一般而言，化學工業程序在本質上都具有相當複雜的非線性動態特性。為了精確地操控這些程序，我們必須透過程序鑑別技術得到可靠的程序與擾動模型以便深入解析。因此本研究主要目標便是發展實用且有效的非線性模型與隨機模型之鑑別方法。

在本論文中，吾人首先提出一疊代式方法，可鑑別由非線性靜態方塊與線性動態方塊串聯而成的連續時間Hammerstein與Wiener模型。此類方塊導向參數模型不僅能夠涵蓋更廣泛的程序特性，且經適度修改後可直接引用線性控制技術。但由於此類模型中存在無法量測的內部變數，因此不利於以最小平方法同時對非線性與線性單元進行參數估測，吾人藉由逐步疊代更新內部變數估測值的方式克服此困難。對於疊代式鑑別會遭遇的參數估測收斂性與正確性問題，尤其在面對線性動態結構不吻合、未知特性的高度非線性效應與嚴重的量測雜訊干擾時，吾人利用包含移動區間平滑技巧(moving-horizon smoothing)與解答引導機制(solution-guiding mechanism)之兩階段估測演算法加以處理。在第一階段中，利用多段式函數或多項式以疊代方式達到對非線性靜態的良好近似，此時可容忍線性動態結構不吻合的情況。在第二階段，由於內部變數已被準確估測出來，鑑別問題便簡化為一線性模型鑑別問題，可以非疊代方式獲得準確的線性動態結構與參數。數個實際程序之模擬與實驗鑑別結果顯示，本文所提鑑別法對於各種不同非線性系統動態與測試條件均十分有效。

此外在本文中吾人亦提出Wiener模型之非疊代式鑑別方法，主要是藉由Laguerre展開式來描述線性動態方塊與可調參考點之反逆多項式或多段線性函數來近似非線性靜態方塊，如此導出的回歸方程式將不含未知的內部變數，有效解決了參數估測的收斂性問題。另外可調參考點的應用使得此法受到測試實驗設計和量測雜訊的影響減小，這也增強了此鑑別法的實際應用價值。

當製程包含未知動態隨機性擾動(非量測雜訊)時，為了將隨機程序鑑別為參數模型，傳統的最小平方法往往因未知隨機擾動產生的相關殘差而得到有偏差的參數估測。雖然該法之參數估測的一致性可透過有益變數(instrumental variable)法獲得改善，但不適當的有益變數與預濾波器之選擇卻可能導致無效的估測。本文提出鑑別ARARX、ARMAX或BJ模型的方法，利用EWMA技巧來將程序輸出數據平滑化，所得優點有二：其一，所提離線和線上演算法能夠從開環或閉環操作之鑑別測試數據中，獲得無偏且有效的參數估測；其二，已鑑別出的程序暨擾動模型能夠用於移除程序輸出數據的自相關性，以獲得正確的統計程序監視結果。蒙地卡羅模擬研究證實本法無論取樣時間、取樣大小及雜訊訊號比如何選擇均能提供可靠之參數模型。

Generally speaking, chemical and industrial processes in essence consist of sophisticated nonlinear dynamic characteristics. To operate and control these processes precisely, we must find reliable process and disturbance models via a process identification technique for thorough analysis. The major objective of this dissertation is then to develop practical and effective identification methods to obtain such nonlinear models and stochastic models.

The dissertation first presents an iterative algorithm to identify continuous-time Hammerstein and Wiener models, characterized by a series connection of a nonlinear static block and a linear dynamic block. Such types of block-oriented parametric models not only cover a wide variety of process characteristics but can also be easily adapted to linear control techniques. However, for such models, the internal variable is inaccessible to measurements so that simultaneous parameter estimation of the nonlinear and linear elements cannot be easily achieved in a least-squares fashion. This difficulty could be circumvented by updating the internal variable at each iteration step. A two-stage estimation algorithm, in conjunction with moving-horizon smoothing and a solution-guiding mechanism, is established to ensure the convergence and accuracy of the iterative method in the face of linear structure mismatch, high static nonlinearity with an unknown characteristic, and severe measurement noise. At the first stage, a good description of the static nonlinearity is given by a multi-segment function or a polynomial in an iterative manner. Linear structure mismatch is allowed for this stage of estimation. At the second stage, the identification problem is reduced to a simple linear one with the internal variable gained at the first stage. A noniterative procedure can then be applied to determine accurately the structure and parameters of the linear dynamic element. Studies with simulated and experimental practical examples demonstrate that the proposed identification method is valid for a wide variety of nonlinear system dynamics and test conditions.

A noniterative identification method is also proposed to deal with the identification of Wiener models. This method represents the linear dynamic element by Laguerre expansions and approximates the nonlinear static element by an inverse polynomial (or an inverse piecewise linear function) with an adjustable reference point. As a result, the unknown internal variable would not appear in the regression equation, thereby resolving the problem of convergence for parameter estimation. Moreover, the use of adjustable reference points renders the method rather robust with respect to the design of the test experiment as well as measurement noise. This enhances the practical value of the method.

When stochastic disturbances with unknown dynamics (not measurement noise) are present, the standard least-squares method can be employed to identify parametric models for stochastic processes. However, it often yields biased parameter estimates owing to correlated residuals resulting from unknown stochastic disturbances. Although the consistency properties of parameter estimates could generically be secured by instrumental variable methods, the inadequate choices of instruments and prefilters would render them much less efficient. This dissertation establishes a method to identify an ARARX (AutoRegressive AutoRegressive with eXogenous input), an ARMAX (AutoRegressive Moving Average with eXogenous input), or a BJ (Box-Jenkins) model based on the process output data smoothed by the EWMA (Exponentially Weighted Moving Average). The major advantages of the method are twofold. First, the proposed off-line and on-line algorithms can acquire unbiased and efficient parameter estimation from identification tests operating in open loop or closed loop. Second, the resultant process plus disturbance model can be easily employed to remove the autocorrelation in process data for accurate statistical process monitoring. Monte-Carlo simulation studies demonstrate that the proposed method provides reliable parametric models for a wide variety of noise characteristics, and is highly robust with respect to the sampling period, sample size, and noise-to-signal ratio.

Abonyi, J.; Babuska, R.; Botto, M. A.; Szeifert, F.; Nagy, L. Identification and Control of Nonlinear Systems Using Fuzzy Hammerstein Models. Ind. Eng. Chem. Res. 2000, 39, 4302.
Al-Duwaish, H.; Karim, M. N. A New Method for the Identification of Hammerstein Model. Automatica 1997, 33, 1871.
strm, K. J.; Wittenmark, B. Adaptive Control; Addison-Wesley: MA, 1989.
Bai, E. W. Decoupling the Linear and Nonlinear Parts in Hammerstein Model Identification. Automatica 2004, 40, 671.
Bloemen, H. H. J.; Chou, C. T.; van den Boon, T. J. J.; Verdult, V.; Verhaegen, M.; Backx, T. C. Wiener Model Identification and Predictive Control for Dual Composition Control of a Distillation Column. J. Process Control 2001, 11, 601.
Box, G. E.; Jenkins, P.; Reinsel, G. M. Time Series Analysis: Forecasting and Control, 3rd ed.; Prentice Hall: Englewood Cliffs, 1994.
Boyd, S.; Chua, L. O. Fading Memory and the Problem of Approximating Nonlinear Operators with Volterra Series. IEEE Trans. Circuits Syst. 1985, CAS-32, 1150.
Broome, P. W. Discrete Orthonormal Sequences. J. Associ. Comput. Machinery 1965, 12, 151.
Cervantes, A. L.; Agamennoni, O. E.; Figueroa, J. L. A Nonlinear Model Predictive Control System Based on Wiener Piecewise Linear Models. J. Process Control 2003, 13, 655.
Chang, F. H. I.; Luss, R. A Noniterative Method for Identification Using Hammerstein Model. IEEE Trans. Autom. Control 1971, AC-16, 464.
Chen, H. F. Pathwise Convergence of Recursive Identification Algorithms for Hammerstein Systems. IEEE Trans. Autom. Control 2004, 49, 1641.
Clarke, D. W. Generalized Least Squares Estimation of Parameters of a Dynamic Model. First IFAC Symposium on Identification in Automatic Control Systems. Prague, 1967.
Clarke, D. W.; Mohtadi, C.; Tuffs, P. S. Generalized Predictive Control – Part I. The Basic Algorithm. Automatica 1987, 23, 137.
Clarke, D. W.; Gawthrop, P. J. Self-Tuning Controller. Proc. IEE 1975, 122, 929.
Cutler, C. R.; Rammker, B. L. Dynamic Matrix Control – A Computer Algorithm; Proc. JACC: New York, 1980.
Doyle III, F. J.; Ogunnaike, B. A.; Pearson, R. K. Nonlinear Model-Based Control Using Second-Order Volterra Models. Automatica 1995, 31, 697.
Eskinat, E.; Johnson, S. H.; Luyben, W. L. Use of Hammerstein Models in Identification of Nonlinear Systems. AIChE J. 1991, 37, 255.
Fruzzetti, K. P.; Palazoglu, A.; McDonald, K. A. Nonlinear Model Predictive Control Using Hammerstein Models. J. Process Control 1997, 7, 31.
Gallman, P. G. An Iterative Method for The Identification of Nonlinear Systems Using Uryson Model. IEEE Trans. Autom. Control 1975, AC-20, 771.
Greblicki, W.; Pawlak, M. Identification of Discrete Hammerstein Systems Using Kernel Regression Estimates. IEEE Trans. Autom. Control 1986, AC-31, 74.
Greblicki, W.; Pawlak, M. Nonparametric Identification of Hammerstein Systems. IEEE Trans. Inf. Theory 1989, IT-35, 409.
Gultekin, M.; Elsayed, E. A.; English, J. R.; Hauksdottir, A. S. Monitoring Automatically Controlled Processes Using Statistical Control Charts. Int. J. Prod. Res. 2002, 40, 2303.
Haber, R.; Unbehauen, H. Structure Identification of Nonlinear Dynamic Systems－A Survey on Input/Output Approaches. Automatica 1990, 26, 651.
Harris, K. R.; Colantonio, M. C.; Palazoglu, A. On the Computation of a Nonlinearity Measure Using Functional Expansions. Chem. Eng. Sci. 2000, 55, 2393.
Hasting-James, R.; Sage, M. W. Recursive Generalised-Least-Squares Procedures for On-Line Identification of Process Parameters. Proceedings IEE 1969, 116, 2057.
Heuberger, P. S. C.; Van den Hof, P. M. J.; Bosgra, O. H. A Generalized Orthonormal Basis for Linear Dynamical Systems. IEEE Trans. Autom. Control 1995, AC-40, 451.
Hsia, T. C. System Identification – Least-Squares Methods; Lexington Books: Massachusetts, 1977.
Hu, X. L.; Chen, H. F. Strong Consistence of Recursive Identification for Wiener Systems. Automatica 2005, 41, 1905.
Huang, H. P.; Lee, M. W.; Tang, Y. T. Identification of Wiener Model Using Relay Feedback Test. J. Chem. Eng. Jpn. 1998, 31, 604.
Hunter, J. S. The Exponentially Weighted Moving Average. Journal of Quality Technology 1986, 18, 203.
Hwang, C.; Shih, Y. P. Parameter Identification via Laguerre Polynomials. Int. J. Syst. Sci. 1982, 13, 209.
Hwang, S. H.; Huang, Y. C. Identification of Continuous-Time Delayed Systems Using an Input Pulse of Arbitrary Shape. J. Chin. Inst. Chem. Engrs. 2005, 29, 301.
Hwang, S. H.; Lin, M. L. A Method for Identification of Discrete Parametric Models with Unknown Orders and Delays. J. Chin. Inst. Chem. Engrs. 2002, 33, 373.
Hwang, S. H.; Lin, M. L. Unbiased Identification of Continuous Time Parametric Models Using a Time-Weighted Integral Transform. Chem. Eng. Commun. 2003, 190, 1170.
Janakiram, M.; Keats, J. B. Combining SPC and EPC in a Hybrid Industry. J. Qual. Technol. 1998, 30, 189.
Jia, L.; Chiu, M. S.; Ge, S. S. A Noniterative Neuro-Fuzzy Based Identification Method for Hammerstein Processes. J. Process Control 2005, 15, 749.
Kalafatis, A.; Arifin, N.; Wang, L.; Cluett, W. R. A New Approach to the Identification of pH Processes Based on the Wiener Model. Chem. Eng. Sci. 1995, 50, 3693.
Landau, I. D.; Zito, G. Digital Control Systems: Design, Identification and Implementation; Springer: Berlin, 2006.
Lang, Z. Q. A Nonparametric Polynomial Identification Algorithm for the Hammerstein System. IEEE Trans. Autom. Control 1997, AC-42, 1435.
Laub, A. J.; Heath, M. T.; Paige, C. C.; Ward, R. C. Computation of System Balancing Transformations and Other Applications of Simultaneous Diagonalization Algorithms. IEEE Trans. Autom. Control 1987, AC-32, 115.
Lecchini, A.; Gevers, M. Explicit Expression of the Parameter Bias in Identification of Laguerre Models from Step Responses. Syst. Control Lett. 2004, 52, 149.
Lee, M. W.; Huang, H. P. Identification and Control of Hammerstein-Type Nonlinear Process. J. Chin. Inst. Chem. Engrs. 2001, 32, 361.
Ljung, L. System Identification: Theory for the User; Prentice Hall: Englewood Cliffs, New Jersey, 1987.
Ljung, L. System Identification: Theory for the User; Prentice Hall: Upper Saddle River, New Jersey, 1999.
MacGregor, J. F. On-Line Statistical Process Control. Chem. Eng. Prog. 1988, 84, 21.
Montgomery, D. C. Introduction to Statistical Quality Control, 4th ed.; John Wiley: New York, 2001.
Montgomery, D. C.; Brown, E. C. Shift Detection Properties of Moving Centerline Control Chart Schemes. J. Qual. Technol. 2000, 32, 67.
Montgomery, D. C.; Mastrangelo, C. M. Some Statistical Process Control Methods for Autocorrelated Data. J. Qual. Technol. 1991, 23, 179.
Murray-Smith, R.; Johansen, T. A. Multiple Model Approaches to Modeling and Control, Taylor and Francis: London, 1997.
Nahas, E. P.; Henson, M. A.; Seborg, D. E. Nonlinear Internal Model Control Strategy for Neural Network Models. Comput. Chem. Eng. 1992, 16, 1992.
Narenda, K. S.; Gallman, P. G. An Iterative Method for the Identification of Nonlinear Systems Using the Hammerstein Model. IEEE Trans. Autom. Control 1997, AC-11, 546.
Neter, J.; Wasserman, W.; Kutner, M. H. Applied Linear Regression Models, 2nd ed.; Richard D. Irwin: Homewood, Illinois, 1989.
Norquary, S. J.; Palazoglu, A.; Romagnoli, J. A. Model Predictive Control Based on Wiener Models. Chem. Eng. Sci. 1998, 53, 75.
Notohardjono, B. D.; Ermer, D. S. Time Series Control Charts for Correlated and Contaminated Data. Journal of Engineering for Industry 1986, 108, 219.
Pajunen, G. A. Adaptive Control of Wiener Type Nonlinear Systems. Automatica 1992, 28, 781.
Palancar, M. C.; Aragon, J. M.; Torrecilla, J. S. pH-Control Systems Based on Artificial Neural Networks. Ind. Eng. Chem. Res. 1998, 37, 2729.
Rivera, D. E.; Morari, M.; Skogestad, S. Internal Model Control: 4. PID Controller Design. Ind. Eng. Chem. Proc. Des. & Dev. 1986, 25, 252.
Seborg, D. E.; Edgar, T. F.; Mellichamp, D. A. Process Dynamics and Control; John Wiley & Sons: New York, 1989.
Singh, M. G.; Elloy, J. P.; Mezencev, R.; Munro, N. Applied Industrial Control; Pergamon Press: Oxford, U.K., 1980.
Smith, C. A.; Corripio, A. B. Principles and Practice of Automatic Process Control; John Wiley & Sons: New York, 1985.
Sderstrom, T. Convergence Properties of the Generalized Least Squares Identification Method. Automatica 1974, 10, 617.
Sderstrom, T.; Stica, P. G. Comparison of Some Instrumental Variable Methods – Consistency and Accuracy Aspects. Automatica, 1981, 17, 101.
Sderstrom, T.; Stica, P. G. Instrumental Variable Methods for System Identification; Springer: Berlin, 1983.
Su, H.; McAvoy, T. J. Integration of Multilayer Perception Networks and Linear Dynamic Models: A Hammerstein Modeling Approach. Ind. Eng. Chem. Res. 1993, 32, 1927.
Sung, S. W. System Identification Method for Hammerstein Processes. Ind. Eng. Chem. Res. 2002, 41, 4295.
van Pelt, T. H.; Bernstein, D. S. Non-Linear System Identification Using Hammerstein and Non-linear Feedback Models with Piecewise Linear Static Maps. Int. J. Control 2001, 74, 1807.
van der Wiel, S.; Tucker, W. T.; Faltin, F. W.; Doganaksoy, N. Algorithmic Statistical Process Control: Concepts and an Application. Technometrics 1992, 34, 286.
Voros, J. Iterative Algorithm for Parameter Identification of Hammerstein System with Two-Segment Nonlinearities. IEEE Trans. Autom. Control 1999, 44, 2145.
Voros, J. Modeling and Identification of Wiener Systems with Two-Segment Nonlinearities. IEEE Trans. Contr. Sys. Tech. 2003, 11, 253.
Voros, J. Parameter Identification of Wiener Systems with Multisegment Piecewise-Linear Nonlinearities. Syst. Control Lett. 2007, 56, 99.
Wahlberg, B. Estimation of Autoregressive Moving-Average Models via High-Order Autoregressive Approximations. J. Time Ser. Anal. 1989, 10, 283.
Wahlberg, B.; Mkil, P. M. Approximation of Stable Linear Dynamical Systems Using Laguerre and Kautz Functions. Automatica 1996, 32, 693.
Wigren, T. Recursive Prediction Error Identification Using the Nonlinear Wiener Model. Automatica 1993, 29, 1011.
Wong, K. Y.; Polak, E. Identification of Linear Discrete Time Systems Using the Instrumental Variable Approach. IEEE Trans. Automat. Contr. 1967, AC-12, 707.