The alarm levels of the vinyl acetate process simulator

The decision tree classifier obtained by the training on the "Max-min" data set is depicted in Figure 3.4. The tree is considered sufficiently simple, yet accurate, however, only the maximum depth of the tree was set at five as the input parameter of the training algorithm.

The sampled continuous process variables form a significantly more complex train-ing data set. Consequently, the obtained decision tree is highly complex, moreover, without any restricting input parameters, it could handle rare cases with just a

Fault ID

Fault

0 no disturbance

1 setpoint of the outlet temperature of the reactor de-creases by 8 ^◦C (from 159 to 151 ^◦C)

2 setpoint of the outlet temperature of the reactor in-creases by 6 ^◦C (from 159 to 165 ^◦C)

3 the vaporizer liquid inlet flowrate increases by 0.44 kmol/min (from 2.2 to 2.64 kmol/min)

4 HAc fresh feed stream lost for 5 minutes 5 O₂ fresh feed stream lost for 5 minutes 6 column feed stream lost for 5 minutes

Table 3.2: The data utilized for alarm design and the characteristics of the resultant alarm system

Figure 3.4: The decision tree classifier obtained by the training on the "Max-min" data set.

few sample points on each leaf. Therefore, after some trial-and-error tuning of the parameters, the maximum depth was set at seven, the maximum number of leaf nodes at 14 and to avoid the over-specific leaves, the minimum number of samples on a leaf was 50. Moreover, in this case, the entropy information measure was chosen over the Gini index. The final decision tree is depicted in Figure 3.5.

The resultant decision trees were evaluated over two steps. Firstly, a tenfold cross-validation was applied and the accuracy measure investigated according to Figure 3.6. Secondly, the online application of the algorithms was mimicked and the re-corded data set of each simulated fault or operating state formed the input of the algorithms. The faults occur at the beginning of the analysed dataset (0^th minute, except for Fault 0 where no fault is implemented) and their temporal period fol-lows the logic of the training set. For the model trained on the "Continuous" data set, the continuous process variables were sampled on the same minute-basis as the training set, while for the one trained on the "Max-min" data set, the min-imal and maxmin-imal values of the process variables within a sliding time window formed the inputs of the decision tree. The length of this sliding time window is a trade-off between accuracy and speed: choosing a long time window with regard to the effect of the fault will basically result in a very precise classification per-formance, however, this renders the classification algorithm exceptionally slow. I have intended to apply sensitivity analysis between a 1 and 20-minute-long time window, however, in this case the results were not significantly dependent on the length of the time window. Hence, after some expert-based investigation, the time window was set at 5 minutes. However, it is important to highlight that the choice of this parameter should always follow some expert-based guidelines or a detailed sensitivity analysis. In the case of expert-based investigations the rule-of-thumb is to set the time window compared to the average time constant of the process.

The detected operation states (or faults) and when a fault was first detected are summarized in Table 3.3. The detailed classification performance of the al-gorithms, i.e. their classification based on the measured process variables over time, can be seen in Figure 3.7.

According to the results, the decision tree trained on the "Continuous" data set provides rapid identification of the faulty states but tends to wrongly classify the operation in some cases. While the correct fault class is present in almost all of the cases, perfect classification cannot be expected from the algorithms as the iden-tifiability of the faults is not investigated. Even in the case of misclassifications,

Figure3.5:Thedecisiontreeclassifierobtainedbythetrainingonthe"Continuous"dataset.

Figure 3.6: The accuracy measure calculated according to Equation 3.6 during the tenfold cross-validation.

"Continuous" "Max-min" (tw = 5 min) Fault

ID

Detected fault

Time of first detection [min]

Detected fault

Time of first detection [min]

0 0 - 0

-1 0, 1, 2 0 0, 1 2

2 0, 2 1 0, 2, 5 4

3 0, 3, 6 0 0, 1, 3 18

4 0, 4 0 0, 4 2

5 0, 2, 5 0 0, 5 0

6 0, 3, 4, 6 1 0, 6 3

Table 3.3: The results of the classification algorithms. The type of the detected faults and time of the detection of the first fault. (tw - time window)

Figure 3.7: The trained classification algorithms tested on simulated faults.

The minute-based process data formed the input of the decision tree trained on the "Continuous" data set, while the minimum and maximum values measured over a 5-minute-long rolling time window were the inputs of the decision tree

trained on the "Max-min" data set.

the first fault to be identified is almost always from the correct class, except for Fault 6, which only occurs in the second minute of operation. In the case of the decision tree trained on the "Max-min" data set, the speed of fault identification is slower, however, the classification performance is much better, a misclassification only occurs in the case of Fault 2, which is mistakenly classified as Fault 5, while Fault 3 is mistakenly classified as Fault 1. It is important to notice the fact that despite the numerous alarm messages applied for fault detection and identification in complex systems, both approaches provided a solution for fault identification using just a very limited number of alarms (of course, however, the complexity of the simulator falls behind the complexity of a modern production plant with numerous failure modes). Yet, in the case of the decision tree classifier trained on the "Max-min" data set, only six alarms are sufficient, while in the case of the decision tree trained on the "Continuous" data set, 13 alarms are required to

identify the six malfunctions and the normal operation.

To interpret the results, consider Fault 3 and how it is misclassified by the decision tree trained on the "Max-min" data set. Fault 3 is the increased flowrate of the inlet liquid of the vaporizer, which is captured by the alarms concerning the temperature of the separator and compressor, which are two closely connected units. The misclassification of this fault with Fault 1 is not a surprise as Fault 1 comprises a decrease in the temperature setpoint of the reactor, moreover, the increase in the flowrate of the inlet liquid of the vaporizer in Fault 3 most likely causes a drop in temperature in the reactor as well. Of course, this similarity is also captured in the data sets, as is presented in Figures 3.8 and 3.9 for Faults 3 and 1, respectively. As can be seen, the algorithm classified well the process based on the extrema: during Fault 3, the temperature of the separator was below its respective limit, while this was not the case when Fault 1 occured. However, when the temperature of the compressor is below its limit, and therefore, a decision with regard to the value of the separator temperature is reached, its value at first exceeds the separator temperature limit. As a result, Fault 1 is identified, which later "evolves" into Fault 3, when the temperature drops below this limit. This issue can be manually fine-tuned. Given the data, it can easily be observed why the detection of this fault also occurs as late as 18 minutes into the process: the temperature of the compressor is above its limit which prevents the decision model on a higher level from reaching these leaves of the tree.