基于神经网络的热力站供热过程预测控制研究
详细信息    本馆镜像全文|  推荐本文 |  |   获取CNKI官网全文
摘要
我国三北地区采暖能耗占全社会能耗的27.2%,供热不但能耗大,而且效率低,单位面积采暖能耗是发达国家的3~4倍,为落实国家节能政策,研究供热节能监控系统意义重大。本文以“十一五”国家科技支撑计划重大项目“建筑节能关键技术研究与示范”(项目编号:2006BAJ01A04)和黑龙江省科技攻关项目“基于LonWorks技术和预测控制的供热FCS研究”(项目编号:GC04A104)为课题背景,研究供热节能控制策略和开发供热节能监控装置。研究中面临的问题是:必须以节能为目标,但同时也要保证优质供热;供热过程是一复杂的动力学对象;在采用先进技术的同时,要降低产品的成本。
     精确的数学模型是供热系统分析与控制的重要依据。将供热过程动态分解为确定部分和随机部分,分别建立这两部分模型:通过机理分析与实验建模法相结合求取确定部分的模型,用ARIMA模型拟合供热过程模型的随机部分。供热过程建模为供热质调量调解耦和预测控制研究的基础。
     供热负荷预报为供热节能提供依据。针对供热负荷具有的非平稳、非线性、时滞等特性,应用时间序列、最大熵、RBF神经网络多种方法对供热负荷进行预报。其中用时间序列法对平稳化处理的随机序列进行预报,用最大熵法对非平稳随机序列进行预报,用神经网络法对非线性负荷序列进行预报。为了进一步提高预报精度,将交叉预报思想引入供热负荷预报中,即用纵向预报跟踪用户对负荷的需求,用横向预报跟踪天气的变化,然后对纵向和横向预报结果进行加权交叉。通过仿真分析、比较各方法的性能。
     供热系统质调、量调通道间存在耦合。给出耦合程度判定方法,对供热耦合模型进行稳态与动态耦合程度分析。分别采用传统解耦方法和时滞递归RBF神经网络解耦方法,将耦合系统解耦成两个相互无干扰的单入单出系统。其中神经网络解耦法采用改进的假近邻法预估神经网络的输入维数,解决时间序列维数确定困难的问题,通过仿真验证其静态和动态性能。
     鉴于预测控制算法能适应供热过程非线性、时变、时滞、不确定等特性,采用预测控制对供热过程质调通道进行控制。对传统预测控制方法DMC和GPC算法进行了改进:用DMC模型简化和预报误差校正结合的方法减少计算量,提高实时性,并解决模型失配问题;对隐式自适应广义预测控制研究,给出改进的辨识和控制算法,以满足实时性要求。进行神经网络预测控制方法的研究,设计基于神经网络的预测控制器,给出其偏差控制算法和控制律求解算
In north areas of China, heating energy consumption has achieved 27.2 percent of total national energy consumption. In fact, energy consumption is not only huge, but also inefficient. Nowadays, the heating energy consumption per unit area is 2 to 3 times than developed countries. In order to implement national policies of energy-saving, it is very important to study the energy-saving monitoring system. Based on above reasons, the heating energy-saving control strategy and corresponding monitoring system are studied in this dissertation. Two projects are taken as background, which are“National Eleventh Five-year Plan Key Project of Ministry of Science and Technology in 2006: Research of Key Technology for Building Energy-saving and Its Engineering Demonstration”(Grant No. 2006BAJ01A04) and“Heilongjiang Province Research Project in 2005: Research of Heat Supply Field Control System Based on LonWorks Technology and Predictive Control Theory”(Grant No. GC04A104). There are some problems to be considered: ensuring the high-quality heating while taking energy-saving as target; Heat supply system is a complex dynamics process; Reducing the product costs when applying advanced technology.
     As accurate mathematical models are foundations of heat supply system analysis and control, the heat supply process is dynamically divided into the certain part and the random part, which models are established separately. The model of the certain part is established by combining mechanism analysis and experimental methods, while the random part of heat supply process model is fitted with ARMA model. The heat supply process modeling is the premise of heat supply decoupling and predictive control.
     Heat load forecasting provides the basis for heating energy-saving. According to the characteristics of nonstationary, nonlinear, time-varying of heat load, several forecasting methods are proposed in this dissertation, which based on time series method, maximum entropy method and neural network theory. The random series stabilized is forecasted by time series method, the random series unstabilized is forecasted with the maximum entropy method, and the nonlinear characteristic is matched with neural network method. To improve the accuracy, crossover forecasting theory is introduced into heat load forecasting. With this method, the household demands are tracked by vertical forecasting, and the outdoor temperature is tracked by the horizontal forecasting. Finally, the performances of above algorithms are analyzed by comparing the simulation results.
     The coupling effect exists between quality-adjust and quantity-adjust channels. Firstly, judgment methods of coupling degree are given to analysis the static and dynamic coupling. Then, two non-interference SISO independent systems are obtained by using conventional decoupling method and decoupling method based on recurrent RBF neural network with delays respectively. The input dimensions of neural network are estimated by modified false neighborhood method. In addition, the static and dynamic performances of the methods are validated by simulation.
     As predictive control can meet the heating characteristics of nonlinear, changeful, time-delay, uncertain, the predictive control is applied in heat supply. The basic DMC and GPC algorithms are improved: improved DMC algorithm combined with model simplified and predictive error correction algorithm is applied to decrease computational complexity, and solve the model mismatch problem; Besides this, control algorithm of implicit adaptive GPC with improved identification algorithm is given to improve real-time ability. Further more, an intelligent predictive control method based on neural network is studied, and its deviation control algorithm along with control rate solving algorithm are presented.
     Finally the engineering application is studied. Through software and hardware design, scheme of heat supply monitoring system based on GPRS and PLC is given. The stability and reliability of control system is guaranteed by advanced technology and components selection. The device prototype achieved the design indexes and passed the technical inspection of national quality inspection department by tested in a substation.
引文
1江亿.我国供热节能中的问题和解决途径.暖通空调. 2006, 36(3):37~41
    2唐卫.热力站自动监控系统基本思路与控制模式分析.区域供热. 2001, (5):9~13
    3郝有志.李德英.基于神经网络的供热计量系统热负荷短期预测.暖通空调. 2003, 33(6):105~107
    4 J. Hensen. Simulation of Building Energy and Indoor Environmental Quality-some Weather Data Issues. Proc. Int. Workshop on Climate Data and Their Application in Engineering. 1999:4~18
    5 S. Werner. The Heat Load in District Heating System. Chalmers University of Technology. 1984
    6 K. Wojdyga. An Influence of Weather Conditions on Heat Demand in District Heating Systems. Energy & Buildings. 2008, 40(11):2009~2014
    7郝有志,李德英.热负荷预测方法评析.建筑热能通风空调. 2003, 22(1):26~27
    8 G. E. P. Box, G. M. Jenkins. Time Series Analysis, Forecasting and Control. San Francisco:Holden-Day. 1970
    9 E. Dotzauer. Simple Model for Prediction of Loads in District-heating Systems. Applied Energy. 2002, 73(3-4):277~284
    10 L. Pedersen, J. Stang, R. Ulseth. Load Prediction Method for Heat and Electricity Demand in Buildings for the Purpose of Planning for Mixed Energy Distribution Systems. Energy & Buildings. 2008, 40(7):1124~1134
    11 C. Ghiaus. Experimental Estimation of Building Energy Performance by Robust Regression. Energy & Buildings. 2006, 38(6):582~587
    12 H. A. Nielsen, H. Madsen. Modelling the Heat Consumption in District Heating System Using a Grey-Box Approach. Energy and Buildings. 2006, 38(1):63~71
    13 J. F. Kreider, J. S. Haberl. Predicting Hourly Building Energy Use: the Great Energy Predictor Shootout-Overview and Discussion of Results. ASHRAE Transactions. 1994, 100(2):1104~1118
    14 B. P. Feuston. Generalized Nonlinear Regression with Ensemble of Neural Nets: the Great Energy Predictor Shootout. ASHARE Transactions. 1994, 100(2):1075~1080
    15 W. J. Stevenson. Using Artificial Neural Nets to Predict Building Energy Parameters. ASHRAE Transactions. 1994, 100(2):1081~1087
    16 M. B. O. Ohlsson. Predicting System Loads with Artificial Neural Network-methodsfrom the Great Energy Predictor Shootout. ASHARE Transactions. 1994, 100(2):1063~1074
    17 S. A. Kalogirou. Long-Term Performance Prediction of Forced Circulation Solar Domestic Water Heating System Using Artificial Neural Networks. Applied Energy. 2000, 66:63~74
    18 G. P. Henze. Building Energy Management as Continuous Quality Control Process. Journal of Architectural Engineering. 2003, 7:97~106
    19 R. H. Dodier, G. P. Henze. Statistical Analysis of Neural Network as Applied to Building Energy Prediction. Journal of Solar Energy Engineering. 2004, 2:19~27
    20 Bing Dong, Cheng Cao, Siew Eang Lee. Applying Support Vector Machines to Predict Building Energy Consumption in Tropical Region. Energy and Buildings. 2005, 37:545~553
    21李玉云,王永骥.人工神经网络在暖通空调领域的应用研究发展.暖通空调. 2001, 31(1):38~41
    22杜进荣,朱能,向天游.民用建筑供热负荷的神经网络法预测.煤气与热力. 2001, 21(1):16~19
    23周恩泽.供热负荷中短期预报理论研究.哈尔滨建筑大学硕士论文. 1998
    24马涛,徐向东.基于多尺度挖掘的区域供热系统负荷预测.暖通空调. 2005, 35(11):16~19
    25黎展求,朱栋华.基于支持向量回归和小波包的供热负荷预测.暖通空调. 2007, 37(2):1~5
    26胡文斌,杨昌智.短期供热负荷的灰色拓扑预报.煤气与热力. 1999, 19(3):51~54
    27冯利华.灰色预报模型的问题讨论.系统工程理论与实践. 1997, 12(17):125~128
    28 J. Richalet, et al. Model Predictive Heuristic Control: Application to industrial Processes. Automatica. 1978, 14(5):413~428
    29 R. Rouhani, R. K. Mehra. Model Algorithmic Control(MAC), Basic Theoretical Properties. Automatica. 1982, 18(4):401~414
    30 C. R. Cutler, B. L. Ramaker. Dynamic Matrix Control—A Computer Control Algorithm. Proc. JACC. SanFranciso. 1980
    31 D. W. Clarke, C. Mohtadi, P. S. Tuffs. Generalized Predictive Control Algorithm. Automatica. 1987, 23:137~160
    32 M. A. Lelic, M. B. Zarrop. Generalized Pole Placement Self-tuning Controller. International Journal of Control. 1987, 46(2):547~568
    33 W. G. Kim, et al. Application of Dynamic Matrix Control to a Boiler-Turbine System.2005 IEEE Power Engineering Society General Meeting. 2005, 2:1595~1599
    34 A.Vahidi, A. Stefanopoulou, H. Peng. Current Management in a Hybrid Fuel Cell Power System: a Model-Predictive Control Approach. IEEE Transactions on Control Systems Technology. 2006, 14(6):1047~1057
    35 M. Zawodniok, S. Jagannathan. Predictive Congestion Control MAC Protocol for Wireless Sensor Networks. Proceedings of the 5th International Conference on Control and Automation, ICCA'05. 2005:185~190
    36 Z. Zeybek, S. Cetinkaya. Generalized Delta Rule (GDR) Algorithm with Generalized Predictive Control (GPC) for Optimum Temperature Tracking of Batch Polymerization. Chemical Engineering Science. 2006, 61(20):6691~6700
    37 L. Zhou, J. Qian. IMC Structure of Multi-Rate Multivariate Predictive Control Systems and an Improved Algorithm. Chinese Journal of Chemical Engineering. 2001, 9(3):273~279
    38 M. A. Duarte, A. M. Suárez, D. F. Bassi. Multivariable Predictive Control of a Pressurized Tank Using Neural Networks. Neural Computing & Applications. 2006, 15(1):18~25
    39 U. Yuzgec, Y. Becerikli, M. Turker. Dynamic Neural-network-based Model Predictive Control of an Industrial Baker's Yeast Drying Process. IEEE Transactions on Neural Networks. 2008, 19(7):1231~1242
    40 S. W. Wang, et al. Adaptive Neural Network Model Based Predictive Control for Air-Fuel Ratio of SI Engines. Engineering Applications of Artificial Intelligence. 2006, 19(2):189~200
    41 Song Ying, Chen Zengqiang, Yuan Zhuzhi. New Chaotic PSO-based Neural Network Predictive Control for Nonlinear Process. IEEE Transactions on Neural Networks. 2007, 18:595~600
    42 M. Jalili, et al. Neural Networks as a Tool for Nonlinear Predictive Control: Application to Some Benchmark Systems. International Journal of Wavelets, Multiresolution and Information Processing. 2007, 5:69~99
    43 C. H. Lu, C. C. Tsai. Generalized Predictive Control Using Recurrent Fuzzy Neural Networks for Industrial Processes. Journal of Process Control. 2007, 17(1):83~92
    44 S. J. Yoo, Y. H. Choi, J. B. Park. Generalized Predictive Control Based on Self-recurrent Wavelet Neural Network for Stable Path Tracking of Mobile Robots: Adaptive Learning Rates Approach. IEEE Transactions on Circuits and Systems I: Regular Papers. 2006, 53(6):1381~1394
    45 Blazic, et al. Design and Stability Analysis of Fuzzy Model-Based Predictive Control—a Case Study. Journal of Intelligent and Robotic Systems:Theory and Applications. 2007, 49(3):279~292
    46 Lei Jia, Hongli Lv, Cai Wenjian. Model Predictive Control Based on Fuzzy Linearization Technique for HVAC Systems Temperature Control. 2006 1st IEEE Conference on Industrial Electronics and Applications. 2006:405~410
    47诸静,黄抗美.复杂系统的广义预测模糊控制.电工技术学报. 1997, 12(2):7~12
    48 R. Kawathekar, J. B. Riggs. Nonlinear Model Predictive Control of a Reactive Distillation Column. Control Engineering Practice. 2007, 15(2):231~239
    49 R. Dubay, M. Abu-Ayyad, J. M. Hernandez. A Nonlinear Regression Model-based Predictive Control Algorithm. ISA transactions. 2009, 48(2):180~189
    50 M. P. de la Parte, et al. Application of Predictive Sliding Mode Controllers to a Solar Plant. IEEE Transactions on Control Systems Technology. 2008, 16(4):819~825
    51 J. Prakash, R. Senthil. Design of Observer Based Nonlinear Model Predictive Controller for a Continuous Stirred Tank Reactor. Journal of Process Control. 2008, 18(5):504~514
    52 J. B. Rawlings, et al. Nonlinear Model Predictive Control: A Tutorial and Survey. IFAC Symposium ADCHEM, Kyoto, Japan. 1994:156~161
    53孙浩,席裕庚.非线性系统基于I/O扩展线性化的预测控制算法.控制理论与应用. 1991., 8(3):261~267
    54曾锋,高东杰,李秀改.一类有约束的分段线性系统双模预测控制.控制与决策. 2006, 21(5):597~600
    55 W. R.Van Soest, Q. P. Chu, J. Mulder. Combined Feedback Linearization and Constrained Model Predictive Control for Entry Flight. Journal of Guidance, Control, and Dynamics. 2006, 29(2):427~434
    56 B. Ding, Y. Xi. A Two-Step Predictive Control Design for Input Saturated Hammerstein Systems. International Journal of Robust and Nonlinear Control. 2006, 16(7):353-367
    57李阳春,许晓呜,杨烃春.一类非线性预测控制系统的鲁棒稳定性.自动化学报. 1999, 25(6):852~855
    58 Xu Min, Li Shaoyuan. Practical Generalized Predictive Control with Decentralized Identification Approach to HVAC Systems. Energy Conversion and Management. 2007, 48(1):292~299
    59 He Ming, Cai Wenjian, Li Shaoyuan. Multiple Fuzzy Model-based TemperaturePredictive Control for HVAC Systems. Information Sciences. 2005, 169(1):155~174
    60 Zhu Xueli, Qi Weigui. Study on Simulation of GPC Implicit Algorithm for Heat Supply Control. Journal of System Simulation. 2005, 17(9):2214~2217
    61 Zhu Xueli, Qi Weigui, Shao Xianhe. Study on the Application of GPC Implicit Adaptive Algorithm in Heat Supply Process. Journal of Harbin Institute of Technology. 2005, 37(2):227~230
    62 Zhang Suying, Pang Zhifeng. Predictive Control Based on Fore-Feed Application in Heat Supply Network. Proceedings of 2004 International Conference on Machine Learning and Cybernetics. 2004, 7:4131~4132
    63 J. Stefanovski. Sufficient Conditions for Linear Control System Decoupling by Static State Feedback. Institute of Electrical and Electronics Engineers Inc. IEEE Transactions on Automatic Control. 2001, 46(6):984~990
    64 D. D. Sourlas. Optimization-based Decoupling Controller Design for Discrete Systems. Chemical Engineering Science. 2001, 56(15):4695~4710
    65 A. Randall, L. Balmer, K. J. Burnham, M. J. Chapman. Hot Strip Mill Tension Control-multivariable Techniques. Systems Science. 1995, 21(4):89~100
    66 F. Borrelli, T. Keviczky. Distributed LQR Design for Identical Dynamically Decoupled Systems. IEEE Transactions on Automatic Contro. 2008, 53(8):1901~1912
    67 Quan Yong, Yang Jie. Identical Matrix Design of The Optimal Decoupling Control System With Kernel Methods. Proceedings of 2002 International Conference on Machine Learning and Cybernetics. 2002, 3:1272~1278
    68 M. Cotsaftis, J. Robert. Applications and Prospect of the Nonlinear Decoupling Method. Computer Methods in Applied Mechanics and Engineering. 1998, 154(3):163~178
    69 Zhu Yubin, Fan Siqi. Multivariable Adaptive Decoupling Control Based on Auto-Tuning Neurons for Aeroengine. Journal of Aerospace Power. 2007, 22(3):490~494
    70 1 L. Zhai, T. Chai. Nonlinear Decoupling PID Control Using Neural Networks and Multiple Models. Journal of Control Theory and Applications. 2006, 4(1):62~69
    71 L. C. Hung, H. Y. Chung. Decoupled Control Using Neural Network-based Sliding-mode Controller for Nonlinear Systems. Expert Systems with Applications. 2007, 32(4):1168~1182
    72董玲,白焰.多变量系统的神经元解耦控制.现代电力. 1999, 16(1):11~16
    73戴先中.感应电机的神经网络逆系统线性化解耦控制.中国电机工程学报. 2004,24(1):112~117
    74张建华,侯国莲,杨黎. 300MW火电单元机组协调控制系统的解耦研究.现代电力. 1998, 15(2):14~18
    75张化光,杨英旭,柴天佑.多变量模糊控制的现状与发展(Ⅱ)—关于解耦、神经网、变结构等问题.控制与决策. 1995, 10(4):289~295
    76 B. Chen, S. Tong, X. Liu. Fuzzy Approximate Disturbance Decoupling of MIMO Nonlinear Systems by Backstepping Approach. Fuzzy Sets and Systems. 2007, 158(10):1097~1125
    77 Liu Hongbo, Li Shaoyuan, Chai Tianyou. Intelligent Decoupling Control of Power Plant Main Steam Pressure and Power Output. International Journal of Electrical Power and Energy System. 2003, 25(10):809~819
    78李旭明.多变量模糊神经网络控制器的研究.控制与决策. 2001, 16(1):107~110
    79 Y. Ying, M. Rao, S. X. Shen, Q. Xia. Bilinear Decoupling Control and Its Industrial Application. Control-Theory and Advanced Technology. 1994, 10(1):97~109
    80 Chen Chung-Cheng, Chien Ting-Li, Wu Chia-Ju. Simultanious Tracking and Almost Disturbance Decoupling for Nonlinear Systems with Uncertainties. Journal of the Chinese Institute of Engineers, Transactions of the Chinese Institute of Engineers, SeriesA/Chung-Kuo Kung Cheng Hsuch Kan. 2004, 27(1):23~34
    81 C. H. Lu, C. C. Tsai. Adaptive Decoupling Predictive Temperature Control for an Extrusion Barrel in a Plastic Injection Molding Process. Institute of Electrical and Electronics Engineers Inc. IEEE Transactions on Industrial Electronics. 2001, 48(5):968~975
    82 Wang Xin, Yue Heng, Chai Tianyou. Multivariable Direct Adaptive Pole Placement Feedforward Decoupling Controller Using Multiple Models. IEEE Proceedings of the 4th World Congress on Intelligent Control and Automation. Institute of Electrical and Electronics Engineers Inc. Proceedings of the World Congress on Intelligent Control and Automation. 2002, 2:852~857
    83 B. Jacimovic, et al. Supply Water Temperature Regulation Problems in District Heating Network with Both Direct and Indirect Connection. Energy & Buildings. 1998, 28(3):317~322
    84 H. Madsen, et al. On Flow and Supply Temperature Control in District Heating Systems. Heat Recovery Systems and CHP-Combined Heat and Power. 1994, 14(6):613~620
    85石兆玉.供热系统运行调节与控制.清华大学出版社. 1998
    86江亿.集中供热网控制调节策略的探讨.区域供热. 1997, (2):10~14
    87原贺新,马卫华,刘海英.热网计算机监控系统.煤气与热力. 2000, 20(2):123~125
    88曹玉强,朱洁,李圣明.供热过程的前馈-串级自适应控制.自动化仪表. 2004, 25(7):55~58
    89 Shou-Heng Huang, Icon M. Nelson. Developtrtent of a Self-Tuning Fuzzy Logic Controller. ASHARE Transaetions. 1999, 105(1):14~31
    90 Masato Kasahara, Tadahiko Matsuba, Yoshiaki Kuzuu. Design and Tuning of Robust PID Controller for HVAC Systems. ASHARE Transactions. 1999, 105(2):154~166
    91 K. R. Prodyut, K. M. George, C. H. Bipul. Fuzzy Rule-adaptive Model Predictive Control for a Multivariable Heating System. Proceedings of 2005 IEEE Conference on Control Applications. 2005:260~265
    92 Liu Chao-ying, Song Xue-Ling. Control System Design of Heat Exchange Station Based on fuzzy Technology. Proceedings of the Fifth International Conference on Machine Learning and Cybernetics, Dalian, 13-16 August 2006. 2006:380~384
    93 Yoshiyuki Sakamoto, Akihiro Nagaiwa, Syuichiro Kobayasi. An Optimization Method of District Heating and Cooling Plant Operation Based on Genetic Algorithm. ASHARE Transactions. 1999, 105(2):104~114
    94 G. Sandou, et al. Predictive Control of a Complex District Heating Network. 44th IEEE Conference on Decision and Control and 2005 European Control Conference. 2005:7372~7377
    95冯雨.预测控制在热力站供暖调节中的应用研究.哈尔滨建筑大学硕士论文. 1999
    96杨建坤.北方小城镇供热模式分析与热网优化控制的研究.同济大学博士论文. 2007
    97张志强.热力站控制系统的设计思想.仪器仪表用户. 2004, 11(1):35~37
    98谢云,刘振全.全自动供热机组与城市集中供热.机械研究与应用. 2003, 16(1):54~55
    99李新刚.集中供热热力站微机监控系统的设计.电力学报. 2000, 15(4):308~31
    100朱学莉,陆亚俊.热力站供热过程建模研究.哈尔滨建筑大学学报. 2002, 35(6):42~46
    101 N. M. Abbasov, et al. Dynamic Models of Heat Exchangers. Chemistry and Technology of Fuels and Oils. 2006, 42(1):25~29
    102杨叔子.平稳时间序列的数学模型及其阶的确定的讨论.华中科技大学学报(自然科学版). 1982, 11(5):9~14
    103 H. Akaike. A New Look at the Statistical Model Identification. IEEE transactions on automatic control. 1974, 19(6):716~723
    104 K. J. Astrom. On the Achievable Accuracy in Identification Problems. IFAC Symposium. 1967:12~17
    105 S. M. Pandit, S. M. Wu. Time Series and System Analysis Modelling an Applications. John Wiley and Sons. 1983
    106 J. P. Burg. Maximum Entropy Spectral Analysis. Proc. 37th Meeting of the Society of Exploration Geophysicists, Oklahoma City, Okla., October, 1967; Reprinted in Modern Spectrum Analysis, D.G. Childers, ed., IEEE Press, New York. 1978:34~39
    107魏海坤.神经网络结构设计的理论与方法.国防工业出版社. 2005
    108 E. Bristol. On a New Measure of Interaction for Multivariable Process Control. IEEE Transactions on Automatic Control. 1966, 11(1):133~134
    109 M. F. Witcher, T. J. McAvoy. Interacting Control Systems: Steady-State and Dynamic Measurement of Interaction. ISA Transactions. 1977, 16(3):35~41
    110 H. Qiao, et al. A Reference Model Approach to Stability Analysis of Neural Networks. IEEE Transactions on Systems, Man, and Cybernetics. 2003, 33(6):925~936
    111 Liangyue Cao. Practical Method for Determining the Minimum Embedding Dimension of a Scalar Time Series. Physica D: Nonlinear Phenomena. 1997, 110:43~50

© 2004-2018 中国地质图书馆版权所有 京ICP备05064691号 京公网安备11010802017129号

地址:北京市海淀区学院路29号 邮编:100083

电话:办公室:(+86 10)66554848;文献借阅、咨询服务、科技查新:66554700