## 5 Case Study and Discussion
### Available Knowledge Acquisition  
#### 5.2.1 Filtering Knowledge Genes with Direct Similarity  
To avoid the loss of valid data and the retention of invalid data, the threshold of direct similarity is set to _TS_ = 0.7. If the direct similarity between the target gene and a knowledge gene is greater than _TS_, then the knowledge gene is in the relevant diagnosis knowledge pool. For instance, according to the Equations (13)-(15), the direct similarity between the target gene and the first knowledge gene, as shown in Table 4 is calculated as follows:  
\[SD(GU(1),KCU(1))=\left( \begin{array}{c}0.83+1.00+1.00+0.75+1.00+0.50+0.63+ 0.81+1.00+0.98\\ +0.67+1.00+0.50+0.67+0.40+0.65+0.76+0.51+0.81+0.50\\ \end{array} \right)/20=0.7485 \tag{38}\] \begin{table}
\begin{tabular}{c c c} \hline \hline
**Element Code** & **Abbreviation** & **Explanation** \\ \hline \multirow{8}{*}{6-1} & sr & It indicates that the surface roughness is too large. \\ \cline{2-3}  & mc1 & It indicates the existence of microcracks on the surface. \\ \cline{2-3}  & ce1 & It indicates that the concentricity error is too large. \\ \cline{2-3}  & de1 & It indicates that the diameter error is greater than the upper deviation. \\ \cline{2-3}  & de2 & It indicates that the diameter error is less than the lower deviation. \\ \cline{2-3}  & de3 & It indicates that the width error is greater than the upper deviation. \\ \cline{2-3}  & de4 & It indicates that the width error is less than the lower deviation. \\ \cline{2-3}  & bh & It indicates the existence of blowholes on the surface. \\ \cline{2-3}  & imp & It indicates the existence of impurities on the surface. \\ \cline{2-3}  & he1 & It indicates that the surface hardness is lower than its design value. \\ \hline \multirow{8}{*}{7-1} & om11 & It indicates that the machine of rough turning or semi-finish turning is too old. \\ \cline{2-3}  & om13 & It indicates that the machine of finish turning is too old. \\ \cline{2-3}  & mat & It indicates that the material is inappropriate or unqualified \\ \cline{2-3}  & mt & It indicates that the error of measuring tools is too large. \\ \cline{2-3}  & pw11 & It indicates that the worker who carries out rough turning is not skilled enough. \\ \cline{2-3}  & pw13 & It indicates that the worker who carries out finish turning is not skilled enough. \\ \cline{2-3}  & pw53 & It indicates that the worker who carries out quenching is not skilled enough. \\ \cline{2-3}  & cm1 & It indicates that the structure of casting mold is unreasonable. \\ \cline{2-3}  & cm2 & It indicates that the casting mold has not been cleaned up. \\ \cline{2-3}  & ht1 & It indicates that the holding time of quenching is too short. \\ \cline{2-3}  & ht2 & It indicates that the holding time of quenching is too long. \\ \cline{2-3}  & tem1 & It means that the temperature of quenching is too high. \\ \cline{2-3}  & tem2 & It means that the temperature of quenching is too low. \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Meanings of abbreviations of quality defects and causes. \[SD(GU(2),KQU(2))=\left( \begin{array}{c}0.83+1.00+0.00+0.92+0.85+0.50+0.64+0.99+ 0.95+0.67\\ +1.00+0.50+0.67+0.73+0.73+0.76+0.69+0.81+0.00\end{array} \right)/19=0.6968 \tag{39}\]  
\[SD(GU(3),KQU(3))=\left( \begin{array}{c}0.83+1.00+0.00+0.75+0.50+0.33+0.63+0. 48+0.98+0.98\\ +0.67+1.00+0.50+0.67+0.95+0.95+0.76+0.61+0.81+0.00\end{array} \right)/20=0.6700 \tag{40}\]  
\[SD(PG,KPG)=\frac{\sum\limits_{k=1}^{3}SD(GU(k),KQU(k))n_{k}}{\sum\limits_{k=1} ^{m}n_{k}}=0.71 \tag{41}\]  
Where _SD_(_PG_, _KPG_)\(>\)_TS_, the first knowledge gene should be in the relevant diagnosis knowledge pool. According to the calculation method mentioned above and _TS_, relevant knowledge genes, as shown in Table 6 are obtained. The corresponding values of direct similarity are shown in Table 7.  
Here, 19 knowledge genes are found to be related to the target gene.