Passive extraction of dynamic transfer function from arbitrary ambient excitations: Application to high-speed rail inspection from wheel-generated waves

The general topic of this paper is the passive reconstruction of an acoustic transfer function from an unknown, generally nonstationary excitation. As recently shown in a study of building response to ground shaking, the paper demonstrates that, for a linear system subjected to an unknown excitation, the deconvolution operation between two receptions leads to the Green's function between the two reception points that is independent of the excitation. This is in contrast to the commonly used cross-correlation operation for passive reconstruction of the Green's function, where the result is always filtered by the source energy spectrum (unless it is opportunely normalized in a manner that makes it equivalent to a deconvolution). This concept is then applied to high-speed ultrasonic inspection of rails by passively reconstructing the rail's transfer function from the excitations naturally caused by the rolling wheels of a moving train. A first-generation prototype based on this idea was engineered using noncontact air-coupled sensors, mounted underneath a test railcar, and field tested at speeds up to 80 mph at the Transportation Technology Center (TTC), Pueblo, CO. This is the first demonstration of passive inspection of rails from train wheel excitations and, to the authors' knowledge, the first attempt ever made to ultrasonically inspect the rail at speeds above ∼30 mph (that is the maximum speed of common rail ultrasonic inspection vehicles). Once fully developed, this novel concept could enable regular trains to perform the inspections without any traffic disruption and with great redundancy.