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The Complex System Modeling Method Based on Uniform Design and Neural Network 被引量:1
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作者 Zhang Yong(Beijing Simulation Center, P.O.Box 142-23, Beijing 100854, P.R. China) 《Journal of Systems Engineering and Electronics》 SCIE EI CSCD 1996年第4期27-36,共10页
In this paper, the method based on uniform design and neural network is proposed to model the complex system. In order to express the system characteristics all round, uniform design method is used to choose the model... In this paper, the method based on uniform design and neural network is proposed to model the complex system. In order to express the system characteristics all round, uniform design method is used to choose the modeling samples and obtain the overall information of the system;for the purpose of modeling the system or its characteristics, the artificial neural network is used to construct the model. Experiment indicates that this method can model the complex system effectively. 展开更多
关键词 modeling method uniform design Neural network Complex system Simulation.
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Enhancing Collaborative Filtering via Topic Model Integrated Uniform Euclidean Distance 被引量:1
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作者 Tieliang Gao Bo Cheng +1 位作者 Junliang Chen Ming Chen 《China Communications》 SCIE CSCD 2017年第11期48-58,共11页
Recommendation system can greatly alleviate the "information overload" in the big data era. Existing recommendation methods, however, typically focus on predicting missing rating values via analyzing user-it... Recommendation system can greatly alleviate the "information overload" in the big data era. Existing recommendation methods, however, typically focus on predicting missing rating values via analyzing user-item dualistic relationship, which neglect an important fact that the latent interests of users can influence their rating behaviors. Moreover, traditional recommendation methods easily suffer from the high dimensional problem and cold-start problem. To address these challenges, in this paper, we propose a PBUED(PLSA-Based Uniform Euclidean Distance) scheme, which utilizes topic model and uniform Euclidean distance to recommend the suitable items for users. The solution first employs probabilistic latent semantic analysis(PLSA) to extract users' interests, users with different interests are divided into different subgroups. Then, the uniform Euclidean distance is adopted to compute the users' similarity in the same interest subset; finally, the missing rating values of data are predicted via aggregating similar neighbors' ratings. We evaluate PBUED on two datasets and experimental results show PBUED can lead to better predicting performance and ranking performance than other approaches. 展开更多
关键词 recommendation system topic model user interest uniform euclidean distance
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Decomposition of Independence Using the Logit Uniform Association Model and Equality of Concordance and Discordance for Two-Way Classifications
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作者 Kouji Tahata Nobuko Miyamoto Sadao Tomizawa 《Open Journal of Statistics》 2015年第6期514-518,共5页
For two-way contingency tables with ordered categories, the present paper gives a theorem that the independence model holds if and only if the logit uniform association model holds and equality of concordance and disc... For two-way contingency tables with ordered categories, the present paper gives a theorem that the independence model holds if and only if the logit uniform association model holds and equality of concordance and discordance for all pairs of adjacent rows and all dichotomous collapsing of the columns holds. Using the theorem, we analyze the cross-classification of duodenal ulcer patients according to operation and dumping severity. 展开更多
关键词 CONCORDANCE DISCORDANCE INDEPENDENCE LOGIT uniform Association model
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Modeling of Few-Mode Multi-Core Optical Fiber Channel Based on Non-Uniform Mode Field Distribution
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作者 Hang Zhou Bo Liu +6 位作者 Fu Wang Dandan Song Li Li Xiangjun Xin Qinghua Tian Qi Zhang Feng Tian 《China Communications》 SCIE CSCD 2016年第8期184-191,共8页
In this paper, the influencing factors that affect few-mode and multi core optical fiber channel are analyzed in a comprehensive way. The theoretical modeling and computer simulation of the information channel are car... In this paper, the influencing factors that affect few-mode and multi core optical fiber channel are analyzed in a comprehensive way. The theoretical modeling and computer simulation of the information channel are carried out and then the modeling scheme of few-mode multicore optical fiber channel based on non-uniform mode field distribution is put forward. The proposed modeling scheme can not only exponentially increases the system capacity through fewmode multi-core optical fiber channel, but has better transmission performance compared to the channel of the same type to the uniform channel revealing from the simulation results. 展开更多
关键词 few-mode multi-core optical fiber channel non-uniform channel channel modeling
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Stability and Uniform Boundedness for a Class of Anaerobic Digestion Ecological Models
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作者 李明奇 《Journal of Electronic Science and Technology of China》 2004年第2期87-89,共3页
Stability, boundedness and persistence are three important aspects for an ecological model. In this paper, a further analysis of a class of anaerobic digestion ecological models is performed. Based on the Liupunov Met... Stability, boundedness and persistence are three important aspects for an ecological model. In this paper, a further analysis of a class of anaerobic digestion ecological models is performed. Based on the Liupunov Method, the local stability of all equilibria in the system is got. According to the vector fields described by the system, the proof of the boundedness of the solution on the anaerobic digestion processes is completed in three steps. The method proposed in the discussion on the boundedness can be generalized to the similar problems. Results in this paper give information on how to run the ecological system well by adjusting the system parameters. 展开更多
关键词 anaerobic digestion processes ecological models of microbes STABILITY uniform Boundedness
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Comparison of Uniform and Kernel Gaussian Weight Matrix in Generalized Spatial Panel Data Model
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作者 Tuti Purwaningsih Erfiani   《Open Journal of Statistics》 2015年第1期90-95,共6页
Panel data combine cross-section data and time series data. If the cross-section is locations, there is a need to check the correlation among locations. ρ and λ are parameters in generalized spatial model to cover e... Panel data combine cross-section data and time series data. If the cross-section is locations, there is a need to check the correlation among locations. ρ and λ are parameters in generalized spatial model to cover effect of correlation between locations. Value of ρ or λ will influence the goodness of fit model, so it is important to make parameter estimation. The effect of another location is covered by making contiguity matrix until it gets spatial weighted matrix (W). There are some types of W—uniform W, binary W, kernel Gaussian W and some W from real case of economics condition or transportation condition from locations. This study is aimed to compare uniform W and kernel Gaussian W in spatial panel data model using RMSE value. The result of analysis showed that uniform weight had RMSE value less than kernel Gaussian model. Uniform W had stabil value for all the combinations. 展开更多
关键词 Component uniform WEIGHT KERNEL GAUSSIAN WEIGHT GENERALIZED Spatial PANEL Data model
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基于UniformLBP特征的镜头检测算法
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作者 赵芳 马玉磊 《计算机应用与软件》 CSCD 2015年第3期145-150,161,共7页
首次将Uniform LBP特征引入镜头检测中,提出一种有效的镜头检测算法。算法的主要思想是:以Uniform LBP特征作为描述视觉信息的主要特征,利用图模型计算图像序列的特征差异信号,采用主动处理策略构造特征向量和选择训练数据,通过SVM分类... 首次将Uniform LBP特征引入镜头检测中,提出一种有效的镜头检测算法。算法的主要思想是:以Uniform LBP特征作为描述视觉信息的主要特征,利用图模型计算图像序列的特征差异信号,采用主动处理策略构造特征向量和选择训练数据,通过SVM分类器识别视频镜头。提出的算法以Trec Vid05实验数据为测试平台,通过与Trec Vid05的测试结果比较可以证明该算法不但对切变镜头检测有很好的实验结果,而且能更为有效地检测渐变镜头。 展开更多
关键词 镜头检测 归一化图像二值特征 图模型 主动学习 支持向量机分类器
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INFLUENCE OF DAMPING MODELS ON DYNAMIC ANALYSES OF A BASE-ISOLATED COMPOSITE STRUCTURE UNDER EARTHQUAKES AND ENVIRONMENTAL VIBRATIONS 被引量:1
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作者 费一凡 田源 +1 位作者 黄羽立 陆新征 《工程力学》 EI CSCD 北大核心 2022年第3期201-211,共11页
Structural design simultaneously governed by earthquakes and environmental vibrations has received a lot of attention in recent years.Base-isolated composite structures are typically used in the above-mentioned struct... Structural design simultaneously governed by earthquakes and environmental vibrations has received a lot of attention in recent years.Base-isolated composite structures are typically used in the above-mentioned structural design.The corresponding analysis involves validating structural safety under earthquakes and human comfort under environmental vibrations through a time-history analysis.Thus,a reasonable damping model is essential.In this work,the representatives of viscous damping model and rate-independent damping model,namely the Rayleigh damping model and uniform damping model,were adopted to investigate the influence of damping models on the time-history analysis of such structural designs.The energy dissipation characteristics of the above-mentioned damping models were illustrated via a dynamic test of recycled aggregate concrete specimens.A case study was performed on a base-isolated steelconcrete composite structure.The dynamic responses under the excitation of earthquakes and environmental vibrations were compared using different damping models.The uniform damping model was found to be more flexible than the Rayleigh damping model in dealing with excitations with different frequency components.The uniform damping model is both theoretically advantageous and easy to use,demonstrating its potential in dynamic analysis of structures designed simultaneously governed by earthquakes and environmental vibrations. 展开更多
关键词 seismic and environmental vibration analysis Rayleigh damping model uniform damping model seismic isolation composite structure
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Influence of Using Parameters on Stirring Uniformity of Mixer 被引量:1
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作者 刘洪海 《Journal of Wuhan University of Technology(Materials Science)》 SCIE EI CAS 2011年第1期172-175,共4页
Stirring uniformity of mixture depends not only on structural parameters of the mixer, motion parameters, but also to a large extent on the using parameters. Based on the analysis of the structure and working principl... Stirring uniformity of mixture depends not only on structural parameters of the mixer, motion parameters, but also to a large extent on the using parameters. Based on the analysis of the structure and working principle of mixer, these factors that affecting mixer performance was studied. The mathematical model of mixer performance characteristics was established by theoretical analysis, which associated with the mechanical structure, motion parameters and using parameters. According to the mathematical model, the effects of the mixer filling rate, stirring time, and other using parameters on the uniformity were studied. In each stirring cycle, the minimum number of revolutions formula for shaft was obtained. In addition, in different filling rates, the relationship between stirring shaft rotation laps and stirring uniformity was obtained too. Finally, full-scale experimental verification was conducted. 展开更多
关键词 structural parameters using parameters uniformITY mathematical model
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Experimental and Modeling Studies on the Chemical Vapor Infiltration with Respect to the Effects of Thermal Gradient and Other Operating Parameters 被引量:1
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作者 Kyung Do Joo Do Hoon Kim Gui Yung Chung 《Journal of Wuhan University of Technology(Materials Science)》 SCIE EI CAS 2018年第3期525-532,共8页
Effects of operating parameters in the thermal gradient chemical vapor infiltration of propane such as thermal gradient, diffusion, infiltrations time, and concentration of propane were studied by focusing on the visu... Effects of operating parameters in the thermal gradient chemical vapor infiltration of propane such as thermal gradient, diffusion, infiltrations time, and concentration of propane were studied by focusing on the visualizations of the intrinsic effects of these parameters. A uniform deposition in the preform was obtained with a gradually increasing temperature along the gas flow. The uniformity of deposition through the preform got improved with increasing deposition time. Results of numerical modeling estimated the experimental data very well when the pre-exponential factor of the overall rate of carbon deposition from propane reported by Vaidyaraman[1] was multiplied by 4. The average density of a preform increased by about 3 times from 0.38 to 1.15 g/cm3 after 60 hr deposition with a thermal gradient under the conditions of 3% propane in nitrogen and 840 to 900 ℃. 展开更多
关键词 TG-CVI propane C/C composites uniform deposition mathematical modeling
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Uniformity evaluation and optimization of fluid flow characteristics in a seven-strand tundish 被引量:8
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作者 Min Wang Chao-jie Zhang Rui Li 《International Journal of Minerals,Metallurgy and Materials》 SCIE EI CAS CSCD 2016年第2期137-145,共9页
The effect of flow control devices(FCDs) on the uniformity of flow characteristics in a seven-strand symmetrical trapezoidal tundish was studied using both an experimental 1:2.5 hydraulic model and a numerical simu... The effect of flow control devices(FCDs) on the uniformity of flow characteristics in a seven-strand symmetrical trapezoidal tundish was studied using both an experimental 1:2.5 hydraulic model and a numerical simulation of a 1:1 geometric model.The variation coefficient(CV) was defined to evaluate the flow uniformity of the seven-strand tundish.An optimized FCD configuration was proposed on the basis of the evaluation of experimental results.It is concluded that a turbulence inhibitor(TI) and U-type dam are essential to improve the uniformity of fluid flow in the seven-strand tundish.In addition,the configuration of inclination T-type dams with a height of 200 mm between the second and third strands and with a height of 300 mm between the third and fourth strands can minimize the proportion of dead zone.After optimizing the configuration of FCDs,the variation coefficient reduces below 20%of the mean value,and the average proportion of dead zone is just 14.6%;in addition,the temperature fluctuation between the strands could be controlled within 0.6 K.In summary,the uniformity of flow and temperature in the seven-strand tundish is greatly improved. 展开更多
关键词 hydraulic models numerical simulation tundishes fluid flow flow characteristics uniformity optimization
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Numerical Simulation of the Impact of Urban Non-uniformity on Precipitation 被引量:2
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作者 Yuqiang SONG Hongnian LIU +2 位作者 Xueyuan WANG Ning ZHANG Jianning SUN 《Advances in Atmospheric Sciences》 SCIE CAS CSCD 2016年第6期783-793,共11页
To evaluate the influence of urban non-uniformity on precipitation, the area of a city was divided into three categories (commercial, high-density residential, and low-density residential) according to the building ... To evaluate the influence of urban non-uniformity on precipitation, the area of a city was divided into three categories (commercial, high-density residential, and low-density residential) according to the building density data from Landsat satel- lites. Numerical simulations of three corresponding scenarios (urban non-uniformity, urban uniformity, and non-urban) were performed in Nanjing using the WRF model. The results demonstrate that the existence of the city results in more precip- itation, and that urban heterogeneity enhances this phenomenon. For the urban non-uniformity, uniformity, and non-urban experiments, the mean cumulative summer precipitation was 423.09 mm, 407.40 mm, and 389.67 mm, respectively. Urban non-uniformity has a significant effect on the amount of heavy rainfall in summer. The cumulative precipitation from heavy rain in the summer for the three numerical experiments was 278.2 mm, 250.6 mm, and 236.5 mm, respectively. In the non- uniformity experiments, the amount of precipitation between 1500 and 2200 (LST) increased significantly. Furthermore, the adoption of urban non-uniformity into the WRF model could improve the numerical simulation of summer rain and its daily variation. 展开更多
关键词 urban non-uniformity urban precipitation WRF model
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A WYNER-ZIV VIDEO CODING METHOD UTILIZING MIXTURE CORRELATION NOISE MODEL 被引量:1
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作者 Hu Xiaofei Zhu Xiuchang 《Journal of Electronics(China)》 2012年第3期197-203,共7页
In Wyner-Ziv (WZ) Distributed Video Coding (DVC), correlation noise model is often used to describe the error distribution between WZ frame and the side information. The accuracy of the model can influence the perform... In Wyner-Ziv (WZ) Distributed Video Coding (DVC), correlation noise model is often used to describe the error distribution between WZ frame and the side information. The accuracy of the model can influence the performance of the video coder directly. A mixture correlation noise model in Discrete Cosine Transform (DCT) domain for WZ video coding is established in this paper. Different correlation noise estimation method is used for direct current and alternating current coefficients. Parameter estimation method based on expectation maximization algorithm is used to estimate the Laplace distribution center of direct current frequency band and Mixture Laplace-Uniform Distribution Model (MLUDM) is established for alternating current coefficients. Experimental results suggest that the proposed mixture correlation noise model can describe the heavy tail and sudden change of the noise accurately at high rate and make significant improvement on the coding efficiency compared with the noise model presented by DIStributed COding for Video sERvices (DISCOVER). 展开更多
关键词 Transform domain Wyner-Ziv (WZ) DIStributed COding for Video sERvices (DISCOVER) Video coding Correlation noise model Mixture Laplace-uniform Distribution model (MLUDM)
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QUALITATIVE ANALYSIS OF A DICRETE POPULATION MODEL 被引量:1
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作者 黄立宏 彭名书 《Acta Mathematica Scientia》 SCIE CSCD 1999年第1期45-52,共8页
In this paper, authors study the qualitative behavior of solutions of the discrete population model xn-xn-1=xn (a+bxn-k-cx2n-k),where a ∈ (0, 1), b ∈ (-∞, 0),c ∈ (0,∞ ), and k is a positive integer. They hot only... In this paper, authors study the qualitative behavior of solutions of the discrete population model xn-xn-1=xn (a+bxn-k-cx2n-k),where a ∈ (0, 1), b ∈ (-∞, 0),c ∈ (0,∞ ), and k is a positive integer. They hot only obtain necessary as well as sufficient and necessary conditions for the oscillation of ail eventually positive solutions about the positive equilibrium, but also obtain some sufficient conditions for the convergence of eventually positive solutions. Furthermore, authors also show that such model is uniformly persistent, and that all its eventually positive solutions are bounded. 展开更多
关键词 Discrete population model OSCILLATION CONVERGENCE uniform persistence boundedness
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Dynamical energy equipartition of the Toda model with additional on-site potentials
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作者 张振俊 唐春梅 +1 位作者 康静 童培庆 《Chinese Physics B》 SCIE EI CAS CSCD 2017年第10期107-111,共5页
We study the dynamical energy equipartition properties in the integrable Toda model with additional uniform or disordered on-site energies by extensive numerical simulations. The total energy is initially equidistribu... We study the dynamical energy equipartition properties in the integrable Toda model with additional uniform or disordered on-site energies by extensive numerical simulations. The total energy is initially equidistributed among some of the lowest frequency linear modes. For the Toda model with uniform on-site potentials, the energy spectrum keeps its profile nearly unchanged in a relatively short time scale. On a much longer time scale, the energies of tail modes increase slowly with time. Energy equipartition is far away from being attached in our studied time scale. For the Toda model with disordered on-site potentials, the energy transfers continuously to the high frequency modes and eventually towards energy equipartition. We further perform a systematic study of the equipartition time teq depending on the energy density ε and the nonlinear parameter α in the thermodynamic limit for the Toda model with disordered on-site potentials. We find teq∝ (1/ε)^a(1/α)^b, where b≈ 2a. The values of a and b are increased when increasing the strengths of disordered on-site potentials or decreasing the number of initially excited modes. 展开更多
关键词 energy transport behaviors Toda model uniform or disordered on-site potentials
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Two-Dimensional Mathematical Model of Tidal Current and Sediment for Oujiang Estuary and Wenzhou Bay 被引量:8
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作者 陆永军 李浩麟 +2 位作者 董壮 陆建宇 郝嘉凌 《China Ocean Engineering》 SCIE EI 2002年第1期107-122,共16页
A 2-D mathematical model of tidal current and sediment has been developed for the Oujiang Estuary and the Wenzhou Bay. This model accomodates complicated features including multiple islands, existence of turbidity, an... A 2-D mathematical model of tidal current and sediment has been developed for the Oujiang Estuary and the Wenzhou Bay. This model accomodates complicated features including multiple islands, existence of turbidity, and significant differ-ence in size distribution of bed material. The governing equations for non-uniform suspended load and bed load transport are presented in a boundary-fitted orthogonal curvilinear coordinate system. The numerical solution procedures along with their initial conditions, boundary conditions, and movable boundary technique are presented. Strategies for computation of the critical condition of deposition or erosion, sediment transport capacity, non-uniform bed load discharge, etc. are suggested. The model verification computation shows that, the tidal levels computed from the model are in good agreement with the field data at the 18 tidal gauge stations. The computed velocities and flow directions also agree well with the values measured along the totally 52 synchronously observed verticals distributed over 8 cross sections. The coraputed tidal water throughputs through the Huangda'ao cross section are close to the measured data. And the computed values of bed deformation from Yangfushan to the estuary outfall and in the outer-sea area are in good agreement with the data observed from 1986 to 1992. The changes of tidal volumes through the estuary, velocities in different channels and the bed form due to the influence of the reclamation project on the Wenzhou shoal are predicted by means of this model. 展开更多
关键词 mathematical model tidal current non-uniform suspended load non-uniform bed load non-equilibrium transport bed deformation
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Literature Review of Single Machine Scheduling Problem with Uniform Parallel Machines 被引量:1
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作者 Panneerselvam Senthilkumar Sockalingam Narayanan 《Intelligent Information Management》 2010年第8期457-474,共18页
This paper presents a survey of single machine scheduling problem with uniform parallel machines. The single machine scheduling problem with uniform parallel machines consists of n jobs, each with single operation, wh... This paper presents a survey of single machine scheduling problem with uniform parallel machines. The single machine scheduling problem with uniform parallel machines consists of n jobs, each with single operation, which are to be scheduled on m parallel machines with different speeds. These parallel machines are also called proportional machines or related machines. There are several measures of performance which are to be optimized in uniform parallel machines scheduling. Since, this scheduling problem is a combinatorial problem;usage of a heuristic is inevitable to obtain solution in polynomial time. This paper gives a classification of the literatures of this scheduling problem in three major categories, viz. offline scheduling, online scheduling and miscellaneous scheduling. In total, the available literatures are classified into 17 subgroups. Under each of the first two categories, the available literatures are discussed under different groups based on different measures of performance and non-preemptive/preemptive nature of the jobs. In the last category, the literatures are discussed under three subgroups, namely non-preemptive jobs, preemptive jobs and periodic jobs. 展开更多
关键词 uniform Parallel MACHINES MEASURE of Performance HEURISTIC model COMPETITIVE Ratio
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The monitoring of burden distribution uniformity and even sintering technology
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作者 MA Luowen 《Baosteel Technical Research》 CAS 2009年第2期27-30,共4页
After expanding the capacity by widening the trolley of the No. 3 sintering machine, severe uneven sintering occurred in the trolley' s lateral distribution, which affected the output and quality of sinter. In this s... After expanding the capacity by widening the trolley of the No. 3 sintering machine, severe uneven sintering occurred in the trolley' s lateral distribution, which affected the output and quality of sinter. In this study, the quantitative evaluation indices of the burden uniform distribution in the width direction of the sintering machine is introduced for the first time. By measuring the temperature of discharged gas, a plane temperature field is constructed. Through analyzing the temperature field and the burden layer' s differential thermal equilibrium, a mathematical model for evaluating the indices, which is an online reflection of the degree of uniform distribution, is built. Following the improvements in burden distribution equipment ,the optimization of the ignition system and the dynamic adjustment of the process ,the problem of uneven sintering in lateral distribution has been solved, and the quality and the yield of sinter have been improved. 展开更多
关键词 uniform distribution index temperature field mathematical model
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Natural Frequency of the Bridge—Vehicle Coupled System Considering Uniform Distributed Moving Load
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作者 Zhang Jun Gou Mingkang Liang Chuan 《仪器仪表学报》 EI CAS CSCD 北大核心 2013年第S1期185-189,共5页
Natural frequencies of the bridge—vehicle coupling system considering uniform distributed load varying with position is investigated in this work.An analytic model of a simply supported beam bridge with constant sect... Natural frequencies of the bridge—vehicle coupling system considering uniform distributed load varying with position is investigated in this work.An analytic model of a simply supported beam bridge with constant section is introduced to establish the frequency equations of the coupled system.Comparisons with the results between analytic model and FEM indicate that the present research is correct and reasonable.In view of an example bridge,natural frequencies are studied on the bridge subjected to uniform distributed moving loads in cases of different weight and span,by which some regular phenomenon are obtained.The present study can apply in the engineering problem of interaction between bridges and moving loads such as trains and tracked vehicles. 展开更多
关键词 bridge-vehicle coupled system frequency analysis uniform DISTRIBUTED MOVING load analytical model
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A Generalized Layered Radiative Transfer Model in the Vegetation Canopy 被引量:6
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作者 戴秋丹 孙菽芬 《Advances in Atmospheric Sciences》 SCIE CAS CSCD 2006年第2期243-257,共15页
In this paper, a generalized layered model for radiation transfer in canopy with high vertical resolution is developed. Differing from the two-stream approximate radiation transfer model commonly used in the land surf... In this paper, a generalized layered model for radiation transfer in canopy with high vertical resolution is developed. Differing from the two-stream approximate radiation transfer model commonly used in the land surface models, the generalized model takes into account the effect of complicated canopy morphology and inhomogeneous optical properties of leaves on radiation transfer within the canopy. In the model, the total leaf area index (LAI) of the canopy is divided into many layers. At a given layer, the influences of diffuse radiation angle distributions and leaf angle distributions on radiation transfer within the canopy are considered. The derivation of equations serving the model are described in detail, and these can deal with various diffuse radiation transfers in quite broad categories of canopy with quite inhomogeneons vertical structures and uneven leaves with substantially different optical properties of adaxial and abaxial faces of the leaves. The model is used to simulate the radiation transfer for canopies with horizontal leaves to validate the generalized model. Results from the model are compared with those from the two-stream scheme, and differences between these two models are discussed. 展开更多
关键词 generalized model of radiation transfer non-uniform canopy distributions of leaf angle and radiation angle optical properties of adaxial and abaxial leaves
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