Just like in Chapter 4, the FDI control data of the GTLP is required to evaluate the perfor- mance of the graph reduction techniques once they are applied to the attributed graph data of the GTLP.
Unlike the TEP, the GTLP simulation is static and, therefore, generates steady-state data.
As a result, measured process data is not generated by sampling over time but rather by using these steady-state measurements. Also, unlike the TEP model, it is possible to simulate different magnitudes of the fault conditions. In the case of the TEP, all 21 process conditions were sampled 501 times over the 25 hours to produce 10521 samples (10521 node signature matrices). The 21 reference attributed graphs were generated by calculating the average of the 501 samples for each process condition.
Figure 7.3: Illustration of fault locations within the GTLP.
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Figure 7.4: Exergy-based attributed graph of the GTLP.
Table 7.2: Summary of the components and input/output streams representing each node.
Node number 1 2 3 4 5 6 7 8 9
Process component - - - - ATR Cooler 1 Separator 1 Mixer 1 Heater 1
Input/output stream Methane Steam Oxygen Carbon dioxide - - - - -
Node number 10 11 12 13 14 15 16 17 18
Process component FTR Separator 2 Cooler 2 3 phase separator Splitter 1 - - Compressor Splitter 2
Input/output stream - - - - - Light liquids Heavy liquids - -
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The GTLP, in turn, has 12 fault conditions and, together with the normal condition, has 13 process conditions in total. The reference attributed graph data for all 13 conditions is generated by inducing each fault condition with a 10 % magnitude, as done by Greyling in [8]. The reference normal attributed graph is simply the steady-state attributed graph while no fault is present. To generate the operational attributed graph data of each fault condition, the induced fault is adjusted to different magnitudes, and the steady-state attributed graph is recorded for each magnitude. These magnitudes are 5 %, 8 %, 12 %, and 25 %.
With the TEP, each fault condition has 501 operational attributed graphs, while in the case of the GTLP, each fault condition has four operational attributed graphs representing the four different fault magnitudes. The attributed graph of the process in NOC remains the same, irrespective of the different magnitudes. The four normal operational attributed graphs are, thus, all the same as the reference normal attributed graph. The difference in the number of graphs for each condition in the TEP and GTLP datasets (501 vs four graphs) prevent the direct comparison of TEP FDI performance with GTLP FDI performance. This is, however, no problem since the study aims to compare the response graph reduction has on the FDI performance of each process and not the FDI performance itself.
The rationale behind using this configuration for the GTLP dataset is to mimic the data configuration used by the FDI methods when applied to the TEP data. Using the attributed graph data at different fault magnitudes, the operational attributed graph data of the GTLP mirrors that of the TEP, which includes sampled measurements as the fault transitions from a minimal magnitude to its rated magnitude. Using the graph data generated at a relatively central fault magnitude as the reference graph data of the GTLP, an effect similar to using the averages of the sampled measurements to construct the reference graph data of the TEP, is achieved.
Seeing as the attributed graph of the GTLP has 18 nodes, the cost matrices generated by the distance parameter and eigendecomposition FDI methods will be an 18 × 18 matrix, which will produce 18 eigenvalues. The eigendecomposition FDI method is once again modified according to the study conducted by Wolmarans [52], whereby only dominant eigenvalues are used by the FDI method to diagnose faults. This is done to reduce the amount of information required by the FDI method to accurately diagnose faults, which reduces the complexity of implementing the FDI method.
Just like with the TEP, a trade-off is done between the number of dominant eigenvalues selected and the FDI performance by evaluating this performance using a range of different CPV values. Equation 4.4 is once again manipulated to determine the number of dominant eigenvalues for a specific CPV value. Table 7.3 contains the results of the trade-off study.
Using only five dominant eigenvalues (CPV of 75 %), the method achieved a higher overall isolation rate while maintaining a very high overall detection rate. The eigendecomposition FDI method is now modified to only consider the number of dominant eigenvalues with a CPV of 75 %. Any future references to the eigendecomposition FDI method refer to this modified version of the eigendecomposition FDI method.
Table 7.3: The performance of the eigendecomposition FDI method applied to the GTLP for different CPV values.
CPV (%) Number of dominant
eigenvalues Overall detection rate (%) Overall isolation rate (%)
75 5 95.83 45.83
80 7 97.92 43.75
85 9 97.92 43.75
90 11 97.92 50.00
100 18 97.92 43.75
Seeing as this chapter explains how the attributed graph data and the FDI methods differ from those applied to the TEP, only the results of each FDI method will be provided here. Table 7.4 contains a summary of the overall detection and isolation rates, as well as the isolation rates of specific fault conditions when the FDI methods are applied to the GTLP. A table containing the specific detection and isolation rates of each fault condition for each of the three FDI methods can be found in Appendix D.
In the case of the TEP, the isolation rates of specific fault conditions, which the FDI methods were highly capable of isolating, were also included in the control data to evaluate the graph reduction techniques. This was done to determine if the graph reduction techniques deteriorate the high-quality isolation capabilities of these specific faults. The same approach is used when generating the control data of the GTLP, except for the specific fault conditions used for the distance parameter FDI method. In the case of this FDI method, all but two fault conditions experienced the same high level of performance. Therefore, one high performing fault condition and the bottom two fault conditions are selected as specific fault conditions to determine if the graph reduction techniques could improve these two faults’ capabilities.
The results, as captured in Table 7.4, now represent the control data that will be used to evaluate the graph reduction techniques when they are applied to the GTLP.
Table 7.4: Summary of the detection and isolation perfor- mance of the FDI methods applied to the GTLP.
Distance parameter FDI method Overall detection rate (%) 87.50
Overall isolation rate (%) 70.83 Isolation of Fault 1 (%) 75.00 Isolation of Fault 10 (%) 50.00 Isolation of Fault 12 (%) 50.00 Eigendecomposition FDI method Overall detection rate (%) 95.83
Overall isolation rate (%) 45.83 Isolation of Fault 1 (%) 75.00 Isolation of Fault 5 (%) 75.00 Isolation of Fault 8 (%) 75.00 Residual-based FDI method Overall detection rate (%) 97.92
Overall isolation rate (%) 39.58 Isolation of Fault 1 (%) 75.00 Isolation of Fault 2 (%) 100.00 Isolation of Fault 11 (%) 100.00