instructions.md

Instructions

Instructions for running the process model, generating the external variable datasets, tuning the feedback and feedforward controllers, performing the fault detection, and quantifying the fault detection performance are provided in this document.

Table of Contents

• 1. Process model [1]
  • 1.1. Running the model
  • 1.2. Process settings
  • 1.3. Output folder structure
  • 1.4. Process states
  • 1.5 Lowpass filter tuning
• 2. External variables
  • 2.1. Running the model
  • 2.2. Output folder structure
  • 2.3. Using the generated external variables
  • 2.4. External variables used in the simulation
• 3. Controller tuning [4]
  • 3.1. Running the model
  • 3.2. Output folder structure
• 4. Fault detection
  • 4.1. Running the fault detection
  • 4.2. Fault detection settings
  • 4.3. Output folder structure
• 5. ROC curves [7]
  • 5.1. Generating the ROC curves
  • 5.2. ROC curve settings
  • 5.3. Constructing the ROC curves
  • 5.4. Output folder structure
• References

1. Process model [1]

1.1. Running the model

1. Run the Simulink model from the MATLAB Live Script process_model/copper_solvent_extraction_model.mlx
2. Run the MATLAB Live Script from the main Process-State-Identification folder

The Simulink model requires the MATLAB Control System Toolbox to be installed.

1.2. Process settings

Table 1: Process settings

Setting	Values	Description
SAVE_IMAGES	true false	Saves the generated images to the respective output folders if set to true.
SAVE_DATA	true false	Saves the simulation data to the respective output folder if set to true.
SENSOR_NOISE	true false	Adds sensor noise to the measurements if set to true.
FEEDBACK_CONTROL	true false	Enables feedback control of the process if set to true.
FEEDFORWARD_CONTROL	true false	Enables feedforward control of the process if set to true.
EXTERNAL_VARIABLES_STEADY_STATE	true false	Sets the external variables to their constant steady-state values when set to true, or loads the non-steady-state external variable dataset selected by EXTERNAL_VARIABLES_DATASET when set to false.
EXTERNAL_VARIABLES_DATASET	'training' 'testing'	Loads the training non-steady-state external variable dataset when set to 'training', or the testing non-steady-state external variable dataset when set to 'testing'. Must specify a dataset to use regardless of the value of EXTERNAL_VARIABLES_STEADY_STATE.
LOWPASS_FILTER_TUNING	true false	Stops the loaded organic and lean electrolyte stiction models from 'sticking' when set to true. This can be used to tune the loaded organic and lean electrolyte stiction lowpass filters (see below). The loaded organic and lean electrolyte stiction models work as expected when set to false.
PROCESS_STATE	see below	Select which process faults occur by selecting the process state. See section 1.4. Process States below.
PROCESS_STATE_PLOTTING_REDUCED	true false	Only plots the single-fault process states (0 to 4) when set to true. Plots all the process states (0 to 8) when set to false.

1.3. Output folder structure

The .gitignore file has been set up to ignore all output folders.

Create the following folder structure to save the simulation results using the SAVE_IMAGES and SAVE_DATA settings:

.
|__ process_model
    |__ output
        |__ data
        |__ graphs
            |__ measured_variables
            |__ process_variables
            |__ valve_states

1.4. Process states

The desired fault combinations can be set using the PROCESS_STATE setting. The following table shows which loaded organic valve faults [2] and which lean electrolyte valve faults occur for the selected process state.

Table 2: Process states

Process State	Loaded Organic Valve	Lean Electrolyte Valve
0	normal	normal
1	stuck	normal
2	stiction	normal
3	normal	stuck
4	normal	stiction
5	stuck	stuck
6	stuck	stiction
7	stiction	stuck
8	stiction	stiction
9	custom	custom

State 9 allows for custom behaviour to be defined in each control valve's custom variant subsystem's Stateflow chart.

The valve states are represented by the following values, and are selected using variant subsystems:

Table 3: Valve states

Value	Valve State
0	normal
1	stuck
2	stiction

The time that the selected process faults occur can be set using the following start_time parameters. Corresponding stop_time parameters are also provided to set the time at which the process faults stop occurring. If no stop time is desired, set the respective stop_time parameter equal to the simulation time plus one.

Table 4: Process fault start and stop time settings

Parameter	Units	Description
valve_LO_fault_start_time	s	Time for the loaded organic valve's fault to occur
valve_LO_fault_stop_time	s	Time for the loaded organic valve's fault to stop
valve_LE_fault_start_time	s	Time for the lean electrolyte valve's fault to occur
valve_LE_fault_stop_time	s	Time for the lean electrolyte valve's fault to stop

1.5 Lowpass filter tuning

The loaded organic and lean electrolyte control valve stiction models use 1^st order Butterworth lowpass filters [3] to account for the sensor noise's effect on the valve stem positions. The valves 'stick' when the filtered valve position reaches a turning point.

The cutoff frequency of the lowpass filters can be tuned by seting the LOWPASS_FILTER_TUNING setting to true. The stiction models then still run, but the control valves will not 'stick'. The filtered signals can be viewed using the Valve LO Lowpass Filter Scope and Valve LE Lowpass Filter Scope scopes found in their respective stiction-valve-model subsytems. The process state has to be set to such a state in which the valve under consideration is experiencing stiction for the lowpass filters to be active.

The cutoff frequency for the loaded organic control valve's lowpass filter can be set using valve_LO_stiction_lowpass_filter_cutoff_frequency (rad/s). The cutoff frequency for the lean electrolyte control valve's lowpass filter can be set using valve_LE_stiction_lowpass_filter_cutoff_frequency (rad/s).

2. External variables

2.1. Running the model

1. Run the Simulink model from the MATLAB Live Script gaussian_external_variables.mlx
2. Run the MATLAB Live Script from the main Process-State-Identification folder

2.2. Output folder structure

Create the following folder structure to save the smoothed external variable data and graphs:

.
|__ external_variables
    |__ output
        |__ data
        |__ graphs

2.3. Using the generated external variables

Copy the generated external variable .mat files over to the following folder to use them in the process model:

.
|__ external_variables
    |__ data

2.4. External variables used in the simulation

The following settings were used in the Signal Builder blocks in the gaussian_external_variables.slx file to generate the non-steady-state external variables used for the process model:

Table 5: External variable properties

Property	Value
Simulation time	200 hours (720 000 seconds)
Sampling time	1 second
Standard deviation	$\sigma$ = 0.10 x steady-state value
Sample frequency	0.00005 Hz

The first and last points of each signal were manually changed to start and stop on the steady-state values of the respective variable.

Table 6: Training external variable properties

Variable	Mean	Standard deviation	Units	Seed
$c_{PLS}$	7	0.7	g/L	1
$c_{LE}$	35	3.5	g/L	2
$f_{PLSP}$	278	27.8	L/s	5
$f_{PLSS}$	278	27.8	L/s	16

Table 7: Testing external variable properties

Variable	Mean	Standard deviation	Units	Seed
$c_{PLS}$	7	0.7	g/L	19
$c_{LE}$	35	3.5	g/L	22
$f_{PLSP}$	278	27.8	L/s	28
$f_{PLSS}$	278	27.8	L/s	30

3. Controller tuning [4]

3.1. Running the model

1. Run the Simulink model from either of the following two MATLAB Live Scripts:
   1. feedback_arx_models.mlx
   2. feedforward_arx_models.mlx
2. Run the above mentioned MATLAB Live Scripts from the main Process-State-Identification folder

3.2. Output folder structure

Create the following folder structure to save the ARX model [5] results:

.
|__ controller_tuning
    |__ output
        |__ feedback
        |__ feedforward

4. Fault detection

4.1. Running the fault detection

1. Run the fault detection MATLAB Live Script from the main Process-State-Identification folder

4.2. Fault detection settings

Table 8: Fault detection settings

Setting	Values	Description
SAVE_IMAGES	true false	Saves the generated images to the respective output folders if set to true.
SAVE_DATA	true false	Saves the fault detection data to the respective output folder if set to true.
NUMBER_OF_PRINCIPLE_COMPONENTS_TO_USE	1 to 11	Specify the number of principal components to use for the reduced principal component subspace.
T2_ALPHA	$T^{2}_{\alpha}\in\mathbb{R}>0$	Upper control limit (UCL) for the Hotelling's T2 statistic control chart [6].
Q_ALPHA	$Q_{\alpha}\in\mathbb{R}>0$	UCL for the Q statistic control chart [6].
NUMBER_CONSECUTIVE_ABOVE_UCL	$n\in{Z}\geq0$	Specify the number of consecutive measurements that must be above the UCL before a fault is detected.
PROCESS_STATE_PLOTTING_REDUCED	true false	Only plots the single-fault process states (0 to 4) when set to true. Plots all the process states (0 to 8) when set to false.
ROC_CURVE_CONSTRUCTION_T2	true false	Appends the Hotelling's T2 ROC curve results for the current $T^{2}_{\alpha}$ to the ROC_CURVE_DATA_T2 table to use for constructing a Hotelling's T2 ROC curve.
ROC_CURVE_CONSTRUCTION_Q	true false	Appends the Q statistic ROC curve results for the current $Q_{\alpha}$ to the ROC_CURVE_DATA_Q table to use for constructing a Q statistic ROC curve.
STATE_1_START_TIME	$n\in{Z}\geq0$	The time at which process state 1 starts in the fault detection dataset in units of seconds. Must be divisable by SAMPLING_RATE.
STATE_1_STOP_TIME	$n\in{Z}\geq0$	The time at which process state 1 stops in the fault detection dataset in units of seconds. Must be divisable by SAMPLING_RATE.
STATE_2_START_TIME	$n\in{Z}\geq0$	The time at which process state 2 starts in the fault detection dataset in units of seconds. Must be divisable by SAMPLING_RATE.
STATE_2_STOP_TIME	$n\in{Z}\geq0$	The time at which process state 2 stops in the fault detection dataset in units of seconds. Must be divisable by SAMPLING_RATE.
STATE_3_START_TIME	$n\in{Z}\geq0$	The time at which process state 3 starts in the fault detection dataset in units of seconds. Must be divisable by SAMPLING_RATE.
STATE_3_STOP_TIME	$n\in{Z}\geq0$	The time at which process state 3 stops in the fault detection dataset in units of seconds. Must be divisable by SAMPLING_RATE.
STATE_4_START_TIME	$n\in{Z}\geq0$	The time at which process state 4 starts in the fault detection dataset in units of seconds. Must be divisable by SAMPLING_RATE.
STATE_4_STOP_TIME	$n\in{Z}\geq0$	The time at which process state 4 stops in the fault detection dataset in units of seconds. Must be divisable by SAMPLING_RATE.
SAMPLING_RATE	$n\in{Z}\geq0$	The sensor sampling rate used for the data in units of seconds.
DETECTION_DELAY_CONSTRUCTION_T2	true false	Appends the Hotelling's T2 detection delay results for the current $T^{2}_{\alpha}$ to the DETECTION_DELAY_DATA_T2 table to use for constructing a Hotelling's T2 detection delay plot.
DETECTION_DELAY_CONSTRUCTION_Q	true false	Appends the Q statistic detection delay results for the current $Q_{\alpha}$ to the DETECTION_DELAY_DATA_Q table to use for constructing a Q statistic detection delay plot.

4.3. Output folder structure

Create the following folder structure to save to fault detection results using the SAVE_IMAGES and SAVE_DATA settings:

.
|__ fault_detection
    |__ output
        |__ data
        |__ fault_detection
        |__ PCA
        |__ training

5. ROC curves [7]

5.1. Generating the ROC curves

1. Run the ROC curves MATLAB Live Script from the main Process-State-Identification folder

5.2. ROC curve settings

Table 9: ROC curve settings

Setting	Values	Description
T2_TRAINING_INDEX	$n\in{Z}\in[1 \ , nr \ of \ T^{2} \ ROC \ datapoints]$	The index of the Hotelling's T2 training $T^{2}_{\alpha}$ point in the Hotelling's T2 ROC curve data file.
Q_TRAINING_INDEX	$n\in{Z}\in[1 \ , nr \ of \ Q \ ROC \ datapoints]$	The index of the Q statistic training $Q_{\alpha}$ point in the Q statistic ROC curve data file.
T2_RECOMMENDED_INDEX	$n\in{Z}\in[1 \ , nr \ of \ T^{2} \ ROC \ datapoints]$	The index of the Hotelling's T2 recommended $T^{2}_{\alpha}$ point in the Hotelling's T2 ROC curve data file.
Q_RECOMMENDED_INDEX	$n\in{Z}\in[1 \ , nr \ of \ Q \ ROC \ datapoints]$	The index of the Q statistic recommended $Q_{\alpha}$ point in the Q statistic ROC curve data file.
T2_OPTIMAL_SENSITIVITY_INDEX	$n\in{Z}\in[1 \ , nr \ of \ T^{2} \ ROC \ datapoints]$	The index of the Hotelling's T2 optimal sensitivity $T^{2}_{\alpha}$ point in the Hotelling's T2 ROC curve data file.
Q_OPTIMAL_SENSITIVITY_INDEX	$n\in{Z}\in[1 \ , nr \ of \ Q \ ROC \ datapoints]$	The index of the Q statistic optimal sensitivity $Q_{\alpha}$ point in the Q statistic ROC curve data file.

5.3. Constructing the ROC curves

Save the ROC_CURVE_DATA_T2 and ROC_CURVE_DATA_Q data tables from the fault detection as .mat files and copy them over to the following folder to use for constructing the ROC curves:

.
|__ roc_curves
    |__ data

5.4. Output folder structure

Create the following folder structure to save to generated ROC curves:

.
|__ roc_curves
    |__ output

References

[1] T. Komulainen, P. Pekkala, A. Rantala, and S.-L. Jämsä-Jounela, “Dynamic modelling of an industrial copper solvent extraction process,” Hydrometallurgy, vol. 81, no. 1, pp. 52–61, Jan. 2006, doi: 10.1016/j.hydromet.2005.11.001.

[2] M. A. A. Shoukat Choudhury, N. F. Thornhill, and S. L. Shah, “Modelling Valve Stiction,” Control Eng Pract, vol. 13, no. 5, pp. 641–658, May 2005, doi: 10.1016/j.conengprac.2004.05.005.

[3] MathWorks, “Butterworth filter with varying coefficients - Simulink,” 2022. https://www.mathworks.com/help/control/ref/varyinglowpassfilter.html (accessed Oct. 25, 2022).

[4] T. Komulainen, F. J. Doyle, A. Rantala, and S. L. Jämsä-Jounela, “Control of an industrial copper solvent extraction process,” J Process Control, vol. 19, no. 1, pp. 2–15, Jan. 2009, doi: 10.1016/j.jprocont.2008.04.019.

[5] T. E. Marlin, Process Control: Designing Processes and Control Systems for Dynamic Performance, 2nd ed. 2015.

[6] A. Bakdi and A. Kouadri, “An improved plant-wide fault detection scheme based on PCA and adaptive threshold for reliable process monitoring: Application on the new revised model of Tennessee Eastman process,” J Chemom, vol. 32, no. 5, p. e2978, May 2018, doi: 10.1002/CEM.2978.

[7] G. James, D. Witten, T. Hastie, and R. Tibshirani, An Introduction to Statistical Learning. New York, NY: Springer US, 2021. doi: 10.1007/978-1-0716-1418-1.