1. Unscented Kalman Filter for a coal run-of-mine bin
IFAC MMM 2015 Workshop
Unscented Kalman Filter for a coal run-of-mine bin
Jonathan Meyer, VICENTE ALVARADO – EXXARO
PROF. IAN CRAIG – UNIVERSITY OF PRETORIA

2. Bin Dynamic Model and INDUSTRIAL DATA identification
Agenda
Introduction
Bin Dynamic Model and INDUSTRIAL DATA identification
Unscented kalman filter
UKF Simulation Results
Summary

3. Introduction General control loop Coal run-of-mine bin operation
State observers and LITERATURE ON DYNAMIC MODELS

4. Introduction
GENERAL CONTROL LOOP:
In scope
Out of scope

5. COAL RUN-OF-MINE BIN OPERATION
Introduction
Manual density control
COAL RUN-OF-MINE BIN OPERATION
Classify run-of-mine (ROM) coal for bin storage
Module one DMC
Manual feeder control
Duff product
Manual level control
Manual density control
Stockpile
Bin
Crush and screen
Module two DMC
Duff product
Manual density control
Plant two DMS
Manual feeder control
Metallurgical coal
Thickeners
Bin scope

6. ESTIMATE VALUES OF STATE VARIABLES:
Introduction
ESTIMATE VALUES OF STATE VARIABLES:
Estimation of the bin model state variables
Various observers include:
Particle filters
Batch filters
Exact recursive filters
Extended Kalman filter
Unscented Kalman filter
Unscented Kalman filter chosen as it uses nonlinear state-space model with no approximations

7. Dynamic models only available for simple fixed area vessels
Introduction
DYNAMIC MODELS:
Dynamic models only available for simple fixed area vessels
No dynamic models for stockpile bin geometry or variable area vessels
Bin models available normally use discrete element methods
Limited minerals processing dynamic models
Screens
Ball mills
Double-roll crushers

8. Bin dynamic model and Industrial data identification
DEVELOPMENT OF DYNAMIC BIN MODEL
SYSTEM IDENTIFIICATION RESULTS
ADVANCED BIN MODEL DEVELOPMENT

9. Bin dynamic model and Industrial data identification
Inputs:
𝑾 𝒃,𝒊 = Feed mass flow rate
𝑾 𝒃,𝒐,𝟑 = Bin 3 mass flow rate
𝒇 𝒃𝒇,𝟏 = Bin 1 feeder frequency
𝒇 𝒃𝒇,𝟐 = Bin 2 feeder frequency
Outputs:
𝑾 𝒃𝒇,𝒐,𝟏 = Bin 1 mass flow rate
𝑾 𝒃𝒇,𝒐,𝟐 = Bin 2 mass flow rate
𝒉 𝒃 = Bin level
Parameters:
𝜷 𝒃 = Bin height ratio
𝝆 𝒃 = Bin bulk density
𝑨 𝒃 = Bin base area
𝝉 𝒃𝒇,𝟏 = Bin 1 feeder time constant
𝑲 𝒃𝒇,𝟏 = Bin 1 feeder constant
𝝉 𝒃 f,2 = Bin 2 feeder time constant
𝑲 𝒃 f,2 = Bin 2 feeder constant
States:
𝒎 𝒃 = Bin mass
𝒎 𝒃𝒇,𝟏 = Bin 1 feeder mass
𝒎 𝒃𝒇,𝟐 = Bin 2 feeder mass

10. Bin dynamic model and Industrial data identification
CONSERVATION OF MASS (SIMPLIFIED):
Found nonlinear relationship in bin level
𝑨𝒄𝒄𝒖𝒎𝒖𝒍𝒂𝒕𝒊𝒐𝒏 𝒐𝒇 𝒎𝒂𝒔𝒔 = 𝑴𝒂𝒔𝒔 𝒊𝒏 − 𝑴𝒂𝒔𝒔 𝒐𝒖𝒕

11. Bin dynamic model and Industrial data identification
SIMPLIFIED BIN MODEL FIT AND CORRELATION:
FURTHER ANALYTICAL ANALYSIS:
Found nonlinear relationship in feeder operation and mass flow proportionality constants
Output
Fit (%)
Correlation
Bin 1 mass flow
75.0
0.97
Bin 2 mass flow
73.7
Bin level
40.7
0.83
Linear
Inverse exponential
Sigmoid

12. Bin dynamic model and Industrial data identification
ADVANCED BIN MODEL SYSTEM IDENTIFICATION:
Three experimental sets of data used for each phase
Experiment one – Primarily phase I and II

13. Bin dynamic model and Industrial data identification
ADVANCED BIN MODEL SYSTEM IDENTIFICATION:
Three experimental sets of data used for each phase
Experiment two– Primarily phase II and III

14. Bin dynamic model and Industrial data identification
ADVANCED BIN MODEL SYSTEM IDENTIFICATION:
Three experimental sets of data used for each phase
Experiment three– Phase III

15. Bin dynamic model and Industrial data identification
ADVANCED BIN MODEL FIT AND CORRELATION:
Experiment
Output
Fit (%)
Correlation
One
Bin 1 mass flow
79.7
0.99
Bin 2 mass flow
64.3
Bin level
71.8
1.00
Two
45.4
0.85
53.8
0.90
49.0
Three
76.2
0.98
66.9
0.95
54.3

16. Bin dynamic model and Industrial data identification
ADVANCED BIN MODEL:
Nonlinear relationship in:
Bin level
Bin feeders
Simulated over same industrial production data as in simplified model

17. Bin dynamic model and Industrial data identification
ADVANCED BIN MODEL FIT AND CORRELATION:
Output
Fit (%)
Correlation
Bin 1 mass flow
88.9
0.99
Bin 2 mass flow
87.1
Bin level
54.2
0.95

18. Unscented Kalman Filter
UNSCENTED KALMAN FILTER ALGORITHM

19. Unscented Kalman Filter
UNSCENTED KALMAN FILTER (UKF) ALGORITHM:
Nonlinear state-space representation of dynamic model
Recursive estimation of 𝒙 𝒌 by,
Unscented transform (UT) is used to calculate the statistics of random variables [sigma vectors 𝜒 𝑖 through nonlinear function 𝛾 𝑖 =g 𝜒 𝑖 ]
Initialise the algorithm with original state ( P 𝟎 𝒂 ), process noise ( P 𝒗 ) and measurement noise ( P 𝒏 )
𝒚=𝒇 𝒙,𝒖,𝜽
𝒅𝒙 𝒅𝒕 =𝒈(𝒙,𝒖,𝜽)
𝒙 𝒌 = (prediction of 𝒙 𝒌 ) + 𝜿 𝒌 [ 𝒚 𝒌 −( prediction of 𝒚 𝒌 )]

20. Unscented Kalman Filter
UNSCENTED KALMAN FILTER (UKF) ALGORITHM:
Original state ( P 𝟎 𝒂 )
Process noise ( P 𝒗 )
Measurement noise ( P 𝒏 )
Initialise
P 𝟎 𝒂 = I 𝟒
Standard deviation of measurements
P 𝒗 = Q 𝟐
Simulate
Scaling factor
Fit acceptable? No
Yes
P 𝒏 = 𝑟 2 I 𝟑
𝑟=0.01
Complete

21. UKF Simulation results
SIMPLIFIED BIN UKF RESULTS
ADVANCED BIN UKF RESULTS

22. UKF Simulation Results
SIMPLIFIED BIN MODEL:

23. UKF Simulation Results
SIMPLIFIED BIN UKF FIT AND CORRELATION:
Output
Fit (%)
Correlation
Bin 1 mass flow
99.5
1.00
Bin 2 mass flow
99.3
Bin level
99.8

24. UKF Simulation Results
ADVANCED BIN MODEL:

25. UKF Simulation Results
ADVANCED BIN UKF FIT AND CORRELATION:
Output
Fit (%)
Correlation
Bin 1 mass flow
99.5
1.00
Bin 2 mass flow
99.3
Bin level
99.7

26. Summary
SUMMARY OF ALL RESULTS
FUTURE WORK

27. MODEL AND UKF FIT RESULTS COMPARISON SUMMARY: Simplified bin model:
Advanced bin model
Output
Model Fit (%)
UKF Fit (%)
Bin 1 mass flow
75.0
99.5
Bin 2 mass flow
73.7
99.3
Bin level
40.7
99.8
Output
Model Fit (%)
UKF Fit (%)
Bin 1 mass flow
88.9
99.5
Bin 2 mass flow
87.1
99.3
Bin level
54.2
99.7

28. Summary
PROPOSED FUTURE WORK:
Implement UKF online over longer time period to validate
Develop model-based controller for bin system
Implement model-based controller with UKF state estimator
Explore the use of the UKF for online parameter identification

29. Thank you