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Optimizing Average Electric Power During the Charging of Lithium-Ion Batteries Through the Taguchi Method
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作者 Mohd H.S.Alrashdan 《Transactions of Tianjin University》 EI CAS 2024年第2期152-166,共15页
In recent times, lithium-ion batteries have been widely used owing to their high energy density, extended cycle lifespan, and minimal self-discharge rate. The design of high-speed rechargeable lithium-ion batteries fa... In recent times, lithium-ion batteries have been widely used owing to their high energy density, extended cycle lifespan, and minimal self-discharge rate. The design of high-speed rechargeable lithium-ion batteries faces a significant challenge owing to the need to increase average electric power during charging. This challenge results from the direct influence of the power level on the rate of chemical reactions occurring in the battery electrodes. In this study, the Taguchi optimization method was used to enhance the average electric power during the charging process of lithium-ion batteries. The Taguchi technique is a statistical strategy that facilitates the systematic and efficient evaluation of numerous experimental variables. The proposed method involved varying seven input factors, including positive electrode thickness, positive electrode material, positive electrode active material volume fraction, negative electrode active material volume fraction, separator thickness, positive current collector thickness, and negative current collector thickness. Three levels were assigned to each control factor to identify the optimal conditions and maximize the average electric power during charging. Moreover, a variance assessment analysis was conducted to validate the results obtained from the Taguchi analysis. The results revealed that the Taguchi method was an eff ective approach for optimizing the average electric power during the charging of lithium-ion batteries. This indicates that the positive electrode material, followed by the separator thickness and the negative electrode active material volume fraction, was key factors significantly infl uencing the average electric power during the charging of lithium-ion batteries response. The identification of optimal conditions resulted in the improved performance of lithium-ion batteries, extending their potential in various applications. Particularly, lithium-ion batteries with average electric power of 16 W and 17 W during charging were designed and simulated in the range of 0-12000 s using COMSOL Multiphysics software. This study efficiently employs the Taguchi optimization technique to develop lithium-ion batteries capable of storing a predetermined average electric power during the charging phase. Therefore, this method enables the battery to achieve complete charging within a specific timeframe tailored to a specificapplication. The implementation of this method can save costs, time, and materials compared with other alternative methods, such as the trial-and-error approach. 展开更多
关键词 Lithium-ion batteries average electric power during charging Taguchi method COMSOL Multiphysics software C rate L27 orthogonal array
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Improved Double Deep Q Network Algorithm Based on Average Q-Value Estimation and Reward Redistribution for Robot Path Planning
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作者 Yameng Yin Lieping Zhang +3 位作者 Xiaoxu Shi Yilin Wang Jiansheng Peng Jianchu Zou 《Computers, Materials & Continua》 SCIE EI 2024年第11期2769-2790,共22页
By integrating deep neural networks with reinforcement learning,the Double Deep Q Network(DDQN)algorithm overcomes the limitations of Q-learning in handling continuous spaces and is widely applied in the path planning... By integrating deep neural networks with reinforcement learning,the Double Deep Q Network(DDQN)algorithm overcomes the limitations of Q-learning in handling continuous spaces and is widely applied in the path planning of mobile robots.However,the traditional DDQN algorithm suffers from sparse rewards and inefficient utilization of high-quality data.Targeting those problems,an improved DDQN algorithm based on average Q-value estimation and reward redistribution was proposed.First,to enhance the precision of the target Q-value,the average of multiple previously learned Q-values from the target Q network is used to replace the single Q-value from the current target Q network.Next,a reward redistribution mechanism is designed to overcome the sparse reward problem by adjusting the final reward of each action using the round reward from trajectory information.Additionally,a reward-prioritized experience selection method is introduced,which ranks experience samples according to reward values to ensure frequent utilization of high-quality data.Finally,simulation experiments are conducted to verify the effectiveness of the proposed algorithm in fixed-position scenario and random environments.The experimental results show that compared to the traditional DDQN algorithm,the proposed algorithm achieves shorter average running time,higher average return and fewer average steps.The performance of the proposed algorithm is improved by 11.43%in the fixed scenario and 8.33%in random environments.It not only plans economic and safe paths but also significantly improves efficiency and generalization in path planning,making it suitable for widespread application in autonomous navigation and industrial automation. 展开更多
关键词 Double Deep Q Network path planning average Q-value estimation reward redistribution mechanism reward-prioritized experience selection method
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Stability of average acceleration method for structures with nonlinear damping 被引量:4
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作者 李妍 吴斌 欧进萍 《Earthquake Engineering and Engineering Vibration》 SCIE EI CSCD 2006年第1期87-92,共6页
The energy approach is used to theoretically verify that the average acceleration method (AAM), which is unconditionally stable for linear dynamic systems, is also unconditionally stable for structures with typical ... The energy approach is used to theoretically verify that the average acceleration method (AAM), which is unconditionally stable for linear dynamic systems, is also unconditionally stable for structures with typical nonlinear damping, including the special case of velocity power type damping with a bilinear restoring force model. Based on the energy approach, the stability of the AAM is proven for SDOF structures using the mathematical features of the velocity power function and for MDOF structures by applying the virtual displacement theorem. Finally, numerical examples are given to demonstrate the accuracy of the theoretical analysis. 展开更多
关键词 unconditional stability average acceleration method nonlinear systems nonlinear damping
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Average vector field methods for the coupled Schrdinger KdV equations 被引量:3
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作者 张弘 宋松和 +1 位作者 陈绪栋 周炜恩 《Chinese Physics B》 SCIE EI CAS CSCD 2014年第7期242-250,共9页
The energy preserving average vector field (AVF) method is applied to the coupled Schr6dinger-KdV equations. Two energy preserving schemes are constructed by using Fourier pseudospectral method in space direction di... The energy preserving average vector field (AVF) method is applied to the coupled Schr6dinger-KdV equations. Two energy preserving schemes are constructed by using Fourier pseudospectral method in space direction discretization. In order to accelerate our simulation, the split-step technique is used. The numerical experiments show that the non-splitting scheme and splitting scheme are both effective, and have excellent long time numerical behavior. The comparisons show that the splitting scheme is faster than the non-splitting scheme, but it is not as good as the non-splitting scheme in preserving the invariants. 展开更多
关键词 coupled Schrodinger-KdV equations average vector field method splitting method Fourier pseu-dospectral method
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Probability distribution of wind power volatility based on the moving average method and improved nonparametric kernel density estimation 被引量:4
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作者 Peizhe Xin Ying Liu +2 位作者 Nan Yang Xuankun Song Yu Huang 《Global Energy Interconnection》 2020年第3期247-258,共12页
In the process of large-scale,grid-connected wind power operations,it is important to establish an accurate probability distribution model for wind farm fluctuations.In this study,a wind power fluctuation modeling met... In the process of large-scale,grid-connected wind power operations,it is important to establish an accurate probability distribution model for wind farm fluctuations.In this study,a wind power fluctuation modeling method is proposed based on the method of moving average and adaptive nonparametric kernel density estimation(NPKDE)method.Firstly,the method of moving average is used to reduce the fluctuation of the sampling wind power component,and the probability characteristics of the modeling are then determined based on the NPKDE.Secondly,the model is improved adaptively,and is then solved by using constraint-order optimization.The simulation results show that this method has a better accuracy and applicability compared with the modeling method based on traditional parameter estimation,and solves the local adaptation problem of traditional NPKDE. 展开更多
关键词 Moving average method Signal decomposition Wind power fluctuation characteristics Kernel density estimation Constrained order optimization
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Hyperstatic reaction method for calculations of tunnels with horseshoe-shaped cross-section under the impact of earthquakes 被引量:1
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作者 Thanh Nguyen Chi Gospodarikov Alexandr 《Earthquake Engineering and Engineering Vibration》 SCIE EI CSCD 2020年第1期179-188,共10页
Tunnels are now an integral part of the infrastructure in major cities around the world. For many reasons, these tunnels have horseshoe-shaped cross-sections with round top and flat bottom. This paper presents some im... Tunnels are now an integral part of the infrastructure in major cities around the world. For many reasons, these tunnels have horseshoe-shaped cross-sections with round top and flat bottom. This paper presents some improvements to the use of the Hyperstatic Reaction Method-HRM for analysing tunnels with horseshoe-shaped cross-sections when these tunnels operate under the influence of earthquakes, particularly in cases when the tunnel lining is a continuous lining. The analysis used parameters of a tunnel from the Hanoi metro system, as well as parameters of the strongest earthquake that may occur in the central Hanoi area in the improved HRM and 2 D numerical methods using the ABAQUS software. On the basis of the results obtained, the paper gives conclusions about the HRM methodology when it is used to calculate tunnels that have horseshoe cross-sections operating under the influence of earthquakes. 展开更多
关键词 hyperstatic reaction method earthquake horseshoe cross-section impact tunnel
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Solving Multi-Objective Linear Programming Problem by Statistical Averaging Method with the Help of Fuzzy Programming Method
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作者 Samsun Nahar Marin Akter Md. Abdul Alim 《American Journal of Operations Research》 2023年第2期19-32,共14页
A multi-objective linear programming problem is made from fuzzy linear programming problem. It is due the fact that it is used fuzzy programming method during the solution. The Multi objective linear programming probl... A multi-objective linear programming problem is made from fuzzy linear programming problem. It is due the fact that it is used fuzzy programming method during the solution. The Multi objective linear programming problem can be converted into the single objective function by various methods as Chandra Sen’s method, weighted sum method, ranking function method, statistical averaging method. In this paper, Chandra Sen’s method and statistical averaging method both are used here for making single objective function from multi-objective function. Two multi-objective programming problems are solved to verify the result. One is numerical example and the other is real life example. Then the problems are solved by ordinary simplex method and fuzzy programming method. It can be seen that fuzzy programming method gives better optimal values than the ordinary simplex method. 展开更多
关键词 Fuzzy Programming method Fuzzy Linear Programming Problem Multi-Objective Linear Programming Problem Statistical averaging method New Statistical averaging method
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Quantum generative adversarial networks based on a readout error mitigation method with fault tolerant mechanism
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作者 赵润盛 马鸿洋 +2 位作者 程涛 王爽 范兴奎 《Chinese Physics B》 SCIE EI CAS CSCD 2024年第4期285-295,共11页
Readout errors caused by measurement noise are a significant source of errors in quantum circuits,which severely affect the output results and are an urgent problem to be solved in noisy-intermediate scale quantum(NIS... Readout errors caused by measurement noise are a significant source of errors in quantum circuits,which severely affect the output results and are an urgent problem to be solved in noisy-intermediate scale quantum(NISQ)computing.In this paper,we use the bit-flip averaging(BFA)method to mitigate frequent readout errors in quantum generative adversarial networks(QGAN)for image generation,which simplifies the response matrix structure by averaging the qubits for each random bit-flip in advance,successfully solving problems with high cost of measurement for traditional error mitigation methods.Our experiments were simulated in Qiskit using the handwritten digit image recognition dataset under the BFA-based method,the Kullback-Leibler(KL)divergence of the generated images converges to 0.04,0.05,and 0.1 for readout error probabilities of p=0.01,p=0.05,and p=0.1,respectively.Additionally,by evaluating the fidelity of the quantum states representing the images,we observe average fidelity values of 0.97,0.96,and 0.95 for the three readout error probabilities,respectively.These results demonstrate the robustness of the model in mitigating readout errors and provide a highly fault tolerant mechanism for image generation models. 展开更多
关键词 readout errors quantum generative adversarial networks bit-flip averaging method fault tolerant mechanisms
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The Method of Calculating Average Skidding Distance
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作者 张志贤 冯志丽 《Journal of Forestry Research》 SCIE CAS CSCD 1997年第1期47-49,共3页
By analyzing the existing average skidding distance formulac and the shape of the landing area, theauthors put forward that the average skidding distance is the shortest when the ratio of length and width is 1, and th... By analyzing the existing average skidding distance formulac and the shape of the landing area, theauthors put forward that the average skidding distance is the shortest when the ratio of length and width is 1, and the landing collectioll area is in proportion to of average geometrical skidding distance. The new models of calculating average distance are presented. 展开更多
关键词 average DISTANCE CALCULATION method Loggingarea
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Methodology for Extraction of Tunnel Cross-Sections Using Dense Point Cloud Data 被引量:2
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作者 Yueqian SHEN Jinguo WANG +2 位作者 Jinhu WANG Wei DUAN Vagner G.FERREIRA 《Journal of Geodesy and Geoinformation Science》 2021年第2期56-71,共16页
Tunnel deformation monitoring is a crucial task to evaluate tunnel stability during the metro operation period.Terrestrial Laser Scanning(TLS)can collect high density and high accuracy point cloud data in a few minute... Tunnel deformation monitoring is a crucial task to evaluate tunnel stability during the metro operation period.Terrestrial Laser Scanning(TLS)can collect high density and high accuracy point cloud data in a few minutes as an innovation technique,which provides promising applications in tunnel deformation monitoring.Here,an efficient method for extracting tunnel cross-sections and convergence analysis using dense TLS point cloud data is proposed.First,the tunnel orientation is determined using principal component analysis(PCA)in the Euclidean plane.Two control points are introduced to detect and remove the unsuitable points by using point cloud division and then the ground points are removed by defining an elevation value width of 0.5 m.Next,a z-score method is introduced to detect and remove the outlies.Because the tunnel cross-section’s standard shape is round,the circle fitting is implemented using the least-squares method.Afterward,the convergence analysis is made at the angles of 0°,30°and 150°.The proposed approach’s feasibility is tested on a TLS point cloud of a Nanjing subway tunnel acquired using a FARO X330 laser scanner.The results indicate that the proposed methodology achieves an overall accuracy of 1.34 mm,which is also in agreement with the measurements acquired by a total station instrument.The proposed methodology provides new insights and references for the applications of TLS in tunnel deformation monitoring,which can also be extended to other engineering applications. 展开更多
关键词 cross-section control point convergence analysis z-score method terrestrial laser scanning dense point cloud data
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Correlation Method of Average Plasma Velocity Measurement in Hall-Effect Thrusters
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作者 宁中喜 李鸿 于达仁 《Plasma Science and Technology》 SCIE EI CAS CSCD 2009年第6期709-713,共5页
A new method to measure the average plasma velocity in a Hall-effect thruster is presented. The method is brought forward in virtue of the characteristics of low frequency oscillation induced by the propellant ionizat... A new method to measure the average plasma velocity in a Hall-effect thruster is presented. The method is brought forward in virtue of the characteristics of low frequency oscillation induced by the propellant ionization in the channel and the oriented movement feature of the plasma density out of the channel. The method, equivalent to the correlation method generally used in the signal processing field, provides a solution to the problem of specific impulse measurement on a timescale of hundreds of microseconds and makes the time evolution of average plasma velocity clear. The comparison between the measured value and the calibrated value shows that the relative error is about 3%. 展开更多
关键词 Hall-effect thruster average plasma velocity correlation method
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Indoor air quality risk assessment on the Canadian campus by a multilevel integrated weighted average method
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作者 夏瑞 张远 +4 位作者 ZHANG Meng-heng LIU Ke-xin WU Jie-yun ZHENG Zhi-rong GONG Yao 《Journal of Chongqing University》 CAS 2015年第3期87-100,共14页
Increasing incidents of indoor air quality(IAQ) related complaints lead us to the fact that IAQ has become a significant occupational health and environmental issue. However, how to effectively evaluate IAQ under diff... Increasing incidents of indoor air quality(IAQ) related complaints lead us to the fact that IAQ has become a significant occupational health and environmental issue. However, how to effectively evaluate IAQ under different scale of multiple indicators is still a challenge. The traditional single-indicator method is subjected to uncertainties in assessing IAQ due to different subjectivity on good or bad quality and scalar differences of data set. In this study, a multilevel integrated weighted average IAQ method including initial walking through assessment(IWA) and two-layers weighted average method are developed and applied to evaluate IAQ of the laboratory building at the University of Regina in Canada. Some important chemical parameters related to IAQ in terms of volatile organic compounds(VOCs), methanol(HCHO), carbon dioxide(CO2), and carbon monoxide(CO) are evaluated based on 5 months continuous monitoring data. The new integrated assessment result can not only indicates the risk of an individual parameter, but also able to quantify the overall IAQ risk on the sampling site. Finally, some recommendations based on the result are proposed to address sustainable IAQ practices in the sampling area. 展开更多
关键词 indoor air quality risk assessment weighted average method CAMPUS CANADA
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Average Rainfall Estimation: Methods Performance Comparison in the Brazilian Semi-Arid
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作者 Fernando D. Barbalho Gabriela F. N. da Silva Klebber T. M. Formiga 《Journal of Water Resource and Protection》 2014年第2期97-103,共7页
Considering the rainfall’s importance in hydrological modeling, the objective of this study was the performance comparison, in convergence terms, of techniques often used to estimate the average rainfall over an area... Considering the rainfall’s importance in hydrological modeling, the objective of this study was the performance comparison, in convergence terms, of techniques often used to estimate the average rainfall over an area: Thiessen Polygon (TP) Method;Reciprocal Distance Squared (RDS) Method;Kriging Method (KM) and Multiquadric Equations (ME) Method. The comparison was done indirectly, using GORE and BALANCE index to assess the convergence results from each method by increasing the rain gauges density in a region, through six scenarios. The Coremas/Mae D’água Watershed employed as study area, with an area of 8385 km2, is situated on Brazilian semi-arid. The results showed the TP, as RDS and ME techniques to be employed successfully to obtain the average rainfall over an area, highlighting the MEM. On the other hand, KM, using two variograms models, had an unstable behavior, pointing the prior study of data and variogram’s choice as a need to practical applying. 展开更多
关键词 average RAINFALL Interpolation Techniques MULTIQUADRIC Equations Reciprocal Distance Squared method SEMIARID RAINFALL Thiessen’s method
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Evaluation of Double Average Asian Options by the Legendre Spectral Method
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作者 盛慧莉 马和平 《Journal of Shanghai University(English Edition)》 CAS 2003年第3期206-213,共8页
In this paper, the evaluation of discretely sampled Asian options was considered by numerically solving the associated partial differential equations with the Legendre spectral method. Double average options were disc... In this paper, the evaluation of discretely sampled Asian options was considered by numerically solving the associated partial differential equations with the Legendre spectral method. Double average options were discussed as examples. The problem is a parabolic one on a finite domain whose equation degenerates into ordinary differential equations on the boundaries. A fully discrete scheme was established by using the Legendre spectral method in space and the Crank-Nicolson finite difference scheme in time. The stability and convergence of the scheme were analyzed. Numerical results show that the method can keep the spectral accuracy in space for such degenerate problems. 展开更多
关键词 double average Asian options discretely sampled arithmetic Asian options Legendre spectral method degenerate parabolic problem.
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RADAR CROSS-SECTION COMPUTATIONS OF ARBITRARILY COMPLICATED TARGETS BY APPLYING THE PANEL METHOD
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作者 周建江 舒永泽 《Journal of Electronics(China)》 1992年第2期140-145,共6页
The present paper deals with the method for the radar cross-section (RCS)computations of arbitrarily complicated targets based on the work by D. Klement et al.(1988).This method is convenient in use, fast in operatio... The present paper deals with the method for the radar cross-section (RCS)computations of arbitrarily complicated targets based on the work by D. Klement et al.(1988).This method is convenient in use, fast in operation and precise in calculating RCS of a complicatedtarget. With this method, the RCS of classic scatterers, for example, a cone and a cylinder, arecomputed with the result of good agreement with experimental data. Furthermore, the RCS’of an aircraft model at various attitudes are calculated with the result of good agreement withexperimental data also. 展开更多
关键词 RADAR cross-section PANEL method RADAR target Electromagnetic SCATTERING
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Three Measurement Methods of Two-photon Absorption Cross-section
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作者 LI De-sheng DAI Qin +1 位作者 MA Yu-guang WANG Xi-jun 《Semiconductor Photonics and Technology》 CAS 2006年第4期276-279,共4页
Through the experimental design and theoretical analysis, three technologies used for characterizing the two-photon absorption(TPA) properties, such as nonlinear transmission experiment and theory, Z-scan technology a... Through the experimental design and theoretical analysis, three technologies used for characterizing the two-photon absorption(TPA) properties, such as nonlinear transmission experiment and theory, Z-scan technology and two-photon induced fluorescence method, are introduced. The properties of the three experiments to be utilizable and realizable under desirable limitation are simply analyzed. The advantages of the measurements for TPA characterization are also analyzed. 展开更多
关键词 TPA TPA cross-section Measurement method FLUORESCENCE
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Experimental Assessment of the Battery Lifetime in WSN Based on the <i>Duty</i>-<i>Cycle</i><i>Current</i><i>Average</i>Method
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作者 Leonardo Barboni Maurizio Valle 《Wireless Sensor Network》 2014年第10期212-220,共9页
A great amount of work addressed methods for predicting the battery lifetime in wireless sensor systems. In spite of these efforts, the reported experimental results demonstrate that the duty-cycle current average met... A great amount of work addressed methods for predicting the battery lifetime in wireless sensor systems. In spite of these efforts, the reported experimental results demonstrate that the duty-cycle current average method, which is widely used to this aim, fails in accurately estimating the battery life time of most of the presented wireless sensor system applications. The aim of this paper is to experimentally assess the duty-cycle current average method in order to give more effective insight on the effectiveness of the method. An electronic metering system, based on a dedicated PCB, has been designed and developed to experimentally measure node current consumption profiles and charge extracted from the battery in two selected case studies. A battery lifetime measurement (during 30 days) has been carried out. Experimental results have been assessed and compared with estimations given by using the duty-cycle current average method. Based on the measurement results, we show that the assumptions on which the method is based do not hold in real operating cases. The rationality of the duty-cycle current average method needs reconsidering. 展开更多
关键词 Battery Lifetime CURRENT Consumption TINYOS Measurement Duty-Cycle CURRENT average method
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Application of Weighted Average Method in Evaluation System for Rural Cadre Distance Education
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作者 DAI Li-na1,ZHENG Bo-wei1,DONG Hai-ge2 1.Institute of Agricultural Scientech Information,Beijing Academy of Agriculture and Forestry Sciences,Beijing 100097,China 2.Food Quality Supervision and Management Section,Chaoyang Branch of Beijing Administration for Industry and Commerce,Beijing 100125,China 《Asian Agricultural Research》 2012年第3期66-68,共3页
We elaborate the application method,process and effect of weighted average method in the examination and evaluation system for modern distance education of rural party members and cadres.The study shows that this meth... We elaborate the application method,process and effect of weighted average method in the examination and evaluation system for modern distance education of rural party members and cadres.The study shows that this method reflects the evaluation results objectively and comprehensively and plays a remarkable role in establishing and improving the examination and evaluation system,thus will have an important reference value for the development of modern distance education of rural party members and cadres in the future. 展开更多
关键词 RURAL modern DISTANCE education WEIGHTED average m
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Average temperature calculation for straight single-row-piped frozen soil wall 被引量:8
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作者 XiangDong Hu SiYuan She RuiZhi Yu 《Research in Cold and Arid Regions》 2011年第2期124-131,共8页
The average temperature of frozen soil wall is an essential parameter in the process of design, construction, and safety manage- ment of artificial ground freezing engineering. It is the basis of calculating frozen s... The average temperature of frozen soil wall is an essential parameter in the process of design, construction, and safety manage- ment of artificial ground freezing engineering. It is the basis of calculating frozen soil's mechanical parameters, fiarther prediction of bearing capacity and, ultimately, safety evaluation of the frozen soil wall. Regarding the average temperature of sin- gle-row-piped frozen soil wall, this paper summarizes several current calculation methods and their shortcomings. Furthermore, on the basis of Bakholdin's analytical solution for the temperature field under straight single-row-piped freezing, two new calcula- tion models, namely, the equivalent trapezoid model and the equivalent triangle model, are proposed. These two approaches are used to calculate the average temperature of a certain cross section which indicates the condition of the whole frozen soil wall. Considering the possible parameter range according to the freezing pipe layout that might be applied in actual construction, this paper compares the average temperatures of frozen soil walls obtained by the equivalent trapezoid method and the equivalent tri- angle method with that obtained by numerical integration of Bakholdin's analytical solution. The results show that the discrepancies are extremely small and these two new approaches are better than currently prevailing methods. However, the equivalent triangle method boasts higher accuracy and a simpler formula compared with the equivalent trapezoid method. 展开更多
关键词 artificial ground freezing single-row-piped freezing frozen soil wall average temperature equivalent trapezoid method equivalent triangle method Bakholdin's solution
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Studies on Stochastic Parametric Roll of Ship with Stochastic Averaging Method 被引量:4
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作者 WANG Li-yuan TANG You-gang +2 位作者 LI Yan ZHANG Jing-chen LIU Li-qin 《China Ocean Engineering》 SCIE EI CSCD 2020年第2期289-298,共10页
The paper studies the parametric stochastic roll motion in the random waves.The differential equation of the ship parametric roll under random wave is established with considering the nonlinear damping and ship speed.... The paper studies the parametric stochastic roll motion in the random waves.The differential equation of the ship parametric roll under random wave is established with considering the nonlinear damping and ship speed.Random sea surface is treated as a narrow-band stochastic process,and the stochastic parametric excitation is studied based on the effective wave theory.The nonlinear restored arm function obtained from the numerical simulation is expressed as the approximate analytic function.By using the stochastic averaging method,the differential equation of motion is transformed into Ito’s stochastic differential equation.The steady-state probability density function of roll motion is obtained,and the results are validated with the numerical simulation and model test. 展开更多
关键词 parametric roll random wave stochastic averaging method probability density function
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