Abstract
In this article, we construct a new physically motivated model for the grain scattering noise (clutter). We assume the clutter is the output of a random linear time-invariant (LTI) filter, the impulse response of which is considered to be a realization of a Gaussian wide sense stationary (WSS) random process, when the transmitted ultrasonic pulse is at the input. In an ultrasonic non-destructive testing (NDT) session, the clutter noise, which is signal-dependent and caused by the microstructure of the material, presents a substantial challenge in identifying defects in the material under testing. The model is used to aid in the detection of a defect in the material. The model incorporates, explicitly, many important physical characteristics of the generated clutter, such as the average grain size, the random shape, and orientation of the grains, and emphasizes the single scatterer assumption (Rayleigh region). The statistical properties of the model are formulated and derived. A comparison with the usual matched filter to indicate the model advantage is performed. An application to real ultrasonic data is conducted with excellent results. Furthermore, we explored the effect of the choice of the model parameters, and the model shows robustness toward parameter misspecification. We then tested the performance under a deviation from the single scatterer assumption, for a more complex target, using simulated noise and obtained promising results.
Highlights
The problem of detecting a target in signal-dependent noise has been researched extensively throughout the years
The stainless steel samples were placed in water bath and scanned with A KB-Aerotech Alpha transducer (0.5-in diameter unfocused), where the surface of the flat-bottom hole was perpendicular to the axial transducer field
To compare between the Gaussian amplitude modulated sinusoid (GAMS) signal and the linear frequency modulated (LFM) signal we generated clutter noise using our model for both signals using the following parameters: a material with an average grain size of 150 μm which corresponds to M = 5, a speed of sound in the material equals 6000 meter/second similar to many stainless steel material, an ambient white noise with σw2 = 1 × 10−5, and the amplitude variance of σA2 = 0.05
Summary
To start we assume that the signal model is known, the observation window is aligned with the actual defect location (n0 is known), and the amplitude is known and positive (A0 > 0 and known) In this manner, the problem becomes a classical known deterministic signal in colored Gaussian noise. Even though the matrix R depends on the energy of the transmitted pulse s[n], as mentioned before, we will not pursue that in this work and, without loss of generality in computing (9), we can assume Es = 1
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