基于混合模型的软测量方法研究及其在发酵过程中的应用
|
摘要
软测量技术是解决复杂测量任务、实现难测变量在线估计的有效方法，生物量是发酵过程中的重要过程参数之一，生物量在线测量对发酵工程的优化和控制具有重要意义，是典型的复杂测量对象。微生物发酵过程具有非线性、时变性、高维数、非结构化等特点，并且缺乏对生物过程机理的先验知识和相对有限的实验测量数据，研究软测量技术的理论、推动软测量技术在生物工程中的应用具有广泛的工程应用前景，是亟待解决的重要研究课题。
传统软测量技术的主要内容之一是对象建模，目前的建模方法主要有基于机理分析的“白箱”模型，基于统计学习的“黑箱”模型，以及这两种模型的简单结合构成的“灰箱”模型。“白箱”模型在理论处理上进行了简化，适应性差，且很多未知微生物反应过程根本无法直接建模：“黑箱”模型没有有效地利用对象先验知识：而目前“灰箱”模型的结构存在很大的随意性，无法保证模型的有效性。本课题抓住这一前沿研究，从经验知识与经验数据的综合利用入手，对软测量模型的结构、模型构建方法以及软测量系统的关键技术进行深入研究。具有重要的理论意义和应用价值。
课题主要从软测量模型结构、软测量统计建模、软测量系统滤波三个方面进行深入的理论研究，并对软测量系统的实现技术进行仿真实验研究。
论文从广义信息论的角度对软测量技术进行了讨论，提出一种混合软测量模型结构。混合软测量模型能够充分地利用先验知识和实验数据的全部信息，构建出完整的软测量模型，并且该软测量模型具备与多种知识表达方式进行融合的能力。课题细致深入地讨论和研究了软测量模型的三个基本问题，首先是软测量模型的可实现性，即软测量模型存在唯一解的条件，以及知识利用的度量等一些相关的概念，体现出混合软测量模型在知识利用有效性上的优势；然后对模型不确定性的概念进行了讨论，研究了模型可靠性问题，得出测量精度与软测量模型可靠性之间的关系；最后讨论了软测量模型与传统软测量方法的关系，说明软测量模型是传统软测量方法的发展。
在统计建模方面，集中研究基于统计学习理论的支持向量机技术。从全新的思考角度建立了支持向量分类和支持向量回归的统一表达形式，并重点研究了数据中包含噪声干扰时的支持向量回归问题，提出了两种误差加权支持向量机，试验说明使用加权法考虑不同取值范围内的噪声分布情况，可以获得更好的回归结果。最后，针对模一支持向量机重新推导了多乘子优化算法，并针对模二支持向量机引入了一种改进的Gilbert几何算法，成功地将其用于支持向量回归问题。
在软测量系统的研究中，主要研究基于混合软测量模型的Kalman滤波器技术。论文重新考虑滤波器对模型的鲁棒性问题，研究了一类鲁棒Kalman滤波器，并证明强跟踪滤波器只是一种鲁棒Kalman滤波器的实现。进而提出一种全新的不敏变换鲁棒Kalman滤波器算法，采用不敏变换方法来处理期望和方差的非线性传播问题，并利用新息序列方差阵中所包含的大量模型摄动误差信息，通过补偿使得非线性系统的一步估计更加准确。最后，将该滤波算法应用于混合软测量模型，给出了完整的软测量系统，并将基于混合软测量模型构建的软测量系统应用于微生物发酵过程中生物量的测量，以Matlab形式实现了完整的软测量系统。
仿真实验表明：基于误差加权的支持向量机算法具有较好的回归结果；基于不敏变换的鲁棒Kalman滤波器具有更好的滤波性能，对初值和模型都具有很强的鲁棒性；在知识缺失和数据缺失的情况下，基于混合模型的软测量系统能够充分地利用先验知识和数据，能够得到更可靠的测量估计。
论文提出的软测量混合建模方法和所构建的软测量系统，能够充分地利用被测系统和被测变量的先验知识，充分地利用已有的实验数据，为实现微生物发酵过程中难测变量和参数的在线测量提供理论支撑，并为软测量系统的实用化提供了一种实现技术。
Soft-sensor technology is a kind of valid method to solve complex measuring tasks. Especially in bioengineering, the measuring tasks have the characteristics of non-linear, time-variant, high-dimension, unstructured model, ignorance of principle mechanism, and scarcity of experimental data, etc. This makes it a very important job to restudy and extend the soft-sensor techniques.
Currently, there are no clear definitions for soft-sensor technology, and it is considered to solve the primary problems of modeling and identifying. One method called "white-box" modeling just gather the most important process mathematical relations, another method called "black-box" modeling only approximates the process outside behavior. The mixed modeling method attempts to take advantage of the above two methods, but the selection of secondary variables and model structure is haphazard. The research of hybrid modeling method, which could make the most of prior knowledge and experimental data, has great value in theoretics and engineering.
In this dissertation, the research focuses on three aspects, includes modeling structure, learning machine and filtering technique.
Firstly, the soft-sensor concept is discussed from the view of generalized information theory, and a novel hybrid model structure is proposed in this paper. The hybrid model is a combination of non-linear algebraic equation group and differential or difference equation group, and possesses the ability to integrate equations in inhomogeneous expression form. Three essential problems are studied in chapter two. The first is the unique existence condition of model root, and some relative concepts such as the amount of knowledge utility, etc. The second is the relationship between measuring accuracy and model reliability, which is analyzed from the view of error theory by introducing model uncertainty concept. The third is the expression capability of some kinds of traditional soft-sensor models.
Support vector machine method is a fine realization of statistical learning theory, some kinds of statistical modeling methods based on the support vector machine technique are researched. After theoretic analyzing support vector machine technique, the equipollence of support vector classification and regression problems is proofed, and a uniformed expression of support vector machine problem is gotten. The noise stained case is studied emphatically, and the experiment shows that a better result will be obtained by assigning weight factor to fit noise distribute characteristic. A multi-multiplier minimal optimization algorithm for norm-1 problems is deduced, and a kind of improved Gilbert geometric algorithm for norm-2 problems is introduced, which is applied in regression problems successfully.
After the research of filtering techniques, the filter based on hybrid soft-sensor model is presented. By considering the filter robustness on modal, a kind of robust Kalman filter is studied. The proof shows that the innovation covariance matrix contains the information of model perturbation, and the one-step linear prediction of non-linear model could be more precise after compensation. The strong tracking filter proposed in current reference is a moderate implementation. A novel algorithm, unscented transformation robust Kalman filter, which use the unscented transformation to calculate the non-linear transform expectation and covariance is developed. Further, applying the improved Kalman filter to the hybrid model, a complete soft-sensor system is presented.
At the experimentation part, the soft-sensor system implemented in Matlab program is put into the practice of biomass estimation in fermentation process. There are three main objectives. The first is to approve the better regression result based on weighted support vector machine. The second is to approve the robustness of unscented transformation robust Kalman filter on initial value and model perturbation, and to validate the new filter provided better performance. The third is to approve the validity of the presented hybrid model under the condition of uncertainty in prior knowledge or imprecision in experiment data.
This dissertation proposes a theoretically perfect and practically convenience hybrid soft-sensor model and the method to construct the soft-sensor system based on it. This system avoids the adverse effects, and can improve the measuring accuracy, precision and reliability. It greatly improves the validity of the utility of the prior knowledge and experiment of the target system and primary variables, and can be applied effectively in complex measuring tasks.
传统软测量技术的主要内容之一是对象建模，目前的建模方法主要有基于机理分析的“白箱”模型，基于统计学习的“黑箱”模型，以及这两种模型的简单结合构成的“灰箱”模型。“白箱”模型在理论处理上进行了简化，适应性差，且很多未知微生物反应过程根本无法直接建模：“黑箱”模型没有有效地利用对象先验知识：而目前“灰箱”模型的结构存在很大的随意性，无法保证模型的有效性。本课题抓住这一前沿研究，从经验知识与经验数据的综合利用入手，对软测量模型的结构、模型构建方法以及软测量系统的关键技术进行深入研究。具有重要的理论意义和应用价值。
课题主要从软测量模型结构、软测量统计建模、软测量系统滤波三个方面进行深入的理论研究，并对软测量系统的实现技术进行仿真实验研究。
论文从广义信息论的角度对软测量技术进行了讨论，提出一种混合软测量模型结构。混合软测量模型能够充分地利用先验知识和实验数据的全部信息，构建出完整的软测量模型，并且该软测量模型具备与多种知识表达方式进行融合的能力。课题细致深入地讨论和研究了软测量模型的三个基本问题，首先是软测量模型的可实现性，即软测量模型存在唯一解的条件，以及知识利用的度量等一些相关的概念，体现出混合软测量模型在知识利用有效性上的优势；然后对模型不确定性的概念进行了讨论，研究了模型可靠性问题，得出测量精度与软测量模型可靠性之间的关系；最后讨论了软测量模型与传统软测量方法的关系，说明软测量模型是传统软测量方法的发展。
在统计建模方面，集中研究基于统计学习理论的支持向量机技术。从全新的思考角度建立了支持向量分类和支持向量回归的统一表达形式，并重点研究了数据中包含噪声干扰时的支持向量回归问题，提出了两种误差加权支持向量机，试验说明使用加权法考虑不同取值范围内的噪声分布情况，可以获得更好的回归结果。最后，针对模一支持向量机重新推导了多乘子优化算法，并针对模二支持向量机引入了一种改进的Gilbert几何算法，成功地将其用于支持向量回归问题。
在软测量系统的研究中，主要研究基于混合软测量模型的Kalman滤波器技术。论文重新考虑滤波器对模型的鲁棒性问题，研究了一类鲁棒Kalman滤波器，并证明强跟踪滤波器只是一种鲁棒Kalman滤波器的实现。进而提出一种全新的不敏变换鲁棒Kalman滤波器算法，采用不敏变换方法来处理期望和方差的非线性传播问题，并利用新息序列方差阵中所包含的大量模型摄动误差信息，通过补偿使得非线性系统的一步估计更加准确。最后，将该滤波算法应用于混合软测量模型，给出了完整的软测量系统，并将基于混合软测量模型构建的软测量系统应用于微生物发酵过程中生物量的测量，以Matlab形式实现了完整的软测量系统。
仿真实验表明：基于误差加权的支持向量机算法具有较好的回归结果；基于不敏变换的鲁棒Kalman滤波器具有更好的滤波性能，对初值和模型都具有很强的鲁棒性；在知识缺失和数据缺失的情况下，基于混合模型的软测量系统能够充分地利用先验知识和数据，能够得到更可靠的测量估计。
论文提出的软测量混合建模方法和所构建的软测量系统，能够充分地利用被测系统和被测变量的先验知识，充分地利用已有的实验数据，为实现微生物发酵过程中难测变量和参数的在线测量提供理论支撑，并为软测量系统的实用化提供了一种实现技术。
Soft-sensor technology is a kind of valid method to solve complex measuring tasks. Especially in bioengineering, the measuring tasks have the characteristics of non-linear, time-variant, high-dimension, unstructured model, ignorance of principle mechanism, and scarcity of experimental data, etc. This makes it a very important job to restudy and extend the soft-sensor techniques.
Currently, there are no clear definitions for soft-sensor technology, and it is considered to solve the primary problems of modeling and identifying. One method called "white-box" modeling just gather the most important process mathematical relations, another method called "black-box" modeling only approximates the process outside behavior. The mixed modeling method attempts to take advantage of the above two methods, but the selection of secondary variables and model structure is haphazard. The research of hybrid modeling method, which could make the most of prior knowledge and experimental data, has great value in theoretics and engineering.
In this dissertation, the research focuses on three aspects, includes modeling structure, learning machine and filtering technique.
Firstly, the soft-sensor concept is discussed from the view of generalized information theory, and a novel hybrid model structure is proposed in this paper. The hybrid model is a combination of non-linear algebraic equation group and differential or difference equation group, and possesses the ability to integrate equations in inhomogeneous expression form. Three essential problems are studied in chapter two. The first is the unique existence condition of model root, and some relative concepts such as the amount of knowledge utility, etc. The second is the relationship between measuring accuracy and model reliability, which is analyzed from the view of error theory by introducing model uncertainty concept. The third is the expression capability of some kinds of traditional soft-sensor models.
Support vector machine method is a fine realization of statistical learning theory, some kinds of statistical modeling methods based on the support vector machine technique are researched. After theoretic analyzing support vector machine technique, the equipollence of support vector classification and regression problems is proofed, and a uniformed expression of support vector machine problem is gotten. The noise stained case is studied emphatically, and the experiment shows that a better result will be obtained by assigning weight factor to fit noise distribute characteristic. A multi-multiplier minimal optimization algorithm for norm-1 problems is deduced, and a kind of improved Gilbert geometric algorithm for norm-2 problems is introduced, which is applied in regression problems successfully.
After the research of filtering techniques, the filter based on hybrid soft-sensor model is presented. By considering the filter robustness on modal, a kind of robust Kalman filter is studied. The proof shows that the innovation covariance matrix contains the information of model perturbation, and the one-step linear prediction of non-linear model could be more precise after compensation. The strong tracking filter proposed in current reference is a moderate implementation. A novel algorithm, unscented transformation robust Kalman filter, which use the unscented transformation to calculate the non-linear transform expectation and covariance is developed. Further, applying the improved Kalman filter to the hybrid model, a complete soft-sensor system is presented.
At the experimentation part, the soft-sensor system implemented in Matlab program is put into the practice of biomass estimation in fermentation process. There are three main objectives. The first is to approve the better regression result based on weighted support vector machine. The second is to approve the robustness of unscented transformation robust Kalman filter on initial value and model perturbation, and to validate the new filter provided better performance. The third is to approve the validity of the presented hybrid model under the condition of uncertainty in prior knowledge or imprecision in experiment data.
This dissertation proposes a theoretically perfect and practically convenience hybrid soft-sensor model and the method to construct the soft-sensor system based on it. This system avoids the adverse effects, and can improve the measuring accuracy, precision and reliability. It greatly improves the validity of the utility of the prior knowledge and experiment of the target system and primary variables, and can be applied effectively in complex measuring tasks.
引文
[1]De Assis A.J.,Filho R.M..Soft Sensors Development for On-line Bioreactor State Estimation [J].Computers and Chemical Engineering,2000,24:1099-1103.
[2]Brosilow C.B..Inferential Control of Process Control [J].AIChE Journal,1978,24(3):475-484.
[3]Brosilow C.B..The Structure and Dynamics of Inferential Control System [J]. AIChEJournal,1978,24(3):485-499.
[4]韩大伟，邹志云．软测量与推断技术初探[J]．南京理工大学学报(自然科学版)，2005，29(1)：206-210．
[5]刘瑞兰，陈渭泉，苏宏业．基于改进GA-PLS算法的最优辅助变量选择及其在软测量建模中的应用[J]．南京邮电大学学报(自然科学版)，2006，26(1)：76-86．
[6]Komives C.,Parker R.S..Bioreactor State Estimation and Control [J].Current Opinion in Biotechnology,2003,14:468-474.
[7]Olsson L.,Nielson J..On-Line and in Situ Monitoring of Biomass in Submerged Cultivations [J].Trends in Biotechnology,1997,15..517-522.
[8]王贻俊，樊育，Olsson L.，Nielson J．．生物量浓度实时在线检测方法的研究[J]．生物化学与生物物理进展，2000，27(4)：387-390．
[9]王武，吕霞付．超声波在生物发酵工程中的应用[J]．无锡轻工大学学报，2002，2l(3)：322-326．
[10]Tatiraju S.,Soroush M.,Mutharasan R..Multi-Rate Nonlinear State and Parameter Estimation in a Bioreactor [J].Biotechnology and Bioengineering,1999,63:22-32.
[11]Chae H.J.,DeLisa M.E,Cha H.J.,Weigand W.A.,Rao G.,Bentley W.E..Framework for Online Optimization of Recombinant Protein Expression in High-Cell-Density Escherichia Coli Cultures Using GFP-Fusion Monitoring [J].Biotechnology and Bioengineering,2000,69:275-285.
[12]Yuan Z.G.,Bogaert H.,Devisscher M.,Vanrolleghem P.,Verstraete W..On-Line Estimation of the Maximum Specific Growth Rate of Nitrifiers in Activated Sludge Systems [J]. Biotechnology and Bioengineering, 1999, 65: 265-273.
[13] Pinchuk R.J., Brown W.A., Hughes S.M., Cooper D.G.. Modeling of Biological Processes Using Self-Cycling Fermentation and Genetic Algorithms [J]. Biotechnology and Bioengineering, 2000, 67: 19-24.
[14] Nilsson A., Taherzadeh G., Liden G.. On-line Estimation of Sugar Concentration for Control of Fed-Batch Fermentation of Lignocellulosic Hydrolyzates by Saccharomyces Cerevisiae [J]. Bioprocess and Biosystems Engineering, 2002, 25: 183-191.
[15] Schuegerl K.. Progress in Monitoring, Modeling and Control of Bioprocesses During the Last 20 Years [J]. Journal of Biotechnology, 2001, 85: 149-173.
[16] Ferreira L.S., De Souza M.B., Trierweiler J.O., Broxtermann O., Folly R.O.M., Hitzmann B.. Aspects Concerning the Use of Biosensors for Process Control: Experimental and Simulation Investigations [J]. Computer and Chemical Engineering, 2003, 27: 1165-1173.
[17] Lubenova V.. On-line Estimation of Biomass Concentration and Non-stationary Parameters for Aerobic Bioprocesses [J]. Journal of Biotechnology, 1996, 46: 197-207.
[18] Beluhan D., Gosak D., Pavlovic N., Vampola M.. Biomass Estimation and Optimal Control of the Baker's Yeast Fermentation Process [J]. Computers and Chemical Engineering, 1995, 19: S387-S392.
[19] Takiguchi N., Shimizu H., Shioya S.. An On-line Physiological State Recognition System for the Lysine Fermentation Process Based on a Metabolic Reaction Model [J]. Biotechnology and Bioengineering, 1997, 55: 170-182.
[20] Woo S.H., Park J.M., Rittmann B.E.. Evaluation of the Interaction Between Biodegradation and Sorption of Phenanthrene in Soil-Slurry Systems [J]. Biotecnology and Bioengineering, 2001, 73: 12-24.
[21] Zupke C., Stephanopoulos G. Intracellular Flux Analysis in Hybridomas Using Mass Balances and in Vitro 13C NMR [J]. Biotechnology and Bioengineering, 1995, 45: 292-303.
[22] El Massaoudi M., Spelthahn J., Drysch A., De GraafA., Takors R.. Production Process Monitoring by Serial Mapping of Microbial Carbon Flux Distributions Using a Novel Sensor Reactor Approach: I-Sensor Reactor System [J]. Metabology Engineering, 2003, 5: 86-95.
[23] Drysch A., El Massaoudi M., Mack C., Takors R., De Graaf A., Sahm H.. Production Process Monitoring by Serial Mapping of Microbial Carbon Flux Distributions Using a Novel Sensor Reactor Approach: Ⅱ-13C-Labeling-Based Metabolic Flux Analysis and L-Lysine Production [J]. MetabologyEngineering, 2003, 5: 96-107.
[24] Sainz J., Pizarro F., Perez-Correa R., Agosin E.. Modeling of Yeast Metabolism and Process Dynamics in Batch Fermentation [J]. Biotechnology and Bioengineering, 2002, 81: 818-828.
[25] Herwig C., Marison I., Von Stockar U.. On-Line Stoichiometry and Identification of Metabolic State under Dynamic Process Conditions [J]. Biotechnology and Bioengineering, 2001, 75: 345-354.
[26] Wang N., Stephanopoulos G.. Application of Macroscopic Balances to the Measurement of Gross Measurement Errors [J]. Biotechnology and Bioengineering, 1983, 25: 2177-2208.
[27] Mahadevan R., Edwards J., Doyle F.. Dynamic Flux Balance Analysis of Diauxic Growth in Escherichia Coli [J]. Biophysics Journal, 2002, 83: 1331-1340.
[28] Lennox B., Montague G.A., Hiden H.G., Kornfeld G., Goulding P.R.. Process Monitoring of an Industrial Fed-Batch Fermentation [J]. Biotechnology and Bioengineering, 2001, 74: 125-135.
[29] Wilson J.A., Zorzetto L.F.M.. A Generalised Approach to Process State Estimation Using Hybrid Artificial Neural Network/Mechanistic Model [J]. Computers and Chemical Engineering, 1997, 21: 951-963.
[30] Te Braake H., Babuska R., Van Can E., Hellinga C.. Predictive Control in Biotechnology Using Fuzzy and Neural Models [A]. In: Van Impe J.F.M., Vanrolleghem E, Iserentant D.. Advanced Instrumentation, Data Interpretation, and Control of Biotechnological Processes [C]. Kluwer Academic Publishers, 2000, 437-464.
[31] Bhowmik U.Kr., Saha G., Barua A., Sinha S.. On-Line Detection of Contamination in a Bioprocess Using Artificial Neural Networks [J]. Chemical Engineering and Technology, 2000, 23(6): 543-549.
[32] Shene C., Diez C., Bravo S.. Neural Networks for the Prediction of the State of Zymomonas Mobilis CP4 Batch Fermentations [J]. Computers and Chemical Engineering, 1999, 23: 1097-1108.
[33] Van Can H.J.L., Te Braake H.A.B., Bijman A., Hellinga C., Luyben K.Ch.A.M., Heijnen J.J.. An Efficient Model Development Strategy for Bioprocesses Based on Neural Networks in Macroscopic Balances [Part Ⅱ] [J]. Biotechnology and Bioengineering, 1999, 62: 666-680.
[34] Prasad Y.J., Bhagwat S.S.. Simple Neural Network Models for Prediction of Physical Properties of Organic Compounds [J]. Chemical Engineering and Technology, 2002, 25: 1041-1046.
[35] Bachinger Th., Martensson P., Mandenius C.-F.. Estimation of Biomass and Specific Growth Rate in a Recombinant Escherichia coli Batch Cultivation Process Using a Chemical Multisensor Array [J]. Journal of Biotechnology, 1998, 60: 55-66.
[36] Glassey J., IgnovaM., Ward A.C., Montague G.A., Morris A.J.. Bioprocess Supervision: Neural Networks and Knowledge Based Systems [J]. Journal of Biotechnology, 1997, 52: 201-205.
[37] Cimander C., Carlsson M., Mandenius C.-F.. Sensor Fusion for On-line Monitoring of Yoghurt Fermentation [J]. Journal of Biotechnology, 2002, 99: 237-248.
[38] Ronen M., Shabtai Y., Guteman H.. Hybrid Model Building Methodology Using Unsupervised Fuzzy Clustering and Supervised Neural Networks [J]. Biotechnology and Bioengineering, 2002, 77: 420-429.
[39] Rallo R., Ferre-Gine J., Arenas A., Giralt F.. Neural Virtual Sensor for the Inferential Prediction of Product Quality From Process Variables [J]. Computers and Chemical Engineering, 2002, 26: 1735-1754.
[40] Fu P.-C., Barford J.P.. A Hybrid Neural Network-First Principles Approach for Modelling of Cell Metabolism [J]. Computers and Chemical Engineering, 1996, 20: 951-958.
[41] Dacosta P., Kordich C., Williams D., Gomm J.B.. Estimation of Inaccessible Fermentation States With Variable Inoculum Sizes [J]. Artificial Intelligence in Engineering, 1997, (11): 383-392.
[42] Ignova M., Montague G.A., Ward A.C., Glassey J.. Fermentation Seed Quality Analysis With Self-Organising Neural Networks [J]. Biotechnology and Bioengineering, 1999, 64: 82-91.
[43] Valdez-Castro L., Baruch I., Barrera-Cortes J.. Neural Networks Applied to the Prediction of Fed-Batch Fermentation Kinetics of Bacillus Thuringiensis [J]. Bioprocess and Biosystems Engineering, 2003, 25: 229-233.
[44]Buckland B.,Fermentation Exhaust Gas Analysis Using Mass Spectrometry [J],Bio/Technology,1985,3:982-988.
[45]Gerigk M.,Bujnicki R,Ganpo-Nkwenkwa E.,Bongaerts J.,Sprenger G.,Takors R..Process Control for Enhanced L-Phenylalanine Production Using Different Recombinant Escherichia Colt Strains [J].Biotechnology and Bioengineering,2002,80:747-754.
[46]Wu L.,Lance H.,Van Gulik W.,Heijnen J..Determination of in Vivo Oxygen Uptake and Carbon Dioxide Evolution Rates from Off-Gas Measurments under Highly Dynamic Conditions [J].Biotechnology and Bioengineering,2002,81:449-458.
[47]James S.,Legge R.,Budman H..Comparative Study of Black-box and Hybrid Estimation Methods in Fed-batch Fermentation [J].Journal of Process Control,2002,(12):113-121.
[48]汪永生，邵惠鹤．微生物生长过程中菌体浓度的软测量[J]．无锡轻工大学学报，2000，19(5)：491-494．
[49]乔晓艳，贾莲风，RBF神经网络在菌体细胞浓度软测量中的应用[J]，计算机工程与设计，2003，24(3)：55-57．
[50]Zhong W.M.,Pi D.Y.,Sun Y.X..SVM Based Soft Sensor for Antibiotic Fermentation Process [A].In:IEEE 2003 International Conference of Systems,Man and Cybermetics [C].Washington D.C.,2003,160-165.
[51]冯瑞，宋春林，张艳珠，邵惠鹤．基于支持向量机与RBF神经网络的软测量模型比较研究[J]．上海交通大学学报，2003，37(增刊)：122-125．
[52]阎威武，朱宏栋，邵惠鹤．基于最小二乘支持向量机的软测量建模[J]．系统仿真学报，2003，15(10)：1494-1496．
[53] 罗健旭，张兆宁，邵惠鹤．应用基于粗集的模糊神经网络进行软测量建模的研究[J]．化工自动化及仪表，2003，30(2)：14-18．
[54]冯瑞，张浩然，邵惠鹤．基于SVM的软测量建模[J]．信息与控制，2002，31(6)：567-571．
[55]Echegaray O.E,Carvalho J.C.M.,Femandes A.N.R.,Sato S.,Aquarone E.,Vitolo M..Fed-Batch Culture of Sacchoromyces Cerevisiae in Sugar-Cane Blackstrap Molasses:Invertase Activity of Intact Cells in Ethanol Fermentation [J].BiomassandBioenergy, 2000,19:39-50.
[56]Gu Z.R.,Lain L.H.,Prasad S.D..Feature Correlation Method for Enhancing Fermentation Development:A Comparison of Quadratic Regression with Artificial Neural Networks [J].Computers and Chemical Engineering,1996,20:S407-S412.
[57]Georgiev Tz.,Ratkov AI.,Tzonkov St..Mathematical Modelling of Fed-Batch Fermentation Processes for Amino Acid Production [J].Mathematics and Computers in Simulation,1997,44:271-285.
[58]Warnes M.R.,Glassey J.,Montague G.A.,Kara B..On Data-Based Modelling Techniques for Fermentation Processes [J].Process Biochemistry,1996,31:147-155.
[59]Fellner M.,Delgado A.,Becker T..Functional Nodes in Dynamic Neural Networks for Bioprocess Modeling [J].Bioprocess and Biosystems Engineering,2003,25:263-270.
[60]Kurtz T.,Fellner M.,Becker T.,Delgado A..Observation and Control of the Beer Fermentation Using Cognitive Methods [J].Journal of Instruments Brewing,2000,107:241-252.
[61]KordonA.K.,Smits G.F.,Jordaan E.,Rightor E..Robust Soft Sensors Based on Integration of Genetic Programming, Analytical Neural Networks,and Support Vector Machines [A].In:Proceedings of WCCI 2002 [C].Honolulu:IEEEPress,2002,896-901.
[62]Zorzetto L.F.M.,Filho R.Maciel,Wolf-Maciel M.R..Process Modelling Development Through Artificial Neural Networks and Hybrid Models [J].Computers and Chemical Engineering,2000,24:1355-1360.
[63]Lee D.S.,Jeon C.O.,Park J.M.,Chang K.S..Hybrid Neural Network Modeling of a Full-Scale Industrial Wastewater Treatment Process [J].Biotechnology and Bioengineering,2002,78:670-682.
[64]Hagedom A.,Legge R.L.,Budman H..Evaluation of Spectrofluorometry as a Tool for Estimation in Fed-batch Fermentations [J].Biotechnology and Bioengineering,2003,83:104-111.
[65]王建林，于涛．发酵过程生物量软测量技术的研究进展．现代化工，2005，25(6)：22-25．
[66]Cover T.M.,Thomas J.A..Elements of Information Theory,2nd Edition [M].New York:John Wiley& Sons,2006.
[67]肖明耀．误差理论与应用[M]．北京：计量出版社，1985．
[68]Sydenham EH.,Thom R..Handbook of Measurement Science [M].New York:John Wiley & Sons,1991.
[69]Cochran W.G.Sampling Techniques,3rd Edition [M].New York:John Wiley &Sons,1977.
[70]Russell S.,Norvig P..Artificial Intelligence:A Modern Approach,Second Edition [M].New Jersey:Prentice Hall,2003.
[71]Nilsson N.J..Artificial Intelligence:A New Synthesis [M].San Fransisco:Morgan Kaufmann,1998.
[72]Vapnik V.N..Estimation of Dependences Based on Empirical Data [M].New York:Springer-Verlag,1982.
[73]Vapnik V.N..The Nature of Statistical Learning Theory [M].New York:Springer,1995.
[74]Vapnik V.N..Statistical Learning Theory [M].New York:Wiley,1998.
[75]邓乃扬，田英杰．数据挖掘中的新方法——支持向量机[M]．北京：科学出版社，2004．
[76]Wang J.L.,Yu T..On-line Estimation of Biomass in Fermentation Process Using Support Vector Machine. Chinese Journal of Chemical Engineering,2006,14(3):383-388.
[77]Osuna E.,Freund R.,Girosi F..Improved Training Algoritym for Support Vector Machines [A].In:Proceedings oflEEE NNSP'97 [C].Amelia Island,1997,276-285.
[78]Platt J.C..Sequential Minimal Optimization:A Fast Algorithm for Training Support Vector Machines [R].Microsoft Research Technical Report MSR-TR-98-14,1998.
[79]Keerthi S.S.,Shevade S.K.,Bhattacharyya C..Improvements to Platt's SMO Algorithm for SVM Classifier Design [J].Neural Computation,2001,13(3):637-649.
[80]Bennett K.P.,Bredensteiner E.J..Duality and Geometry in SVM Classifiers [A].In:Proceedings of the 17th International Conference on Machine Learning [C].2000,57-64.
[81]Keerthi S.S.,Shevade S.K.,Bhattacharyya C.,Murthy K.R.K.. A Fast Iterative Nearest Point Algorithm for Support Vector Machine Classifier Design [J].IEEETransNeuralNetworks,2000,11(1):124-136.
[82]Crisp D.J.,Burges C.J.C..A Geometric Interpretation of v-SVM Classifiers.NIPS,2000.
[83]Dai L.L.,Huang H.Y.,Chen Z.X..Ternary Sequential Analytic Optimization Algorithm for SVM Class Design [J].Asian Journal of Information Technology,2005,4(3):2-8.
[84]业宁，孙瑞祥，董逸生．多拉格朗日乘子协同优化的SVM快速学习算法研究[J]．计算机研究与发展，2006，43(3)：442-448．
[85]业宁，孙瑞祥，董逸生．MLSVM4——一种多乘子协同优化的SVM快速学习算法[J]．计算机研究与发展，2005，42(9)：1467-1471．
[86]Martin S..Techniques in Support Vector Classification [D].Fort Collins: Colorado State University,2001.
[87]Gilbert E.G..An Iterative Procedure for Computing the Minimum of a Quadratic Form on a Convex Set [J].SIAM Journal on Control,4(1):61-79.
[88]Haykin S..Adaptive Filter Theory,4th Edition [M].New Jersey:Prentice Hall,2002.
[89]Xie X.Q.,Zhou D.H.Jin Y.H..Strong Tracking Filter Based Adaptive Generic Model Control [J].Joumal of Process Control,1999,(9):337-350.
[90]文成林，周东华．多尺度估计理论及其应用[M]．北京：清华大学出版社，2002．
[91]范文兵，张素贞．带未知时变噪声的非线性系统卡尔曼滤波器算法研究[J]．华东理工大学学报，2003，29(3)：299-302．
[92]Wan E.A.,Van der Merwe R..The Unscented Kalman Filter for Nonlinear Estimation [A].In:Proceedings of Symposium 2000 on Adaptive Systems for Signal Processing,Communication and Control (AS-SPCC) [C].IEEE,Lake Louise,2000.
[93]Julier S.J.,Uhlmann J.K..A New Extension of the Kalman Filter to Nonlinear Systems [A].In: Proceedings of AeroSense: The 11th International Symposium on Aerosoace/Defence Sensing,Simulation and Control [C].1997.
[94]黄象鼎．非线性数值分析的理论与方法[M]．武汉：武汉大学出版社，2004．
[95]山根恒夫．生物反応工学(第3版)(M]．東京：産業(?)書，2003．
[96]Nielsen J.,Villadsen J.,Liden G..Bioreaction Engineering Principles,Second Edition [M].New York:KluwerAcademic/PlenumPublishers,2002.
[97]朱启忠．生物化学[M]．北京：化学工业出版社，2006．
[98]Lee S.H..Application of Tendency Modeling to State Estimation of Fermentation Processes [D]. Benthlehem: Lehigh University, 1997.
[99] Shimizu H., Araki K., Shioya S., Suga K.. Optimal production of glutathione by controlling the specific growth rate of yeast in fed-batch culture [J]. Biotechnology and Bioengineering, 1991, 38: 196-205.
[100] Sonnleitner B., Kappeli O.. Growth of Saccharomyces cerevisiae is Controlled by its Limited Respiratory Capacity: Formulation and Verification of a Hypothesis[J]. Biotechnology and Bioengineering, 1986, 28- 927-937.
[2]Brosilow C.B..Inferential Control of Process Control [J].AIChE Journal,1978,24(3):475-484.
[3]Brosilow C.B..The Structure and Dynamics of Inferential Control System [J]. AIChEJournal,1978,24(3):485-499.
[4]韩大伟，邹志云．软测量与推断技术初探[J]．南京理工大学学报(自然科学版)，2005，29(1)：206-210．
[5]刘瑞兰，陈渭泉，苏宏业．基于改进GA-PLS算法的最优辅助变量选择及其在软测量建模中的应用[J]．南京邮电大学学报(自然科学版)，2006，26(1)：76-86．
[6]Komives C.,Parker R.S..Bioreactor State Estimation and Control [J].Current Opinion in Biotechnology,2003,14:468-474.
[7]Olsson L.,Nielson J..On-Line and in Situ Monitoring of Biomass in Submerged Cultivations [J].Trends in Biotechnology,1997,15..517-522.
[8]王贻俊，樊育，Olsson L.，Nielson J．．生物量浓度实时在线检测方法的研究[J]．生物化学与生物物理进展，2000，27(4)：387-390．
[9]王武，吕霞付．超声波在生物发酵工程中的应用[J]．无锡轻工大学学报，2002，2l(3)：322-326．
[10]Tatiraju S.,Soroush M.,Mutharasan R..Multi-Rate Nonlinear State and Parameter Estimation in a Bioreactor [J].Biotechnology and Bioengineering,1999,63:22-32.
[11]Chae H.J.,DeLisa M.E,Cha H.J.,Weigand W.A.,Rao G.,Bentley W.E..Framework for Online Optimization of Recombinant Protein Expression in High-Cell-Density Escherichia Coli Cultures Using GFP-Fusion Monitoring [J].Biotechnology and Bioengineering,2000,69:275-285.
[12]Yuan Z.G.,Bogaert H.,Devisscher M.,Vanrolleghem P.,Verstraete W..On-Line Estimation of the Maximum Specific Growth Rate of Nitrifiers in Activated Sludge Systems [J]. Biotechnology and Bioengineering, 1999, 65: 265-273.
[13] Pinchuk R.J., Brown W.A., Hughes S.M., Cooper D.G.. Modeling of Biological Processes Using Self-Cycling Fermentation and Genetic Algorithms [J]. Biotechnology and Bioengineering, 2000, 67: 19-24.
[14] Nilsson A., Taherzadeh G., Liden G.. On-line Estimation of Sugar Concentration for Control of Fed-Batch Fermentation of Lignocellulosic Hydrolyzates by Saccharomyces Cerevisiae [J]. Bioprocess and Biosystems Engineering, 2002, 25: 183-191.
[15] Schuegerl K.. Progress in Monitoring, Modeling and Control of Bioprocesses During the Last 20 Years [J]. Journal of Biotechnology, 2001, 85: 149-173.
[16] Ferreira L.S., De Souza M.B., Trierweiler J.O., Broxtermann O., Folly R.O.M., Hitzmann B.. Aspects Concerning the Use of Biosensors for Process Control: Experimental and Simulation Investigations [J]. Computer and Chemical Engineering, 2003, 27: 1165-1173.
[17] Lubenova V.. On-line Estimation of Biomass Concentration and Non-stationary Parameters for Aerobic Bioprocesses [J]. Journal of Biotechnology, 1996, 46: 197-207.
[18] Beluhan D., Gosak D., Pavlovic N., Vampola M.. Biomass Estimation and Optimal Control of the Baker's Yeast Fermentation Process [J]. Computers and Chemical Engineering, 1995, 19: S387-S392.
[19] Takiguchi N., Shimizu H., Shioya S.. An On-line Physiological State Recognition System for the Lysine Fermentation Process Based on a Metabolic Reaction Model [J]. Biotechnology and Bioengineering, 1997, 55: 170-182.
[20] Woo S.H., Park J.M., Rittmann B.E.. Evaluation of the Interaction Between Biodegradation and Sorption of Phenanthrene in Soil-Slurry Systems [J]. Biotecnology and Bioengineering, 2001, 73: 12-24.
[21] Zupke C., Stephanopoulos G. Intracellular Flux Analysis in Hybridomas Using Mass Balances and in Vitro 13C NMR [J]. Biotechnology and Bioengineering, 1995, 45: 292-303.
[22] El Massaoudi M., Spelthahn J., Drysch A., De GraafA., Takors R.. Production Process Monitoring by Serial Mapping of Microbial Carbon Flux Distributions Using a Novel Sensor Reactor Approach: I-Sensor Reactor System [J]. Metabology Engineering, 2003, 5: 86-95.
[23] Drysch A., El Massaoudi M., Mack C., Takors R., De Graaf A., Sahm H.. Production Process Monitoring by Serial Mapping of Microbial Carbon Flux Distributions Using a Novel Sensor Reactor Approach: Ⅱ-13C-Labeling-Based Metabolic Flux Analysis and L-Lysine Production [J]. MetabologyEngineering, 2003, 5: 96-107.
[24] Sainz J., Pizarro F., Perez-Correa R., Agosin E.. Modeling of Yeast Metabolism and Process Dynamics in Batch Fermentation [J]. Biotechnology and Bioengineering, 2002, 81: 818-828.
[25] Herwig C., Marison I., Von Stockar U.. On-Line Stoichiometry and Identification of Metabolic State under Dynamic Process Conditions [J]. Biotechnology and Bioengineering, 2001, 75: 345-354.
[26] Wang N., Stephanopoulos G.. Application of Macroscopic Balances to the Measurement of Gross Measurement Errors [J]. Biotechnology and Bioengineering, 1983, 25: 2177-2208.
[27] Mahadevan R., Edwards J., Doyle F.. Dynamic Flux Balance Analysis of Diauxic Growth in Escherichia Coli [J]. Biophysics Journal, 2002, 83: 1331-1340.
[28] Lennox B., Montague G.A., Hiden H.G., Kornfeld G., Goulding P.R.. Process Monitoring of an Industrial Fed-Batch Fermentation [J]. Biotechnology and Bioengineering, 2001, 74: 125-135.
[29] Wilson J.A., Zorzetto L.F.M.. A Generalised Approach to Process State Estimation Using Hybrid Artificial Neural Network/Mechanistic Model [J]. Computers and Chemical Engineering, 1997, 21: 951-963.
[30] Te Braake H., Babuska R., Van Can E., Hellinga C.. Predictive Control in Biotechnology Using Fuzzy and Neural Models [A]. In: Van Impe J.F.M., Vanrolleghem E, Iserentant D.. Advanced Instrumentation, Data Interpretation, and Control of Biotechnological Processes [C]. Kluwer Academic Publishers, 2000, 437-464.
[31] Bhowmik U.Kr., Saha G., Barua A., Sinha S.. On-Line Detection of Contamination in a Bioprocess Using Artificial Neural Networks [J]. Chemical Engineering and Technology, 2000, 23(6): 543-549.
[32] Shene C., Diez C., Bravo S.. Neural Networks for the Prediction of the State of Zymomonas Mobilis CP4 Batch Fermentations [J]. Computers and Chemical Engineering, 1999, 23: 1097-1108.
[33] Van Can H.J.L., Te Braake H.A.B., Bijman A., Hellinga C., Luyben K.Ch.A.M., Heijnen J.J.. An Efficient Model Development Strategy for Bioprocesses Based on Neural Networks in Macroscopic Balances [Part Ⅱ] [J]. Biotechnology and Bioengineering, 1999, 62: 666-680.
[34] Prasad Y.J., Bhagwat S.S.. Simple Neural Network Models for Prediction of Physical Properties of Organic Compounds [J]. Chemical Engineering and Technology, 2002, 25: 1041-1046.
[35] Bachinger Th., Martensson P., Mandenius C.-F.. Estimation of Biomass and Specific Growth Rate in a Recombinant Escherichia coli Batch Cultivation Process Using a Chemical Multisensor Array [J]. Journal of Biotechnology, 1998, 60: 55-66.
[36] Glassey J., IgnovaM., Ward A.C., Montague G.A., Morris A.J.. Bioprocess Supervision: Neural Networks and Knowledge Based Systems [J]. Journal of Biotechnology, 1997, 52: 201-205.
[37] Cimander C., Carlsson M., Mandenius C.-F.. Sensor Fusion for On-line Monitoring of Yoghurt Fermentation [J]. Journal of Biotechnology, 2002, 99: 237-248.
[38] Ronen M., Shabtai Y., Guteman H.. Hybrid Model Building Methodology Using Unsupervised Fuzzy Clustering and Supervised Neural Networks [J]. Biotechnology and Bioengineering, 2002, 77: 420-429.
[39] Rallo R., Ferre-Gine J., Arenas A., Giralt F.. Neural Virtual Sensor for the Inferential Prediction of Product Quality From Process Variables [J]. Computers and Chemical Engineering, 2002, 26: 1735-1754.
[40] Fu P.-C., Barford J.P.. A Hybrid Neural Network-First Principles Approach for Modelling of Cell Metabolism [J]. Computers and Chemical Engineering, 1996, 20: 951-958.
[41] Dacosta P., Kordich C., Williams D., Gomm J.B.. Estimation of Inaccessible Fermentation States With Variable Inoculum Sizes [J]. Artificial Intelligence in Engineering, 1997, (11): 383-392.
[42] Ignova M., Montague G.A., Ward A.C., Glassey J.. Fermentation Seed Quality Analysis With Self-Organising Neural Networks [J]. Biotechnology and Bioengineering, 1999, 64: 82-91.
[43] Valdez-Castro L., Baruch I., Barrera-Cortes J.. Neural Networks Applied to the Prediction of Fed-Batch Fermentation Kinetics of Bacillus Thuringiensis [J]. Bioprocess and Biosystems Engineering, 2003, 25: 229-233.
[44]Buckland B.,Fermentation Exhaust Gas Analysis Using Mass Spectrometry [J],Bio/Technology,1985,3:982-988.
[45]Gerigk M.,Bujnicki R,Ganpo-Nkwenkwa E.,Bongaerts J.,Sprenger G.,Takors R..Process Control for Enhanced L-Phenylalanine Production Using Different Recombinant Escherichia Colt Strains [J].Biotechnology and Bioengineering,2002,80:747-754.
[46]Wu L.,Lance H.,Van Gulik W.,Heijnen J..Determination of in Vivo Oxygen Uptake and Carbon Dioxide Evolution Rates from Off-Gas Measurments under Highly Dynamic Conditions [J].Biotechnology and Bioengineering,2002,81:449-458.
[47]James S.,Legge R.,Budman H..Comparative Study of Black-box and Hybrid Estimation Methods in Fed-batch Fermentation [J].Journal of Process Control,2002,(12):113-121.
[48]汪永生，邵惠鹤．微生物生长过程中菌体浓度的软测量[J]．无锡轻工大学学报，2000，19(5)：491-494．
[49]乔晓艳，贾莲风，RBF神经网络在菌体细胞浓度软测量中的应用[J]，计算机工程与设计，2003，24(3)：55-57．
[50]Zhong W.M.,Pi D.Y.,Sun Y.X..SVM Based Soft Sensor for Antibiotic Fermentation Process [A].In:IEEE 2003 International Conference of Systems,Man and Cybermetics [C].Washington D.C.,2003,160-165.
[51]冯瑞，宋春林，张艳珠，邵惠鹤．基于支持向量机与RBF神经网络的软测量模型比较研究[J]．上海交通大学学报，2003，37(增刊)：122-125．
[52]阎威武，朱宏栋，邵惠鹤．基于最小二乘支持向量机的软测量建模[J]．系统仿真学报，2003，15(10)：1494-1496．
[53] 罗健旭，张兆宁，邵惠鹤．应用基于粗集的模糊神经网络进行软测量建模的研究[J]．化工自动化及仪表，2003，30(2)：14-18．
[54]冯瑞，张浩然，邵惠鹤．基于SVM的软测量建模[J]．信息与控制，2002，31(6)：567-571．
[55]Echegaray O.E,Carvalho J.C.M.,Femandes A.N.R.,Sato S.,Aquarone E.,Vitolo M..Fed-Batch Culture of Sacchoromyces Cerevisiae in Sugar-Cane Blackstrap Molasses:Invertase Activity of Intact Cells in Ethanol Fermentation [J].BiomassandBioenergy, 2000,19:39-50.
[56]Gu Z.R.,Lain L.H.,Prasad S.D..Feature Correlation Method for Enhancing Fermentation Development:A Comparison of Quadratic Regression with Artificial Neural Networks [J].Computers and Chemical Engineering,1996,20:S407-S412.
[57]Georgiev Tz.,Ratkov AI.,Tzonkov St..Mathematical Modelling of Fed-Batch Fermentation Processes for Amino Acid Production [J].Mathematics and Computers in Simulation,1997,44:271-285.
[58]Warnes M.R.,Glassey J.,Montague G.A.,Kara B..On Data-Based Modelling Techniques for Fermentation Processes [J].Process Biochemistry,1996,31:147-155.
[59]Fellner M.,Delgado A.,Becker T..Functional Nodes in Dynamic Neural Networks for Bioprocess Modeling [J].Bioprocess and Biosystems Engineering,2003,25:263-270.
[60]Kurtz T.,Fellner M.,Becker T.,Delgado A..Observation and Control of the Beer Fermentation Using Cognitive Methods [J].Journal of Instruments Brewing,2000,107:241-252.
[61]KordonA.K.,Smits G.F.,Jordaan E.,Rightor E..Robust Soft Sensors Based on Integration of Genetic Programming, Analytical Neural Networks,and Support Vector Machines [A].In:Proceedings of WCCI 2002 [C].Honolulu:IEEEPress,2002,896-901.
[62]Zorzetto L.F.M.,Filho R.Maciel,Wolf-Maciel M.R..Process Modelling Development Through Artificial Neural Networks and Hybrid Models [J].Computers and Chemical Engineering,2000,24:1355-1360.
[63]Lee D.S.,Jeon C.O.,Park J.M.,Chang K.S..Hybrid Neural Network Modeling of a Full-Scale Industrial Wastewater Treatment Process [J].Biotechnology and Bioengineering,2002,78:670-682.
[64]Hagedom A.,Legge R.L.,Budman H..Evaluation of Spectrofluorometry as a Tool for Estimation in Fed-batch Fermentations [J].Biotechnology and Bioengineering,2003,83:104-111.
[65]王建林，于涛．发酵过程生物量软测量技术的研究进展．现代化工，2005，25(6)：22-25．
[66]Cover T.M.,Thomas J.A..Elements of Information Theory,2nd Edition [M].New York:John Wiley& Sons,2006.
[67]肖明耀．误差理论与应用[M]．北京：计量出版社，1985．
[68]Sydenham EH.,Thom R..Handbook of Measurement Science [M].New York:John Wiley & Sons,1991.
[69]Cochran W.G.Sampling Techniques,3rd Edition [M].New York:John Wiley &Sons,1977.
[70]Russell S.,Norvig P..Artificial Intelligence:A Modern Approach,Second Edition [M].New Jersey:Prentice Hall,2003.
[71]Nilsson N.J..Artificial Intelligence:A New Synthesis [M].San Fransisco:Morgan Kaufmann,1998.
[72]Vapnik V.N..Estimation of Dependences Based on Empirical Data [M].New York:Springer-Verlag,1982.
[73]Vapnik V.N..The Nature of Statistical Learning Theory [M].New York:Springer,1995.
[74]Vapnik V.N..Statistical Learning Theory [M].New York:Wiley,1998.
[75]邓乃扬，田英杰．数据挖掘中的新方法——支持向量机[M]．北京：科学出版社，2004．
[76]Wang J.L.,Yu T..On-line Estimation of Biomass in Fermentation Process Using Support Vector Machine. Chinese Journal of Chemical Engineering,2006,14(3):383-388.
[77]Osuna E.,Freund R.,Girosi F..Improved Training Algoritym for Support Vector Machines [A].In:Proceedings oflEEE NNSP'97 [C].Amelia Island,1997,276-285.
[78]Platt J.C..Sequential Minimal Optimization:A Fast Algorithm for Training Support Vector Machines [R].Microsoft Research Technical Report MSR-TR-98-14,1998.
[79]Keerthi S.S.,Shevade S.K.,Bhattacharyya C..Improvements to Platt's SMO Algorithm for SVM Classifier Design [J].Neural Computation,2001,13(3):637-649.
[80]Bennett K.P.,Bredensteiner E.J..Duality and Geometry in SVM Classifiers [A].In:Proceedings of the 17th International Conference on Machine Learning [C].2000,57-64.
[81]Keerthi S.S.,Shevade S.K.,Bhattacharyya C.,Murthy K.R.K.. A Fast Iterative Nearest Point Algorithm for Support Vector Machine Classifier Design [J].IEEETransNeuralNetworks,2000,11(1):124-136.
[82]Crisp D.J.,Burges C.J.C..A Geometric Interpretation of v-SVM Classifiers.NIPS,2000.
[83]Dai L.L.,Huang H.Y.,Chen Z.X..Ternary Sequential Analytic Optimization Algorithm for SVM Class Design [J].Asian Journal of Information Technology,2005,4(3):2-8.
[84]业宁，孙瑞祥，董逸生．多拉格朗日乘子协同优化的SVM快速学习算法研究[J]．计算机研究与发展，2006，43(3)：442-448．
[85]业宁，孙瑞祥，董逸生．MLSVM4——一种多乘子协同优化的SVM快速学习算法[J]．计算机研究与发展，2005，42(9)：1467-1471．
[86]Martin S..Techniques in Support Vector Classification [D].Fort Collins: Colorado State University,2001.
[87]Gilbert E.G..An Iterative Procedure for Computing the Minimum of a Quadratic Form on a Convex Set [J].SIAM Journal on Control,4(1):61-79.
[88]Haykin S..Adaptive Filter Theory,4th Edition [M].New Jersey:Prentice Hall,2002.
[89]Xie X.Q.,Zhou D.H.Jin Y.H..Strong Tracking Filter Based Adaptive Generic Model Control [J].Joumal of Process Control,1999,(9):337-350.
[90]文成林，周东华．多尺度估计理论及其应用[M]．北京：清华大学出版社，2002．
[91]范文兵，张素贞．带未知时变噪声的非线性系统卡尔曼滤波器算法研究[J]．华东理工大学学报，2003，29(3)：299-302．
[92]Wan E.A.,Van der Merwe R..The Unscented Kalman Filter for Nonlinear Estimation [A].In:Proceedings of Symposium 2000 on Adaptive Systems for Signal Processing,Communication and Control (AS-SPCC) [C].IEEE,Lake Louise,2000.
[93]Julier S.J.,Uhlmann J.K..A New Extension of the Kalman Filter to Nonlinear Systems [A].In: Proceedings of AeroSense: The 11th International Symposium on Aerosoace/Defence Sensing,Simulation and Control [C].1997.
[94]黄象鼎．非线性数值分析的理论与方法[M]．武汉：武汉大学出版社，2004．
[95]山根恒夫．生物反応工学(第3版)(M]．東京：産業(?)書，2003．
[96]Nielsen J.,Villadsen J.,Liden G..Bioreaction Engineering Principles,Second Edition [M].New York:KluwerAcademic/PlenumPublishers,2002.
[97]朱启忠．生物化学[M]．北京：化学工业出版社，2006．
[98]Lee S.H..Application of Tendency Modeling to State Estimation of Fermentation Processes [D]. Benthlehem: Lehigh University, 1997.
[99] Shimizu H., Araki K., Shioya S., Suga K.. Optimal production of glutathione by controlling the specific growth rate of yeast in fed-batch culture [J]. Biotechnology and Bioengineering, 1991, 38: 196-205.
[100] Sonnleitner B., Kappeli O.. Growth of Saccharomyces cerevisiae is Controlled by its Limited Respiratory Capacity: Formulation and Verification of a Hypothesis[J]. Biotechnology and Bioengineering, 1986, 28- 927-937.