United States Department of Transportation
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Abstract:Mathematical representations of railroad track geometry variations are derived from time series analyses of track measurements. Since the majority of track is free of anomalies (turnouts, crossings, bridges, etc.), representation of anomaly-free track is first considered. Anomalies are then represented by using a combination of processes used to describe joints or welds in the anomaly-free track. In practice, anomaly-free track is constructed by joining many rails of the same length together so that periodic behavior is expected. Results indicate that the geometry of such track structures is completely represented by a periodically modulated random process whose first, second, and higher order statistics are a function of position along the rail relative to a joint or weld. This process is the synthesis of two simpler processes. The first is a stationary random process completely described by its power spectral density (PSD), which is modeled as a smooth function described by a roughness parameter and a set of corner frequencies (wavelengths). This process gives a complete representation of a homogeneous track structure free of joints or welds. The second process, which represents the joints or welds, involves a shape function, a decay rate away from the peak, and a correlation between joint amplitudes. The sequence of shape amplitudes is also a stationary random process having a non-zero mean. The mean amplitude and the decay rate of the shape function can be estimated from track geometry PSD's. Roughness parameters, corner frequencies, mean shape amplitudes and decay rates of the processes are related to track classes as defined by FRA Track Safety Standards, and to the measurements prescribed by those standards.
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