On the Use of Wigner Distribution in Ultrasonic NDE

Chen, C. H.; Guey, Jiann‐Ching

doi:10.1007/978-1-4615-3344-3_124

Cited by 6 publications

(4 citation statements)

References 2 publications

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“…1 were developed. The Wigner distribution is the most well known example [2] [3]. Though the Wigner distribution possesses the merits of high resolution in both time and frequency domains, the interference terms produced by the interaction of two signal components make it hard to interpret the result.…”

Section: A Brief Description Of Time Frequency Representationsmentioning

confidence: 98%

“…A set of ultrasonic signals as tabulated in Table 3 has been used to determine accurately the bond thickness using Wigner distribution [3]. In the present study the Gabor transform is used and the results are compared with the use of short time Fourier transform and cepstrum.…”

Section: Application To Nde Of Bonded Materialsmentioning

confidence: 99%

“…3 and 4, where T and F are the sampling interval in time and frequency, respectively. STFT(mT, nF) = f x(t)g*(t -mT'2tdt (3) x(t) = STFT(mT, nF)g(t -mT)e32t…”

Section: A Brief Description Of Time Frequency Representationsmentioning

confidence: 99%

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<title>Signal processing in ultrasonic NDE using time-frequency representations</title>

Cheng

Chen

1997

SPIE Proceedings

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Signal processing has been used in the ultrasonic nondestructive evaluation (NDE) of materials for a number of years. The time domain analysis of NDE signals includes signal enhancement, deconvolution, matched filtering, etc. and the results can often be linked to physical parameters. Frequency (Fourier) analysis of NDE singals provides information about the major frequency components which may be closely related to the geometry of hidden defects, material properties, etc.It is clear that the use of frequency domain or time domain information alone is not adequate for effective NDE. Recent advances in digital signal processing have resulted in new and effective approaches to joint time-frequency representations that provide more information from the data which may be useful for defect characterization and classffication. Among all time-frequency analysis methods, both Wigner distributions and wavelet transforms have been considered for use in ultrasonic NDE. However the full potential of time-frequency representation in ultrasonic NDE is yet to be explored. In this paper, a fundamental analysis of time frequency representations is briefly presented. Several application areas of the timefrequency representation in ultrasonic NDE including geometrical defect discrimination, NDE ofbonded materials, sizing problem with geometrical defects, and waveform decomposition are examined in detail. The fundamental time-frequency analysis is the short-time Fourier transform. A signal function x(t) issegmented into a number of sections by using a window function. The STFT is defined as (see e.g. [1]) STFT(t,f) = fx(t)g*(t _ t)e2dt(1) where g(t) is the window function. The asterisk '*' denotes the complex conjugate. The plane formed by the twodimensional function STFT(t,J) is called the complex spectrogram. The square value of the magnitude of STF7(t,j) is termed spectrogram. The inverse STFT can be obtained straightforwardly by taking the inverse Fourier transform. Taking the inverse Fourier transform of Eq. 1, we have : STFT('c, f)e32'df = xQ)g * (tLet t = t and move g(.) to the other side of equality sign.x(t) = J STFT(t f)e2'df (2) g (0) if the window function g(t) satisified the unity energy constraint, j'g(t)2dt = 1 , the inverse STFT can also be derived by taking the inverse Fourier transform of the windowed STFT(t,J). The derivation is omitted here.Equations 1 and 2 together are called STFT pairs. The sampled version STFT pairs are given in Eqs. 3 and 4, where T and F are the sampling interval in time and frequency, respectively. STFT(mT, nF) = f x(t)g*(t -mT'2tdt (3) x(t) = STFT(mT, nF)g(t -mT)e32t (4) SPIE Vol. 2921 • 0277-786X197/$lO.OO 319 Downloaded From: http://proceedings.spiedigitallibrary.org/ on 06/23/2016 Terms of Use: http://spiedigitallibrary.org/ss/TermsOfUse.aspx

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Section: A Brief Description Of Time Frequency Representationsmentioning

confidence: 98%

Section: Application To Nde Of Bonded Materialsmentioning

confidence: 99%

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<title>Signal processing in ultrasonic NDE using time-frequency representations</title>

Cheng

Chen

1997

SPIE Proceedings

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“…some of the commonly used statistical features are: mean, variance, skewness, kurtosis, peak positions and amplitudes with respect to the reference signal, higher order moments, and correlation coefficients. other features that have been developed by different researchers are time-frequency-based features, wavelet coefficients, and higher-order statistics-based model coefficients [17]- [21]. Whereas time-frequency and wavelet analysis tools are considered to be one of the best methods to handle non-linearities, the time and complexity can prevent these techniques to be used in near-real-time applications.…”

Section: B Ultrasonic Inspectionmentioning

confidence: 99%

Autonomous corrosion detection in gas pipelines: a hybrid-fuzzy classifier approach using ultrasonic nondestructive evaluation protocols

Qidwai

2009

IEEE Trans. Ultrason., Ferroelect., Freq. Contr.

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In this paper, a customized classifier is presented for the industry-practiced nondestructive evaluation (NDE) protocols using a hybrid-fuzzy inference system (FIS) to classify the corrosion and distinguish it from the geometric defects or normal/healthy state of the steel pipes used in the gas/petroleum industry. The presented system is hybrid in the sense that it utilizes both soft computing through fuzzy set theory, as well as conventional parametric modeling through H(infinity) optimization methods. Due to significant uncertainty in the power spectral density of the noise in ultrasonic NDE procedures, the use of optimal H(2) estimators for defect characterization is not so accurate. A more appropriate criterion is the H(infinity) norm of the estimation error spectrum which is based on minimization of the magnitude of this spectrum and hence produces more robust estimates. A hybrid feature set is developed in this work that corresponds to a) geometric features extracted directly from the raw ultrasonic A-scan data (which are the ultrasonic echo pulses in 1-Dtraveling inside the metal perpendicular to its 2 surfaces) and b) mapped features from the impulse response of the estimated model of the defect waveform under study. An experimental strategy is first outlined, through which the necessary data are collected as A-scans. Then, using the H(infinity) estimation approach, a parametric transfer function is obtained for each pulse. In this respect, each A-scan is treated as output from a defining function when a pure/healthy metal's A-scan is used as its input. Three defining states are considered in the paper; healthy, corroded, and defective, where the defective class represents metal with artificial or other defects. The necessary features are then calculated and are then supplied to the fuzzy inference system as input to be used in the classification. The resulting system has shown excellent corrosion classification with very low misclassification and false alarm rates.

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Ultrasonic non-destructive evaluation with spatial combination of Wigner?Ville Transforms

Rodríguez-Hernández¹

2003

NDT & E International

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On the Use of Wigner Distribution in Ultrasonic NDE

Cited by 6 publications

References 2 publications

<title>Signal processing in ultrasonic NDE using time-frequency representations</title>

<title>Signal processing in ultrasonic NDE using time-frequency representations</title>

Autonomous corrosion detection in gas pipelines: a hybrid-fuzzy classifier approach using ultrasonic nondestructive evaluation protocols

Ultrasonic non-destructive evaluation with spatial combination of Wigner?Ville Transforms

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