# Kohonen Mapping of the Space of Vibration Parameters of an Intact and Damaged Wheel Rim Structure
## 1 Introduction
This idea can be realised by using artificial neural networks (ANNs), Bayesian networks [17; 18], genetic algorithms, or fuzzy logic [9]. Particular attention should be paid to diagnostic models that take into account current monitoring data and historical degradation data [19]. While this approach is promising for future diagnostic processes, it may be excessive for assessing conditions during production. Therefore, simpler methods are required-methods capable of providing sufficient diagnostic information for damage detection while being fast enough not to disrupt the manufacturing process. Deep neural networks are of interest, mainly because they outperform alternative machine learning methods such as support vector machines (SVMs) or kernel machines in many key applications. Recently, such models have been developed for fault detection and diagnosis in mechanical engineering [16; 20]. In 2017, a study explored using a 1-D convolutional neural network (CNN) for structural fault detection [21]. [PERSON] et al. [22] presented the concept of combining a system's dynamic response analysis with neural networks. Their work highlighted the potential for real-time identification of vibration signals and image mapping using artificial neural networks, which could effectively locate and predict structural changes with high accuracy. Non-invasive methods for diagnosing wheel rims using intelligent neural networks have yet to incorporate self-organising Kohonen maps (SOM), despite their potential effectiveness in quality control processes for vehicle wheels during manufacturing. This paper aims to explore this potential. Previous research [23] demonstrated the usefulness of SOM maps in identifying defects in concrete structures. Similarly, the authors of the paper [24] concluded that SOMs significantly improve damage classification, underscoring the validity of using this tool in the proposed approach. There remains a need to verify and further develop the methodology for a non-invasive diagnostic approach [13; 14], based on the analysis of rim vibration spectra collected on a diagnostic bench following the application of impact-induced vibrations. Table 1 shows the main approaches to damage detection, distinguishing between signal characteristics and damage detection strategies based on vibration analysis. Highlighted  
within the table are the methods and measures chosen to assess the condition of the rim as the test object. The aim of this paper is to address the problem of 'three-dimensional adequacy' regarding the non-uniform structure of a vehicle wheel rim, including welded joints. The personal observations of the authors, who have experience in the field of appraisal, prompted the development of a fast and precise assessment method. The proposed approach achieves a reduction in the dimensionality of the problem through synergistic application of dynamic system response and self-organising Kohonen maps. It is anticipated that by analysing the dispersion of energy delivered via impact, it will be possible to precisely locate damage within the structure. The practical significance of this work lies in its applicability during the manufacturing process of the rim. Compared to existing methods cited in the literature, this approach is less time-consuming (e.g., does not require the development of a mathematical model) and allows unskilled personnel to draw conclusions using self-organising Kohonen maps, based on visual divergences for different rim positions. The implementation of a diagnostic method for assessing rim conditions (e.g., defects such as cracks related to welding errors) can be implemented prior to the painting process. The goal is to eliminate defective components before they progress to later production stages, which can yield economic benefits by reducing material waste and mitigating potential product complaints.