# Kohonen Mapping of the Space of Vibration Parameters of an Intact and Damaged Wheel Rim Structure
## 4 Conclusions  
This paper presents original results that significantly improve the non-invasive identification process for wheel rims. The proposed method synergistically combines frequency spectrum identification with Kohonen self-organising maps for rapid identification of structural damage in wheel rims during production. The study utilised cycles of acceleration amplitude times as a measure of the structural response. These cycles underwent Fast Fourier Transform (FFT) analysis, identifying four diagnostic symptoms described by 20 features of the diagnostic signals, which in turn allowed the definition of the condition vector, \(P_{j}\). Subsequently, the amplitude and frequency cycles served as input data for a neural network, and based on these inputs, SOM images were created to define a condition vector, PSOM, describing the condition of the wheel rim at different measurement angles. The developed diagnostic model employed a two-state classification system for condition identification (serviceable vs. unserviceable), applied similarly across all symptoms, and provided unconditional differentiation between these states. The accuracy testing of Kohonen maps, conducted with various features and input data types, led to the following conclusions:It is possible to detect structural damage in wheel rims using a 10 \(\times\) 10 SOM. It takes approximately 11 s (from the generation of the dynamic response of the system to the decision on the quality of the part) to generate such a map, which is acceptable for use in a series production verification process. - The best results using Kohonen maps were obtained when data were presented in the form of frequency series. Using a time series as input data may lead to ambiguity in interpreting SOM images, as shown in a comparison between time and frequency domain SOMs in Tables 4 and 6. SOMs in the frequency domain successfully detected a defect in the test object at a position of 270 degrees. The outcome of this work is an innovative diagnostic system that identifies the condition of a wheel rim based on vibration and acoustic analysis, complemented by neural network techniques using Kohonen maps. The presented diagnostic method has proven its effectiveness and has been incorporated into the quality control system for disc wheel rim production. The paper focuses on a methodology for the synergetic identification of damage in the three-dimensional structure of a technical object using a Kohonen SOM. Future work may involve developing a diagnostic method for monitoring wheel rim conditions during service, which would require expanding the dimension of the condition vector and accounting for the degradation history of the wheel disc structure. Compared to other methods such as Fast Fourier Transform (FFT) or Discrete Cosine Transform (DCT), DTT [49] may offer advantages in representing local image features, which is beneficial for image processing and pattern recognition. Future work could include comparing the results from FFT and DTT, which may provide insights into the effectiveness and accuracy of FFT for this particular application. The DTT may allow more efficient analysis or reveal aspects that FFT could miss. The discrete Chebyshev transform is known for its ability to represent certain signal types better, especially those with specific patterns or noise, and may be more suitable for describing shape or geometric features, such as those in circular structures. Conceptualization, A.R. and O.V. ; methodology, A.R. and O.V. ; software, D.S. and O.V. ; validation, D.S. and O.V. ; investigation, A.R., D.S. and O.V. ; writing--original draft preparation, O.V. ; writing--review and editing, A.R. and D.S. ; funding acquisition, A.R. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. Not applicable. Not applicable. Data Availability Statement: The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.