# Kohonen Mapping of the Space of Vibration Parameters of an Intact and Damaged Wheel Rim Structure
## 1 Introduction  
The vehicle wheel (comprising the tyre and rim) is a crucial structural component of a car, as it facilitates the transmission of all forces between the vehicle and the road. Although detailed analyses of tyre design, manufacturing, and use are abundant in the literature [1; 2; 3], the wheel rim--which is essential for the proper functioning of the tyre--has received comparatively little attention in terms of measurement methods aimed at characterising its condition. The rim, also known as the disc wheel, plays a key role as the component connecting the tyre to the suspension. Research on wheel rims can be categorised into several areas. One primary area of focus is the identification of technical conditions through simulation studies and their verification on real-world objects [4; 5]. Another area involves strength testing of wheel rims based on approval and in-service tests [2; 6]. Post-test evaluations are typically limited to examining the geometry and conducting visual assessments of the rim material using VT and X-ray methods. In addition, some studies discuss identifying the modal parameters of wheel rims--[PERSON] et al. [7] focused on these aspects--while others explore rim strength ([PERSON] et al. [1]) and operational problems [8]. Despite the existing body of research, there remains a significant gap regarding the development of effective measurement methods for rapid and unambiguous assessment of wheel rim conditions. Innovative diagnostic approaches could be of benefit particularly in the production process, where quality control is critical to prevent defective products from entering distribution. Ideally, a non-invasive diagnostic technique should be used to characterise manufactured parts without causing any degradation. Non-invasive diagnostic methods have been widely applied to assess the structural integrity of engineering components [9]. These methods are based on detecting changes in the dynamic responses and characteristics of a structure, which may relate to different damage states and their locations. The traditional approach involves creating a mathematical model of the object [10] to understand its behaviour and to determine the relationship between damage and changes in characteristics (especially dynamic characteristics). Subsequent steps include identifying damage causes, which may involve joint failures, material defects, wear and tear, accidents, and corrosion. As noted by [PERSON] et al. [11], damage identification through vibration characteristics can be considered a pattern recognition problem. Many researchers have proposed methods for estimating structural damage based on analyses of dynamic responses before and after damage occurs. Some methods focus solely on forced vibration frequencies as responses to applied static or dynamic load [12; 13; 14]. However, while mathematical models of complex structures may be suitable for analysis and design purposes, they may not be practical for diagnostics. The cited research shows that a structure's dynamic response to forcing can be a valuable source of information about its condition. This approach is expected to be effective for wheel rims as technical objects. The authors of the paper [15] highlighted the challenges of using spectral analysis of vibration for rigid structural plates due to the numerous degrees of freedom and various features of the frequency response function. Consequently, the vibration characteristics of an object alone may be insufficient for diagnostic purposes without reference standards for undamaged structures. Moreover, the need to operate with many object benchmarks underscores the necessity for enriching condition assessment methodologies with pattern recognition capabilities, especially to detect damage through changes in structural responses. For instance, deep neural networks have been employed to classify data, representing cracks in plate structures [16].