Flaw signature estimation in ultrasonic nondestructive evaluation using the Wiener filter with limited prior information

Abstract

Flaw signals measured in ultrasonic testing include the effects of the measurements system and are corrupted by noise. The measurement system response is both bandlimited and frequency dependent within the bandwidth, resulting in measured signals which are blurred and distorted estimates of actual flaw signatures. The Wiener filter can be used to estimate the flaw's scattering amplitude by removing the effect of the measurement system in the presence of noise. A method is presented for implementing an optimal form of the Wiener filter that requires only estimates of the noise distribution parameters. The theoretical error for scattering amplitude estimation, assuming various levels of available prior information, is analyzed. Three estimation techniques, one a maximum-likelihood based method and the other two residual-sum-of-squares methods, are formulated and tested. The results demonstrate that any of the three approaches could be used to optimally implement the alternative form of the Wiener filter with limited prior information.

Creating Noise-Corrupted Flaw Signals for Ultrasonic Nondestructive Evaluation

“…The application of the Wiener filter with Q2( m) taken to be of sub-optimal form has also been studied [10] and should be addressed to complete this discussion. The most common sub-optimal form has been to take Q2 equal to 10% of the maximum value of IH(m)l. If the SNR is changed by scaling H(m), then the filter reflects this change through the change in the maximum value of IH(m)l. Conversely, if the SNR is changed by scaling the noise or by scaling or changing A(m), the filter does not change with SNR since Q2 is insensitive to these changes.…”

“…The most common sub-optimal form has been to take Q2 equal to 10% of the maximum value of IH(m)l. If the SNR is changed by scaling H(m), then the filter reflects this change through the change in the maximum value of IH(m)l. Conversely, if the SNR is changed by scaling the noise or by scaling or changing A(m), the filter does not change with SNR since Q2 is insensitive to these changes. Further, Neal et al [10] have studied the application of the filter when it is assumed that an estimate of Sn (m) is known, but it is not possible to establish Clearly, changing the SNR without understanding the implication of the change could lead to problems.…”

“…On the other hand, if deconvolution approaches are being studied, then each type of scaling affects a different input to the filter. Consider the case where the randop:1 variable scattering amplitude has zero mean, and a scattering amplitude estimate, A(w), is determined via the Wiener filter as [10] A(m,tP8,tPf) is changed by changing tP8 or tPf, then, in general, new scattering amplitudes must be calculated, and a new associated SA ( m) must also be calculated.…”

“…One method of changing the SNR, which has been successfully used by the authors for a number of years, involves scaling the acoustic noise prior to addition to the noise-free flaw signal [9,10]. Scaling the noise in this manner does not change its frequency.…”

“…In this paper, an approach is presented for creating "known flaw" noise-corrupted flaw signals which was frrst introduced by the authors in 1985 [8] and which has been used in a number of studies since that time [9][10][11]. Significant inspiration for this approach came from the work of Gray and Thompson in creating noise-free flaw signals [4,5].…”