## 5 Case Study
### Case Analysis  
A new FR is used to analyze the predicted results using KNN-SVM. We randomly sample the values of this FR to be missing in four cases, where cases 1, 2, 3, 4 contain 2, 5, 7, and 13 missing values, respectively. As shown in Table 4, the specific values under four cases are the predicted values using KNN-SVM. Comparing the predicted values with ground truth, we make a concrete analysis to different cases as following. \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline \multirow{2}{*}{**Method**} & \multicolumn{2}{c}{**RMSE**} & \multicolumn{2}{c}{**Ang**} & \multicolumn{2}{c}{**FSN**} & \multicolumn{2}{c}{**Time (s)**} \\ \cline{2-11}  & **10\%** & **30\%** & **50\%** & **10\%** & **30\%** & **50\%** & **10\%** & **30\%** & **50\%** & **10\%** & **30\%** & **50\%** \\ \hline \multicolumn{11}{c}{ Cold-start scenario 1: 10 incomplete FRs without reference} \\ \hline KNN-SVM & 0.44 & 0.52 & 0.63 & 0.04 & 0.09 & 0.17 & – & – & – & 1.13 & 0.51 & 1.56 \\ KNN-Bay & 0.58 & 0.56 & 0.78 & 0.06 & 0.14 & 0.26 & – & – & – & 2.19 & 1.92 & 3.19 \\ KNN-Tree & 0.56 & 0.53 & 0.76 & 0.11 & 0.14 & 0.30 & – & – & – & 0.19 & 0.11 & 0.18 \\ KNN & – & – & – & – & – & – & – & – & – & – & – & – \\ GRNN & 0.59 & 0.71 & 0.66 & 0.04 & 0.22 & 0.26 & – & – & – & 9 & 11 & 18 \\ \hline \multicolumn{11}{c}{ Warm-start scenario 1: 10 incomplete FRs with rest 81 complete FRs for reference} \\ \hline KNN-SVM & 0.09 & 0.18 & 0.23 & \(4\times 10^{-5}\) & \(1\times 10^{-3}\) & \(1\times 10^{-3}\) & 1.00 & 1.00 & 1.00 & 0.33 & 0.69 & 0.60 \\ KNN-Bay & 0.28 & 0.37 & 0.38 & \(1\times 10^{-3}\) & \(2\times 10^{-3}\) & \(4\times 10^{-3}\) & 0.99 & 0.97 & 0.96 & 1.36 & 1.68 & 1.81 \\ KNN-Tree & 0.32 & 0.33 & 0.29 & \(1\times 10^{-3}\) & \(3\times 10^{-3}\) & \(5\times 10^{-3}\) & 0.99 & 0.97 & 0.96 & 0.24 & 0.27 & 0.28 \\ KNN & 0.49 & 0.53 & 0.50 & \(1\times 10^{-3}\) & \(2\times 10^{-3}\) & \(4\times 10^{-3}\) & 0.98 & 0.96 & 0.96 & 0.19 & 0.21 & 0.20 \\ GRNN & 0.63 & 0.56 & 0.60 & \(3\times 10^{-3}\) & \(6\times 10^{-3}\) & \(1\times 10^{-2}\) & 0.98 & 0.97 & 0.96 & 5 & 15 & 24 \\ \hline \multicolumn{11}{c}{ Cold-start scenario 2: 50 incomplete FRs without reference} \\ \hline KNN-SVM & 0.31 & 0.39 & 0.42 & 0.01 & 0.02 & 0.04 & 1.00 & 0.99 & 0.99 & 0.50 & 0.49 & 0.42 \\ KNN-Bay & 0.56 & 0.59 & 0.59 & 0.06 & 0.10 & 0.17 & 0.95 & 0.86 & 0.92 & 3.54 & 2.77 & 2.18 \\ KNN-Tree & 0.51 & 0.59 & 0.55 & 0.04 & 0.08 & 0.14 & 0.96 & 0.90 & 0.90 & 0.63 & 0.21 & 0.16 \\ KNN & 0.68 & 0.62 & 0.61 & 0.07 & 0.15 & 0.17 & 0.95 & 0.92 & 0.93 & 0.08 & 0.07 & 0.05 \\ GRNN & 0.66 & 0.66 & 0.67 & 0.09 & 0.16 & 0.21 & 0.94 & 0.91 & 0.91 & 29 & 95 & 127 \\ \hline \multicolumn{11}{c}{ Warm-start scenario 2: 50 incomplete FRs with rest 41 complete FRs for reference} \\ \hline KNN-SVM & 0.14 & 0.30 & 0.30 & \(3\times 10^{-3}\) & \(6\times 10^{-3}\) & \(1.2\times 10^{-2}\) & 1.00 & 0.95 & 0.92 & 0.76 & 0.78 & 0.80 \\ KNN-Bay & 0.26 & 0.31 & 0.36 & \(5\times 10^{-3}\) & \(9\times 10^{-3}\) & \(1.0\times 10^{-2}\) &(1) In cases 1 and 3, where the values of speed (\(r_{13}\)) is missing, the predicted value is 3.64 m/s and the difference is acceptable comparing with 4.1 m/s. The shaft height (\(r_{19}\)) is 43 m, the time cost is 11.8 vs. 10.5 s, where 1.3 s are negligible for passengers. (2) The predicted results of categorical variables are accurate against the ground truth. For the binary classification, the predicted values using KNN-SVM are the same as the ground truth in gear of hoisting machine (\(r_{3}\)), door opening (\(r_{6}\)), and counterweight position (\(r_{8}\)). For the multi-class classification, such as hoisting rope size (\(r_{2}\)), number of hoisting roper (\(r_{9}\)), and number of guides (\(r_{10}\)), the predicted values are accurate. In addition, the predicted values of hoisting motor power (\(r_{1}\)) are larger than the ground truth. One reason is the missing rate of case 4 is high. From another perspective, the candidate values of \(r_{1}\) in the product family are [8, 10, 11, 12, 15, 17, 18] kW.