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 TakadaMitsubishi Chemical Corporation,

Mizushima, Japan

2Outline

• Problem Description

• Detection• Theory (Autocorrelation function)

• Application Results

• Diagnosis• Theory (Valve Stiction)

• Application Results

• Future Directions

3Problem Description

Feed

Condenser

Top ProductReflux Drum

Side Stripper

Stripper

Distillation Column

Oscillations in

Condenser Level

Bottom Product

4Problem 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

6Scope of Analysis

Column 1

FC8

LC10

LC9

FC7

LC8

FC6

FC5

LC7

LI1

LC2

PC1

LI2

LC1

FI1

FI3

AC1

FC2

TC1

AC2

LC3

FI2

LC4

LC5

LI3

SI1

PC2 PC

3

PC4

PC5

TI4 TI

5

TI6

TC2

FC3

FC4

LC11

TI1

Column 2

Compressor

LC6

TI2

TI3

FC1

FI4

Heat Exchanger

Chain

LI5

LI4

7Data 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

8Detection 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

9Detection 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

10Detection using ACFAuto Correlation

Function

Effect of Noise Reduced

ACF oscillates at same frequency as signal

Regularity of oscillations – Zero Crossings of ACF

Power SpectrumTime Trend

11Detection using ACF

Period of Oscillation Oscillation regular if

ACF

ZeroCrossings

12Clustering 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) >

13Multiple Oscillations

Fourier Transform

Two peaks in Spectra

Use Band pass filters

Calculate ACF for each filtered signal

14Detection 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

15Detection: ResultsLow 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

16Low frequency detections

158 samples/cycle

137 samples/cyclePV OP PV OP

Column 1

FC8

LC10

LC9

FC7

LC8

FC6

FC5

LC7

LI1

LC2

PC1

LI2

LC1

FI1

FI3

AC1

FC2

TC1

AC2

LC3

FI2

LC4

LC5

LI3

SI1

PC2 PC

3

PC4

PC5

TI4 TI

5

TI6

TC2

FC3

FC4

LC11

TI1

Column 2

Compressor

LC6

TI2

TI3

FC1

FI4

Heat Exchanger

Chain

LI5

LI4

17Summary 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

19Possible Reasons

• Poorly tuned Controller

• External disturbances

• Process induced oscillations

• Valve Problems

• MPC model mismatch

20Definition of Stiction

valv

e ou

tput

(m

v)

valve input (op)

deadband stickband

slip jump, j

stickband + deadband

mov

ing

phas

e

A BC

D

EF

G

s

21

Central Idea:Nonlinear interactions between different frequencies

Normalized Bispectrum – squared Bicoherence

Test of Nonlinearity

Bispectrum DFT

22Linear and nonlinear Signal

23

Non-Gaussianity Index and Nonlinearity Index

NGI <= 0 NGI>0 , NLI=0

NGI>0, NLI>0

Frequency independent Frequency dependent

GaussianLinear

Non-GaussianLinear

Non-GaussianNonlinear

Critical Values of bic2crit is determined at 95% or 99%

confidence interval of the squared bicoherence

Test of Non-linearity (cont’d)

24

NGI = 0.02 andNLI = 0.55

200 400 600 800 10001.1

1.12

1.14

x 104

PV

and S

P

PVSP

200 400 600 800 100038

38.2

38.4

38.6

38.8

CO

sampling instants

CO

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

OP

PV

PV

OP

Pattern of Stiction in PV-OP Plot

apparent stiction = maximum width of the cycles in pv-op plot

26

4

38.1 38.2 38.3 38.4 38.5 38.6 38.7 38.8 38.91.105

1.11

1.115

1.12

1.125

1.13

1.135

1.14

1.145x 10

P Q

a b

OP

PV

Quantification of Apparent Stiction

Apparent Stiction = 0.35 %

27Nonlinearity Analysis

28Stiction QuantificationFC5 PC1 TC2

No Stiction 0.5% 1.25%

29Research 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

30Acknowledgements

• NSERC

• Dr. Nina Thornhill, UK

• Ebara San, Amano San, Oonodera San

• Computer Process Control group