# Vibration Velocity Prediction with Regression and Forecasting Techniques for Axial Piston Pump
## 2 Materials and Methods
### Feature Importance Analysis  
During the experiments, many different measurements were available. On the other hand, in the production environment, it will be difficult or sometimes impossible to use all variables indicated in Table 1. There are two main reasons for this. The first is the cost of sensors and second is the difficulty in mounting them properly on monitored device. Pumps are used in different conditions; in some use cases there is no space to fix a sensor on the device. For instance, in cases where other machines work nearby. Domain experts from PONAR Wadowice suggested that sensors they consider the easiest to mount are sensors that measure outlet pressure, bleed pressure, outlet temperature and outlet flow. However, vibration sensor is the most desired factor because of its non-invasiveness and mobility. Considering possibilities of interference in the pump and advantages and disadvantages of mounting vibration sensors as presented in the article [32], sticking sensors with glue was performed on a test stand. Two vibration sensors were available, however, in the production environment only one sensor is desired due to constraints and conditions described in the previous paragraph. To meet this requirement, an analysis of \(V_{RMS}\) value from both sensors for all carried out experiments for a constant load was performed. \(V_{RMS}\) values from only steady state periods were taken into consideration. Median values of analyzed variables were calculated. The results are shown in Figure 4.  
Based on analysis of Figure 4, several conclusions could be drawn. Measurements from a sensor mounted in radial position are more informative in the context of distinguishing between an undamaged and damaged pump. It is possible to set a threshold visually for every load that separates the pump with and without faults for all fault types, except bearing faults. However, this is not the case for every load or for every experiment, as the differences between \(V_{RMS}\) values are significant. On the other hand, for sensors mounted in axial position, such a simple threshold is not possible to establish. Taking the above factors into consideration, it could be deduced that measurements from sensors mounted in radial position are more informative for the description of pump condition. The goal of the article is therefore to estimate vibration velocity root-mean-square value that comes from a radial mounted sensor. This variable will be further denoted as \(V_{RMS-Radial}\). After selecting the most informative vibration sensor and choosing \(V_{RMS-Radial}\) as the output variable of the model, input variables should be chosen. As presented in [33; 34],  
Figure 4: Median values for \(V_{RMS-Radial}\) for each load value distinguishing between types of failures. among all the available measured quantities, selecting the most informative ones to improve the quality of the deep learning model prediction could be performed using Pearson Correlation Coefficients (PCC). The higher the PCC absolute value between the output and the input variable, the more useful the input variable is. According to this approach, to select useful variables, PCC between \(V_{RMS-Radial}\) and variables acquired from flow, pressure and temperature sensors were computed. The results are presented in the Figure 5. Among the variables considered, outlet pressure, outlet flow, inlet and bleed pressure are good potential candidates for input variables. One more factor that influences the choice of input variable is that the number of variables will be crucial in the context of training duration for models [35]. Generally, the more variables are chosen, the longer training lasts. This aspect harmonizes with the business requirement to minimize the amount and cost of sensors to be mounted.