## 2 State of the Art
### The Previous Predictive Models Tested Separately  
In the area of analyzing and predicting the state of a technical object on an example of pantograph's sliding strips, previous research has been published in [38; 39], and the following predictive models have been described, developed based on real data from maintenance systems:  
* Model based on the decision trees method.
* Model based on artificial neural networks.  
The paper by [38] described a predictive model based on decision trees. To predict the technical condition of the object, a three-valued prediction method based on machine learning and failure analysis was developed. The results from the developed model were in a discrete form. Therefore, the anticipated technical conditions can be described as follows:  
\[\begin{array}{l}S_{1}\Longleftrightarrow[y_{13}=1]\\ S_{2}\Longleftrightarrow[y_{13}=2]\\ S_{3}\Longleftrightarrow[y_{13}=3]\end{array} \tag{7}\]  
Based on the results, it can be determined that the correctness of the classification was about 81%. However, correct classification of Class 2 is the most important. Class 2 indicates that the technical object will fail soon (which defines Class 3). In the confusion matrix, 49.6% of cases in Class 2 were identified as Class 1 (class 1--possibility of further use). In practice, it means that about half of cases can be identified before failure (i.e., reach Class 3--no use, it is necessary to replace the object).  
In a second paper by [39], a predicting method based on an ANN was developed. Due to the large number of conducted studies, it was decided to include only representative models based on artificial neural networks. The most representative models are presented in Table 1.  
The selected model can be described as follows:  
\[\text{a2}=\text{f2}(\text{IW2},\text{1f1}(\text{IW1},\text{1p}+\text{b1})+\text {b2}) \tag{8}\]  
Since the simulation results were continuous, to determine the technical condition, it was necessary to define the ranges of values belonging to a given technical condition. For example, for the model giving the best results, it was defined as follows:  
\[\begin{split} S_{1}&\Longleftrightarrow[0\leq y_{12}<1.25] \\ S_{2}&\Longleftrightarrow[1.25\leq y_{12}\leq 2.5]\\ S_{3}&\Longleftrightarrow[2.5<y_{12}\leq 3.5]\end{split} \tag{9}\]  
where  
\(S_{1}\) is the first technical condition, i.e., able to further use;  
\(S_{2}\) is the second technical condition, i.e., the limited ability of further use, it will be necessary to replace the sliding strip for the next inspection;  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Model No.** & **Type of Learning Method** & **Model Parameters** \\ \hline \(1\) & & & Number of hidden layers: 5 (14-14-14-14-3) \\ \hline \(2\) & Activation function: & Learning algorithm: & Number of hidden layers: 5 (12-12-12-12-3) \\ \hline \(3\) & & & Number of hidden layers: 5 (12-12-12-12-3) \\ \hline \(12\) & & & Number of hidden layers: 5 (12-12-12-12-3) \\ \hline \(4\) & Feed-forward artificial neural network with backpropagation & & Number of hidden layers: 1 (12-3) \\ \hline \(5\) & & & \\ \(6\) & & & \\ \(7\) & & & \\ \(8\) & & & \\ \(9\) & & & \\ \(10\) & & & \\ \(11\) & & & \\ \(12\) & & & \\ \(13\) & & & \\ \(14\) & & & \\ \(15\) & & & \\ \(16\) & & & \\ \(17\) & & & \\ \(18\) & & & \\ \(19\) & & & \\ \(19\) & & & \\ \(10\) & & & \\ \(11\) & & & \\ \(12\) & & & \\ \(13\) & & & \\ \(14\) & & & \\ \(15\) & & & \\ \(16\) & & & \\ \(17\) & & & \\ \(18\) & & & \\ \(19\) & & & \\ \(19\) & & & \\ \(17\) & & & \\ \(18\) & & & \\ \(19\) & & & \\ \(19\) & & & \\ \(18\) & & & \\ \(19\) & & & \\ \(19\) & & & \\ \(17\) & & & \\ \(18\)\(S_{3}\) is the third technical condition, i.e., not able to further use, it is necessary to replace the sliding strip/pantograph;  
\(y_{12}\) is the value obtained during the prediction based on use of the ANN predictive model.  
The simulation results based on the ANN allowed us to obtain the correctness of the classification of State 2 at the level of 85.1%.