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研究生:田立德
研究生(外文):Lester-Lik-Teck Chan
論文名稱:高斯程序於模型辨識,控制與效能評估:數據選擇以改善模型不確定性
論文名稱(外文):Gaussian Process Model Based Process Identification, Control and Performance Assessment: Data Selection for Model Uncertainty Improvement
指導教授:陳榮輝陳榮輝引用關係
指導教授(外文):Jung-Hui Chen
學位類別:博士
校院名稱:中原大學
系所名稱:化學工程研究所
學門:工程學門
學類:化學工程學類
論文種類:學術論文
論文出版年:2014
畢業學年度:102
語文別:英文
論文頁數:173
中文關鍵詞:高斯程序模型辨識控制效能評估數據選擇模型不確定性
外文關鍵詞:controlmodel uncertaintyperformance assessmentdata selectionprocess identificationgaussian process model
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全球產業都很重視提高效率,降低運營成本因此具有重要意義。通過新的方法,以及資源的增強減少對環境和健康的影響,有很大的重要性。因此,有必要提昇現有的方法,並引入新的,突破性的技術。在化學工程的研究,程序識別,控制和性能評估是活躍的研究領域。本文旨在提出基於高斯過程 (Gaussian Process) 方法來改進序程在上述方面的運作。在高斯過程模型方法會有因為矩陣的求逆的高計算量問題。本研究提出了一遞歸更新協方差矩陣的方法。該更新方法是有選擇性,只對需要改善的區域進行更新,避免高運算的需求。此外,配合修剪過程除去冗餘數據使得模型的數據量維持精簡。目前工業使用的主要控制器仍然是PID 控制,其調整方法則是基於程序的模型。因此,該模型的完整性是非常重要的,而有關模型預測的可信度的資訊則是有利的。高斯過程模型能提供可信度的資訊,因此本研究提出了基於高斯過程模型PID控制調整。利用方差信息於控制,達到安全與性能權衡的控制。此外方差信息提供了改善模型的一個方法。控制器性能評估的目的是衡量控制系統的能力,以改善系統的運作。過去性能評估,模型被認為完整的,但在實際情況下,這可能並非如此。該模型的準確性方取決於數據的品質。其結果是,基於模型所得到的性能指標實際上的不是最佳值。因此在考慮改善目前的程序時,有必要提供操作員更多的資訊。本研究提出基於高斯過程 (Gaussian Process) 的性能評估架構,利用方差作為模型的可信度資訊,以及對應的性能指標,並判定改善的可能性。此外,該方法可應用在非線性系統的評估。本研究方法的特性會透過測試範例來呈現。
The global industries place a great importance in increasing efficiency to reduce operating costs. This also have a great importance in minimizing environmental and health impacts, through new industrial approaches, as well as an enhancement of resources. Therefore, there is a need to upgrade existing approaches and introduce new, breakthrough technologies. In chemical engineering research process identification, control and performance assessment are three areas of active research. This thesis aims to propose methodologies to improve the operation of process with regards to the aforementioned areas of research based on the Gaussian Process (GP) model. The GP model based method can encounter a high computation load because of the inversion of matrix. In this work, a method which recursively updates the covariance matrix is proposed. The update scheme is selective by admitting data to the region requiring improvement. This enables the model to be updated without placing a high computation demand. In addition, the process is augmented by a pruning process which removes redundant data from the model to keep the data size compact. The predominant controllers used in most process industries are still mainly PIDs and model based method is used for controller tuning. The integrity of the model is therefore very important and information on the model based prediction can be invaluable. The GP model gives the information on the reliability of the prediction. A GP model based PID tuning control has been proposed in this study. The variance information is used for control which results in a safety-performance trade-off control. In addition the variance information provides a mean for the selection of data to improve the model at successive control stage. The aim of the controller performance assessment is to determine and measure the capability of control systems in order to improve the degradation performance. Conventionally it is assumed the model is perfect but in actual situation this may not be the case. In terms of accuracy of the model it is only as accurate as the quality of the data available. The consequence is that the performance index based on the identified model is not the actual optimum. This leads to a need for the providence of trust on the performance index that provides the operators with better information when considering improving the current process. A GP model based performance assessment framework is proposed using the variance of the predictive distribution as a confidence level of the model and thus the corresponding performance index. The proposed index is used to provide a trust region on the performance index. Based on the indication of the model quality the reliability of the evaluated performance index can be indicated. It is used to provide a framework for judging whether improvement to the control structure as well as model is worthwhile. Moreover the proposed method provides a framework for nonlinear process assessment. The capabilities of the proposed methods are demonstrated through a series of case studies.
Table of Contents
摘要 I
Abstract III
Acknowledgment V
Table of Contents VII
List of Figures XI
List of Tables XV
Chapter 1: Introduction 1
1.1 Motivation 1
1.2 Research Objectives 5
1.3 Thesis Outline 7
Chapter 2: Gaussian Process Models 9
2.1 Introduction 9
2.2 Preliminaries 9
2.2.1 Inference and Bayes’ rule 10
2.2.2 Random Variables, Joint, Marginal and Conditional Probability 10
2.2.3 Gaussian Random Functions 11
2.3 Regression Using Gaussian Processes 12
2.4 Covariance Functions 17
2.4.1 Stationary Covariance Functions 17
2.4.2 Non-stationary Covariance Functions 18
2.5 Determination of the Hyper-Parameters 20
2.5.1 Likelihood Maximization 20
2.5.2 Monte Carlo Method 21
2.6 Case Study: Mathematical Model 23
2.7 Gaussian Process Regression Based Optimal Design of Combustion Systems Using Flame Images 25
2.7.1 Combustion System Description 26
2.7.2 Modeling of Combustion Systems Using GP 27
2.7.3 Modeling Flame Image Process 32
2.7.4 Combustion Design 34
Chapter 3: Nonlinear System Identification with Selective Recursive Gaussian Process Models 39
3.1 Introduction 39
3.2 Active Recursive Gaussian Process Model 43
3.2.1 Illustration of Concept 43
3.2.2 Addition of Data by Recursive Updating 46
3.2.3 Removal of Data by Recursive Pruning 47
3.3 Case Studies 52
3.3.1 Case I: Numerical Example 53
3.3.2 Case II: Application to Industrial Cogeneration Plant 61
3.4 Conclusion 76
Chapter 4: Progressive Gaussian Process Model Based PID Controller Tuning for Nonlinear Processes 79
4.1 Introduction 79
4.2 Problem statement 81
4.3 Progressive GP model 83
4.3.1 Heuristic for Progressive GP Model 83
4.3.2 GP Model Based PID Tuning 86
4.3.2.1 GP Based PID Tuning with Gradient Method (Direct Method) 86
4.3.2.2 Instantaneous GP PID Tuning 88
4.4. Case studies 90
4.4.1 pH Neutralization system 90
4.4.1.1 GP Model with Rich Data 92
4.4.1.2 GP Model with Sparse Data 93
4.4.1.3 Model Update with New Data 98
4.4.2 Fed-Batch Fermentation 102
4.5. Conclusion 109
Chapter 5: Gaussian Process Model Based Performance Assessment of Control Loop 111
5.1 Introduction 111
5.2 Problem Statement 115
5.3 GP model based LQG benchmark 123
5.4 Case Studies 128
5.4.1 Numerical Simulation 128
5.4.2 pH Neutralization System 130
5.5 Conclusions 138
Chapter 6: Conclusions and Future Directions 141
6.1 Concluding Remarks 141
6.2 Recommendations for Future Work 142
References 145


List of Figures
Figure 2 1 Samples drawn from prior distribution. The shaded region denotes twice the standard deviation at each input value . 19
Figure 2 2 Posterior after two data-points have been observed. The shaded region denotes twice the standard deviation at each input value . 20
Figure 2 3 Model identification of Mathematical example 28
Figure 2 4 Variance prediction of Mathematical example 29
Figure 2 5 Flame imaging system 31
Figure 2 6 Five flame images collected in a normal operation condition 31
Figure 2 7 Unfolded structures of the flame image data. 35
Figure 2 8 (a) Reconstructed image using the first two components from (b) a sample image 36
Figure 2 9 Discrepancy in design of combustion design 37
Figure 2 10 Variance prediction on score 1 when score 2 value fixed at 5 40
Figure 2 11 Flame imaging control system 40
Figure 2 12 Flame imaging multivariable control system 41
Figure 3 1 Concept of the active recursive update GP model 54
Figure 3 2 Active recursive updating and pruning of the GP model 60
Figure 3 3 Model trained with initial data in Case I 64
Figure 3 4 First update of the model in Case I: (a) addition of data, (b) pruning of data 66
Figure 3 5 Model after the second update in Case I: (a) addition of data, (b) pruning of data 68
Figure 3 6 Absolute relative error for each update: (*) initial, (∆) after first update , (o) after second update. 69
Figure 3 7 Schematic of boiler 70
Figure 3 8 Data distribution for 2 daily operation of the boiler, where the circle (o) and plus (+) represent data from day 1 and day 2, respectively. 72
Figure 3 9 ARE for the predictions in Case II when the training data contain the high and the low loads data: (a) model with update; (b) model without update. 75
Figure 3 10 Predicted results in Case II when the training data contain the high and the low loads data: (a) model with update; (b) model without update. 77
Figure 3 11 Prediction results for sampling points (200-300) in Case II when the training data contain the high and the low loads data: (a) model with update; (b) model without update. 79
Figure 3 12 ARE for the predictions in Case II when the training data contain the low load data only: (a) model with update; (b) model without update. 81
Figure 3 13 Predicted results in Case II when the training data contain the low load data only: (a) model with update; (b) model without update. 83
Figure 4 1 The GP model based PID control scheme 92
Figure 4 2 The data admission region 95
Figure 4 3 Instantaneous linearization of the GP model 98
Figure 4 4 pH CSTR systems 101
Figure 4 5 Comparison of direct GP PID control with variance and direct GP PID control without variance when the model is accurate 104
Figure 4 6 Comparison of direct GIP PID control, approximate GP PID control and linearized neural-network when the model is accurate 105
Figure 4 7 Comparison of direct GP PID control with variance, direct GP PID control without variance when the model is inaccurate. 106
Figure 4 8 PID parameter tuning: (a) GP with variance (b) GP without variance 108
Figure 4 9 GP PID control with initial data which is rich in region of pH 8; dotted-line region are regions where data are to be used to update the model. 110
Figure 4 10 Historical data (○) and new admitted (*) input vector 111
Figure 4 11 GP PID control with updated model from admitted data. 112
Figure 4 12 Evolution of GP PID control: (a) Initial batch (b) Batch no.2 (c) Batch no. 3 117
Figure 4 13 Control performance at each batch 118
Figure 5 1 SISO feedback control 127
Figure 5 2 A sample of LQG trade-off curve 129
Figure 5 3 Input data: (a) poor model (b) rich model 132
Figure 5 4 Output data: (a) poor (b) rich 134
Figure 5 5 Trade-off curve for SISO process and model with rich and poor data 135
Figure 5 6 The predictive variance and actual variance. 138
Figure 5 7 The GP based LQG trade-off curve and its performance bound 139
Figure 5 8 Trade-off curves for (a) poor and (b) rich data 142
Figure 5 9 Data for modeling in pH neutralization system (a) pH (b) input 144
Figure 5 10 Comparison of conventional LQG and GP based performance assessment. 145
Figure 5 11 Prediction performance of GP and LQG model 146
Figure 5 12 pH output for (a) LQG controller (b) GP controller 148
Figure 5 13 Performance for (a) old model (b) new model 150

List of Tables
Table 2 1 The design score values for different oxygen contents 39
Table 3 1. RMSE and RRMSE of different updates in Case I 69
Table 3 2. RMSE and RRMSE of the predictions with and without update in Case II when the training data contain the high and the low loads. 83
Table 3 3. RMSE and RRMSE of the predictions with and without update in Case II when the training data contain only the low loads. 84
Table 4 1 Parameters for case study 1 102


[1]Altınten A.; Ketevanlioğlu F.; Erdoğan S.; Hapoğlu H.; Alpbaz M. Self-tuning PID control of jacketed batch polystyrene reactor using genetic algorithm. Chemical Engineering Journal. 2008, 138, 490
[2]Aström K. J.; Wittenmark B. Self-tuning controllers based on pole-zero placements. Control Theory and Applications, IEE Proceedings D. 1980, 127, 120
[3]Azman, K.; Kocijan, J. Application of Gaussian processes for black-box modelling of biosystems. ISA Transactions. 2007, 46 (4), 443
[4]Bitenc, A.; Cretnik, J.; Petrovcic, J.; Strmcik, S.; . Design and application of an industrial controller. Computing &; Control Engineering Journal. 1992, 3, 29
[5]Beer J. M. Combustion technology developments in power generation in response to environmental challenges. Pro. Energy Combust Sci. 2000, 26, 301
[6]Boyle, P. Gaussian processes for regression and optimization. Ph.D. Thesis, Victoria University of Wellington. 2007
[7]Bouzouita B.; Bouani F.; Ksouri M., Efficient implementation of multivariable MPC with parametric uncertainties. In: Proc. ECC. 2007
[8]Burkardt H. Image analysis and control of combustion processes. The International Seminar on Imaging in Transport Processes, Athen, Greece, 1992Cameron F.; D.E. Seborg. A self-tuning controller with a PID structure, Int. J. Control. 1983, 30, 401
[9]Cameron F.; Seborg D. E. A self-tuning controller with a PID structure. Int. J. of Control. 1983, 38, 401
[10]Casavola A.; Famularo D.; Franze G. Robust constrained predictive control of uncertain norm-bounded linear systems. Automatica. 2004, 4, 1865
[11]Chan L. L. T.; Liu Y.; Chen J. Nonlinear system identification with selective recursive Gaussian process models. Ind. &; Eng. Chem. Res. 2013, 52, 18276
[12]Chen J.; Chan L. L. T.; N. Cheng. Gaussian Process Regression Based Optimal Design of Combustion Systems Using Flame Images, Applied Energy. 2012,111, 153
[13]Chen J.; Chang Y-H.; Cheng Y-C.; Hsu C-K. Design of image-based control loops for industrial combustion processes. Applied Energy. 2012, 94, 13
[14]Chen J.; Huang T-C. Applying neural networks to on-line updated PID controllers for nonlinear process control. J. Process Control. 2004, 14, 211
[15]Chen T.; Zhang J. On-line multivariate statistical monitoring of batch processes using Gaussian mixture model. Computers and Chemical Engineering. 2010, 34, 500
[16]Chiang L.H.; Russell EL, Braatz RD. Fault detection and diagnosis in industrial systems. Springer, London, 2001Clark D.W.; P.J. Gawthrop. Self-tuning control, in: Proc. IEE, Pt-D. 1979, 126, 633
[17]Clarke D.W.; Gawthrop P. J. Self-tuning control. Proc. of the Inst. of Electr. Eng. 1979, 126, 633
[18]Csato, L.; Opper, M. Sparse on-line Gaussian processes. Neural Computation. 2002, 14(3), 641
[19]dela Pena D.M., Alamo T., Ramirez T., Camacho E., Min-max model predictive control as a quadratic program. In: Proc. of 16th IFAC World Congress. 2005
[20]di Sciascio F.; Amicarelli A. N. Biomass estimation in batch biotechnological processes by Bayesian Gaussian process regression. Comput. &; Chem. Eng. 2008, 32, 3264
[21]Decquier N.; Candel S. Combustion control and sensors, a review. Progress in Energy and Combustion Science. 2002, 28, 107
[22]Desborough L.; Harris, T. J. Performance assessment measures for univariate feedback control. Can. J. Chem. Eng. 1992, 70, 1186
[23]Desborough L.; Harris T.J. Harris. Performance assessment measures for univariate feedforward/feedback Control, Can. J. Chem. Eng. 1993, 7,605
[24]DeVries W. R.; Wu S. M. Evaluation of process control effectiveness and diagnosis of variation in paper basis weight via multivariate time-series analysis. IEEE Trans. Automat Control. 1978, 23, 702
[25]Draper, T.S.; Zeltner, D.; Tree, D. R.; Xue Y.; Tsiava R. Two-dimensional flame temperature and emissivity measurements of pulverized oxy-coal flames. Applied Energy. 2012, 95, 38
[26]Eriksson P.-G.; Isaksson A.J. Some aspects of control loop performance monitoring Proceedings of the Third IEEE Conference on Control Applications. 1994
[27]Gang L.; Yong Y.; Mike C. A digital imaging based multifunctional flame monitoring system. IEEE Trans. Inst. Meas. 2004, 53, 1152-1158.
[28]Gawthrop P. J. Self-tuning PID controllers: Algorithms and implementation. Autom. Control, IEEE Trans. on. 1986, 31, 201
[29]Gibbs, M. N.; Mackay, D. J. C. Efficient implementation of Gaussian process. In Technical report, Cavendish Laboratory. Cambridge University, U.K.,1997
[30]Golub, G.H.; Van Loan, C.F. Matrix Computations 3rd Edition, The John Hopkins University Press, Baltimore, 1996
[31]González-Cencerrado, A.; Peña, B.; Gil, A. Coal flame characterization by means of digital image processing in a semi-industrial scale PF swirl burner. Applied Energy. 2012, 94, 375
[32]Grancharova, A.; Kocijan, J.; Johansen, T. A. Explicit stochastic predictive control of combustion plants based on Gaussian process models. Automatica. 2008, 44, 1621
[33]Gregorcic G.; Ligthbody G. Local model network identification with GP. IEEE Transactions on Neural Network. 2007, 18, 1404Gawthrop P.J. Self-tuning PID controllers: algorithm and implementation, IEEE Trans. Autom. Control. 1986 31, 201
[34]Gregorcic, G.; Lightbody G. Gaussian process approach for modeling of nonlinear systems. Engineering Application of Artificial Intelligence. 2009, 22, 522
[35]Harris T.J. Assessment of control loop performance, Can. J. Chem. Eng. 1989, 67,856.
[36]Hernandez R.; Ballester J. Flame imaging as a diagnostic tool for industrial combustion. Combust Flame. 2008, 155, 509
[37]Herzallah R.; Lowe D. A mixture density network approach to modeling and exploiting uncertainty in nonlinear control problems. Engineering Applications of Artificial Intelligence. 2004, 17, 145
[38]Himmelblau, D.M. Accounts of experiences in the application of artificial neural networks in chemical engineering. Ind. Eng. Chem. Res. 2008, 47(16), 5782
[39]Huang B.; Kadali R. Dynamic Modeling, Predictive Control and Performance Monitoring A Data-driven Subspace Approach. 2008
[40]Huang, B.; Shah, S.L. Control loop performance assessment: theory and application. Springer-Verlag, London. 1999
[41]Huang, B.; Shah S. L.; Kwok K. Y. Good, bad or optimal? Performance assessment of MIMO processes. Automatica. 1997, 33(6), 1175.
[42]Huang, H. W.; Zhang, Y. Flame colour characterization in the visible and infrared spectrum using a digital camera and image processing, Measurement Science and Technology. 2008, 19, 085406
[43]Huang, H. W.; Zhang, Y. Syngas Combustion Radiation Profiling through Spectrometry and DFCD Processing Techniques, International Journal of Hydrogen Energy. 2012, 37, 5257Huang B. Minimum variance control and performance assessment of time-variant processes. J. Proc. Cont. 2002, 12, 707
[44]Jelali M. An overview of control performance assessment technology and industrial applications. Control Engineering Practice. 2006, 14, 441
[45]Iino N.; Tsuchino F.; Torii S.; Yano T. Timewise variation of turbulent jet diffusion flame shape by means of image processing. J. Flow Visualization and Image Processing. 1998, 5, 275
[46]Jackson J. E. A user’s guide to principal components. New York,John Wiley &; Sons NY, 1991
[47]Kadali R.; Huang B. Controller Performance Analysis with LQG-Benchmark Obtained under Closed-loop Conditions, ISA Trans. 2002, 41, 521
[48]Kammer L. C.; Bitmead R. R.; Bartlett P. L. Optimal controller properties from closed-loop experiments. Automatica. 1998, 34, 83
[49]Kansha Y.; Jia L.; Chiu M-S. Self-tuning PID controllers based on the Lyapunov approach. Chem. Eng. Sci. 2008, 63, 2732
[50]Kadlec, P.; Grbic, R.; Gabrys, B. Review of adaptation mechanisms for data drive soft sensors. Com. Chem. Eng. 2011, 35, 1
[51]Keerthi, S.S.; Chu, W. A matching pursuit approach to sparse Gaussian process regression. In Advances in Neural Information Processing Systems. 18, 2005
[52]Ko B.S.; Edgar T.F. PID control performance assessment: the single-loop case, AIChE J. 2004 50, 1211
[53]Ko, B.; Edgar T. F. Assessment of achievable PI control performance for linear processes with dead time. In American Control Conf., Philadelphia, PA, 1998
[54]Kocijan J.; Murray-Smith R.; Rasmussen C. E.; Girard A. Gaussian process model based predictive control. Proc. of Am. Control Conf. 2004, 2214
[55]Kolmogorov, A. N. Interpolation und extrapolation von stationären zufälligen folgen. Bull Acad. Sci. USSR 1941, 5, 3 (Russian)
[56]Kohse-Hoinghaus K.; Barlow R.S.; Alden M.; Wolfrum J. Combustion at the focus, laser diagnostic and control. Proceedings of the Combustion Institute. 2005, 30, 89
[57]Kuwata Y.; Richards A.; How J. Robust receding horizon using generalized constraint tightening. In: Proc. ACC. 2007
[58]Kwakernaak H.; Sivan R. Linear optimal control systems, John Wiley &; Sons. 1972.
[59]Lee M.H.; Harashima F. Flame detection for the steam boiler using neural networks and image information in the ulsan steam power generation plant. IEEE Trans Ind Electron. 2006, 53, 338
[60]Lee C-H.; Teng C-C. Calculation of PID controller parameters by using a fuzzy neural network. ISA Trans. 2003, 42, 391
[61]Likar B.; Kocijan J. Predictive control of a gas liquid separation plant based on a Gaussian process model. Comput. &; Chem. Eng. 2007, 31, 142
[62]Liu, Y.; Yang, D.C.; Wang, H.Q.; Li P. Modeling of fermentation processes using online kernel learning. In Proceedings of 17th IFAC World Congress, Seoul, South Korea. 2008, 9679
[63]Ljung, L.; Hjalmarsson, H.; Ohlsson, H. Four encounters with system identification. Eur. J. Control. 2011, 17(5-6), 449
[64]Lovas C.; Seron M.M.; Goodwin G.C. Robust model predictive control of input constrained stable systems with unstructured uncertainty. In: Proc. ECC. 2007
[65]Lundgren, A.; Sjoberg, J. Gaussian processes framework for validation of linear and nonlinear models. In 13th IFAC Symposium on System Identification (SYSID 2003), Rotterdam, The Netherlands, 67
[66]Lu G.; Gilabert G.; Yan Y. Vision based monitoring and characterization of combustion flames. Journal of Physics, Conference Series. 2005, 15, 194
[67]Mackay, D. J. C. Introduction to Gaussian processes. In Neural networks and Machine Learning, F: Computer and Systems Sciences, Bishop, C. M. (Ed.). 1998, 133
[68]Nahas E. P.; Henson M.A.; Seborg D. E. Nonlinear internal model control strategy for neural network models. Comput. &; Chem. Eng. 1992, 16, 1039
[69]Ni, W.; Tan, S.; Ng, W. Recursive GPR for nonlinear dynamic process modeling. Chem. Eng. J. 2011, 173, 636
[70]Ni, W.; Tan S.; Ng W.; Brown S. D. Moving-window GPR for nonlinear dynamic system modeling with dual updating and dual preprocessing. Ind. Eng. Chem. Res. 2012, 51(18), 6416
[71]Ni, W.; Wang, K.; Chen, T.; Tan, S.; Ng, W. GPR model with signal preprocessing and bias update for dynamic processes modeling, Control Eng. Pract. 2012b, 20(12), 1281
[72]O’Hagan, A. Curve fitting and optimal design for prediction, J. Royal Statistical Society B. 1978, 40 (1), 1
[73]Ortega R.; Kelly R. PID self-tuners: some theoretical and practical aspects. Ind. Electr., IEEE Trans. on IE. 1984, 31, 332
[74]Pan T.; Li S.; Cai W-J. Lazy learning-based online identification and adaptive PID Control:A case study for CSTR process. Ind. &; Eng. Chem. Res. 2007, 46, 472
[75]Papoulis, A. Probability, Random Variables and Stochastic Processes. McGraw-Hill, 1991
[76]Petelin, D.; Grancharova, A.; Kocijan J. Evolving Gaussian process models for prediction of ozone concentration in the air. Simulation modelling practice and theory. 2013, 33, 68
[77]Polak E.; Yang T. H. Moving horizon control of linear systems with input saturation and plant uncertainty Part 1. Robustness, International Journal of Control. 1993, 58, 613
[78]Qin S. J. Control performance monitoring – a review and assessment, Computers and Chemical Engineering. 1998, 23, 173
[79]Proudfoot C. G.; Gawthrop P. J.; Jacobs O. L. R. Self-tuning PI control of a pH neutralisation process. Control Theory and Appl., IEE Proc. D. 1983, 130, 267
[80]Pugachev, V. S. Theory of random functions and its application to control problems. Pergamon Press, 1967
[81]Radke F.; Isermann R. A parameter-adaptive PID-controller with stepwise parameter optimization. Automatica. 1987, 23, 449
[82]Ranganathan, A.; Yang, M.-H.; Ho, J. Online Sparse Gaussian Process Regression and Its Applications. IEEE Trans. Image Processing. 2011, 20(2), 391
[83]Rasmussen, C.E. Evaluation of Gaussian processes and other methods for non-linear regression. Ph.D. Thesis, University of Toronto. 1996
[84]Rasmussen, C.E.; Williams, C.K.I. Gaussian Processes for Machine Learning; MIT Press, 2006
[85]Sciascio F.D.; Amicarelli A.N. Biomass estimation in batch biotechnological processes by Bayesian Gaussian process regression. Com. Chem. Eng. 2008, 32, 3264
[86]Seeger, M.; Williams, C.K.I.; Lawrence, N.D. Fast forward selection to speed up sparse Gaussian process regression. In Proceedings of the Ninth International Workshop on Artificial Intelligence and Statistics, 2003
[87]Tang, H.S.; Xue, S.T.; Chen, R.; Sato, T. Online weighted LS-SVM for hysteretic structural system identification. Engineering Structure 2006, 28 (12), 1728
[88]Tao, C.; Ren, J. Bagging for Gaussian process regression. Neurocomputing, 2009, 72, 1605
[89]Vesely V.; Rosinova D.; Foltin M. Robust model predictive control design with input constraints, ISA Trans. 2010, 49, 114
[90]Vincent, V. Nonlinear system identification: A state-space approach. Ph.D. Thesis, University of Twente. 2002
[91]Wang, H.Q.; Li, P.; Gao, F.R.; Song Z.H.; Ding S.X. Kernel classifier with adaptive structure and fixed memory for process diagnosis. AIChE J. 2006, 52(10), 3515
[92]Wang L.; Du W.; Wang H.; Wu H. Fuzzy self-tuning PID control of the operation temperatures in a two-staged membrane separation process. Journal of Natural Gas Chemistry. 2008, 17, 409
[93]Wang, X.D.; Laing, W.F.; Cai, X.S.; Lv, G.Y.; Zhang, C.J.; Zhang, H.R. Application of adaptive least square support vector machines in nonlinear system identification. In Proceedings of The Sixth World Congress on Intelligent Control and Automation, Dalian, China. 2006, 1897
[94]Wiener, N. Extrapolation, Interpolation and Smoothing of Stationary Time Series. MIT Press, Cambridge. 1949
[95]Williams, C. K. I. Prediction with Gaussian processes: From linear regression to linear prediction and beyond. In Learning in Graphical Models, Jordan, M. I. (Ed.). 1999, 599
[96]Wittenmark B. Self-tuning PID Controllers Based on Pole Placement, Lund Institute Technical Report TFRT-7179. 1979
[97]Yan, W.; Hu, S.; Yang, Y.; Gao, F.; Chen, T. Bayesian migration of Gaussian process regression for rapid process modeling and optimization. Chem. Eng. J. 2011, 166, 1095
[98]Yan Y.; Lu G.; Colechin M. Monitoring and characterization of pulverized coal flames using digital imaging techniques. Fuel. 2002, 81, 647
[99]Yan Z.; Liang Q.; Guo Q.; Yu G.; Yu, Z. Experimental investigations on temperature distributions of flame sections in a bench-scale opposed multi-burner gasifier. Applied Energy. 2009, 86, 1359
[100]Yoshioka, T.; Ishii, S. Fast Gaussian process regression using representative data. In Proceedings of International Joint Conference on neural networks. 2001, 11, 132
[101]Zafiriou E.; Marchal A. Stability of SISO quadratic dynamic matrix control with hard output constraints. AIChE Journal.1991, 37, 1550
[102]Zhang H.; Zou Z.; Li J.; Chen X. J. Flame image recognition of alumina rotary kiln by artificial neural network and support vector machine methods. Cent South Univ. Tech. 2008, 15, 39
[103]Zhang, Q; Benveniste, A. Wavelet networks. IEEE Trans. Neural Networks. 1992, 3(6), 889
[104]Zheng Z.Q.; Morari M. Robust stability of constrained model predictive control. In: Proc. ACC. 1993 379
[105]Zhou H.; Zheng L.; Cen K. Computational intelligence approach for NOx emissions minimization in a coal-fired utility boiler. Energy Conversion and Management. 2010, 51, 580
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