## 3 Results and Potential IIoT instantiation  
### Results and Findings  
#### 3.1.1 Measurement System Analysis  
Figure 9 below shows the relative pooled standard deviation (RPSD) for the historical process data recorded over the four-week period. In the case of the degradation scenarios, the maximum standard deviation of data recorded relative to the mean was 950 rpm for  
Figure 7: Recurrent neural network architecture used for each component in the water distribution system.  
the clogged filter failure condition scenario, with the minimum occurring at 700 rpm for a leaking pipe scenario. The healthy condition scenario showed near zero RPSD for the varying pump speeds over the four-week period. Even though Figure 9 provides insights into the variation in the data, it was difficult to determine the source of the variation, whether it was from the measurement system or the process itself. Figure 10 shows the nature of data recorded by the measurement system of the water distribution testbed. Over the four weeks, the data quality scores as defined in this paper showed data characterising the conditions of the pump with the lowest data-quality score at 0.986 and that of the valve at 0.9942. The quality of one of the synthetic datasets generated is also shown in Figure 10, with data characterising the conditions of the filter with the lowest data-quality score at 0.76 and that of the valve at 0.8.  
Figure 8: Process for benchmarking the FDI algorithms.  
Figure 9: RPSD for different faulty condition data at varying pump speeds.  
3.1.2. The Nexus between Data Quality and FDI Model Performance  
The relationship between the quality of data defined by the MSA process and its impact on the development of fault detection and isolation algorithms varies depending on the nature of the principles that underpin the mathematical foundations and development process of those algorithms. The performance of the models trained with both historical and synthetic datasets is presented below, with Appendix A.2 (Tables A1 and A2) showing the best classification algorithm for each component. Figure 11 shows a radar plot of the data-quality score for every component and its impact on test degradation data T13. In the case of the SPC model, the impact of the synthetic data with lower data quality compared to the historical dataset resulted in an increase in model performance, where the synthetic dataset produced a mean accuracy for all components of 85.55% and the historical dataset producing a mean accuracy of 49.7%. The same pattern was seen in T17 as well, where the performance of the data-driven models decreased with a decrease in data quality (see Figure 12). Tables 5 and 6 show a summary of the performance of the FDI algorithms using historical and synthetic data respectively. Figures 13 and 14 also show the average performance of the FDI models in the rest of the test degradation scenarios. It was observed that there was no direct relationship between data quality as defined and the performance of the SPC FDI algorithms in the detection MCD scenarios.  
Figure 11: Impact of data quality (a) on performance of FDI models (b-Historical) and (b-Synthetic) for T13.  
Figure 10: Data-quality assessment.  
Figure 12: Impact of data quality (a) on performance of FDI models (b-Historical) and (b-Synthetic) for T17.  
\begin{table}
\begin{tabular}{l l l l l} \hline \hline  & \multicolumn{3}{c}{**Historical Dataset with Average Data Quality of 0.99**} \\ \hline Model & SPC & Best Classifier & Ensemble & Neural Network \\ Mean accuracy (\%) & 49.7 & 86.10 & 46.84 & 63.81 \\ \hline \multicolumn{5}{c}{Synthetic Dataset with Average Data Quality of 0.794} \\ \hline Model & SPC & Best Classifier & Ensemble & Neural Network \\ Mean accuracy (\%) & 80.55 & 83.82 & 16.18 & 46.71 \\ \hline \hline \end{tabular}
\end{table}
Table 5: Summary of average performance of FDI models for T13.  
Figure 13: Performance of FDI models using historical dataset for test degradation scenarios.