# A Data-Knowledge Hybrid Driven Method for Gas Turbine Gas Path Diagnosis
## 3 Methodology
### Virtual Distance Mapping Algorithm  
The CPA method is a mathematical model that extracts the fault feature from the field data of a gas turbine. On the other hand, the fault diagnosis ontology model represents the heterogeneous knowledge with a unified semantics. A mapping method is needed to relate the GPA result to a specific _FeatureCriteria_ individual in the developed ontology model. The reference fault feature (\(FF_{\textit{ref}}\)) from the fault criteria analysis is stored in the data property of the _FeatureCriteria_ individuals. According to the fault criteria analysis knowledge from previous works [32; 33; 34], the reference fault features corresponding to several typical gas path fault modes are summarized in Table 3.  
The mapping process consists of three steps. Firstly, the virtual distance is calculated by measuring the Euclidean distance between the GPA result and each \(FF_{\textit{ref}}\). Secondly, a fault probability algorithm based on the virtual distance is presented to identify the most likely _FeatureCriteria_ individual. Finally, the mapping rule script is generated based on the data property of the identified _FeatureCriteria_ individual. It is noted that there are two turbine components in a two-shaft gas turbine system. The high pressure turbine and power turbine should both consider the turbine fault modes 5, 6, and 7. In summary, ten fault mode individuals are included to analyze the two-shaft gas turbine. For the ten defined _FeatureCriteria_ individuals, the reference fault features stored in the \(i\)-th _FeatureCriteria_ individual are \(FF^{i}_{\textit{ref}}\) (\(i=1\), \(2\), \(3\), \(\ldots\), \(10\)). The first four reference fault features \(FF^{i}_{\textit{ref}}\) (\(i=1\), \(2\), \(3\), \(4\)) belong to the compressor component, and the next three reference fault features \(FF^{i}_{\textit{ref}}\) (\(i=5\), \(6\), \(7\)) belong to the high pressure turbine component. The last three reference fault features \(FF^{i}_{\textit{ref}}\) (\(i=8\), \(9\), \(10\)) belong to the power turbine component. As shown in Table 1, the GPA results are the fault features of the compressor (\(DGC\), \(DEC\)), high pressure turbine (\(DGT\), \(DET\)), and power turbine (\(DGP\), \(DEP\)). In the compressor component, the virtual distance between the compressor fault features, and the \(i\)-th compressor \(FF^{i}_{\textit{ref}}\) (\(i=1\), \(2\), \(3\), \(4\)) in Euclidean space is defined as follows. \[d_{i}(DGC,DEC)=\sqrt{\left(DGC-DG^{i}_{\textit{ref}}\right)^{2}+\left(DEC-DE^{i }_{\textit{ref}}\right)^{2}}(i=1,2,3,4) \tag{6}\]  
where \(d_{i}\) is the virtual distance. \(DG^{i}_{\textit{ref}}\) and \(DE^{i}_{\textit{ref}}\) are values of the \(FF^{i}_{\textit{ref}}\). In the high pressure turbine and power turbine components, the virtual distance is defined as follows:  
\[ \begin{array}{l}d_{i}(DGT,DET)=\sqrt{\left(DGT-DG^{i}_{\textit{ref}}\right) ^{2}+\left(DET-DE^{i}_{\textit{ref}}\right)^{2}}(i=5,6,7)\\ d_{i}(DGP,DEP)=\sqrt{\left(DGP-DG^{i}_{\textit{ref}}\right)^{2}+\left(DEP- DE^{i}_{\textit{ref}}\right)^{2}}(i=8,9,10)\end{array}  \tag{7}\] \begin{table}
\begin{tabular}{c c c c} \hline \hline
**No.** & **Fault Modes** & \
\begin{tabular}{c} **Reference Flow Rate** \\ **Degradation** \(DG_{\textit{ref}}\) **(\%)** \\ \end{tabular} &
\begin{tabular}{c} **Reference Efficiency** \\ **Degradation** \(DE_{\textit{ref}}\) **(\%)** \\ \end{tabular} \\ \hline
**Compressor** & & & \\
1 & blade fouling & 7 & 2 \\
2 & blade tip clearance increasing & 4 & 0 \\
3 & blade wear and erosion & 0 & 2 \\
4 & Foreign objects damage & 1 & 5 \\
**Turbine** & & & \\
5 & blade fouling & 6 & 2 \\
6 & blade erosion & \(-6\) & 2 \\
7 & Foreign objects damage & 0 & 5 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Reference fault features for the typical gas path fault modes. Finally, the virtual distance set is as follows:  
\[\mathbf{d}=\{d_{1},d_{2},\ldots,d_{10}\} \tag{8}\]  
The next step is to estimate the probability based on the virtual distance set.