Time–frequency analysis of axle box accelerations in railway systems: experimental insights on ballasted tracks and bridge transition zone

Abstract Railway track structural health monitoring (SHM) plays a critical role in modern railway systems. Axle box acceleration (ABA) signals serve as a valuable information source for track SHM. However, the relationship between ABA frequency components and train–track dynamics, especially the muti-tone harmonics interaction, remains underexplored. This paper investigates the frequency components of ABA signals with time–frequency analysis methods, including short-time Fourier transform, continuous wavelet transform, and wavelet synchro squeezed transform. Through experimental field studies on a ballasted railway track and an embankment–bridge transition zone, the interactions between the sleeper passing frequency ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:msub> <mml:mi>f</mml:mi> <mml:mrow> <mml:mrow> <mml:mtext>sp</mml:mtext> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> </mml:mrow> </mml:math> ) and wheelset rotation frequency ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:msub> <mml:mi>f</mml:mi> <mml:mrow> <mml:mrow> <mml:mtext>wr</mml:mtext> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> </mml:mrow> </mml:math> ) are identified as the result of multi-tone harmonic coupling. The revealed empirical coupling relationship is shown by <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:msub> <mml:mi>f</mml:mi> <mml:mrow> <mml:mtext>c</mml:mtext> </mml:mrow> </mml:msub> </mml:mrow> <mml:mo>=</mml:mo> <mml:mrow> <mml:mo>(</mml:mo> <mml:mrow> <mml:mn>1</mml:mn> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> <mml:mo>)</mml:mo> </mml:mrow> <mml:mrow> <mml:msub> <mml:mi>C</mml:mi> <mml:mn>1</mml:mn> </mml:msub> </mml:mrow> <mml:mrow> <mml:msub> <mml:mi>f</mml:mi> <mml:mrow> <mml:mrow> <mml:mtext>sp</mml:mtext> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> <mml:mo>±</mml:mo> <mml:mrow> <mml:mo>(</mml:mo> <mml:mrow> <mml:mn>1</mml:mn> <mml:mrow> <mml:mo>/</mml:mo> </mml:mrow> <mml:mn>2</mml:mn> </mml:mrow> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mrow> <mml:mrow> <mml:msub> <mml:mi>C</mml:mi> <mml:mn>2</mml:mn> </mml:msub> </mml:mrow> <mml:mrow> <mml:msub> <mml:mi>f</mml:mi> <mml:mrow> <mml:mrow> <mml:mtext>wr</mml:mtext> </mml:mrow> </mml:mrow> </mml:msub> </mml:mrow> </mml:mrow> </mml:math> , which remains consistent across different train speeds on the embankment and could also be observed on bridge sections. Additionally, the influence of differential settlement in the transition zone on the collected ABA signals from experimental campaigns has also been considered. The novelty of this paper lies in the identification of multi-tone harmonic interactions in ABA signals, and the empirical validation of frequency coupling relationships across varying track conditions using the time–frequency analysis methods. These contributions give insights into practical applications for ABA signal analysis and potentially offer a guideline for future practical applications.