Improving the Ultrasonic Nondestructive Evaluation Signals by Iterative Wiener Filtering

abstract-Signals measured in ultrasonic nondestructive evaluation (NDE) of materials are masked by the characteristics of the measuring instruments, the propagation paths taken by the ultrasonic waves, and noise originating from various sources, including the electrical noise. Due to the band-limited characteristics of ultrasonic transducers, the received echoes are degraded by the transducer impulse response and show a relatively low time resolution. In order to remove the transducer impulse response in the presence of noise, deconvolution techniques are usually implemented. One of these deconvolution techniques is the Wiener filter. Implementation of an optimal Wiener filter requires estimation of the statistical distributions of both the desired signal and the noise present in this signal. In practical applications, this information is not readily available and needs to be somehow estimated. In this paper an iterative algorithm is proposed for estimating the power spectral density of the desired signal. This method uses the signal processed by the Wiener filter as an improved signal to update the power spectral density estimates. The results obtained from synthetic data indicate that the proposed method outperforms the conventional Wiener filter and could significantly improve the time resolution of the ultrasonic signals. The ultrasonic nondestructive technique aims to determine the physical properties of reflectors in terms of their location, size, shape, and orientation. However, the extraction of this information is sometimes difficult due to low signal to noise ratio (SNR) or overlapping of returned echoes. The mathematical model considered for an ultrasonic NDE signal is of the form [4]: ›ሺ–ሻൌšሺ–ሻȗŠሺ–ሻ൅ሺ–ሻ ሺͳሻ where * denotes the linear convolution operator, ›ሺ–ሻ is the measured signal, Šሺ–ሻ and šሺ–ሻ are respectively the impulse response functions of the measurement system and flaw, and ሺ–ሻ is the additive noise. Characteristics of the reflectors are included in the impulse response function of the flaw. The main assumptions in Eq. (1) are: 1) the ultrasonic pulse propagates through a linear medium, and 2) ሺ–ሻ and šሺ–ሻ are statistically independent. The first assumption allows us to isolate the impulse response of reflectors from the transducer and propagation medium as much as possible, while the second assumption is at the heart of a variety of well known identification methods. If the overall system is modeled as a cascade of many linear time invariant (LTI) systems, then Eq. (1) becomes: where are respectively the driving impulse to the transducer, forward transducer impulse response (IR), forward path IR, target (e.g. …