Date of Award


Degree Type


Degree Name

Doctor of Philosophy in Electrical Engineering


Electrical, Computer, and Biomedical Engineering

First Advisor

Steven Kay


The problem of detecting a defect inside the material in an ultrasonic non-destructive testing (NDT) session is addressed in this dissertation. What makes this problem a difficult one is the presence of clutter noise, which is signal-dependent noise. The clutter noise in the material is caused by the microstructure of the material under test. When an ultrasonic wave travels through a coarse-grained material, the traveled pulse hits the grain boundaries, which will cause some of its energy to propagate back to the transducer and mask the echo from the defect if it exists. We tackle the problem by first establishing the statistical framework (using the hypothesis testing approach). Then, we propose a new physically motivated model for the clutter noise. We construct the physically motivated clutter model as the output of a random linear time-invariant (LTI) filter, whose impulse response can be assumed to be a realization of a Gaussian wide sense stationary (WSS) random process. Next, we determine the model mean, autocorrelation sequence (ACS), and power spectral density (PSD). The model implementation leads to the generalized matched filter (GMF) statistic and showed an advantage of more than 10 dB over the conventional matched filter (MF). Moreover, the model worked well on real ultrasonic data and showed robustness towards parameter misspecification. Next, we pursue the problem of the optimal signal design to be used in combination with our model. A new proof is provided for a finite data record that is lacking in the literature. We found that the optimal signal is an impulse and as a result, the signal has an impulsive ACS. Since an impulsive ACS signal is not realizable in practice a study for an alternative signal is conducted. Signals from four different categories are explored: linear frequency modulated (LFM) signal, non-linear frequency modulated (NLFM) signals, phase coded modulated (PCM) signals, and finally what we called other signals. A comparative analysis in terms of the clutter to ambient noise ratio (CNR) versus the deflection coefficient is performed between these signals themselves and the most commonly used excitation signal in practice, which is the Gaussian amplitude modulated sinusoid (GAMS) signal. Next, we show that the LFM signal has a large advantage over the GAMS signal in terms of detectability. In addition, a comparison between the LFM signal and the GAMS signal under a deviation from the single scatterer assumption, indicating a more complex target, using simulated noise is performed.



To view the content in your browser, please download Adobe Reader or, alternately,
you may Download the file to your hard drive.

NOTE: The latest versions of Adobe Reader do not support viewing PDF files within Firefox on Mac OS and if you are using a modern (Intel) Mac, there is no official plugin for viewing PDF files within the browser window.