## 4 Results of the Proposed Algorithm for the Automatic Parameters Set up and the Prediction Results  
In this research, there was used a NAR neural network with two hidden layers. This NAR network had hyperbolic tangent activation functions in each layer. The first hidden layer was consisting of 100 neurons and the other one was consisting of 75 neurons. The size of these two hidden layers was constant. The algorithm was correcting in this test only the time delay input layer size and the steps ahead parameter. For the algorithm tests presented in this article, we decided to set up the initial parameters with these specific values given in Table 1 below. After the first parameter correction, the correlation coefficient between the real measured data and the predicted data for 100-time steps ahead reached a value of R = 0.20548. There is a given regression plot and a preview of the prediction on specific samples in the figures below. This value was far from the desired R = 0.75 so there was necessary for the algorithm to do multiple parameter corrections. After 7 corrections of the model parameters, the final NAR model accuracy reached a value of R = 0.76128 which is larger than the desired accuracy defined in the previous table. The input layer was increased from the initial value of 100 to 300 and the _stepsAheadParam_ was corrected from 100 to 60. After this correction, the model was able to reach the desired accuracy. The results of the correlation coefficient between the estimated predictions and the real data during of each parameter correction is given in the table below. The performance of the initial configuration of the model is given in the Figure 10. The performance after the algorithm ended is given in the Figure 11.  
The process of the parameter corrections is given in Figure 12 and Table 2. The algorithm started with the initial values which are given in the Table 1. The blue line represents the value of the input layer size during the modifying process of the model parameters. This parameter is increased by a constant value of 100 until the reach of the 4 th correction of the model. In the 4 th step of the parameter correction the value of the chosen criterion of the accuracy drops, so the algorithm sets the previous value of the size of the input layer of the NAR neural network model in the next parameter correction. In the next \begin{table}
\begin{tabular}{c c} \hline \hline
**Name of the Parameter** & **Value** \\ \hline stepsAheadParam & 100 \\ \hline inputLayerSize & 100 \\ \hline Maximum inputLayerSize & 1000 \\ \hline Minimum stepsAheadParam & 30 \\ \hline Minimum R-value & 0.75 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Initial parameters settings for the algorithm. Figure 10: Performance of the NAR neural network model with the initial parameter values. stages of the analysis of sensed vibrations without interfering with the actual structure of the industrial machine itself. The way in which this module should be deployed in a real machine was tested on a Siemens ET 200 SP device using a written.NET framework console application using libraries such as _S7 NETplus_, _npgsql_[30], and _encog_[31]. It is often necessary to choose the appropriate settings for these models to be able to predict the specified time into the future with sufficient prediction accuracy. Therefore, an algorithm is introduced in this article that automatically searches for specific parameter values so that the model meets the prediction accuracy criteria as a result. Testing of this algorithm took a place in the MATLAB environment. Firstly, the parameter was set to the specific values from Table 1. At initialization, the model achieved a prediction accuracy of R = 0.20548. With _stepsAheadParam_ = 100, the model calculates the estimated values for one step in advance and moves the estimated value to the input layer. With the _inputLayerSize_ = 100, after calculating the 100 th prediction, the entire layer is filled with values which are containing inaccuracies.