A Mathematical Methodology for the Detection of Rail Corrugation Based on Acoustic Analysis: Toward Autonomous Operation

In autonomous railway systems, where there is no driver acting as the primary fault detector, annoying interior noise caused by track defects can go unnoticed for long periods. One of the main contributors to this phenomenon is rail corrugation, a recurring defect that generates vibrations and acoustic emissions, directly affecting passenger comfort and accelerating infrastructure deterioration. This work presents a methodology for the automatic detection of corrugated track sections, based on the mathematical modeling of the spectral content of onboard-recorded acoustic signals. The hypothesis is that these defects produce characteristic peaks in the frequency domain, whose position depends on speed but whose wavelength remains constant. The novelty of the proposed approach lies in the formulation of two functional spectral indices—IIAPD (permissive) and EWISI (restrictive)—that combine power spectral density (PSD) and fast Fourier transform (FFT) analysis over spatial windows, incorporating adaptive frequency bands and dynamic prominence thresholds according to train speed. This enables robust detection without manual intervention or subjective interpretation. The methodology was validated under real operating conditions on a commercially operated metro line and compared with two reference techniques. The results show that the proposed approach achieved up to 19% higher diagnostic accuracy compared to the best-performing reference method, maintaining consistent detection performance across all evaluated speeds. These results demonstrate the robustness and applicability of the method for integration into autonomous trains as an onboard diagnostic system, enabling reliable, continuous monitoring of rail corrugation severity using reproducible mathematical metrics.