# Kohonen Mapping of the Space of Vibration Parameters of an Intact and Damaged Wheel Rim Structure
## 2 Research Methodology  
There are two approaches to the identification of damage. The first approach is the inverse problem and the second approach is the problem of recognising patterns. The inverse problem usually uses the mathematical model of processes in a structure and \begin{table}
\begin{tabular}{l l} \hline \hline
**Research Object: Mechanical Structure–Wheel rim** \\ \hline \hline \multicolumn{2}{l}{Damage detection major approaches} \\ \hline \(\bullet\) & Mechanical Vibration [25; 26] \\ \(\bullet\) & Acoustic emission [25; 27] \\ \(\bullet\) & Elastic-wave-based (Lamb Wave Tomography) [28] \\ \hline \multicolumn{2}{l}{Damage detection strategies based on vibration analysis} \\ \hline \(\bullet\) & Principal Component Analysis (PCA) [5] \\ \(\bullet\) & Wavelet Transform (WT) [29] \\ \(\bullet\) & PCA-WT [15] \\ \(\bullet\) & Adaptive Harmonic Wavelet Transform (AHWT) [30] \\ \(\bullet\) & Genetic Algorithm (GA) [31] \\ \(\bullet\) & Data fusion and random forests [32] \\ \(\bullet\) & Autoregressive Models (AR) [33], \\ \(\bullet\) & Autoregressive Moving Average (ARMA) [34] \\ \(\bullet\) & Autoregressive Integrated Moving Average (ARIMA) [10; 35] \\ \hline \multicolumn{2}{l}{Different domains from wave propagation perspective} \\ \hline \(\bullet\) & Frequency domain [25; 36] \\ \(\bullet\) & Time domain [25; 26] \\ \(\bullet\) & Joint Time-Frequency domain analysis [37] \\ \hline \multicolumn{2}{l}{Data analysis method} \\ \hline \(\bullet\) & ANN [15; 21; 22; 38] \\ \(\bullet\) & SOM [39] \\ \(\bullet\) & Bayesian Network [17] \\ \(\bullet\) & Wiener process [18] \\ \(\bullet\) & MLP [40] \\ \(\bullet\) & Hidden Markov (HMM) [41] \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Non-invasive methods for fault detection with highlighting signal features and fault detection strategies based on vibration analysis. changes in the measured data of the physical structure are consistent with changes in the elaborated model, e.g., MES (Manufacturing Execution System) [10; 42]. The second approach is based on measurement data of the researched structure and classification of damage (type, location), assigned by pattern recognition algorithms [34]. The second approach was adopted in the presented paper. The proposed ZRTOK (dynamic response test station for wheel rims) station, as well as the method, is intended for quality control of products at a production line of wheel rims. The aim of its employment is to rapidly identify the technical condition of the ready-made products through pinpointing wheel rims which, in the production process, were manufactured with a faulty welded joint of the wheel rim coil and/or the wheel rim with wheel disc. The presented diagnostic station was constructed on a wheel-balancing machine furnished with: additional vibration acceleration sensors, vibration inductor (mechanical percusise hammer) and computing unit with software for data analysis and visualization. In Figure 1, the general view of the ZRTOK test station is presented, in which the assembly location of measurement sensors and basic station's components are highlighted. The station is equipped with two accelerators: front (4a, Figure 1) and rear (4b). The exact construction and assembly of the sensors is described in the patent application [43]. During verification tests of the elaborated diagnostic method, an extensive analysis of the usability of vibration signals from these sensors was conducted. The performed analysis indicated that the front sensor feeds a signal with much higher amplitude than the rear sensor. This is due to the fact that the amount of induction energy fed during the measurement is sourced with a mechanical vibration inductor. During automation of the measurement process of the elaborated method, a minimum induction force was defined and connected with the mass of a tested wheel rim. With low induction energy, suppression of the station's frame is considerable and vibrations detected by the rear sensor are at a noise level.