# A Diagnosability-Integrated Design Approach Based on Graph Theory
## 5 Instance Verification
### Experimental Analysis  
Table 3 and Figure 9 show the diagnosis of different fault modes in one experiment. From the results, the fault diagnosis scheme designed by this paper's method can identify the faults of the system well, and the methods in the literature can only identify some of the fault modes, while there were difficulties in identifying other faults. For example, the KNN and random forest methods had poorer results in the identification of fault mode 4 compared to other fault modes. In terms of diagnosis correctness, the correctness of this paper's method was improved by 3.25 percentage points compared to the average correctness of the four methods in the literature. Figure 11 shows the statistical results of the diagnosis of different fault modes in 50 repeated experiments. From the statistical results, the median number of incorrectly diagnosed samples of this paper's method was 0, and the maximum value was 2, which indicates that at least in half of the experiments, this paper's method was able to correctly diagnose all the samples, and the number of incorrectly diagnosed samples of the worst diagnosis result was 2. This diagnosis result was already better than that of the KNN and the random forest (the minimum value of the number of incorrectly diagnosed samples of the two methods was 5 and 2, respectively), while for the use of discriminative classifier  
Figure 11: Distribution of multiple simulation experimental results of different diagnostic methods. \begin{table}
\begin{tabular}{c c c c c c c} \hline
**NO.** & **Method** & \(f_{0}\) & \(f_{1}\) & \(f_{2}\) & \(f_{3}\) & \(f_{4}\) & **Total** \\ \hline
1 & KNN & 0 & 2 & 0 & 0 & 3 & 5 (5\%) \\
2 & RF & 0 & 0 & 0 & 0 & 6 & 6 (6\%) \\
3 & discriminative classifier & 0 & 0 & 0 & 0 & 1 & 1 (1\%) \\
4 & SVM & 0 & 0 & 0 & 0 & 1 & 1 (1\%) \\ \hline \end{tabular}
\end{table} 
Table 3: Other diagnosis methods results. and SVM, both methods performed stably in 50 repetitions, and their number of incorrectly diagnosed samples was 1. In the comparison method, the design of the fault diagnosis method can only be based on the measurement points that have been selected, which does not guarantee that the information provided by the selected measurement points is best adapted to the current fault diagnosis method. Since the information provided by two groups of measurement points, measurement point 5 and measurement point 6, was used in the experiments to diagnose the faults of the system, in order to handle multiple groups of measurement points, the method adopted in the literature was to splice the signal features of multiple measurement points horizontally to form new feature vectors to be used, which seems to be a fast and easy way, but the implied premise of doing so is that the distinguishing ability of each signal for the faults is the same, and the same features on different signals for the faults, which makes the implied premise obviously over-idealized. In the actual classifier, the classification is based on the relative position of the sample features in the feature space, in this case, when the features used are not sensitive to faults, the addition of these features will make the originally clear relative position become blurred, and, thus, the phenomenon of misclassification occurs. This leads to the situation in the experiment: although the information of two measurement points was used in the comparison experiment, which provided more diagnosis information, the diagnosis effect was not satisfactory. Therefore, it is not the case that the more measurement point information is used, the better the diagnosis effect is, but only by combining the information of the measurement points with the specific fault diagnosis method can the best fault diagnosis effect be produced.