# Kohonen Mapping of the Space of Vibration Parameters of an Intact and Damaged Wheel Rim Structure
## 2 Research Methodology
\begin{table}
\begin{tabular}{l c c c c c c c c c} \hline \hline  & **f\({}_{\text{L}}\) Hz** & **A\({}_{\text{r}}\) m/s\({}^{2}\)** & **f\({}_{\text{2z}}\) Hz** & **A\({}_{\text{r}}\) m/s\({}^{2}\)** & **f\({}_{\text{3z}}\) Hz** & **A\({}_{\text{r}}\) m/s\({}^{2}\)** & **f\({}_{\text{4z}}\) Hz** & **A\({}_{\text{r}}\) m/s\({}^{2}\)** & **f\({}_{\text{5z}}\) Hz** & **A\({}_{\text{r}}\) m/s\({}^{2}\)** \\ \hline Experimental tests & 152 & 0.28 & 370.51 & 0.85 & 727.51 & 2.55 & 995.49 & 0.29 & 1239.05 & 0.14 \\ \hline Mathematical model & 151.39 & 0.3 & 369.14 & 0.9 & 728.51 & 2.44 & 992.14 & 0.26 & 1236.5 & 0.12 \\ \hline Relative error (\%) & 0.4 & \(-\)7.14 & 0.37 & \(-\)5.88 & \(-\)0.14 & 4.31 & 0.34 & 10.35 & 0.2 & 14.29 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of characteristic frequencies and vibration amplitudes obtained in experimental and simulation tests. number of hidden layers, the number of processing units in each layer and the relations between layers. In this study, a simple connection pattern was used: each processor features outgoing connections with all processors at the next level. The capacity of a neural network is somehow connected with the amount of information contained in teaching data and the complexity of knowledge contained in the data. To date, no credible rules have been established for defining the throughput of the leading MLN, as this question is still not well understood. The subjects of testing were steel wheel rims, size 9 \(\times\) 15.3 (the first digit in such a notation indicates the width of the rim in inches, while the second refers to its diameter, also in inches, weighing 12.25 kg. This is a wheel rim commonly used in duty vehicles and agricultural machines. The ZRTOK measuring system was equipped with a piezoelectric acceleration sensor (ICP, 100 series--100 mV/g)-this sensor records system vibrations, shaft position sensor-encoder (resolution of 1.40\({}^{\circ}\)). The sampling rate of all diagnostic signals of the test machine was 2 kHz. The wheel rim vibration induction force during testing amounted to 250 N \(\pm\) 10 N. The utilised ZRTOK testing station has been extensively described in papers [10; 13; 14]--an innovation in the stand compared to previous publications is the use of a single piezoelectric acceleration sensor and a shaft position sensor. With all non-invasive diagnostic methods regarding the condition of technical objects, there is a problem with the analysis of results. For this purpose, the method of converting the space of parameters characterising an object's condition is employed, e.g., Fast Fourier Transform (FFT). In each case, there is the problem of rapid recognition of the condition, based on a comparison of the collected data (individual values and process curve) with the reference values or values predicted with the use of the known methods (e.g., artificial neural network [ANN]). These are interesting methods, which make it possible to reduce the dimension of the vector of tested parameters to present the results of verification of the object's condition at an intuitive level. In this aspect, one should consider the possibilities of the Kohonen artificial neural network (ANN). In this case, the processing of input data results in a self-organising map (SOM), which is trained to obtain a two-dimensional, discrete representation of input space of training samples using the method  
Figure 3: Graphical interpretation of the data acquisition process at the ZRTOK testing station: 1—the tested wheel rim; 2—framework with shaft for mounting the tested wheel rim; 3—wheel rim pressure nut; 4—sensor of vibration acceleration; 5—shaft rotation angle sensor (encoder); 6—vibration inductor; 7—wheel valve bore. of dimension reduction. As is well-known, SOMs use the neighbourhood function for displaying topological characteristics of the input space. In this paper, SOM is used in mapping mode. The used SOM consists of a competitive layer (Figure 4), which may classify a data set of four-dimensional vectors.