在化學工業中，填充塔是一類常用於氣液系統的分離設備，填充塔能夠達到高質傳效率且能適用於劇烈流量波動的情況，還能夠維持相對低的操作壓力。然而液泛現象常會使得工作效率降低，影響製程的正常運作，甚至還會讓整條生產線故障，造成巨大的損失。為了避免嚴重液泛發生，相關的經驗式和模型常被用來預測液泛點─即會發生液泛的臨界氣體流量。然而預測的準確度須取決於經驗式參數，不同的填料塔會有對應不同的經驗參數，在填充塔設計未知的情況下，要取得這些參數是相當困難的，更何況實際運用於工業上的填料塔類型不計其數。因此，對填充塔操作的製程變數做即時的線上監控變得相當重要。且在先前的研究裡發現塔內的壓力差的變化為液泛發生判斷的重要依據。然而，即使是在正常的操作條件下，填料塔內壓力差也是隨著流量調整持續變化的，導致常規的統計製程監控方法無法直接使用於監控壓力差變數。本研究提出一種藉由一種穩定度指標來提取變數特徵進而監控填料塔製程，因為在液泛發生前後，壓力差變數所計算出的穩定度指標會有顯著的不同。另外，由於缺乏穩定度指標的正確統計分佈，無母數統計管制方法將適用於建立穩定度指標的管制圖。此外，對壓力差數據進行時間序列分析亦能有效的提取變數特徵。因此，指數型廣義自回歸條件異變異數模型(Exponential Generalized AutoRegressive Conditional Heteroskedasticity，簡稱之EGARCH模型)被提出用來建立壓力差變數的時間序列模型。在本研究中，主要期望能藉由EGARCH模型來描述液泛發生前後的壓力差數據波動幅度差異。而根據實驗結果，本研究發現液泛發生前後所建立出的模型之係數將有顯著性的變化。最終透過無母數統計管制方法來建立模型係數的管制圖即能達成即時監控與預警的目的。

In chemical industries, packed tower is a commonly used operating unit for separation, which is capable to achieve high mass transfer rates even in the situations of strong flow fluctuations and relatively low pressure drop. However, the flooding phenomenon often reduces the efficiency of packed tower, interferes with the normal performance of the operating system, and even shuts down the entire production line. In order to avoid the occurrence of flooding, empirical correlations and models have been used to predict the flooding point velocity, i.e. the operating limit of a packed power. However, the accuracy of prediction depends on some empirical parameters related to the specific packed tower under consideration which are difficult to obtain. Due to this reason, the research on the real-time monitoring system for preventing flooding becomes an important field. Previous research shows that pressure drop is the most indicative process variable for flooding. However, the mean and variance of such variable varies with the changes in gas velocity or liquid velocity even in normal operation, breaking the requirements of conventional statistical process control (SPC) methods. In this research, it is proposed to monitor the operation of packed tower via a steadiness index, since the inherent distinction before and after the occurrence of flooding is the shift in the degree of steadiness (DOS) of pressure drop trajectory, which motivates the research in this research. Due to the lack of knowledge of the exact distribution of DOS, a nonparametric charting technique is adopted. In addition, time series analysis of pressure drop data is also a useful method to extract the characteristic of variable. Hence, the Exponential Generalized autoregressive conditional heteroskedastic (EGARCH) model is proposed as the technique for fitting pressure drop data. In this research, the EGARCH is expected to model the difference fluctuation behaviors of operation status. Then, the experimental results show that the model coefficients have significant variations after flooding onset. Finally, a nonparametric control chart technique is utilized to achieve real-time monitoring and prognosis.

1. 蒋维钧,余立新. 化工原理: 化工分离过程. 清华大学出版社有限公司, 2005.
2. Kister, H. Z., Scherffius, J., Afshar, K., & Abkar, E. "Realistically predict capacity and pressure drop for packed columns. " Chem. Eng. Prog, 103(7) (2007), 28-36.
3. Parthasarathy, Srinivasan, Hitesh Gowan, and Praveen Indhar. "Prediction of flooding in an absorption column using neural networks." Control Applications, 1999. Proceedings of the 1999 IEEE International Conference on. Vol. 2. IEEE, (1999).
4. Strigle, Ralph F. "Random packings and packed towers: Design and applications." (1987).
5. Dzyacky, George E. "Process and apparatus for predicting and controlling flood and carryover conditions in a separation column." U.S. Patent No. 5,784,538. 21 Jul. (1998).
6. Hansuld, Erin, Lauren Briens, and Cedric Briens. "Acoustic detection of flooding in absorption columns and trickle beds." Chemical Engineering and Processing: Process Intensification 47.5 (2008): 871-878.
7. Pihlaja, Roger Kenneth, and John Philip Miller. "Detection of distillation column flooding." U.S. Patent No. 8,216,429. 10 Jul. 2012.
8. Stichlmair, J., J. L. Bravo, and J. R. Fair. "General model for prediction of pressure drop and capacity of countercurrent gas/liquid packed columns." Gas Separation & Purification 3.1 (1989): 19-28.
9. Chakraborti, Subhabrata, and Mark A. van de Wiel. A nonparametric control chart based on the Mann-Whitney statistic. Institute of Mathematical Statistics, (2008).
10. L.-a. Yip, "Realtime empirical mode decomposition for intravascular bubble detection," Bachelor, School of engineering and physical sciences, James Cook University, (2010).
11. Von Neumann, J., Kent, R. H., Bellinson, H. R., & Hart, B. T. "The mean square successive difference." The Annals of Mathematical Statistics 12.2 (1941): 153-162.
12. Cao, Songling, and R. Russell Rhinehart. "An efficient method for on-line identification of steady state." Journal of Process Control 5.6 (1995): 363-374.
13. R. Russell Rhinehart, “Automated Steady and Transient State Identification in Noisy Processes”, 2013 American Control Conference
14. Crow, E.; Davis, F., Statistics Manual; Dover Publications: Mineola,NY, (1960).
15. Ranjan, Nikhil, Hema A. Murthy, and Timothy A. Gonsalves. "Detection of SYN flooding attacks using generalized autoregressive conditional heteroskedasticity (GARCH) modeling technique." Communications (NCC), 2010 National Conference on. IEEE, (2010).
16. Box, G. E., Jenkins, G. M., Reinsel, G. C., & Ljung, G. M. Time series analysis: forecasting and control. John Wiley & Sons, (2015).
17. Cheung, Yin-Wong, and Kon S. Lai. "Lag order and critical values of the augmented Dickey–Fuller test." Journal of Business & Economic Statistics 13.3 (1995): 277-280.
18. Engle, Robert F. "Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation." Econometrica: Journal of the Econometric Society (1982): 987-1007.
19. Bollerslev, Tim. "Generalized autoregressive conditional heteroskedasticity."Journal of econometrics 31.3 (1986): 307-327.
20. Bollerslev, Tim, and Eric Ghysels. "Periodic autoregressive conditional heteroscedasticity." Journal of Business & Economic Statistics 14.2 (1996): 139-151.
21. Nelson, Daniel B. "Conditional heteroskedasticity in asset returns: A new approach." Econometrica: Journal of the Econometric Society (1991): 347-370.
22. Box, G. E. P., G. M. Jenkins, and G. C. Reinsel. "Time Series Analysis: Forecasting and Control. "
3rd ed. Englewood Cliffs, NJ: Prentice Hall, (1994).
23. Ljung, G. and G. E. P. Box. "On a Measure of Lack of Fit in Time Series Models." Biometrika. Vol. 66, (1978), pp. 67–72.
24. Engle, Robert F. "Autoregressive Conditional Heteroskedasticity with Estimates of the Variance of United Kingdom Inflation." Econometrica. Vol. 50, (1982), pp. 987–1007.
25. Engle, Robert F., and Victor K. Ng. "Measuring and testing the impact of news on volatility." The journal of finance 48.5 (1993): 1749-1778.
26. Kirchgässner, Gebhard, Jürgen Wolters, and Uwe Hassler. "Introduction to modern time series analysis. " Springer Science & Business Media, (2012).
27. Posada, David, and Thomas R. Buckley. "Model selection and model averaging in phylogenetics: advantages of Akaike information criterion and Bayesian approaches over likelihood ratio tests." Systematic biology 53.5 (2004): 793-808.
28. Montgomery, Douglas C. Statistical quality control. John Wiley, (1985).
29. Chakraborti, Subhabrata, P. Laan, and M. A. Wiel. "A class of distribution‐free control charts." Journal of the Royal Statistical Society: Series C (Applied Statistics) 53.3 (2004): 443-462.
30. Gibbons, J. D. and Chakraborti, S. "Nonparametric Statistical Inference.", 4th ed. Dekker, New York, (2003).
31. Jensen, Jens Ledet. "Saddlepoint approximations. " No. 16. Oxford University Press, (1995).