# Vibration Velocity Prediction with Regression and Forecasting Techniques for Axial Piston Pump
## 3 Results and Discussion
### Performance
#### 3.2.1 Neural Networks  
To check the legitimacy of the trained models in context of assessing condition of the pump, metrics were computed on the whole experiments with both damaged and not damaged devices. A distinction between four types of damage was indicated as mentioned in Section 2.1. The models were trained on data from experiments where the pump had no damage, so it is expected that they would obtain a significant difference between the prediction quality calculated on the scenarios for the pump with and without damage. The best models for the purpose of the following analysis were chosen by the lowest test MAPE value among Tables 6-8 for dense, RNN and LSTM models, respectively. The metrics computed for these models on all experiments are presented in Tables 10-12. These results are the basis for drawing several conclusions. The more input variables the model has, the greater the difference between metrics for scenarios for the pump with and without damage. For many models that take one or two variables on the input, it emerges that the bearing fault scenario has better fitness metrics than scenarios that involve pump without faults. A high MSE value in combination with low MAPE and MAE values means for all types of models for experiment called Reference tests v1, that the outliers are present in the experiment. However, there are some models, for example the best LSTM model with one input variable, that are able to handle outliers better than models that have lower values of MAE and MAPE metrics. A similar situation appears for an experiment called Bearing fault. However, in that case, the MSE value is high for all types of models for all number of input variables. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Metric** & **GB Dense** & **GB RNN** & **GB LSTM** & **Median** & **Mean** & **Linear Regression** \\ \hline \multicolumn{7}{c}{Experiment: Swash plate fault} \\ \hline MAE & 2.2711 & 2.3352 & 2.1457 & 2.2727 & 2.2522 & 2.245 \\ MAPE & 65.0 & 66.83 & 61.37 & 65.04 & 64.45 & 64.25 \\ MSE & 5.1945 & 5.4953 & 4.6474 & 5.2011 & 5.1085 & 5.0758 \\ \hline \multicolumn{7}{c}{Experiment: Bearing fault} \\ \hline MAE & 0.1397 & 0.1943 & 0.1555 & 0.1726 & 0.1573 & 0.1192 \\ MAPE & 10.8 & 14.67 & 11.57 & 13.03 & 11.88 & 9.2 \\ MSE & 0.0304 & 0.053 & 0.0399 & 0.0407 & 0.0355 & 0.0226 \\ \hline \hline \end{tabular}
\end{table} 
Table 9: _Cont._ \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline
**Experiment** & \(MAPE_{1 war}\) & \(MAE_{1 war}\) & \(MSE_{1 war}\) & \(MAPE_{2 war}\) & \(MAE_{2 war}\) & \(MSE_{2 war}\) & \(MAPE_{2 war}\) & \(MSE_{2 war}\) & \(MSE_{2 war}\) \\ \hline Reference tests v1 & 9.85 & 0.12 & 0.47599 & 13.27 & 0.23 & 15.3615 & 5.46 & 0.15 & 15,4813 \\ Reassembling v1 & 12.52 & 0.19 & 0.10032 & 9.45 & 0.14 & 0.11833 & 5.37 & 0.09 & 0.01366 \\ Reference tests v2 & 11.16 & 0.13 & 0.09743 & 10.09 & 0.12 & 0.07467 & 7.27 & 0.08 & 0.03478 \\ Reference tests with check valve & 18.42 & 0.17 & 0.17454 & 13.23 & 0.13 & 0.11489 & 7.24 & 0.08 & 0.11464 \\ Axial play fault & 35.63 & 0.7 & 0.54233 & 35.09 & 0.67 & 0.57356 & 22.11 & 0.45 & 0.29764 \\ Timing plate fault & 27.9 & 0.46 & 0.25225 & 34.78 & 0.56 & 0.39376 & 19.98 & 0.33 & 0.14984 \\ Swash plate fault & 62.3 & 1.85 & 3.57135 & 59.99 & 1.79 & 3.31754 & 57.75 & 1.72 & 3.14876 \\ Bearing fault & 8.66 & 0.23 & 39.9357 & 7.6 & 0.21 & 39.0417 & 14.49 & 0.29 & 39.3965 \\ \hline \end{tabular}
\end{table} 
Table 10: MAPE, MAE and MSE metrics for whole dataset evaluated for best dense model for following sets of input variables: 1 var—[Outlet pressure], 2 var—[Outlet pressure, Outlet flow, liked pressure].