When looking at the specific isolation rates of all the FDI methods as more attributes are reduced by the various reduction techniques, it can further be seen that specific attributes can obscure or bolster the isolation capability of the FDI method with regards to a particular fault condition, while having the opposite or even no effect on the capability of the method with regards to other fault conditions. Such is the case with the specific isolation rates of the distance FDI method, which are recorded in Table 6.1. For example, once the 30th percentile threshold was increased to the 40th percentile threshold, the isolation rate of Fault 1 fell from 70 % to 4 %, the isolation rate of Fault 2 only dropped by one percent, and the isolation rate of Fault 6 increased by 23 %.
This can be ascribed to the fact that a specific reduction operation can alter the structural information so that the attribute features that the FDI method uses to diagnose a particular fault are accentuated. In contrast, the attribute features that the same method uses to diagnose a different fault are attenuated.
By conducting an intertechnique comparison, it is possible to determine which reduction tech- niques better complement each of the three FDI methods. This comparison involves assessing the overall detection and isolation rates, as well as the specific isolation rates of each FDI method as stated in Tables 6.1 - 6.5. For example, for the distance FDI method, Techniques 1, 2, and 5 at specific thresholds were the most complementary reduction techniques when examining the performance of the FDI method after these techniques were applied to the graph data.
When looking at the performance of the eigendecomposition FDI method after the various reduction techniques were applied to the graph data, Techniques 2 and 5 at specific thresh- olds were also able to maximally reduce attributes while minimally affecting performance.
Techniques 1, 2, and 5 at specific thresholds were once again able to maximally reduce the attributed graph data while minimally deteriorating the performance of the residual-based FDI method. While Techniques 3 & 4 positively affected the overall detection and isolation rates at certain reduction intervals, the specific isolation rates were adversely affected in most instances.
This intertechnique comparison also allows for the evaluation of the different types of tech- niques used to reduce the attributed graph data. For this evaluation, it is essential to note the scale of attribute reduction, seeing as the techniques that reduce nodes can reduce far more non-zero attributes than the techniques that are link attribute orientated. It should also be taken into account that the scale of the x-axes in Figures 6.1 - 6.10 are not neces- sarily displayed linearly. This evaluation serves to determine which techniques are better at maintaining the level of performance achieved before reduction while still reducing non-vital
structural information.
From assessing the trajectories of the performance indicators of the three FDI methods for each of the five reduction techniques, it is evident that the techniques which rely on attribute variation analysis (Techniques 1 & 2) outperformed the techniques which rely on attribute size analysis (Techniques 3 & 4) across all three FDI methods when the same range of reduction is used for the evaluation. This proves the validity of the argument, which stated that the process noise does not significantly influence the variation analysis performed by Techniques 1 & 2.
Furthermore, when comparing the trajectories of the overall detection rates, overall isolation rates, and the specific isolation rates of the three FDI methods for Technique 5 with that of the other techniques over the same reduction range, it is also evident that Technique 5 resulted in the most stable and consistent response. This indicates that Technique 5 is highly effective at reducing graph complexity while not significantly affecting FDI performance.
Seeing as the aim of graph reduction is to reduce the complexity of the attributed graph, and subsequently the complexity of implementing the FDI methods, it is also necessary to compare the influence that different styles of reduction (node attribute or link attribute) have on the execution time of these methods. Table 6.6 contains a comparison of the execution times of the unreduced graph data, the graph data reduced by Technique 1 with a 10th percentile threshold, and the graph data reduced by Technique 2 with a 20th percentile threshold.
The percentage attributes reduced by the node attribute reduction technique (Technique 1) and the link attribute reduction technique (Technique 2) at those respective thresholds are approximately the same. The distance FDI method is used to diagnose graph data sets since it has the longest execution time.
From the table, it is evident that while these two techniques reduced approximately the same percentage of attributes, the node attribute reduction technique (Technique 1) far outper- formed the link attribute reduction technique (Technique 2) in terms of reducing the execu- tion time. This is because the node attribute reduction technique reduces the size of the NSM while the link attribute reduction technique only sets attributes within the NSM to zero. To emphasize the usefulness of graph reduction, it is noted that after applying Technique 1 at that specific reduction interval, the FDI execution time decreased by 17 %, while none of the performance indicators decreased by more than 1 %.
Table 6.6: Comparison of the execution times of the distance FDI method after applying different reduction techniques.
Reduction Type Attribute Reduction (%) Execution Time (s)
Unreduced 0.00 1365.42
Technique 1 12.90 1133.10
Technique 2 11.29 1323.04