УДК 620.179.16
NOISE SUPPRESSION AND FLAW DETECTION OF ULTRASONIC SIGNALS USING EMPIRICAL MODE DECOMPOSITION
Yimei Mao, Peiwen Que
Institute of Automatic Detection, Shanghai Jiaotong University, Shanghai
200240, China
ПОДАВЛЕНИЕ ШУМОВ И ДЕТЕКТИРОВАНИЕ ДЕФЕКТОВ
В УЛЬТРАЗВУКОВЫХ СИГНАЛАХ С ИСПОЛЬЗОВАНИЕМ
СПОСОБА ДЕКОМПОЗИЦИИ НА ЭМПИРИЧЕСКИЕ МОДЫ
Имей Мао, Пейвен Ке Институт автоматического детектирования, Джиао Тонь университет, Шанхай 200240, Китай
Важной задачей неразрушающего контроля является надежное детектирование скрытых в шумах эхо-сигналов в сильно рассеивающих материалах. В этой статье предложен новый метод декомпозиции сигнала для исследования нестационарных и нелинейных у. з. сигналов. Разработана методика фильтрации, которая сочетает разложение на эмпирические моды и рассмотрение частотной области для подавления шумов и более четкого детектирования эхо-сигналов. Как модельные, так и экспериментальные сигналы были очищены от шумов с использованием этой техники фильтрации. Представлены и проанализированы результаты моделирования, показывающие, что предлагаемый метод имеет высокую эффективность даже для очень низкого отношения сигнал/шум (-23 дБ). Улучшение в поиске дефектов было экспериментально подтверждено на образце трубы с искусственными дефектами.
Abstract: In ultrasonic non-destructive testing, the precise detection of flaw echoes buried in backscattering noise caused by highly scattering materials is a problem of great importance. In this paper, a new signal decomposition method for analyzing non-stationary or nonlinear data called empirical mode decomposition, is proposed to deal with ultrasonic signals. A new de-noising technique that combines empirical mode decomposition and filtering simultaneously in time domain and frequency domain is designed to suppress noise and enhance flaw signals. Sythetic and experimental signals are de-noised using this EMD-based filtering technique. Simulated results are presented and analyzed, showing that the proposed technique has an excellent performance even when the signal-to-noise ratio is very low (-23 dB). The improvement in flaw detection was experimentally verified on a pipeline sample with artificial flaws.
Keywords: Ultrasonic Non-destructive Testing, Empirical Mode Decomposition, Noise suppression, Flaw detection
1. INTRODUCTION
Ultrasonic technique is one of widely used techniques for nondestructive testing of materials [1]. The signals reflected by defects possess useful information about defects size and orientation. However, in ultrasonic testing and evaluation of highly scattering materials such as austenitic and stainless steel, the noise from grain boundaries is one of the most important limitations in the detection of small cracks or flaws. In some cases, the backscattering noise may be greater than the searched flaw echo. Therefore, de-noising of ultrasonic signals is extremely important as to correctly identify small defects.
In order to reduce background noise, different signal processing techniques have already been widely utilized. Various linear and non-linear signal processing techniques including signal averaging, matched filtering, frequency spectrum analysis, neural networks, and autoregressive analysis have all been used to analyze ultrasonic signals. In all these techniques the signal is analyzed in the time domain or in the frequency domain [2]. However, in ultrasonic flaw detection the ultrasonic signals are non-stationary and noisy in nature due to back scattering caused by material microstructure. Thus, time-frequency representations of ultrasonic signals are useful for detecting and characterizing flaw echoes in highly scattering materials.
In this work, empirical mode decomposition (EMD), proposed by Huang et al. [3], is used to deal with de-noising of ultrasonic signals. EMD-based time-frequency signal processing provids a two-dimensional filtering of signals in both time and frequency domains. This time-frequency filtering technique preserves non-stationary characteristics of the ultrasonic signals simultaneously in the time and the frequency domains. The major advantage of the EMD is that the basis functions are derived from the sugnal itself, unlike another time-frequency analysis method, Wavelet analysis, where the basis functions are fixed. Hence, the analysis is adaptive and fully data-driven.
In the following discussion, EMD is briefly introduced and its application in ultrasonic signals is presented. The proposed technique is applied to both simulated and exprerimental ultrasonic signals for flaw detection. Simulated results are presented and analyzed, showing that the proposed time-frequency filtering technique has an excellent performance on signal-to-noise ratio (SNR) enhancement and is suitable for dealing with heavy noised ultrasonic signals.
2. BASICS OF EMD
The EMD, developed based on the simple assumption that any signal consists of many simple intrinsic modes of oscillation, can effectively decomposes a complicated signal into a set of inherent physical modes of motion. Each component of this set, which is narrow band and may be non-stationary, is termed an intrinsic mode function (IMF) of the original signal. An IMF is a function that satisfies the following two conditions: (a) the number of extrema and the number of zero crossings must be either equal or differ at most by one in the entire data set, and 0b) the mean value of the envelope defined by the local maxima and the envelope defined by local minima is zero at evergy point. Thus, an IMF represents simple oscillatory mode imbedded in the signal.
The procedure to decompose a signal into IMFs is as follows. First, is as follows. First, all the local extrema of the signal are edentified. Using a cubic spline, the local maxima and minima are interpolated to form the upper and lower envelopes. The mean of the upper and lower envelopes, designated as mv is extracted from the signal x(t) and the first component /?, is obtained as
=x(t)-mv (1)
The component h] is examined if it satisfies all the requirements to be an IMF. If not, the shifting process is to be repeated treating /?, as new data until /;, is an IMF designated as cr Next, the first IMF is separated from the rest data giving a residue ri as
rl=x(t)-cl. (2)
If the residue r, still constains information of longer period components, the procedure can then be applied to this residue, considered as a new signal and subjected to the same shifting process as described above. Successive constiturive components of a signal can therefore be iteratively extracted.
The shifting process can stop when the residue residue beomes constant or a monotonic function from which no furher IMF can be extracted. In this paper, a stopping criterion is accomplished by limiting the size of the standard deviation SD computed from the two consecutive sifting results. Usually, SD is set between 0.2 to 0.3.
At the end of the procedure we have a residue rn and a collection of n IMFs c. (i = 1,2, ..., «). Summing up all IMFs and the final residue r , the signal can be expressed as
n
x(t) = Xе/ + r«-i=i
(3)
Note that the EMD does not use any pre-determined filter of Wavelet function. It is a fully data-driven method.
The extracted IMFs satisfy the following properties: they are symmetric, have a unique local frequency and different IMFs do not exhibit the same frequency at the same time. Thus, another way to explain how the wmpirical mode decomposition works is that it picks out the highest frequency oscillation that remains in the signal. Thus, locally, each IMF contains lower frequency oscillations than the one extracted just before. The residue includes almost no frequency components at all. This property of the EMD can be very useful to pick up frequency changes, and thus extremely useful for detecting ultrasonic flaw echoes embedded in background noise.
Traditionally, filtering is carried out in frequency space only. But there is great difficulty in applying the frequency filtering to ultrasonic signals for ultrasonic data are non-stationary. Any filtering will eliminate some of the harmonics, which will cause deformation of the signal filtered. Using IMFs, however, we can devise a time-frequency filtering. For example, a low pass filtered results of a signal having »-IMF components can be simply expressed as
n
V)= Xc'+r«; (4)
i=k
a high pass results can be expressed as
k
**(')= Xci (5)
1=1
and a band pass result can be expressed as
k
(6)
i=b
where I < b < k < n. In such a case, EMD acts like a dyadic filter bank resembling those involved in wavelet decompositions [4]. The main advantage of this time-frequency filring is that the results preserve the full non-stationarity characteristics of the ultrasonic flaw sognals.
3. DE-NOISING ALGORITHM
EMD-based de-noising procedures for a signal corrupted by Gaussian white random noise can be summarized as follows:
1. EMD of the noisy ultrasonic signal;
2. selection of IMFs based on both instantaneous frequency band and threshold;
(a) selection of IMFs according to the instantaneous frequency band of each IMF;
(b) estimating the "noise only" model according to the SNR of the input ultrasonic signal;
(c) comparing the IMF energies with the "noise only" model used as threshold, selection of IMFs whose energy exceeds the threshold in time domain.
In practice, the enerhy of each IMF can be estimated as
E(i)=j^cf(n), (7)
n=\
where N is the total data points.
3. preprocessing each IMF selected in step 2 using thresholoding.
A smooth version of the input signal can be obtained by thresholding the IMFs before signal reconstruction. Different kinds of preprocessing can be used: hard and soft thresholding. In this work, we use soft type and level dependent thresholding.
,WJ° . KMN'A, (8)
1 l^hwHM'Oi-"',)' M»];>«<,'
where thi is the threshold corresponding to the i'h IMF c.. The selection of threshold value has several methods [5]. I
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