Spectral Differentiation of Vehicle Vibration States Using FFT, ANOVA and Effect Size Analysis

The objective of this study was to identify vibration frequency bands that most effectively differentiate vehicle operating conditions in real driving. Vehicle vibration signals acquired along three measurement axes and as a resultant signal were analyzed together with synchronized CAN bus parameters. The vibration signals were divided into 5-s segments and analyzed using the fast Fourier transform (FFT). Mean spectra and spectral variability were evaluated for different RPM classes. To quantitatively assess spectral differences, one-way analysis of variance (ANOVA) with False Discovery Rate correction and frequency-dependent Cohen’s d effect-size analysis were applied. The results demonstrated that engine operating conditions significantly influence the vibration spectrum across a broad frequency range, with the most diagnostically relevant changes occurring within the 8–12 Hz and 25–35 Hz bands. The strongest spectral separation was observed during the transition from idle to low-RPM operation, yielding very large effect sizes. An additional assessment of the usefulness of the selected descriptors was conducted using a Random Forest classifier, accounting for group-based temporal partitioning and five-fold cross-validation. The classifier achieved an accuracy of 88.28% and a balanced accuracy of 74.51% on a separate test set. The results indicate high recognition rates for the idle state and greater difficulty in distinguishing between low and medium engine speeds. Global spectral descriptors demonstrated the greatest predictive power, whereas the energies of selected narrow frequency bands did not provide significant additional information to the classification model.