6 Unsupervised Learning for Operational State
6.4 Application of AR Tnet to the FCC Process
The FCC process and the data used is described in appendix B. To demonstrate the procedure, 64 data patterns are used. Discussion is limited to 64 data patterns in order to keep the discussion manageable and to assist in presentation of the results.
The data sets include the following faults or disturbances:
• fresh flow rate is increased or decreased
• preheat temperature for the mixed feed increases or decreases
• recycle slurry flow rate increases or decreases
• opening of the hand valve V20 increases or decreases
• air flow rate increases or decreases
• the opening of the fully open valve 40 I-ST decreases
• cooling water pump fails
• compressor fails
• double faults occur
The sixty four data patterns were obtained from a customised dynamic training simulator, to which random noise was added using a zero-mean noise generator (MATLAB®). In the following discussions, the term "data patterns" refers to these sixty four data patterns and "identified patterns" to the patterns estimated by ARTnet.
Figure 6.5(a) shows a reactor temperature transient when the fresh feed flowrate increases by 70%. Figure 6.5(b) is the same transient with random noise. The corresponding four scales from multiresolution analysis for this transient are shown in Figure 6.6, together with the corresponding extrema on the right hand side of Figure 6.6.
2 0
·2
·4
·6
·8
·10
·12
·14
·16 0 20 40 60 80 100
(a)
-2 -4
·6 -8 -10 -12 -14 -16
(b)
Figure 6.S A signal from the simulator (a) and the signal with random noise (b).
128 Data Mining and Knowledge Discovery for Process Monitoring and Control
after noise removal (a) after piece-wise analysis (b)
Figure 6.6 Multiresolution analysis (left) and extrema (right),
As stated in Chapter 3, the extrema that are mostly influenced by noise fluctuations are those (1) where the amplitude decreases on average as the decomposition scale increases and (2) do not propagate to large scales. Using these criteria, noise extrema are removed.
The extrema representation after the noise extrema are removed is a sparse vector, so a piece-wise technique is employed to reduce the dimensionality of the signal.
The extrema after removing noise and carrying out piece-wise processing are shown in Figure 6.7.
Figure 6.8 shows the result after noise removal and compares it with the multiresolution analysis of the original noise-free signal. The extrema are the same in positions but are slightly different in value. The noise removal algorithm is therefore suitable in this case and the 4th scale extrema are selected as input to the ARTnet for pattern identification
It is important that a suitable threshold for pattern recognition is used when applying ARTnet. For a threshold p
=
0.8, all 64 data patterns are identified as individual patterns. A more suitable threshold is obtained by analysing clustering results for increased threshold values as shown in Table 6.1.Table 6.1 ARTnet clustering result using different distance thresholda.
Threshold p Number of
patterns Identified grouping of data samples identified
0.8 64
1.0 63 r56571
2.0 60 r5 71 r25 261 r27 281 r56 571
3.0 57 r5 71 r19 2023241 r25 261
m
281 r56 571 4.0 54 r5 6 7 81 r19 20 21 23 241 r25 26] r27 281 r56 5714.5 49 [3456789] [192021222324] [25 26] [2728]
r35 361 r56 57]
5.0 48 r34 5 6 7 8 91 r 19 20 21 22 23 24 291 r25 261 r27 281 r35 361 r56 57]
6.0 47 r34 5 6 7 8 91 r 19 20 21 22 23 24 29 611 r25 261 r27 281 [35 361 r56 571
a -[56 57] means that data patterns 56 and 57 are identified in the same cluster.
130 Data Mining and Knowledge Discovery for Process Monitoring and Control
With the threshold p increased to 1.0, data patterns 56 and 57, which represent cases where the opening of valve 401-ST is decreased from 100% by 80% and 90%
are grouped together. When p is 2.0, further groupings are [5, 7], representing the fresh feed flowrate increasing by 50% and 70%, [25, 26] recycle oil flowrate increasing by 70% and 90%, and [27, 28] recycle oil flowrate decreasing by 70%
and 90%. It is obvious that these are all reasonable groupings.
When the threshold value is 4.5, the groupings are [3,4,5,6,7,8,9], [192021 22 2324], [2526], [27,28], [35,36] and [56 57]. The pairing of identified patterns and original data patterns are shown in Table 6.2. The clustering is justified by inspecting the results in detail. Figure 6.9 shows the trends of three measurements for data pattern 5. It shows that regenerator temperature and concentration of oxygen in regenerator flue gas drop sharply while catalyst hold-up in reactor increases dramatically. All of which mean abnormal operations. Very similar scenarios can be found for data patterns 3, 4, 5, 6, 7, 8, and 9, so the result of regarding them as a single pattern is acceptable. The grouping [35, 36] can also be justified by inspecting the dynamic responses (Figure 6.10). In both cases, the dynamic responses of catalyst recycle rate lead to a steady state with the process remaining under control.
Table 6.2 ATRnet identified clusters when the distance threshold is 4.5 and the corresponding data patterns . a
Identified Corresponding Identified Corresponding Identified Corresponding clusters data patterns clusters data natterns clusters data patterns
1 I 19 32 37 51
4 4
aft'nriseremMII (a) after pece-\\ise (b)
Figure 6.7 Extrema after removing noise (left) and piece wise analysis (right).
Di -detail of multiscale wavelet analysis; Ai -approximation.
132 Data Mining and Knowledge Discovery for Process Monitoring and Control
However, any further increase in threshold is not useful because some data patterns that are significantly different are grouped in the same cluster. For instance, when the threshold value is 5, data pattern 29 (opening ratio of the hand-valve V20 increasing by 5%) is merged with the clusters representing increase and decrease in the preheat temperature of the mixed feed. Therefore, the threshold p
=
4.5 isconsidered as the most appropriate value for this case.
10
10
200~ -~--'-:::0 ----:!15:----:::2o----!2·5
(a)
·10
~200L -~--,-:::0-~,5:---:::20---:!25
(b)
Figure 6.8 Comparison of the result after noise removal (b) with the multiresolution analysis of the original simulation signal (a).
o ,...,--,---....---,----,----, 0.05 I-:;::X::::::::=;;:--""--'---'
-10
Regenemtor Temperature
_201---_ _ -+-_---< _ _ +-_-1 Time
300
200 100
-0.15
Oxygen in outlet of Regenerator
-0.35'--_-'-_--... _ _ "--_-'-_--'
Time Catalyst holdup
Time
Figure 6.9 Variable dynamic trends of data pattern 5.
'
.. ~-~----~---.Catalyst rElC)de rate #36
.,
Tine Tim!
Figure 6.10 Dynamic trends of catalyst recycle rate for data patterns 35 and 36.
134 Data Mining and Knowledge Discovery for Process Monitoring and Control
6.4.1 Comparison between ARTnet and ART2
It is apparent that the data pre-processing part of ARTnet is able to effectively reduce the dimension of the dynamic trend signals using wavelet feature extraction and piece wise processing. ARTnet has also shown other advantages over ART2 in operational data analysis. These include the determination of threshold values, the ability to deal with noise and computational speed. In the comparison followed only the fIrst fIfty seven data patterns were used.
6.4.1.1 Threshold Determination
In this case, only 57 data patterns are used to compare the distance threshold for using ARTnet and the vigilance value in ART2 using noise-free data. For noise free data, ARTnet and ART2 give the same results if the ARTnet distance threshold and the ART2 vigilance are appropriately adjusted, as shown in Table 6.3. To understand the table, consider the last row, which shows that when the distance threshold of ARTnet is 4.5 it gives the same grouping result as ART2 with a vigilance value of 0.9985. From Table 6.3, for the same groupings, the ARTnet distance threshold changes from 0.8 to 4.5 while the vigilance of ART2 varies from 0.9998 down to 0.9985. So the distance threshold for ARTnet is less sensitive than the vigilance of ART2. The ART2 clustering is too sensitive to the vigilance value, making it difficult to set a value.
6.4.1.2 Robustness with Respect to Noise
The following demonstrates that ARTnet gives consistent clustering result regardless of the magnitude of noise to signal ratio, providing it is in a reasonable range. ART2 gives fewer clusters at a low noise to signal ratio and more clusters at a larger ratio. 57 data patterns are considered with white noise added. A constant
Cnoise is introduced to control the magnitude of noise defIned by The magnitude of noise from
the noise generator
The magnitude of noise = =
-c'lOi.\'e
(6.5)
Table 6.3 Comparison of the value ranges of the distance threshold of ARTnet and the vigilance value of AR T2, for the same grouping schemes' , . abc
ARTnet ART2
distance vigilance Grouping of data samples threshold value
0.8 0.9998
1.0 0.9996 [5657]
2.0 0.9992 [5 7] [2526] [2728] [5657]
3.0 0.9990 [57] [19202324] [25 26] [2728] [5657]
4.0 0.9987 [5 67 8] [192021 2324] [2526] [2728] [56 57]
4.5 0.9985 [3456789] [192021222324] [25 26] [2728]
[35 36] [5657]
a [56 57] means that data patterns 56 and 57 are grouped in the same cluster, b Only the first 57 data patterns are considered and the data is noise free, cThe ARTnet distance threshold changes in a wider range while ART2 vigilance is too sensitive making it difficult to set a value.
Table 6.4 Clusters predicted by ARTnet when the distance threshold is 4.5 and
'd fi 0 0 100a
Cnoise varies over a Wi e range, rom .0 1 to
Identified Corresponding Identified Corresponding Identified Corresponding patterns data patterns patterns data patterns patterns data patterns
1 I 15 [27,28] 29 43
2 2 16 29 30 44
3 [34 5 6 7 8 9] 17 30 31 45
4 10 18 31 32 46
5 II 19 32 33 47
6 12 20 33 34 48
7 13 21 34 35 49
8 14 22 [35 36] 36 50
9 15 23 37 37 51
10 16 24 38 38 52
11 17 25 39 39 53
12 18 26 40 40 54
13 [19202122 27 41 41 55
23241
14 [25 26] 28 42 42 [5657]
a[3 4 5 6 7 8 9] means that data patterns 3 to 9 are grouped in the same cluster.
136 Data Mining and Knowledge Discovery for Process Monitoring and Control
In Equation 6.5, Cnoise changes ranging from 0.001 to 100 are examined in what follows where the smaller the Cnoise, the larger the noise to signal ratio.
The best clustering results are obtained when the distance threshold of ARTnet is 4.5. This result is not affected by changing Cnoise from 0.001 to 100, as can be seen in Table 6.4. For ART2, the best value of the vigilance is 0.9985 and Cnoise = 100, and is the same result as ARTnet (Table 6.4). However, as Cnoise decreases to 10, i.e., larger noise to signal ratio, ART2 splits the cluster [3 4 5 6 7 8 9] into two [3 4 5 6 7] and [8 9]. As Cnoise decreases to 0.001, i.e., a much larger noise to signal ratio, there are further new groupings, [20 42] and [29 51]. The new groups are not able to be satisfactorily explained. Although the inappropriate groupings [20 42]
and [29 51] can be avoided by changing the vigilance value, other unreasonable groupings are generated.
6.3.1.3 Computational Speed
It is found that ARTnet is faster than ART2. After optimum values of the distance threshold of ARTnet and the vigilance of ART2 are found, for the same data, ARTnet is typically two times faster than ART2.