## 3 Selected Research Results
### Machine Learning Methods  
Neural networks provide innovative solutions in the classification of technical states. In this work, a neural network was used to detect a developing crack in a marine internal combustion engine component. This study aims to develop a neural network-based classification system for identifying signals in various technical states. The neural network was established considering the diagnostic parameters of the recorded signals in multiple domains, and predictive models capable of classifying unknown state symptoms were developed. A graphical diagram of the stages of the procedure, from the acquisition of signals from the internal combustion engine to the development of the classification and recognition model, is shown in Figure 11.  
Classification is supervised, and semisupervised learning algorithms have been applied to binary problems. A semisupervised algorithm is a type of supervised machine learning in which the algorithm \"learns\" to classify new measurement data based on examples of selected data. The classification learner application was used to apply classification models interactively. Techniques such as machine learning and deep learning were employed, which enable machines to use the environment to improve tasks. In machine learning, a neural network classifier was chosen for all the neural networks. Figure 10: Kurtosis values \(K\) for individual cylinders of the tested engine with limit values: _llv_—lower limit value, _ulv_—upper limit value. The classifier divides the feature space of a technical condition into decision areas in a part of the feature space such that all points located in the distinguished area correspond to the same class. The boundaries between these areas are called decision surfaces or decision boundaries. The following decision rules were used in this study:  
* If \(S(\tau_{j})\geq l\upsilon\) and \(S(\tau_{j})\leq\upsilon\upsilon\), then it indicates a suitable state;
* If \(S(\tau_{j})\leq l\upsilon\) and \(S(\tau_{j})\geq\upsilon\upsilon\), then it indicates a state of unfitness. The results from neural network classification depend on many factors, the most important of which is the quality of learning, testing, and validation. The error generated using a neural network depends on the weighting coefficients present in the network and can be refined using machine learning algorithms [35, 36]. In practice, the learning coefficient determines the error correction amount and can change during the learning of the network, improving the quality of the results. To evaluate the quality of learning, the GIGO (garbage in, garbage out) rule [37] was used to evaluate the quality of learning and learning data. Networks were evaluated using statistics as network quality coefficients for learning, testing, and validation sets [38]. The quality of the network was assessed in terms of its ability to generalize, and the measure was the quality of the validation sample, that is, the new data that had not been subjected to the learning process. In the classification model, \"accuracy\" was determined as the ratio of the number of correct predictions to the total number of predictions. These qualities can be expressed are Pearson correlation coefficients between the expected values and the network's prediction:  
\[k=\frac{\sum_{i=1}^{n}\left(x_{i}-\overline{x}\right)\left(y_{i}-\overline{y} \right)}{\sqrt{\sum_{i=1}^{n}\left(x_{i}-\overline{x}\right)^{2}\sum_{i=1}^{n }\left(y_{i}-\overline{y}\right)^{2}}} \tag{19}\]  
where \(i\) is the consecutive number of the component of the diagnostic parameter, \(x_{i}\) is the consecutive value of the given input, \(\overline{x}\) is the average value of the given input in the set of observations, and \(y_{i}\) is the consecutive value of the given diagnostic parameter. These qualities are Pearson correlation coefficients between the expected values and the network's prediction, so a linear correlation of \(\geq\)70% in the learning set was considered a good result.