1. Detection and Diagnosis of Plant-wide Oscillations: An Application Study Vinay Kariwala M.A.A. Shoukat Choudhury, Sirish L. Shah, J. Fraser Forbes, Edward S. Meadows Department of Chemical and Materials Engineering University of Alberta Hisato Douke, Haruo Takada Mitsubishi Chemical Corporation, Mizushima, Japan

2. 2 Outline Problem Description Detection Theory (Autocorrelation function) Application Results Diagnosis Theory (Valve Stiction) Application Results Future Directions

3. 3 Problem Description Feed Condenser Top Product Reflux Drum Side Stripper Stripper Distillation Column Oscillations in Condenser Level Bottom Product

4. 4 Problem Description Condenser Level Oscillations with Large amplitude Back-off from Optimal operating point Economic Potential 1% increase in set points ~ 20M Yen/year Previous attempts PID tuning, MPC model Not successful

5. 5

6. 6 Scope of Analysis

7. 7 Data Description Data Set: 2880 samples, 1 min. data, Variables: 45 Tags + 15 Controller Outputs (MV) 15 SISO control loops 5 cascade control loops 2 DMCs

8. 8 Detection Philosophy Which variables are oscillating? Which variables have common oscillations? Important to find All variables with common oscillations Root cause likely to lie within this set

9. 9 Detection by Visual Inspection Fourier Transform Time trends Presence of Oscillation – Peak in Spectra Period and Regularity – Difficult to Judge Multiple oscillations destroy Regularity Noise overshadows Oscillations Power Spectrum

10. 10 Detection using ACF Auto Correlation Function Effect of Noise Reduced ACF oscillates at same frequency as signal Regularity of oscillations – Zero Crossings of ACF Power Spectrum Time Trend

11. 11 Detection using ACF Period of OscillationOscillation regular if ACF Zero Crossings

12. 12 Clustering using ACF Two signals – same frequency oscillation if Ref: Thornhill et al., JPC, 2003 Oscillation considered significant if (Power in selected band)/(Power in entire spectrum) >

13. 13 Multiple Oscillations Fourier Transform Two peaks in Spectra Use Band pass filters Calculate ACF for each filtered signal

14. 14 Detection Algorithm Remove Non-stationary trends Repeat if more than one oscillations present in every filter range OR stop Detect and cluster oscillations Narrow ranges of band pass filters around detected oscillations

15. 15 Detection: Results Low frequency range 158 min./cycle – 27 tags 137 min./cycle – 10 tags Medium frequency range 62 min./cycle – 11 tags 75 min./cycle – 23 tags 86 min./cycle – 5 tags High frequency range 43 min./cycle – 5 tags 25 min./cycle – 1 tag 4 min./cycle – 1 tag Condenser Level

16. 16 Low frequency detections 158 samples/cycle 137 samples/cycle PV OP PV OP

17. 17 Summary of Detection Low frequency oscillations 158 minute/cycle 26 tags other than condenser level Plant wide nature of oscillations revealed Root cause should lie in this set

18. 18

19. 19 Possible Reasons Poorly tuned Controller External disturbances Process induced oscillations Valve Problems MPC model mismatch

20. 20 Definition of Stiction valve output (mv) valve input (op) deadband stickband slip jump, j stickband + deadband moving phase A B C D E F G s

21. 21 Central Idea: Nonlinear interactions between different frequencies Normalized Bispectrum – squared Bicoherence Test of Nonlinearity BispectrumDFT

22. 22 Linear and nonlinear Signal

23. 23 Non-Gaussianity Index and Nonlinearity Index NGI <= 0 NGI>0, NLI=0NGI>0, NLI>0 Frequency independentFrequency dependent Gaussian Linear Non-Gaussian Linear Non-Gaussian Nonlinear Critical Values of bic 2 crit is determined at 95% or 99% confidence interval of the squared bicoherence Test of Non-linearity (contd)

24. 24 NGI = 0.02 andNLI = 0.55 Loop is Nonlinear 1.The process is locally linear in the current operating region 2.Disturbances entering the loop are linear Assumptions: Flow Control Loop in a Refinery

25. 25 OP PV OP Pattern of Stiction in PV-OP Plot apparent stiction = maximum width of the cycles in pv-op plot

26. 26 4 38.138.238.338.438.538.638.738.838.9 1.105 1.11 1.115 1.12 1.125 1.13 1.135 1.14 1.145 x 10 PQ a b OP PV Quantification of Apparent Stiction Apparent Stiction = 0.35 %

27. 27 Nonlinearity Analysis

28. 28 Stiction Quantification FC5PC1TC2 No Stiction0.5%1.25%

29. 29 Research Directions ACF based Detection Algorithm –False Detection, Premature Termination Stiction Quantification –Assumption of linear disturbance Path Analysis –Oscillation Propagation Model Predictive Controller –Oscillations due to model mismatch

30. 30 Acknowledgements NSERC Dr. Nina Thornhill, UK Ebara San, Amano San, Oonodera San Computer Process Control group