Coherent Flaw Reflectivity Estimation in Nonstationary Noise

Abstract

INTRODUCTIONThis paper presents a model for RF broadband ultrasonic A-scans obtained from materials composed of microstructures, in which isolated flaws or impurities may exist. The model incorporates both the RF phase and magnitude differences between the microstructure and coherent flaw echo spectra. An adaptive implementation of the maximumlikelihood estimator (MLE) is presented for estimating A-scan amplitudes associated with coherent scatterers embedded in grain echoes. The adaptive implelllentation is motivated by the nonstationary behavior of the back-scattered energy received over the duration of the A-scan [1]. This nonstationarity results from the frequency dependent absorption, scattering, and diffraction that occurs as the pulse propagates through the material [2,3].The experimental results indicate that the model's covariance matrix characterizes phase information related to the microstructures in the material. While no experiments have been performed to directly demonstrate this conjecture, the MLE performance is compared for cases when the phase elements of the covariance matrix are and are not included in the MLE computation. Significant performance increases are demonstrated for cases where the MLE uses the phase elements of the covariance matrix. Experimental A-scans, obtained from stainless-steel cylinders with flat-bottom holes, are used in the performance comparisons. COHERENT GRAIN-ECHO MODELThis section constructs a statistical model for the discrete Fourier transform (DFT) components corresponding to an A-scan segment received from a volume of scatterers. The A-scan segment length used in this model corresponds to the volume illuminated by the pulse at a single instant of time. This volume will be referred to as aresolution celloThe ultrasonic cross-section (UCS), or reflectivity of the scatterer characterizes the relationship between the scattering center and its back-scattered energy measured at the transducer. The UCS is defined as the ratio of ultrasonic energy received at the transducer, over the incident energy illuminating the scattering center. The UCS value for a given target is dependent on the size and acoustic impedance of the target relative to the surrounding scatterers.Consider an A-scan received from a broadband uItrasonic pulse. Let the strength and position of scatterers within a single resolution cell be modeled by a train of scaled and delayed Dirac Delta functions:(1)where Vk and Sk in the summation represent the UCS and delay associated with each of the Kn unresolvable scattering centers (corresponding to the microstructures), and 0. and 't represent the UCS and delay associated with a coherent target scatterer. In cells where no target scatterer exits, 0. is zero.Let an A-scan segment that corresponds to aresolution cell, be modeled by the an impulse response convolved with the scatterer model:where hs(t, 1..) is the impulse response of the pulse-echo system for the unresolvable scatterers located in the neighborhood corresponding to t. This impulse response depends...