# Vibration Velocity Prediction with Regression and Forecasting Techniques for Axial Piston Pump
### Related Work  
Common applications of neural networks in industry include projects related to the subject of intelligent machine maintenance [15]. The purpose of this kind of project is to track the condition of a machine, so that potential failure of the machine could be detected or even predicted in case of Predictive Maintenance [16] implementation. Such an approach allows manufacturers to keep production flow undisturbed as much as possible. Data acquisition plays a crucial role in intelligent maintenance. Without the proper measurement of quantities related to monitored machine or process, it is impossible to implement intelligent maintenance strategies based on machine condition monitoring. Data from sensors is the main source of information regarding the state of a machine [17]. In simple maintenance strategies, tracking the value of a chosen variable and applying a threshold to it can provide enough information. In such a case, it may not be necessary to implement more complex strategies, as the costs of development of complex strategies could be too high to ensure a return of investment, considering potential profits from the reduction of disturbances in machine work [18]. An example of such an implementation in industry could be vibration monitoring of a suspension bridge, as presented in [19]. In the article, the authors set warning threshold of RMS of vibration acceleration at \(5\frac{\text{cm}}{\text{s}^{2}}\). In many industrial implementations, the application of a threshold on measurements may be not enough in processes that work at different operating points [20]. Significant process nonlinearities make handmade determination of threshold values related to specific operating points difficult--that is where neural networks come into play. By training a network using data from different machine conditions at various operating points, a neural network is able to \"learn\" the behavior of the piston pump, even if this behavior is strongly nonlinear [21]. In the literature, applications of using neural networks for regression and forecasting purposes in different industry domains are presented. As an example, neural networks models were used for forecasting electricity consumption in the Brazilian industrial sector [22]. The presented results show that neural network-based approaches outperform classical forecasting algorithms over a longer prediction horizon in terms of mean absolute percentage error (MAPE), which for a 24 h prediction horizon equals 3.42%. In the paper [23], the authors present the facilitation of a neural network for production schedule optimization. For the purpose of the present article, axial piston pump vibration velocity monitoring and prediction is the particular subject of research. Previous research described in [21] presents failure analysis and intelligent identification of critical friction pairs of an axial piston pump. Diagnostics of the pump were implemented with the use of pressure signal analysis transformed using wavelet transform and convolutional neural networks (CNN). The authors claim that the proposed approach achieved 100% accuracy for recognition of different faults. These faults include wear of the slipper, wear of the swash plate, failure of the loose slipper, wear of the central spring, and no visible failure. Another application of neural networks in piston pump state recognition and failure prediction is presented in the paper [24]. By using a feed forward neural network, 92.8% accuracy was achieved for the recognition of six distinct failures. Statistical features extracted from vibration data were input to the network. The prediction of vibration velocity of an axial piston pump was presented in [25]. However, instead of using neural networks to model the course of pump vibration, a set of equations was used and frequency of vibration was a particular interest. The presented approach leads to an 8.85% error in vibration frequency estimation. Similar work was carried out and presented in [26].