# MIMO LS-SVR-Based Multi-Point Vibration Response Prediction in the Frequency Domain
## 3 Experimental Verification
### Comparison of Results among Different Multi-Point Vibration Response Prediction Methods  
In order to verify the model performance of MIMO LS-SVR-based method, it was compared with the transmissibility matrix based method, transfer function with load based method (a method for predicting vibration response using known load and transfer function), multiple linear regression (MLR)-based method, MIMO neural network-based method (layers: 16-64-32-2, activation function:Rectified Linear Unit (ReLU), loss: MSE, epochs: 50, optimizer: Root Mean Square prop(RMSprop), learning rate: 0.0001, batch size: 2) and MIMO LS-SVR with load-based method (prediction of vibration response from known load using MIMO LS-SVR). Table 2 shows the percentage of the number of frequencies whose energy prediction error was over 3 dB for different methods, where t1 and t2 represent two predicted vibration responses in the MIMO model. Figure 4 shows the energy dB of the true vibration response and predicted vibration response, the results within two horizontal lines indicate that the errors between the predicted results and the real results do not exceed 3 dB. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & & **t1** & **t2** & **t1** & **t2** & **t1** & **t2** \\  & & **1** & **5** & **2** & **6** & **8** & **9** \\ \hline \multirow{4}{*}{Transmissibility matrix} & \(>\)3 dB & 1.31 & 0.44 & 3.25 & 0.69 & 1.12 & 1.37 \\  & \(<\)–3 dB & 1.06 & 0.37 & 0.75 & 0.75 & 1.19 & 1.06 \\  & total & 2.37 & 0.81 & 4.00 & 1.44 & 2.31 & 2.44 \\  & \(>\)3 dB & 1.75 & 1.37 & 4.56 & 1.87 & 1.87 & 2.00 \\ \multirow{4}{*}{Transfer function with loads} & \(<\)–3 dB & 1.81 & 1.56 & 1.25 & 1.94 & 1.50 & 1.50 \\  & total & 3.56 & 2.94 & 5.81 & 3.81 & 3.37 & 3.50 \\  & \(>\)3 dB & 1.44 & 1.69 & 5.25 & 1.75 & 1.62 & 1.75 \\ \multirow{4}{*}{Multiple linear regression} & \(<\)–3 dB & 3.94 & 4.31 & 6.93 & 4.62 & 3.94 & 5.37 \\  & total & 5.37 & 6.00 & 12.18 & 6.37 & 5.56 & 7.12 \\ \multirow{4}{*}{MIMO Neural network} & \(>\)3 dB & 3.56 & 1.62 & 2.81 & 2.44 & 4.25 & 4.56 \\  & total & 2.75 & 2.06 & 3.25 & 2.62 & 4.81 & 4.93 \\ \multirow{4}{*}{MIMO LS-SVR with loads} & total & 6.31 & 3.69 & 6.06 & 5.06 & 9.06 & 9.49 \\  & \(>\)3 dB & 1.87 & 1.75 & 3.62 & 2.44 & 2.25 & 2.44 \\ \multirow{4}{*}{MIMO LS-SVR with loads} & \(<\)–3 dB & 0.31 & 0.31 & 0.12 & 0.56 & 0.37 & 0.19 \\  & total & 2.19 & 2.06 & 3.75 & 3.00 & 2.62 & 2.62 \\ \multirow{4}{*}{MIMO LS-SVR} & \(>\)3 dB & 0.56 & 0.25 & 2.25 & 0.50 & 0.69 & 0.94 \\  & \(<\)–3 dB & 0.12 & 0.00 & 0.81 & 0.12 & 0.12 & 0.19 \\ \cline{1-1}  & total & 0.69 & 0.25 & 3.06 & 0.62 & 0.81 & 1.12 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Percentage of the number of frequencies whose energy prediction error is over 3 dB for different models (%). Figure 4: _Cont._  
Table 3 shows the RMSE value of predicted vibration response in different methods, and Table 4 shows the MAPE value of predicted vibration response in different methods. In order to verify the influence of different number of measurement points on accuracy, different number of measurement responses were selected to predict the unmeasured responses of point 1 and point 5 under different levels of noise. The results are shown in Table 5: \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Model**} & **t1** & **t2** & **t1** & **t2** & **t1** & **t2** \\ \cline{2-7}  & **1** & **5** & **2** & **6** & **8** & **9** \\ \hline Transmissibility matrix & 0.01566 & 0.02220 & 0.01597 & 0.03056 & 0.00726 & 0.01261 \\ Transfer function with loads & 0.02529 & 0.06562 & 0.02980 & 0.05101 & 0.01718 & 0.01667 \\ MLR & 0.02631 & 0.02149 & 0.03983 & 0.05477 & 0.02524 & 0.03301 \\ MIMO Neural network & 0.07172 & 0.12726 & 0.05926 & 0.05644 & 0.03049 & 0.03019 \\ MIMO LS-SVR with loads & 0.03348 & 0.06137 & 0.02546 & 0.04523 & 0.01780 & 0.01565 \\ MIMO LS-SVR & 0.01682 & 0.03723 & 0.02047 & 0.02704 & 0.00906 & 0.01653 \\ \hline \hline \end{tabular}
\end{table}