## 4 Experiments and Results
### Experiments in Cost Prediction of WMS  
In order to verify the effectiveness of this method in the application of WSM cost prediction, the cost data of WSM are studied. In the WSM cost data collection, we collected all repair records from different undertaking factories for different types of warships in the past five years, including the basic information of the repaired warship and undertaking factory. The collected index system of WSM maintenance incidents is shown in Figure 4.  
As is shown in Figure 4, the maintenance cost is not only related to the performance parameters of the warship, but also to the context of the maintenance such as the factory of the maintenance, and the maintenance time. Based on the index system shown in Figure 4, the input-output characteristic feature sets shown in Table 3 is constructed, where the input feature set is the quantifiable basic information index of the warship collected and various indexes related to the repairing factory, and the output corresponds to the subentry costs of WSM. In Table 3, the power unit type (\(C_{5}\)) and the maintenance unit (\(C_{10}\)) are one-hot encoded. Hence, the input dimension of the sample set after pre-processing is 23, and the output target number is 5. In order to ensure a good similarity between the WSM samples or events involved in the prediction, the sample set is preliminarily divided into multiple datasets according to the warship type (combat support warships, surface combat warships and submarines) and maintenance grade (second-grade and third-grade maintenance, because there are few instances of first-grade maintenance, so it is not considered). Then, considering the similarity of WSM cost data in distance and angle, define the similarities between the maintenance instance \(\varphi_{i}=\{\mathbf{x}_{i},\mathbf{y}_{i}\}\) and \(\varphi_{j}=\left\{\mathbf{x}_{j},\mathbf{y}_{j}\right\}\) as follows:  
\[sim\big{(}\varphi_{i},\varphi_{j}\big{)}=\sigma\cdot\exp\big{(}-\|\varphi_{i}- \varphi_{j}\|_{2}\big{)}+(1-\sigma)\cdot\cos\Bigg{(}\frac{<\varphi_{i},\varphi _{j}>}{\|\varphi_{i}\|_{2}\cdot\|\varphi_{j}\|_{2}}\Bigg{)} \tag{25}\]  
Figure 3: Bonferroni-Dunn test with comparisons of MTR-MLS against other compared methods. Formula (25) clusters the instances by using the hybrid similarity function based on the angle cosine and the Euclidean distance and obtains several representative instances sets of WSM. As shown in Table 4, the WSM dataset with different ship categories and maintenance grades are obtained by nearest neighbour clustering [42] based on the similarity  
Figure 4: Index system of WSM maintenance incidents. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Feature Sets** & **Feature Type** & **Denotes** \\ \hline Displacement & Continuous & \(C_{1}\) \\ Shipment length & Continuous & \(C_{2}\) \\ Shipment width & Continuous & \(C_{3}\) \\ Maximum speed & Continuous & \(C_{4}\) \\ Power unit type & Semantic & \(C_{5}\) \\ Power unit number & Enumerates & \(C_{6}\) \\ Construction cost & Continuous & \(C_{7}\) \\ Shaft horsepower & Continuous & \(C_{8}\) \\ \multirow{2}{*}{Input features} & Warship age & Continuous & \(C_{9}\) \\ Repairing factory & Semantic & \(C_{10}\) \\ Maintenance time & Continuous & \(C_{11}\) \\ Total task work & Continuous & \(C_{12}\) \\ Number of repairmen & Continuous & \(C_{13}\) \\ Proportion of repairmen & Continuous & \(C_{14}\) \\ Original value of fixed assets & Continuous & \(C_{15}\) \\ Operating income of repairing factory & Continuous & \(C_{16}\) \\ Operating profit of repairing factory & Continuous & \(C_{17}\) \\ \hline \hline \multirow{4}{*}{Output targets} & Material cost & Continuous & \(D_{1}\) \\ Labor cost & Continuous & \(D_{2}\) \\ Manufacturing cost & Continuous & \(D_{3}\) \\ Special cost & Continuous & \(D_{4}\) \\ Period cost & Continuous & \(D_{5}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Feature sets for WSM cost prediction. function (25), to ensure good similarity among different samples under the same datasets.