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.
The focus of this paper is the estimation of the dynamic transfer function between two outputs of a linear system subjected to an uncontrolled and generally unknown excitation, and accounting for possible uncorrelated noise present at both outputs. Several applications of this case exist in the passive identification of dynamic systems including the health monitoring and/or non-destructive evaluation of structures subjected to natural "ambient" excitations. It is well known that noise-robust transfer function estimation of a single-input-single-output system can be achieved by a normalized cross-power spectrum operation. This paper shows that, for the subject case of a dual-output system, particular caution must be placed in the choice of the normalization factor to apply to the cross-power spectrum of the two outputs. In particular, an "inter-segment" averaging method is proposed for the normalization factor in combination with the classical "intra-segment" averaging of the cross-power spectrum in order to estimate the transfer function between the two outputs without the influence of the excitation spectrum and of the uncorrelated noise at the two receivers. Validating results are presented for synthetic signals and for experimental signals from an application to high-speed ultrasonic rail inspection exploiting the train wheels as the "ambient" excitation.
An interposed coupling material between an ultrasonic transducer and the test medium can be present in various non-destructive inspections and structural health monitoring imaging applications. One example is the wedge medium often used to direct ultrasonic beams into the test material for optimal interaction with internal defects. Another example is the ultrasonic imaging of multilayered structures. This article discusses the ways to perform synthetic aperture focus ultrasonic imaging in these cases where signal losses and complicated refractions at the coupling material/medium interface take place. Three main steps are proposed to maximize image quality. The first step is the delay-multiply-and-sum algorithm that increases the number of independent terms in the beamforming equation compared to the delay-and-sum algorithm. The second step is the utilization of a ray tracing algorithm to properly account for the refraction of the waves in both transmission and reflection paths, and accounting for both L-waves and S-waves that can potentially propagate. The compounding of multiple wave mode combinations is the third step proposed to significantly improve image quality. Validation experiments are presented for a transducer array on a wedge to image two closely spaced holes in an aluminum block. The delay-multiply-and-sum algorithm and wave mode compounding algorithm are also in principle applicable to other structural health monitoring imaging approaches that use, for example, sparse transducer arrays and guided-wave probing.
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