高炉冶炼过程的子空间辨识、预测及控制
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摘要
钢铁工业是国民经济的重要支柱产业,也是大量消耗能源的产业。而作为钢铁生产体系中能耗最大的环节,高炉炼铁的每一个技术进步都将带来巨大的经济和社会效益。本文以内蒙古包钢6#高炉在线采集的冶炼过程数据为基础,针对高炉的实际情况及炼铁生产中工长关注的实际问题,对高炉冶炼过程的辨识、预测及控制进行研究,从而为高炉冶炼过程的闭环控制提供了一种新的思路,具有一定的理论意义和应用价值。
高炉冶炼过程自动控制的核心难题是炉温的预测和控制。其复杂性来源于几种复杂动力学的交叉。一个良好的预测模型对实际生产有重要指导价值,而如果能够得到一个有效的控制模型,其意义则更为显著。因此,高炉冶炼过程的预测控制问题成为本篇论文研究的核心问题。论文的第二章简要介绍了高炉生产流程以及高炉专家系统的最新设计思路,通过炼铁工艺机理模型、炉况诊断推理模型、系统优化的数理模型以及炉温预测控制模型的智能化集成,为实现高炉冶炼过程的闭环控制奠定基础。论文的第三章针对高炉实际数据中经常出现的缺失值和异常值分别进行处理,对于数据中的缺失值,通过将离散属性的数据进行分类从而利用C4.5决策树算法进行填充,取得了较好的填充效果。对于数据中的异常值,基于马氏距离等4种多变量异常值检测方法来判定异常值并将其从原始数据中删除。对异常值和缺失值的合理处置大大降低了数据的波动性。在此基础上,论文第四章介绍了一种较新的系统辨识方法—子空间方法。这种方法基于输入输出数据,对模型结构的先验知识需求较少,其算法实现依赖于一些简单可靠的线性代数工具因而在数值计算中具有一定的鲁棒性并且能够较好地适用于高炉冶炼过程等多变量系统。利用子空间方法对第三章的数据处理效果进行验证,结果表明数据处理能够对高炉冶炼的辨识和预测产生较好的效果。
为进一步提高辨识效果,论文第五章基于子空间方法分别对高炉冶炼过程采用Wiener模型和Hammerstein-Wiener模型结构进行辨识。对于Wiener模型辨识,通过对非线性模块的逆函数进行逼近从而显式地得到系统的非线性特性,将多输入单输出非线性问题转化成为一个多输入多输出的模型进行辨识,利用辨识得到的模型对包钢数据进行预测,预测命中率达到81%。对于Hammerstein-Wiener模型,在辨识过程中利用径向基函数良好的逼近能力及其对多变量系统的方便处理分别对Hammerstein非线性和Wiener非线性部分进行逼近,并利用BFGS最优化方法对参数进行优化。利用四种径向基函数:Laplacian径向基函数、Logistic径向基函数、Gaussian径向基函数和薄板样条径向基函数进行建模,结果表明利用薄板样条径向基函数对高炉冶炼过程进行辨识和预测得到的效果更佳,其命中率达到85%。
在探讨了高炉冶炼过程的辨识和预测问题之后,论文的第六章对高炉冶炼过程的控制做进一步的研究。在现行的生产实践中,高炉工长对冶炼过程的控制主要是以专业知识和实践经验为基础的人工控制。由于高炉工长控制水平各不相同,造成了高炉冶炼过程的不稳定。本章针对这个问题,基于子空间方法构造了一种适合于高炉冶炼过程的自适应预测控制方法,提出了一种更为简便的约束处理方法,同时在方法中对各个输入变量调整的优先级进行考虑。结合高炉的实际情况,从实际数据的计算出发得到了保持高炉高产低耗的最佳炉温水平。仿真结果表明,设计的预测控制模型能够有效降低高炉冶炼过程的波动性,而各个输入变量的调整均没有超出约束,这表明预测控制算法的有效性和可行性。此外,这种思路克服了之前预测模型的“预测—控制”模式所带来的“模型悖论问题”,即工长利用了炉温预测信息对高炉行程进行调控后,炉温的发展改变了轨迹,从而与初始预测值产生了偏差的问题。而自适应预测控制方法将静态预测-控制-动态预测结合在一起,整体考虑炉温预测控制问题,因而能达到更好的应用效果。论文第七章对全文的研究内容以及创新点做了归纳,并对课题的后续研究做了展望。
As the pillar industry of national economy, steel industry is among the most energy intensive, while for all the sub-processes in steel industry, blast furnace (BF) ironmaking consumes the largest part of energy. Thus every technological progress in BF ironmaking will bring enormous economic and social benefits. By investigation into the actual situation of BF ironmaking and BF operators? concerns, the current study discussed the identification and predictive control of blast furnace ironmaking with data collected from No. 6 BF at Baotou Steel. The study introduces a new idea for closed-loop control of BF ironmaking and is meaningful both in theory and practice.
In the efforts to achieve closed loop control of BF ironmaking, the crucial problem is prediction and control of silicon content in hot metal, whose complexity is the result of interaction between chemical reaction dynamics and kinetics. An accurate predictive model for silicon content will greatly enhance BF ironmaking, while an effective controller will bring significant benefits. These two problems become the main research efforts in this dissertation. Chapter 2 gave a brief introduction to the blast furnace ironmaking process and some latest development on design of BF expert system. By integration of 4 kinds of models, e.g. mechanism models, inferential models, optimization models and predictive control models a closed loop controller for BF ironmaking is constructed. Chapter 3 dealt with the problem of missing values and outliers in the raw data. For missing values, a C4.5 decision tree based algorithm was adopted by discretizing the missing attribute and good results are achieved. While for the outliers, 4 multivariate outlier detection methods were used and the detected outliers are deleted from the original dataset. The fluctuation of data decreased significantly after processing of missing values and outliers. Chapter 4 introduced a novel method in the theory of system identification- subspace methods and tested the method on data before and after processing. Subspace methods identify system model from input and output data, its algorithm uses some simple and reliable linear algebra methods and is robust and efficient. Its good capacity to deal with multivariate system is very suitable for identification of blast furnace ironmaking process. Simulation experiments were carried out to test the method based on data before and after processing of missing values and outliers. It is shown that processing of missing values and outliers enhances the identification of blast furnace ironmaking process.
To get more accurate models, Chapter 5 identifies the BF ironmaking process based on Wiener model and Hammerstein-Wiener model using subspace methods. For identification of Wiener model, a polynomial function was used to approximate inversion of the nonlinear part of Wiener model. By this technique the multivariate input single output (MISO) nonlinear problem was converted to a multivariate input multivariate output (MIMO) linear system and the identification became simpler. The identified model was then test on data from Baotou Steel and a hit-rate of 81% was achieved. As for the Hammerstein-Wiener model, radial basis functions (RBF) were used to approximate both the Hammerstein and Wiener nonlinearity, a BFGS quasi-Newton method was used to optimize the parameters. Four kinds of RBFs, e.g. Laplacian, Logistic, Gaussian and Thin-plate Spline RBF were tested. Simulation results shown identification using thin-plate spline RBF is the most accurate with the hit-rate of 85%.
After discussion on the identification and prediction problem, Chapter 6 made further research on predictive control of BF ironmaking. Currently, control of BF ironmaking heavily relies on expert experience of operators. However, since different operators have different habits, control of BF ironmaking becomes inconsistent and unstable. To solve this problem, an adaptive predictive control method was constructed based on subspace method. The predictive control method adopts a simpler constraint handling method and priorities of input variables were also taken into consideration. The best level of silicon content was computed from practical data. Simulation results shown that the designed predictive control method can effectively handle the fluctuation of BF ironmaking problem, while the constraints of input variables were not violated. Thus the effectiveness and feasibility of the proposed method was proved. Besides, the adaptive method can overcome the problem of previous predictive models. In practice, the BF operators make control movements based on future information of silicon content obtained through predictive models, which results in deviation between actual and predicted silicon content. The adaptive predictive control method is a combination of static prediction, control and dynamic prediction so that it is capable of handling the overall condition of the ironmaking process. Finally, Chapter 7 gave the conclusion and theoretical innovations in the paper, issues for further research were also investigated.
高炉冶炼过程自动控制的核心难题是炉温的预测和控制。其复杂性来源于几种复杂动力学的交叉。一个良好的预测模型对实际生产有重要指导价值,而如果能够得到一个有效的控制模型,其意义则更为显著。因此,高炉冶炼过程的预测控制问题成为本篇论文研究的核心问题。论文的第二章简要介绍了高炉生产流程以及高炉专家系统的最新设计思路,通过炼铁工艺机理模型、炉况诊断推理模型、系统优化的数理模型以及炉温预测控制模型的智能化集成,为实现高炉冶炼过程的闭环控制奠定基础。论文的第三章针对高炉实际数据中经常出现的缺失值和异常值分别进行处理,对于数据中的缺失值,通过将离散属性的数据进行分类从而利用C4.5决策树算法进行填充,取得了较好的填充效果。对于数据中的异常值,基于马氏距离等4种多变量异常值检测方法来判定异常值并将其从原始数据中删除。对异常值和缺失值的合理处置大大降低了数据的波动性。在此基础上,论文第四章介绍了一种较新的系统辨识方法—子空间方法。这种方法基于输入输出数据,对模型结构的先验知识需求较少,其算法实现依赖于一些简单可靠的线性代数工具因而在数值计算中具有一定的鲁棒性并且能够较好地适用于高炉冶炼过程等多变量系统。利用子空间方法对第三章的数据处理效果进行验证,结果表明数据处理能够对高炉冶炼的辨识和预测产生较好的效果。
为进一步提高辨识效果,论文第五章基于子空间方法分别对高炉冶炼过程采用Wiener模型和Hammerstein-Wiener模型结构进行辨识。对于Wiener模型辨识,通过对非线性模块的逆函数进行逼近从而显式地得到系统的非线性特性,将多输入单输出非线性问题转化成为一个多输入多输出的模型进行辨识,利用辨识得到的模型对包钢数据进行预测,预测命中率达到81%。对于Hammerstein-Wiener模型,在辨识过程中利用径向基函数良好的逼近能力及其对多变量系统的方便处理分别对Hammerstein非线性和Wiener非线性部分进行逼近,并利用BFGS最优化方法对参数进行优化。利用四种径向基函数:Laplacian径向基函数、Logistic径向基函数、Gaussian径向基函数和薄板样条径向基函数进行建模,结果表明利用薄板样条径向基函数对高炉冶炼过程进行辨识和预测得到的效果更佳,其命中率达到85%。
在探讨了高炉冶炼过程的辨识和预测问题之后,论文的第六章对高炉冶炼过程的控制做进一步的研究。在现行的生产实践中,高炉工长对冶炼过程的控制主要是以专业知识和实践经验为基础的人工控制。由于高炉工长控制水平各不相同,造成了高炉冶炼过程的不稳定。本章针对这个问题,基于子空间方法构造了一种适合于高炉冶炼过程的自适应预测控制方法,提出了一种更为简便的约束处理方法,同时在方法中对各个输入变量调整的优先级进行考虑。结合高炉的实际情况,从实际数据的计算出发得到了保持高炉高产低耗的最佳炉温水平。仿真结果表明,设计的预测控制模型能够有效降低高炉冶炼过程的波动性,而各个输入变量的调整均没有超出约束,这表明预测控制算法的有效性和可行性。此外,这种思路克服了之前预测模型的“预测—控制”模式所带来的“模型悖论问题”,即工长利用了炉温预测信息对高炉行程进行调控后,炉温的发展改变了轨迹,从而与初始预测值产生了偏差的问题。而自适应预测控制方法将静态预测-控制-动态预测结合在一起,整体考虑炉温预测控制问题,因而能达到更好的应用效果。论文第七章对全文的研究内容以及创新点做了归纳,并对课题的后续研究做了展望。
As the pillar industry of national economy, steel industry is among the most energy intensive, while for all the sub-processes in steel industry, blast furnace (BF) ironmaking consumes the largest part of energy. Thus every technological progress in BF ironmaking will bring enormous economic and social benefits. By investigation into the actual situation of BF ironmaking and BF operators? concerns, the current study discussed the identification and predictive control of blast furnace ironmaking with data collected from No. 6 BF at Baotou Steel. The study introduces a new idea for closed-loop control of BF ironmaking and is meaningful both in theory and practice.
In the efforts to achieve closed loop control of BF ironmaking, the crucial problem is prediction and control of silicon content in hot metal, whose complexity is the result of interaction between chemical reaction dynamics and kinetics. An accurate predictive model for silicon content will greatly enhance BF ironmaking, while an effective controller will bring significant benefits. These two problems become the main research efforts in this dissertation. Chapter 2 gave a brief introduction to the blast furnace ironmaking process and some latest development on design of BF expert system. By integration of 4 kinds of models, e.g. mechanism models, inferential models, optimization models and predictive control models a closed loop controller for BF ironmaking is constructed. Chapter 3 dealt with the problem of missing values and outliers in the raw data. For missing values, a C4.5 decision tree based algorithm was adopted by discretizing the missing attribute and good results are achieved. While for the outliers, 4 multivariate outlier detection methods were used and the detected outliers are deleted from the original dataset. The fluctuation of data decreased significantly after processing of missing values and outliers. Chapter 4 introduced a novel method in the theory of system identification- subspace methods and tested the method on data before and after processing. Subspace methods identify system model from input and output data, its algorithm uses some simple and reliable linear algebra methods and is robust and efficient. Its good capacity to deal with multivariate system is very suitable for identification of blast furnace ironmaking process. Simulation experiments were carried out to test the method based on data before and after processing of missing values and outliers. It is shown that processing of missing values and outliers enhances the identification of blast furnace ironmaking process.
To get more accurate models, Chapter 5 identifies the BF ironmaking process based on Wiener model and Hammerstein-Wiener model using subspace methods. For identification of Wiener model, a polynomial function was used to approximate inversion of the nonlinear part of Wiener model. By this technique the multivariate input single output (MISO) nonlinear problem was converted to a multivariate input multivariate output (MIMO) linear system and the identification became simpler. The identified model was then test on data from Baotou Steel and a hit-rate of 81% was achieved. As for the Hammerstein-Wiener model, radial basis functions (RBF) were used to approximate both the Hammerstein and Wiener nonlinearity, a BFGS quasi-Newton method was used to optimize the parameters. Four kinds of RBFs, e.g. Laplacian, Logistic, Gaussian and Thin-plate Spline RBF were tested. Simulation results shown identification using thin-plate spline RBF is the most accurate with the hit-rate of 85%.
After discussion on the identification and prediction problem, Chapter 6 made further research on predictive control of BF ironmaking. Currently, control of BF ironmaking heavily relies on expert experience of operators. However, since different operators have different habits, control of BF ironmaking becomes inconsistent and unstable. To solve this problem, an adaptive predictive control method was constructed based on subspace method. The predictive control method adopts a simpler constraint handling method and priorities of input variables were also taken into consideration. The best level of silicon content was computed from practical data. Simulation results shown that the designed predictive control method can effectively handle the fluctuation of BF ironmaking problem, while the constraints of input variables were not violated. Thus the effectiveness and feasibility of the proposed method was proved. Besides, the adaptive method can overcome the problem of previous predictive models. In practice, the BF operators make control movements based on future information of silicon content obtained through predictive models, which results in deviation between actual and predicted silicon content. The adaptive predictive control method is a combination of static prediction, control and dynamic prediction so that it is capable of handling the overall condition of the ironmaking process. Finally, Chapter 7 gave the conclusion and theoretical innovations in the paper, issues for further research were also investigated.
引文
[1]张玉柱,胡长庆.炼铁节能与工艺计算[M].北京:冶金工业出版社,2002.
[2]张群,邵球军,李岭.论中国钢铁工业发展和循环经济[J].冶金管理,2007(8):38-41.
[3]储满生,尚策,艾名星,沈峰满.高炉炼铁技术的最新进展[J].中国冶金,2006(10):4-8.
[4]Jun-ichiro Yagi,Mathematical modeling of the flow of four fluids in a packed bed[J].ISIJ International,1993(33),6(619-639).
[5]Peter Richard Austin,Hiroshi Nogami and Jun-ichiro Yagi,A mathematical model for blast furnace reaction analysis based on the four fluid model[J].1997(37),8:748-755.
[6]Kouji Takatani,Takanobu Inada,Yutaka Ujisawa,Three dimensional dynamic simulator for blast furnace[J].ISIJ International,1999(39),1(15-22).
[7]储满生,郭宪臻,沈峰满,八木顺一郎.高炉数学模型的进展[J].中国冶金,2007(4):10-17.
[8]Chuanhou Gao,Jiming Chen,Jiusun Zeng,Xueyi Liu,Youxian Sun,A chaos-based iterated multistep predictor for blast furnace ironmaking process[J].AIChE Journal,forthcoming.
[9]Hermann Druckenthaner,Josef Scheidi,Bernhard Schurz,VAI blast furnace automation- a powerful solution for highest production economy[C].IEEE Industry Applications Society Annual Meeting,1997(2182-2186).5(1-6).
[10]马竹梧.高炉专家系统的最新进展[J].世界钢铁,2003(3),
[11]刘祥官,曾九孙,刘芳,蒋美华,高炉炉温闭环智能控制的数学建模[C].A Collection of Theses for Communication,Volume 3,2008.
[12]郜传厚.高炉冶炼过程的混沌动力学研究[D].浙江大学博士论文,2004.
[13]郜传厚,周志敏,邵之江.高炉冶炼过程的混沌性解析[J].物理学报,2005(54),4(1490-1494).
[14]M.S.Phadke,S.M.Wu,Identification of multiinput-multioutput transfer function and noise model of a blast furnace from closed-loop data[J].IEEE Transaction on Automatic Control,1974(19),12(944-951).
[15]H Singh,N.V.1 Sridhar,B.Deo,Artificial neural nets for prediction of silicon content of blast furnace hot metal[J].Steel Research,1996(67),12(521-527).
[16]Matias Wailer,Henrik Saxe磏,On the development of predictive models with application to a metallurgical process[J].Industrial Engineering Chemistry Research,2000(39),4(982-988).
[17]T.Miyano,S.Kimoto,H.Shibuta,K.Nakashima et.al,Time series analysis and predictior on complex dynamical behavior observed in a blast furnace[J].Physica D,2000(135),3-4(305-330).
[18]罗世华.高炉冶炼过程的分形特征辨识及其应用研究[D].浙江大学博士论文,2006.
[19]K.Omori,Blast furnace phenomena and modeling[M].London:Elsevier Applied Science,1987.
[20]毕学工.高炉过程数学模型及计算机控制[M].北京:冶金工业出版社,1996.
[21]J.A.Castro,H.Nogami,J.Yagi,Transient mathematical model of blast furnace based on multi-fluid concept,with application to high PCI operation[J].ISIJ International,2000(40),7(637-646).
[22]P.Sungging,H.Nogami,J.Yagi,Numerical analysis of static holdup of fine particles in blast furnace[J].ISIJ International,2002(42),2(304-309).
[23]M.Chu,H.Nogami,J.Yagi,Numerical analysis on charging carbon composite agglomerates into blast furnace[J].ISIJ International,2004(44),5(510-517).
[24]H.Nogami,M.Chu,J.Yagi,Multi-dimensional transient mathematical simulator of blast furnace process based on multi-fluid and kinetic theories[J].Computers and Chemical Engineering,2005(29),6(2438-2448).
[25]安秋顺,马竹梧.专家系统开发工具发展现状及动向[J].冶金自动化,1995(18),1(8-13).
[26]刘金琨,王树青.高炉专家系统知识的实例学习[J].控制理论与应用,1998(15),6(955-958).
[27]S.M.Pandit,J.A.Clum,S.M.Wu,Modelling,prediction and control of blast furnace operation from observed data by multivariate time series[C].Ironmaking Proceedings,Metallurgical Society of AIME,Iron and Steel Division,1975:34-43.
[28]R.謘termark,Henrik Saxe磏VARMAX-modelling of balst fumace process variables[J].European Journal of Operational Research,1996(90),10(85-101).
[29]Waller M,Sax閚 H,Time-varying event-internal trends in predictive modeling-methods with applications to ladlewise analyses of hot metal silicon content[J].Industrial Engineering Chemistry Research,2003(42),1(85-90).
[30]Jiu-sun Zeng,Chuan-hou Gao,Xiang-guan Liu,Ke-ping Yang,Shi-hua Luo,Using nonlinear GARCH model to predict silicon content in blast furnace hot metal[J].Asian Journal of Control,2008(10),6(1-6).
[31]Tathagata Bhattacharya,Prediction of silicon content in blast furnace hot metal using partial least squares(PLS)[J].ISIJ International,2005(45),12(1943-1945).
[32]刘学艺.基于Bayes网络的高炉炉温[si]预测控制模型研究[D].浙江大学硕士论文,2004.
[33]曾九孙,刘祥官,郜传厚,罗世华.基于隐Markov模型的高炉铁水硅质量分数预测算法[J].浙江大学学报:工学版,2008(42),5(742-746).
[34]Ling Jian,Chuanhou Gao,Lei Li,Jiusun Zeng,Application of least squares support vector machines to predict the silicon content in blast furnace hot metal[J].ISIJ International,2008(48),11(1659-1661).
[35]Jian Chen,A predictive system for blast furnaces by integrating a neural network with qualitative analysis[J].Engineering Applications of Artificial Intelligence,2001(14),1(77-85).
[36]V.R.Radhakrishnan,A.R.Mohamed,Neural networks for the identification and control of blast furnace hot metal quality[J].Journal of Process Control,2000(10),6(509-524).
[37]Juan Jim闁ez,Javier Mocha,Jes.(?)Sainz de Ayala,Faustino Obeso,Blast furnace hot metal temperature prediction through neural networks-based models[J].ISIJ International,2004(44),3(573-580).
[38]F.Pettersson,N.Chakraborti,H.Sax閚,A genetic algorithms based multi-objective neural net applied to noisy blast furnace data[J].Applied Soft Computing,2007(7),1(387-397).
[39]Henrik Saxen,Frank Pettersson and Kiran Gunturu,Evolving nonlinear time series models of the hot metal silicon content in the blast furnace[J].Materials and Manufacturing Processes,2007(22),5(577-584).
[40]Li Qihui,Liu Xiangguan,Fuzzy prediction of silicon content for bf hot metal[J].Journal of Iron and Steel Research,International,2007(12),6(1-4).
[41]Zhao Min,Liu Xiangguan,Luo Shihua,An evolutionary artificial neural networks approach for BF hot metal silicon content prediction based on chaotic analysis[J].Lecture Notes in Computer Science,2005(36),10(572-575).
[42]高小强,郑忠,黄庆周.高炉铁水含硅量和含硫量动力学预报研究[J].钢铁,1995(30),4(10-16).
[43]Chuanhou Gao,Jixin Qian,Evidence of chaotic behavior in noise from industrial process[J].IEEE Transaction on Signal Processing,2007(55),6(2877-2884).
[44]罗世华,刘祥官.高炉铁水含硅量的分形结构分析[J].物理学报,2006(55),7(3343-3348).
[45]Shi-hua Luo,Xiang-guan Liu and Jiu-sun Zeng,Identification of multi-fractal characteristics of silicon content in blast furnace hot metal[J].ISIJ International,2007(47),8(1102-1107).
[46]#12
[47]刘祥官,曾九孙,郝志忠,鹿智勇.多模型集成的高炉炼铁智能控制专家系统[J].浙江大学学报:工学版,2007(41),10(1637-1642).
[48]刘祥官,刘芳.高炉炼铁过程优化与智能控制系统[M].北京:冶金工业出版社,2003.
[49]周传典,徐矩良,刘云彩等.高炉操作的第三代技术[J].炼铁,1998(18),5(53-57).
[50]周传典.高炉炼铁生产技术手册[M].北京:冶金工业出版社,2002.
[51]国家自然科学基金委员会.自动化科学与技术-自然科学学科发展战略调研报告[M].北京:科学出版社,1995.
[52]Wooyoung Lee,Veto W.Weekman Jr.Advanced control practice in the chemical process industry:a view from industry[J].AIChE Journal,2004(22),1(27-38).
[53]Liu Xiang-guan,Zeng Jiu-sun,Zhao Min.Mathematical model and its hybrid dynamic mechanism in intelligent control of blast furnace[J].Journal of Iron and Steel Research,International,2007(14),1:7-11.
[54]R.K.Rajput.Engineering Materials[M].Indian:Chand(S.) & Co.Ltd,2000.
[55]Wang Huai-qing,Zhang Ming-yi,Xu Dong-ming et al.A framework of fuzzy diagnosis[J].IEEE Transaction on Knowledge and Data Engineering,2004(16),12(1571-1582).
[56]刘祥官,罗世华,刘元和,吴晓峰.高炉炼铁过程炉温的非线性混合控制[J].控制理论与应用,2006(23),3(391-396).
[57]Manfred Morari,Jay H.Lee,Model predictive control:past,present and future[J].Computers & Chemical Engineering,1999(23),4-5(667-682).
[58]郝晓静,张苹,王鹏,杜钢.高炉操作参数预处理及相互关系的研究[J].材料与冶金学报,2003(2),4(241-245).
[59]Pierre Wikstram.Data mining analysis of the relationship between input variables and hot metal silicon in a blast furnace[D].Master thesis of Lulea University of Technology,2004.
[60]郭景峰,米浦波,刘国华.基于决策树的数据遗矢值填充方法的研究[J].计算机工程与科学,2002(24),5(9-11).
[61]A Ragel,B Cremilleux.MVC- A preprocessing method to deal with missing values[J].Knowledge-Based Systems,1995(12),5(285-291)
[62]R.J.A.Little,D.B.Rubin.Statistical Analysis with Missing Data,Wiley Series in Probability and Mathematical Statistics[M].New York:Wiley,1987.
[63]M.J.Lukac,M.Marincek.Determination of the EM field rotating mirror Q-switch Error,Glass Laser[C].Proceeding of SPIE,1992;13-20.
[64]D Li,J Deogun,W Spaulding,B Shuart.Towards missing data imputation:a study of fuzzy K-means clustering method[C].LNAI(Lecture Notes in Artificial Intelligence),2004(573-579).
[65]Trivellore E.Raghunathan,James M.Lepkowski,John Van Hoewyk,Peter Solenberger.A Multivariate technique for multiply imputing missing values using a sequence of regression models[J].Survey Methodology,2001(27),1(85-95).
[66]Jiawei Han,Micheline Kamber.Data Mining:Concepts and Techniques,2~(nd) ed.[M].San Francisco:Morgan Kuafmann Publishers,2006.
[67]E.B.Hunt.Concept Learning:An Information Processing Problem.[M]New York:Wiley,1962.
[68]J.R.Quinlan.C4.5:Programs for Machine Learning.[M]San Francisco:Morgan Kuafmann Publishers,1993.
[69]高玉蓉.基于决策树的土地利用现状信息提取研究[D].浙江大学硕士学位论文,2006.
[70]Tom Mitchell.Machine Learning.[M]New York:MacGraw Hill,1997.
[71]R.De Maesschalck,D.Jouan-Rimbaud,D.L.Massart.The Mahalanobis distance[J].Chemometrics and Intelligent Laboratory Systems,2000(50),1(1-18).
[72]L.Daviers,U.Gather.The identification of multiple outliers[J].Journal of the American Statistical Association,1993(88),9(782-792).
[73]K.R.Beebe,R.J.Pell,M.B.Seasholtz.Chemometries A Practical Guide[M].New York:Wiley,1998.
[74]M.Hubert,P.J.Rousseeuw,S.Verboven.A fast method for robust principal components with application to chemometrics.[J]Chemometrics and Intelligent Laboratory Systems,2002(60),1 (101-111).
[75]W.J.Egan,S.L.Morgan.Outlier detection in multivariate analytical chemical data[J].Analytical Chemistry,1998(70),11(2372-2379).
[76]R.K.Pearson.Exploring process data[J].Journal of Process Control,2001(11),2(179-194).
[77]Leo H.Chiang,Randy J.Pell,Mary Beth Seasholtz.Exploring process data with the use of robust outlier detection algorithms[J].Journal of Process Control,2003(13),5(437-449).
[78]刘蓉,陈文亮,徐可欣,邱庆军,崔厚欣.奇异点快速检测在牛奶成分近红外光谱测量中的应用[J].光谱学与光谱分析,2005(25),2(207-210).
[79]Tohru Katayama.Subspace methods for system identification[M].Berlin:Springer,2007.
[80]H.J.Palanthandalam-Madapusi,S.Lacy,J.B.Hoagg,D.S.Bernstein.Subspace based identification for linear and nonlinear systems[C].Proceedings of 2005 American Control Conference,2005(2320-2334).
[8l]李幼凤,苏宏业,褚健.子空间模型辨识方法综述[J].化工学报,2006(57),3(473-479).
[82]W.Larimore.Cannonical variate analysis in identification,filtering and adaptive control[C].Proceedings of the 29~(th) IEEE Conference on Decision and Control,1990:596-604.
[83]M.Verhaegen.Identification of the deterministic part of MIMO state space models given in innovations form from input-out data[J].Automatica,1994(30),1(61-74).
[84]P.Van Overschee,B.de Moor.N4SID subspace algorithms for the identification of combined deterministic- stochastic systems[J].Automatica 1994(30),1(75-93).
[85]P.Van Overschee,B.de Moor.A unifying theorem for three subspace system identification algorithms[C].Proceedings of the 1994 American Contod Conference,1994:1645-1649.
[86]杨华.基于子空间方法的系统辨识及预测控制设计[D].上海交通大学博士学位论文,2007.
[87]Wouter Favoreel,Bart De Moor,Peter Van Overschee.Subspace state space system identification for industrial processes[J].Journal of Process Control,2000(10),4:149-155.
[88]Oscar A.Z.Sotomayor,Song Won Park,Claudio Garcia.Multivariable identification of an activated sludge process with subspace-based algorithms[J].Control Engineering Practice,2003(11),8:961-969.
[89]Wouter Favoreel,Sabine Van Huffel,Bart De Moor,Vasile Sima,Michael Verhaegen.Comparative study between three subspace identification algorithms[C].Proceeding of the 5~(th) European Control Conference,1999.
[90]Frans Verbeyst and Marc Vanden Bossche,The Volterra input-output map of a high frequency amplifier as a practical alternative to load-pull measurements[J].IEEE Transaction on Instrumentation and Measurement,1995(44),3(662-665).
[91]朱豫才著,张湘平,虞水俊、孙志强、胡德文译.过程控制的多变量系统辨识[M].长沙:国防科技大学出版社,2005.
[92]S.Boyd,L.Chua.Fading memory and the problem of approximating nonlinear operators with Volterra series[J].IEEE Transaction on Circuit Systems,1985(32),11(1150-1161).
[93]J.C.Gomez,A.Jutan,E.Baeyens.Wiener model identification and predictive control of a pH neutralization process[J].IEEE Proceedings on Control Theory Application,2004(151),3(329-338).
[94]A.Kalafatis,N.Arfin,L.Wang and W.Cluett.A new approach to the identification of pH processes based on the Wiener model[J].Chemical Engineering Science,1995(50),23(3693-3701).
[95]张艳,李少远,王笑波,周坚刚.基于粒子群优化的Wiener模型辨识与实例研究[J].控制理论与应用,2006(23),6(991-995).
[96]H.Bioemen,C.Chou,T.Van den Boom,M.Verhaegen,T.Backy.Wiener model identification and predictive control for dual composition control of a distillation column[J].Journal of Process Control,2001(11),6(601-620).
[97]W.Greblicki.Nonparametric identification of Wiener systems[J].IEEE Transactions on Information Theory,1992(38),5(1487-1493).
[98]H.F.Chen.Recursive identification for Wiener model with discontinuous piecewise linear function[J].IEEE Transactions on Automatic Control,2006(51),3(390-400).
[99]A.Hagenblad,L.Ljung,A.Wills.Maximum likelihood identification of Wiener models[J].Automatica,2008(44),11(2697-2705).
[100]杨建军,刘民,吴澄.基于遗传算法的非线性模型预测控制方法[J].控制与决策,2003(18),2(141-144).
[101]R.Raich,G.Zhou,M.Viberg.Subspace-based approaches for Wiener system identification [J].IEEE Transaction on Automatic Control,2005(50),10(1629-1634).
[102]M.Verhaegen,D.Westwick.Identifying MIMO Wiener systems using subspace model identification methods [C]. Proceedings of the 34~(th) IEEE Conference on Decision and Control, 1995(4206-4211).
[103] E. W. Bai. An optimal two-stage identification algorithm for Hammerstein-Wiener nonlinear systems [J], Automatica, 1998(34), 3(333-338).
[104] Y.C. Zhu Estimation of an N-L-N Hammerstein-Wiener model [J]. Automatica, 2002(38), 9(1607-1614).
[105] H.C. Park, S. W. Sung, J. Lee Modelling of Hammerstein-Wiener processes with special input test signals [J]. Industrial & Engineering Chemistry Research, 2006(45), 3(1029-1038).
[106] H.J. Palanthandalam-Madapusi, S. Dennis, D. S. Bernstein, A. J. Ridley. Identifying periodically switching block-structured models to predict magnetic-field fluctuations [J]. IEEE Control System Magazine, 2007(27), 10(109-123).
[107] H.J. Palanthandalam-Madapusi, J.B. Hoagg, D.S. Bernstein. Basis-function optimization for subspace based nonlinear identification of systems with measured input nonlinearities [C]. Proceedings of the 2004 American Control Conference, 2004(4788-4793).
[108] I. Goethals, K. Pelckmans, J. Suykens, B. De Moor. Subspace intersection identification of Hammerstein-Wiener systems [C]. Proceedings of the 44~(th) IEEE Conference on Decision and Control, 2005(7108-7113).
[109] M.D. Buhmann, M. J. Ablowitz. Radial basis functions: theory and implementation [M]. Cambridge: Cambridge University Press, 2003.
[110] M. Mathron. Spline and Kriging their formal equivalence. Les Cahiers du Centre de Morphologie Mathematique de Fontainebleau, 1980.
[111] R.L. Hardy. Multiquadric equations of topography and other irregular surfaces [J]. Journal of Geophysics Research, 1971(76), 8(1905-1915).
[112] J. Duchon. Splined minimizing rolation-invariate semi-norms in Sobolev space, constructive theory of functions of several variables [M]. Berlin: Springer-Verlag, 1976.
[113] 吴宗敏. 函数的径向基表示[J]. 数学进展, 1998(27), 3(202-208).
[114] A. Mordecai. Nonlinear Programming: Analysis and Methods [M]. Paris: Courier Dover Publications, 2003.
[115] H. Wendland. Piecewise Polynomials, Positive Definite and Compactly Supported Radial Basis Functions of Minimal Degree [J]. Advances in Computational Mathematics, 1995(5), 4(389-396).
[116] J. B. Rawlings, Tutorial overview of model predictive control [J]. IEEE Control System Magazine, 2000(20), 6 (38-52).
[117] Hiroya Seki, Morimasa Ogawa, Satoshi Ooyama et al., Industrial application of a nonlinear model predictive control to polymerization reactors [J]. Control Engineering Practice, 2001(9), 8(819-828).
[118] Alberto Bemporad, Francesco Borrelli, Manfred Morari, Model predictive control based on linear programming- the explicit solution [J]. IEEE Transaction on Automatic Control, 2002(47): 12(1974-1985).
[119] W. Favoreel, B. De Moor, P. Van Overschee. Model free subspace based LQG design [C]. Proceedings of the American Control Conference, 1999: 3372-3376.
[120] T. Elaine, Hale and S. Joe Qin, Subspace model predictive control and a case study [C]. Proceedings of the American Control Conference, 2002: 4758-4763.
[121] Ramesh Kadali, Biao Huang, Anthony Rossiter, A data driven subspace approach to predictive controller design [J]. Control Engineering Practice, 2003(11), 3 (261-278).
[122] Norhaliza A Wahab, Reza Katebi and Jonas Balderud, Data-driven direct adaptive model based predictive control [C]. Proceedings of the 2008 International Conference on Control, 2008: 181-186.
[123] D.W. Clarke, C. Mohtadi, P.S. Tuffs, Generalized predictive control- Part I. The basic algorithm [J]. Automatica, 1987(23), 2 (137:148).
[124] D.W. Clarke, C. Mohtadi, P.S. Tuffs, Generalized predictive control- Part II. Extensions and interpretations [J]. Automatica, 1987(23), 2 (149:160).
[125] W. Favoreel, B. De Moor, SPC: Subspace predictive control. Technical report 98-49, Katholieke Uniersiteit, Leuven.
[126] David Di Ruscio, Model predictive control and identification: a linear state space model approach [C]. Proceedings of the 36~(th) IEEE conference on Decision and Control, 1997:3203-3207.
[127] David Di Ruscio, Bjarne Foss, On state space model based predictive control [C]. Proceedings of the 5~(th) IFAC Symposium on Dynamics and Control of Process Systems, 1998: 203-210.
[128] Yasuo Niwa, Takashi Sumigama, Akira Maki et.al., Blast furnace operation for low silicon content at Fukuyama No.5 blast furnace [J]. ISIJ International, 1991(31), 5:487:493.
[2]张群,邵球军,李岭.论中国钢铁工业发展和循环经济[J].冶金管理,2007(8):38-41.
[3]储满生,尚策,艾名星,沈峰满.高炉炼铁技术的最新进展[J].中国冶金,2006(10):4-8.
[4]Jun-ichiro Yagi,Mathematical modeling of the flow of four fluids in a packed bed[J].ISIJ International,1993(33),6(619-639).
[5]Peter Richard Austin,Hiroshi Nogami and Jun-ichiro Yagi,A mathematical model for blast furnace reaction analysis based on the four fluid model[J].1997(37),8:748-755.
[6]Kouji Takatani,Takanobu Inada,Yutaka Ujisawa,Three dimensional dynamic simulator for blast furnace[J].ISIJ International,1999(39),1(15-22).
[7]储满生,郭宪臻,沈峰满,八木顺一郎.高炉数学模型的进展[J].中国冶金,2007(4):10-17.
[8]Chuanhou Gao,Jiming Chen,Jiusun Zeng,Xueyi Liu,Youxian Sun,A chaos-based iterated multistep predictor for blast furnace ironmaking process[J].AIChE Journal,forthcoming.
[9]Hermann Druckenthaner,Josef Scheidi,Bernhard Schurz,VAI blast furnace automation- a powerful solution for highest production economy[C].IEEE Industry Applications Society Annual Meeting,1997(2182-2186).5(1-6).
[10]马竹梧.高炉专家系统的最新进展[J].世界钢铁,2003(3),
[11]刘祥官,曾九孙,刘芳,蒋美华,高炉炉温闭环智能控制的数学建模[C].A Collection of Theses for Communication,Volume 3,2008.
[12]郜传厚.高炉冶炼过程的混沌动力学研究[D].浙江大学博士论文,2004.
[13]郜传厚,周志敏,邵之江.高炉冶炼过程的混沌性解析[J].物理学报,2005(54),4(1490-1494).
[14]M.S.Phadke,S.M.Wu,Identification of multiinput-multioutput transfer function and noise model of a blast furnace from closed-loop data[J].IEEE Transaction on Automatic Control,1974(19),12(944-951).
[15]H Singh,N.V.1 Sridhar,B.Deo,Artificial neural nets for prediction of silicon content of blast furnace hot metal[J].Steel Research,1996(67),12(521-527).
[16]Matias Wailer,Henrik Saxe磏,On the development of predictive models with application to a metallurgical process[J].Industrial Engineering Chemistry Research,2000(39),4(982-988).
[17]T.Miyano,S.Kimoto,H.Shibuta,K.Nakashima et.al,Time series analysis and predictior on complex dynamical behavior observed in a blast furnace[J].Physica D,2000(135),3-4(305-330).
[18]罗世华.高炉冶炼过程的分形特征辨识及其应用研究[D].浙江大学博士论文,2006.
[19]K.Omori,Blast furnace phenomena and modeling[M].London:Elsevier Applied Science,1987.
[20]毕学工.高炉过程数学模型及计算机控制[M].北京:冶金工业出版社,1996.
[21]J.A.Castro,H.Nogami,J.Yagi,Transient mathematical model of blast furnace based on multi-fluid concept,with application to high PCI operation[J].ISIJ International,2000(40),7(637-646).
[22]P.Sungging,H.Nogami,J.Yagi,Numerical analysis of static holdup of fine particles in blast furnace[J].ISIJ International,2002(42),2(304-309).
[23]M.Chu,H.Nogami,J.Yagi,Numerical analysis on charging carbon composite agglomerates into blast furnace[J].ISIJ International,2004(44),5(510-517).
[24]H.Nogami,M.Chu,J.Yagi,Multi-dimensional transient mathematical simulator of blast furnace process based on multi-fluid and kinetic theories[J].Computers and Chemical Engineering,2005(29),6(2438-2448).
[25]安秋顺,马竹梧.专家系统开发工具发展现状及动向[J].冶金自动化,1995(18),1(8-13).
[26]刘金琨,王树青.高炉专家系统知识的实例学习[J].控制理论与应用,1998(15),6(955-958).
[27]S.M.Pandit,J.A.Clum,S.M.Wu,Modelling,prediction and control of blast furnace operation from observed data by multivariate time series[C].Ironmaking Proceedings,Metallurgical Society of AIME,Iron and Steel Division,1975:34-43.
[28]R.謘termark,Henrik Saxe磏VARMAX-modelling of balst fumace process variables[J].European Journal of Operational Research,1996(90),10(85-101).
[29]Waller M,Sax閚 H,Time-varying event-internal trends in predictive modeling-methods with applications to ladlewise analyses of hot metal silicon content[J].Industrial Engineering Chemistry Research,2003(42),1(85-90).
[30]Jiu-sun Zeng,Chuan-hou Gao,Xiang-guan Liu,Ke-ping Yang,Shi-hua Luo,Using nonlinear GARCH model to predict silicon content in blast furnace hot metal[J].Asian Journal of Control,2008(10),6(1-6).
[31]Tathagata Bhattacharya,Prediction of silicon content in blast furnace hot metal using partial least squares(PLS)[J].ISIJ International,2005(45),12(1943-1945).
[32]刘学艺.基于Bayes网络的高炉炉温[si]预测控制模型研究[D].浙江大学硕士论文,2004.
[33]曾九孙,刘祥官,郜传厚,罗世华.基于隐Markov模型的高炉铁水硅质量分数预测算法[J].浙江大学学报:工学版,2008(42),5(742-746).
[34]Ling Jian,Chuanhou Gao,Lei Li,Jiusun Zeng,Application of least squares support vector machines to predict the silicon content in blast furnace hot metal[J].ISIJ International,2008(48),11(1659-1661).
[35]Jian Chen,A predictive system for blast furnaces by integrating a neural network with qualitative analysis[J].Engineering Applications of Artificial Intelligence,2001(14),1(77-85).
[36]V.R.Radhakrishnan,A.R.Mohamed,Neural networks for the identification and control of blast furnace hot metal quality[J].Journal of Process Control,2000(10),6(509-524).
[37]Juan Jim闁ez,Javier Mocha,Jes.(?)Sainz de Ayala,Faustino Obeso,Blast furnace hot metal temperature prediction through neural networks-based models[J].ISIJ International,2004(44),3(573-580).
[38]F.Pettersson,N.Chakraborti,H.Sax閚,A genetic algorithms based multi-objective neural net applied to noisy blast furnace data[J].Applied Soft Computing,2007(7),1(387-397).
[39]Henrik Saxen,Frank Pettersson and Kiran Gunturu,Evolving nonlinear time series models of the hot metal silicon content in the blast furnace[J].Materials and Manufacturing Processes,2007(22),5(577-584).
[40]Li Qihui,Liu Xiangguan,Fuzzy prediction of silicon content for bf hot metal[J].Journal of Iron and Steel Research,International,2007(12),6(1-4).
[41]Zhao Min,Liu Xiangguan,Luo Shihua,An evolutionary artificial neural networks approach for BF hot metal silicon content prediction based on chaotic analysis[J].Lecture Notes in Computer Science,2005(36),10(572-575).
[42]高小强,郑忠,黄庆周.高炉铁水含硅量和含硫量动力学预报研究[J].钢铁,1995(30),4(10-16).
[43]Chuanhou Gao,Jixin Qian,Evidence of chaotic behavior in noise from industrial process[J].IEEE Transaction on Signal Processing,2007(55),6(2877-2884).
[44]罗世华,刘祥官.高炉铁水含硅量的分形结构分析[J].物理学报,2006(55),7(3343-3348).
[45]Shi-hua Luo,Xiang-guan Liu and Jiu-sun Zeng,Identification of multi-fractal characteristics of silicon content in blast furnace hot metal[J].ISIJ International,2007(47),8(1102-1107).
[46]#12
[47]刘祥官,曾九孙,郝志忠,鹿智勇.多模型集成的高炉炼铁智能控制专家系统[J].浙江大学学报:工学版,2007(41),10(1637-1642).
[48]刘祥官,刘芳.高炉炼铁过程优化与智能控制系统[M].北京:冶金工业出版社,2003.
[49]周传典,徐矩良,刘云彩等.高炉操作的第三代技术[J].炼铁,1998(18),5(53-57).
[50]周传典.高炉炼铁生产技术手册[M].北京:冶金工业出版社,2002.
[51]国家自然科学基金委员会.自动化科学与技术-自然科学学科发展战略调研报告[M].北京:科学出版社,1995.
[52]Wooyoung Lee,Veto W.Weekman Jr.Advanced control practice in the chemical process industry:a view from industry[J].AIChE Journal,2004(22),1(27-38).
[53]Liu Xiang-guan,Zeng Jiu-sun,Zhao Min.Mathematical model and its hybrid dynamic mechanism in intelligent control of blast furnace[J].Journal of Iron and Steel Research,International,2007(14),1:7-11.
[54]R.K.Rajput.Engineering Materials[M].Indian:Chand(S.) & Co.Ltd,2000.
[55]Wang Huai-qing,Zhang Ming-yi,Xu Dong-ming et al.A framework of fuzzy diagnosis[J].IEEE Transaction on Knowledge and Data Engineering,2004(16),12(1571-1582).
[56]刘祥官,罗世华,刘元和,吴晓峰.高炉炼铁过程炉温的非线性混合控制[J].控制理论与应用,2006(23),3(391-396).
[57]Manfred Morari,Jay H.Lee,Model predictive control:past,present and future[J].Computers & Chemical Engineering,1999(23),4-5(667-682).
[58]郝晓静,张苹,王鹏,杜钢.高炉操作参数预处理及相互关系的研究[J].材料与冶金学报,2003(2),4(241-245).
[59]Pierre Wikstram.Data mining analysis of the relationship between input variables and hot metal silicon in a blast furnace[D].Master thesis of Lulea University of Technology,2004.
[60]郭景峰,米浦波,刘国华.基于决策树的数据遗矢值填充方法的研究[J].计算机工程与科学,2002(24),5(9-11).
[61]A Ragel,B Cremilleux.MVC- A preprocessing method to deal with missing values[J].Knowledge-Based Systems,1995(12),5(285-291)
[62]R.J.A.Little,D.B.Rubin.Statistical Analysis with Missing Data,Wiley Series in Probability and Mathematical Statistics[M].New York:Wiley,1987.
[63]M.J.Lukac,M.Marincek.Determination of the EM field rotating mirror Q-switch Error,Glass Laser[C].Proceeding of SPIE,1992;13-20.
[64]D Li,J Deogun,W Spaulding,B Shuart.Towards missing data imputation:a study of fuzzy K-means clustering method[C].LNAI(Lecture Notes in Artificial Intelligence),2004(573-579).
[65]Trivellore E.Raghunathan,James M.Lepkowski,John Van Hoewyk,Peter Solenberger.A Multivariate technique for multiply imputing missing values using a sequence of regression models[J].Survey Methodology,2001(27),1(85-95).
[66]Jiawei Han,Micheline Kamber.Data Mining:Concepts and Techniques,2~(nd) ed.[M].San Francisco:Morgan Kuafmann Publishers,2006.
[67]E.B.Hunt.Concept Learning:An Information Processing Problem.[M]New York:Wiley,1962.
[68]J.R.Quinlan.C4.5:Programs for Machine Learning.[M]San Francisco:Morgan Kuafmann Publishers,1993.
[69]高玉蓉.基于决策树的土地利用现状信息提取研究[D].浙江大学硕士学位论文,2006.
[70]Tom Mitchell.Machine Learning.[M]New York:MacGraw Hill,1997.
[71]R.De Maesschalck,D.Jouan-Rimbaud,D.L.Massart.The Mahalanobis distance[J].Chemometrics and Intelligent Laboratory Systems,2000(50),1(1-18).
[72]L.Daviers,U.Gather.The identification of multiple outliers[J].Journal of the American Statistical Association,1993(88),9(782-792).
[73]K.R.Beebe,R.J.Pell,M.B.Seasholtz.Chemometries A Practical Guide[M].New York:Wiley,1998.
[74]M.Hubert,P.J.Rousseeuw,S.Verboven.A fast method for robust principal components with application to chemometrics.[J]Chemometrics and Intelligent Laboratory Systems,2002(60),1 (101-111).
[75]W.J.Egan,S.L.Morgan.Outlier detection in multivariate analytical chemical data[J].Analytical Chemistry,1998(70),11(2372-2379).
[76]R.K.Pearson.Exploring process data[J].Journal of Process Control,2001(11),2(179-194).
[77]Leo H.Chiang,Randy J.Pell,Mary Beth Seasholtz.Exploring process data with the use of robust outlier detection algorithms[J].Journal of Process Control,2003(13),5(437-449).
[78]刘蓉,陈文亮,徐可欣,邱庆军,崔厚欣.奇异点快速检测在牛奶成分近红外光谱测量中的应用[J].光谱学与光谱分析,2005(25),2(207-210).
[79]Tohru Katayama.Subspace methods for system identification[M].Berlin:Springer,2007.
[80]H.J.Palanthandalam-Madapusi,S.Lacy,J.B.Hoagg,D.S.Bernstein.Subspace based identification for linear and nonlinear systems[C].Proceedings of 2005 American Control Conference,2005(2320-2334).
[8l]李幼凤,苏宏业,褚健.子空间模型辨识方法综述[J].化工学报,2006(57),3(473-479).
[82]W.Larimore.Cannonical variate analysis in identification,filtering and adaptive control[C].Proceedings of the 29~(th) IEEE Conference on Decision and Control,1990:596-604.
[83]M.Verhaegen.Identification of the deterministic part of MIMO state space models given in innovations form from input-out data[J].Automatica,1994(30),1(61-74).
[84]P.Van Overschee,B.de Moor.N4SID subspace algorithms for the identification of combined deterministic- stochastic systems[J].Automatica 1994(30),1(75-93).
[85]P.Van Overschee,B.de Moor.A unifying theorem for three subspace system identification algorithms[C].Proceedings of the 1994 American Contod Conference,1994:1645-1649.
[86]杨华.基于子空间方法的系统辨识及预测控制设计[D].上海交通大学博士学位论文,2007.
[87]Wouter Favoreel,Bart De Moor,Peter Van Overschee.Subspace state space system identification for industrial processes[J].Journal of Process Control,2000(10),4:149-155.
[88]Oscar A.Z.Sotomayor,Song Won Park,Claudio Garcia.Multivariable identification of an activated sludge process with subspace-based algorithms[J].Control Engineering Practice,2003(11),8:961-969.
[89]Wouter Favoreel,Sabine Van Huffel,Bart De Moor,Vasile Sima,Michael Verhaegen.Comparative study between three subspace identification algorithms[C].Proceeding of the 5~(th) European Control Conference,1999.
[90]Frans Verbeyst and Marc Vanden Bossche,The Volterra input-output map of a high frequency amplifier as a practical alternative to load-pull measurements[J].IEEE Transaction on Instrumentation and Measurement,1995(44),3(662-665).
[91]朱豫才著,张湘平,虞水俊、孙志强、胡德文译.过程控制的多变量系统辨识[M].长沙:国防科技大学出版社,2005.
[92]S.Boyd,L.Chua.Fading memory and the problem of approximating nonlinear operators with Volterra series[J].IEEE Transaction on Circuit Systems,1985(32),11(1150-1161).
[93]J.C.Gomez,A.Jutan,E.Baeyens.Wiener model identification and predictive control of a pH neutralization process[J].IEEE Proceedings on Control Theory Application,2004(151),3(329-338).
[94]A.Kalafatis,N.Arfin,L.Wang and W.Cluett.A new approach to the identification of pH processes based on the Wiener model[J].Chemical Engineering Science,1995(50),23(3693-3701).
[95]张艳,李少远,王笑波,周坚刚.基于粒子群优化的Wiener模型辨识与实例研究[J].控制理论与应用,2006(23),6(991-995).
[96]H.Bioemen,C.Chou,T.Van den Boom,M.Verhaegen,T.Backy.Wiener model identification and predictive control for dual composition control of a distillation column[J].Journal of Process Control,2001(11),6(601-620).
[97]W.Greblicki.Nonparametric identification of Wiener systems[J].IEEE Transactions on Information Theory,1992(38),5(1487-1493).
[98]H.F.Chen.Recursive identification for Wiener model with discontinuous piecewise linear function[J].IEEE Transactions on Automatic Control,2006(51),3(390-400).
[99]A.Hagenblad,L.Ljung,A.Wills.Maximum likelihood identification of Wiener models[J].Automatica,2008(44),11(2697-2705).
[100]杨建军,刘民,吴澄.基于遗传算法的非线性模型预测控制方法[J].控制与决策,2003(18),2(141-144).
[101]R.Raich,G.Zhou,M.Viberg.Subspace-based approaches for Wiener system identification [J].IEEE Transaction on Automatic Control,2005(50),10(1629-1634).
[102]M.Verhaegen,D.Westwick.Identifying MIMO Wiener systems using subspace model identification methods [C]. Proceedings of the 34~(th) IEEE Conference on Decision and Control, 1995(4206-4211).
[103] E. W. Bai. An optimal two-stage identification algorithm for Hammerstein-Wiener nonlinear systems [J], Automatica, 1998(34), 3(333-338).
[104] Y.C. Zhu Estimation of an N-L-N Hammerstein-Wiener model [J]. Automatica, 2002(38), 9(1607-1614).
[105] H.C. Park, S. W. Sung, J. Lee Modelling of Hammerstein-Wiener processes with special input test signals [J]. Industrial & Engineering Chemistry Research, 2006(45), 3(1029-1038).
[106] H.J. Palanthandalam-Madapusi, S. Dennis, D. S. Bernstein, A. J. Ridley. Identifying periodically switching block-structured models to predict magnetic-field fluctuations [J]. IEEE Control System Magazine, 2007(27), 10(109-123).
[107] H.J. Palanthandalam-Madapusi, J.B. Hoagg, D.S. Bernstein. Basis-function optimization for subspace based nonlinear identification of systems with measured input nonlinearities [C]. Proceedings of the 2004 American Control Conference, 2004(4788-4793).
[108] I. Goethals, K. Pelckmans, J. Suykens, B. De Moor. Subspace intersection identification of Hammerstein-Wiener systems [C]. Proceedings of the 44~(th) IEEE Conference on Decision and Control, 2005(7108-7113).
[109] M.D. Buhmann, M. J. Ablowitz. Radial basis functions: theory and implementation [M]. Cambridge: Cambridge University Press, 2003.
[110] M. Mathron. Spline and Kriging their formal equivalence. Les Cahiers du Centre de Morphologie Mathematique de Fontainebleau, 1980.
[111] R.L. Hardy. Multiquadric equations of topography and other irregular surfaces [J]. Journal of Geophysics Research, 1971(76), 8(1905-1915).
[112] J. Duchon. Splined minimizing rolation-invariate semi-norms in Sobolev space, constructive theory of functions of several variables [M]. Berlin: Springer-Verlag, 1976.
[113] 吴宗敏. 函数的径向基表示[J]. 数学进展, 1998(27), 3(202-208).
[114] A. Mordecai. Nonlinear Programming: Analysis and Methods [M]. Paris: Courier Dover Publications, 2003.
[115] H. Wendland. Piecewise Polynomials, Positive Definite and Compactly Supported Radial Basis Functions of Minimal Degree [J]. Advances in Computational Mathematics, 1995(5), 4(389-396).
[116] J. B. Rawlings, Tutorial overview of model predictive control [J]. IEEE Control System Magazine, 2000(20), 6 (38-52).
[117] Hiroya Seki, Morimasa Ogawa, Satoshi Ooyama et al., Industrial application of a nonlinear model predictive control to polymerization reactors [J]. Control Engineering Practice, 2001(9), 8(819-828).
[118] Alberto Bemporad, Francesco Borrelli, Manfred Morari, Model predictive control based on linear programming- the explicit solution [J]. IEEE Transaction on Automatic Control, 2002(47): 12(1974-1985).
[119] W. Favoreel, B. De Moor, P. Van Overschee. Model free subspace based LQG design [C]. Proceedings of the American Control Conference, 1999: 3372-3376.
[120] T. Elaine, Hale and S. Joe Qin, Subspace model predictive control and a case study [C]. Proceedings of the American Control Conference, 2002: 4758-4763.
[121] Ramesh Kadali, Biao Huang, Anthony Rossiter, A data driven subspace approach to predictive controller design [J]. Control Engineering Practice, 2003(11), 3 (261-278).
[122] Norhaliza A Wahab, Reza Katebi and Jonas Balderud, Data-driven direct adaptive model based predictive control [C]. Proceedings of the 2008 International Conference on Control, 2008: 181-186.
[123] D.W. Clarke, C. Mohtadi, P.S. Tuffs, Generalized predictive control- Part I. The basic algorithm [J]. Automatica, 1987(23), 2 (137:148).
[124] D.W. Clarke, C. Mohtadi, P.S. Tuffs, Generalized predictive control- Part II. Extensions and interpretations [J]. Automatica, 1987(23), 2 (149:160).
[125] W. Favoreel, B. De Moor, SPC: Subspace predictive control. Technical report 98-49, Katholieke Uniersiteit, Leuven.
[126] David Di Ruscio, Model predictive control and identification: a linear state space model approach [C]. Proceedings of the 36~(th) IEEE conference on Decision and Control, 1997:3203-3207.
[127] David Di Ruscio, Bjarne Foss, On state space model based predictive control [C]. Proceedings of the 5~(th) IFAC Symposium on Dynamics and Control of Process Systems, 1998: 203-210.
[128] Yasuo Niwa, Takashi Sumigama, Akira Maki et.al., Blast furnace operation for low silicon content at Fukuyama No.5 blast furnace [J]. ISIJ International, 1991(31), 5:487:493.