Key Takeaways & Executive Findings
- •• • Hamming window with 4096-point length yields optimal turnout irregularity PSD estimation; a fifth-order polynomial fits the PSD with minimal error, providing a standardized spectral basis for turnout-specific condition monitoring rather than relying on generic track spectra. • • TIFIEM sample size of 250 irregularity realizations minimizes RMSE against the target spectrum; PSD amplitudes at each frequency point follow a Chi-square distribution with 2 degrees of freedom, enabling probabilistic reliability assessment without exhaustive Monte Carlo sampling. • • At 300 km/h on a No. 18 turnout, the straight switch rail 3–7 m from the switch rail tip and the point rail 53–54 m from the tip are the most wear-prone zones, directing inspection resources to specific longitudinal positions where degradation accelerates. • • Vehicle–turnout structural reliability at the crossing panel drops to 95.8% at 300 km/h, quantifying the safety margin erosion under high-speed operation and justifying prioritized maintenance at the crossing panel.
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Abstract
Turnout irregularity governs the stochastic vibration response of vehicle–turnout coupling systems, yet frequency-domain models that preserve the statistical characteristics of each frequency point remain scarce. This study establishes a turnout irregularity full information expression model (TIFIEM) using stochastic harmonic functions (SHF) and applies it to vehicle–turnout stochastic vibration and reliability analysis. Spectral estimation trials identify the Hamming window with a 4096-point window length as optimal for turnout irregularity power spectral density (PSD) estimation, and a fifth-order polynomial is recommended for PSD fitting with minimal error. The TIFIEM reproduces randomness in amplitude, frequency, and phase; a sample size of 250 irregularity realizations minimizes the root-mean-square error against the target spectrum. PSD amplitudes at distinct frequency points follow a Chi-square distribution with 2 degrees of freedom. Application to a No. 18 turnout at 300 km/h identifies the straight switch rail 3–7 m from the switch rail tip and the point rail 53–54 m from the tip as the most wear-susceptible regions. The reliability of the vehicle–turnout structure at the crossing panel decreases to 95.8%, indicating that these zones warrant prioritized inspection.
1. Introduction
Track irregularity constitutes the primary excitation source in vehicle–turnout coupling dynamics, yet turnout-specific power spectral density (PSD) models remain underdeveloped compared with those for plain track. Existing spatial-domain sampling methods—triangular series and inverse Fourier transform—suffer from unclear parameter selection and incomplete representation of per-frequency statistical characteristics. Prior attempts to combine direct PSD sampling with triangular series or segmented inverse Fourier transforms still produce mean-value spectra that neglect the statistical dispersion at each frequency point, limiting their utility for stochastic vibration and reliability analysis of turnout structures.
This study addresses the bottleneck by constructing a turnout irregularity full information expression model (TIFIEM) grounded in stochastic harmonic functions. The model explicitly encodes randomness in amplitude, frequency, and phase, and its parameters are calibrated against an optimally estimated turnout irregularity spectrum. The calibrated TIFIEM is then embedded in a vehicle–turnout coupled dynamic analysis to evaluate stochastic vibration response and structural reliability at 300 km/h, thereby linking spectral characterization directly to wear-prone locations and crossing-panel reliability.
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Xueyang Tang, Xiaopei Cai, Jingmang Xu, Fei Yang (2026). A Full Information Expression Model for Track Irregularity Based on Stochastic Harmonic Functions in Vehicle–Turnout Structure Stochastic Vibration Analysis. Railway Engineering Science (铁道工程科学). https://doi.org/10.1007/s40534-025-00381-9
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Frequently Asked Questions
What spectral estimation parameters were found optimal for turnout irregularity, and why does this matter for field measurement campaigns?
The Hamming window with a window length of 4096 points was identified as optimal for estimating the turnout irregularity spectrum. This specification matters because turnout geometry varies sharply over short distances, and improper windowing inflates spectral leakage or smears localized defects; the 4096-point Hamming configuration provides a validated baseline for processing turnout inspection data.
How many irregularity samples are required for the TIFIEM to achieve acceptable accuracy, and what statistical distribution governs PSD amplitudes?
A sample size of 250 irregularity realizations minimizes the RMSE relative to the target spectrum. The PSD amplitude at each frequency point follows a Chi-square distribution with 2 degrees of freedom, which allows reliability analysis to be conducted with quantified probabilistic confidence rather than deterministic mean-value assumptions.
Which turnout locations are most susceptible to wear under 300 km/h operation, and what is the resulting structural reliability?
For a vehicle passing at 300 km/h through a No. 18 turnout, the straight switch rail 3–7 m from the switch rail tip and the point rail 53–54 m from the tip are the most wear-prone regions. The reliability of the vehicle–turnout structure at the crossing panel decreases to 95.8%, indicating a measurable safety margin reduction that warrants prioritized inspection at these longitudinal positions.
Why is a fifth-order polynomial recommended for fitting the turnout irregularity PSD instead of lower-order or non-parametric representations?
A fifth-order polynomial precisely models the PSD with minimal fitting error, balancing parametric simplicity against spectral fidelity. Lower-order polynomials cannot capture the multi-scale features of turnout irregularity, while non-parametric spectra lack the analytical tractability needed for stochastic harmonic function calibration and subsequent reliability computation.
What limitation of prior spatial-domain irregularity generation methods does the TIFIEM overcome?
Triangular series methods suffer from unclear parameter selection, and inverse Fourier transform methods inadequately represent per-frequency statistical characteristics. Earlier hybrid approaches still produced mean-value PSD models that ignored statistical dispersion at each frequency point. The TIFIEM, built on stochastic harmonic functions, explicitly captures randomness in amplitude, frequency, and phase, enabling full probabilistic representation for vehicle–turnout stochastic vibration analysis.
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