interesting Classification Rules
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作者 YI Yunfei LIN Fang QIN Jun 《现代电子技术》 2008年第10期132-135,138,共5页
Distributed genetic algorithm can be combined with the adaptive genetic algorithm for mining the interesting and comprehensible classification rules.The paper gives the method to encode for the rules,the fitness funct... Distributed genetic algorithm can be combined with the adaptive genetic algorithm for mining the interesting and comprehensible classification rules.The paper gives the method to encode for the rules,the fitness function,the selecting,crossover,mutation and migration operator for the DAGA at the same time are designed. 展开更多
关键词 分析方法 分类规则 计算方法 编码 智能系统
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Localization in modified polar representation: hybrid measurements and closed-form solution 被引量:2
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作者 CONG Xunchao SUN Yimao +2 位作者 YANG Yanbing ZHANG Lei CHEN Liangyin 《Journal of Systems Engineering and Electronics》 SCIE CSCD 2024年第3期575-588,共14页
Classical localization methods use Cartesian or Polar coordinates, which require a priori range information to determine whether to estimate position or to only find bearings. The modified polar representation (MPR) u... Classical localization methods use Cartesian or Polar coordinates, which require a priori range information to determine whether to estimate position or to only find bearings. The modified polar representation (MPR) unifies near-field and farfield models, alleviating the thresholding effect. Current localization methods in MPR based on the angle of arrival (AOA) and time difference of arrival (TDOA) measurements resort to semidefinite relaxation (SDR) and Gauss-Newton iteration, which are computationally complex and face the possible diverge problem. This paper formulates a pseudo linear equation between the measurements and the unknown MPR position,which leads to a closed-form solution for the hybrid TDOA-AOA localization problem, namely hybrid constrained optimization(HCO). HCO attains Cramér-Rao bound (CRB)-level accuracy for mild Gaussian noise. Compared with the existing closed-form solutions for the hybrid TDOA-AOA case, HCO provides comparable performance to the hybrid generalized trust region subproblem (HGTRS) solution and is better than the hybrid successive unconstrained minimization (HSUM) solution in large noise region. Its computational complexity is lower than that of HGTRS. Simulations validate the performance of HCO achieves the CRB that the maximum likelihood estimator (MLE) attains if the noise is small, but the MLE deviates from CRB earlier. 展开更多
关键词 LOCALIZATION modified polar representation time difference of arrival(TDOA) angle of arrival(AOA) closed-form solution
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局部表面拟合的点云模型法向估计及重定向算法 被引量:19
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作者 王醒策 蔡建平 +1 位作者 武仲科 周明全 《计算机辅助设计与图形学学报》 EI CSCD 北大核心 2015年第4期614-620,共7页
为了提高对点云模型处理的有效性,提出一种对点云模型的法向估计和重定向方法.首先利用基于局部平面拟合的主元分析方法得到初步法向估计;然后改进移动最小二乘曲面实现局部曲面拟合,进一步得到更加准确的法向,实现了点云模型的去噪光顺... 为了提高对点云模型处理的有效性,提出一种对点云模型的法向估计和重定向方法.首先利用基于局部平面拟合的主元分析方法得到初步法向估计;然后改进移动最小二乘曲面实现局部曲面拟合,进一步得到更加准确的法向,实现了点云模型的去噪光顺;最后通过增加切向约束规则来修正法向重定向中的法向传播方向.实验结果表明,对于具有复杂细节(如紧邻面、尖角形状等)的点云模型,该方法可以提高法向计算的准确度,并得到光顺的点云模型.在实际应用中,该方法可以很好地应用于点云模型的预处理,为后续的模型处理和分析提供良好的数据基础. 展开更多
关键词 法向估计 法向重定向 主元分析 点邻域 移动最小二乘曲面
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基于微机的面向对象三维图形引擎 被引量:11
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作者 LI Hui 李辉 +1 位作者 吴建国 游志胜 《计算机工程》 CAS CSCD 北大核心 2001年第4期169-171,173,共4页
随着微机三维图形加速硬件性能的不断提高,微机上虚拟现实及三维图形动画应用正在飞速发展,为了提高这方面程序开发的效率与质量,设计了一个面向时象的三维图形引擎Object-3D,它支持动态裁剪,分细节模型(LOD),Billboard以及模型... 随着微机三维图形加速硬件性能的不断提高,微机上虚拟现实及三维图形动画应用正在飞速发展,为了提高这方面程序开发的效率与质量,设计了一个面向时象的三维图形引擎Object-3D,它支持动态裁剪,分细节模型(LOD),Billboard以及模型的结构化组织,在应用系统开发的实践中证明它可以提高应用的开发效率并保障其性能. 展开更多
关键词 计算机动画 OPENGL 计算机图形学 三维图形引擎 微机 面向对象
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A Bayesian Network Learning Algorithm Based on Independence Test and Ant Colony Optimization 被引量:21
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作者 JI Jun-Zhong ZHANG Hong-Xun HU Ren-Bing LIU Chun-Nian 《自动化学报》 EI CSCD 北大核心 2009年第3期281-288,共8页
关键词 最优化 随机系统 自动化 BN
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Cooperative extended rough attribute reduction algorithm based on improved PSO 被引量:10
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作者 Weiping Ding Jiandong Wang Zhijin Guan 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2012年第1期160-166,共7页
Particle swarm optimization (PSO) is a new heuristic algorithm which has been applied to many optimization problems successfully. Attribute reduction is a key studying point of the rough set theory, and it has been ... Particle swarm optimization (PSO) is a new heuristic algorithm which has been applied to many optimization problems successfully. Attribute reduction is a key studying point of the rough set theory, and it has been proven that computing minimal reduc- tion of decision tables is a non-derterministic polynomial (NP)-hard problem. A new cooperative extended attribute reduction algorithm named Co-PSAR based on improved PSO is proposed, in which the cooperative evolutionary strategy with suitable fitness func- tions is involved to learn a good hypothesis for accelerating the optimization of searching minimal attribute reduction. Experiments on Benchmark functions and University of California, Irvine (UCI) data sets, compared with other algorithms, verify the superiority of the Co-PSAR algorithm in terms of the convergence speed, efficiency and accuracy for the attribute reduction. 展开更多
关键词 rough set extended attribute reduction particle swarm optimization (PSO) cooperative evolutionary strategy fitness function.
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Density-based trajectory outlier detection algorithm 被引量:10
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作者 Zhipeng Liu Dechang Pi Jinfeng Jiang 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 2013年第2期335-340,共6页
With the development of global position system(GPS),wireless technology and location aware services,it is possible to collect a large quantity of trajectory data.In the field of data mining for moving objects,the pr... With the development of global position system(GPS),wireless technology and location aware services,it is possible to collect a large quantity of trajectory data.In the field of data mining for moving objects,the problem of anomaly detection is a hot topic.Based on the development of anomalous trajectory detection of moving objects,this paper introduces the classical trajectory outlier detection(TRAOD) algorithm,and then proposes a density-based trajectory outlier detection(DBTOD) algorithm,which compensates the disadvantages of the TRAOD algorithm that it is unable to detect anomalous defects when the trajectory is local and dense.The results of employing the proposed algorithm to Elk1993 and Deer1995 datasets are also presented,which show the effectiveness of the algorithm. 展开更多
关键词 density-based algorithm trajectory outlier detection(TRAOD) partition-and-detect framework Hausdorff distance
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