## 2 Related Work  
The literature analysis shows that machine learning techniques are popular tools for failure prediction including a large family of methods. A good example of a neural network application particularly a convolutional neural network is described [10]. However, it is noted that classic machine-learning algorithms are dominant in this area. One can find examples of the use of a modified KNN algorithm, which in combination with the just-in-time learning rule (JITL) was used to determine the remaining useful life (RUL) [11]. This method was used for hydraulic pumps taking into account pressure measurements. Also, authors of [12,13] use the term RUL in combination with Bayesian regularized radial basis function neural network (Trainbr-RBFNN) during research on external gear pump or modified auto-associative kernel regression (MAAKR) and the monotonicity-constrained particle filtering (MCPF) approach when examining the piston pump. Another application is based on the use of RBF neural networks combined with noise filtering algorithms and the use of vibrodiagnostics [12]. The literature review also includes comparisons of classic machine learning algorithms, including SVM, KNN, and gradient-boosted trees [14]. Another publication [15] describes the use of a method based on empirical wavelet transform (EWT), principal component analysis (PCA), and extreme learning machine (ELM) to analyze data from vibration sensors. Another approach presented in [16,17] is based on using a convolutional neural network. In these articles pressure, vibration, and acoustic signals were used as the input data for the prediction. The authors of [18] present a review of the recent literature touching on ML-based condition monitoring systems. Manyauthors draw attention to artificial neural networks (ANN), multilayer perceptron (MLP), or convolutional neural networks (CNN). Remaining useful life is also predicted in [19] where the Auto-Regressive Integrated Moving-Average (ARIMA) forecasting method is used. The research object was a piston pump for which leakage volume was considered a significant parameter for RUL prediction. Another proposal for the predictive maintenance model was presented in [20]. This paper is focused on a hybrid solution that combines Improved Complete Ensemble Empirical Mode Decomposition with Adaptive Noise (ICEEMDAN), Principal Component Analysis (PCA) and Least Squares Support Vector Machine (LSSVM). The model is optimized by the combination of Coupled Simulated Annealing and Nelder-Mead Simplex optimization algorithms (ICEEMDAN-PCA-LSSVM). The proposed technique is compared with three established methods [Linear Discriminant Analysis (LDA), Support Vector Machine (SVM), and Artificial Neural Network (ANN)] with multiclass classification capabilities. Authors of [21] describe deep learning methods where the Bayesian optimization (BO) algorithm is used to find the best hyperparameters of the model. In this paper, the vibration signal of the piston pump is used as a source of data. The CWT preprocesses the signal and then the preliminary CNN model is prepared. Finally, BO based on the Gaussian process was used to prepare an adaptive CNN model (CNN-BO). Another article [22] presenting research on axial piston pumps proposes a transfer learning method for fault severity recognition. The method is based on adversarial discriminative domain adaptation combined with a convolutional neural network (CNN). Similar to [21] there is also a vibration signal utilized as a data source for ML. In the paper [23], the authors do the research using a one-way analysis of variance ANOVA. This is another article in which the authors rely on the vibration signal and additional pressure on the output port of the pump. Pump wear classification methods used were as follows: decision tree (DT), discriminant analysis (DA), KNN, naive Bayesian classifiers, and SVM.