|NDT.net - September 2002, Vol. 7 No.09|
In collaboration between the Institute of Statics and Dynamics of Aerospace Structures (ISD) and the Institute of Construction Materials (IWB) of the University of Stuttgart new efficient filter techniques are investigated to enhance the signal-to-noise ratio in acoustic emission (AE) analysis. After a brief overview of existing methods a new approach is introduced using wavelet algorithms. Applying this technique to acoustic emission raw data enhances the signal-to-noise ratio significantly. This is a useful tool especially for signal-based analysis, where picking the onset times of the signals is essential for localization. Other applications using wavelet algorithms besides denoising are possible.
Acoustic emission, digital filter, wavelet analysis, denoising
Two different approaches to record and analyze AE signals are typically distinguished: the classical and the quantitative or signal-based AE technique. Both approaches are applied nowadays with success for different applications. If AE events are recorded with one or more sensors such that a set of parameters is extracted from the signal and later stored, but the signal itself is not stored, the procedure is usually referred to as classical (or parameter-based) AE technique. Using the so-called quantitative AE technique, as many signals as possible are recorded and stored along with their waveforms converted from analogue-to-digital (A/D). A more comprehensive (time-consuming) analysis of the data is possible using this approach, but usually only in a post-processing environment and not in real-time. For applications using signal-based analysis techniques, equipment based on transient recorders is typically used. It is easy to apply user-written software tools to extract AE parameters for a statistical analysis of the data obtained with these instruments. This paper deals with certain techniques applied to signal-based AE methods.
The signals obtained during the recording of AE events and storing their waveforms are usually not recorded in a way to apply more sophisticated analysis tools. The so-called raw data have to be processed in a way to extract detailed information about the source in terms of fracture analysis. To do so, all influences not related to source information have to be eliminated. The data processing can include the following steps:
Signal conditioning in AE analysis can be described by terms of filter techniques. A more traditional way to apply such filter techniques is the use of analogue filters (Fig. 1). While the analogue technique using electronic circuits has a lot of disadvantages and is not very flexible, other digital techniques are nowadays preferred. Especially, if the signals have to be recorded or transformed into a digital form anyway, which is essential for signal-based AE techniques to be described in this paper. Besides of real-time applications, these solutions do not need certain hardware and offer numerous advantages. Some are described in the following:
Fig 1: Example of analogue frequency filters. A high-pass and a low-pass can be combined to work as a band-pass filter.
Since digital filter techniques are used for more than 50 years, numerous different methods are described in the literature [e. g. Oppenheim & Schafer 1975] to filter a signal in the frame of time series analysis. Digital filters are applied to the samples of a time series; the samples of the filtered signal are calculated by using convolution techniques applied to the source signal. The number of source signal samples is giving the order N of the filter.
Some of these filters most widely used in non-destructive testing are known as FIR (Finite Impulse Response) and IIR (Infinite Impulse Response) filters and according algorithms are described for example in Stearns et al.  including source codes. The impulse response of an IIR filter is "infinite" because there is feedback in the filter; if you put in an impulse (a single sample followed by many zero samples), an infinite number of non-zero values will come out. Instead, the impulse response of FIR filters is "finite" because there is no feedback in the filter.
IIR filters can achieve a given filtering characteristic using less memory and calculations than a similar FIR filter. FIR filters can easily be designed to be of "zero phase". Zero-phase filters delay the input signal, but dont distort its phase (see next section). Their implementation is simple and they have desirable numeric properties in terms of precision.
The first approach to reduce the noise content in a signal by filters is the application of a high- or a low-pass filter. A combination of both is called band-pass. Applying these techniques reduces low- and/or high-frequency portions in the signal originating from other sources like electric transmitters or machines and interfering with the interesting signal. Some parameters characterizing digital band-pass filters are described in Fig. 2.
|Fig 2: Example of a digital band-pass filter. The filter characteristic is described by several parameters in the frequency domain for a certain frequency range F.|
Noise in between the interesting frequency range of the signal (pass-band range) can be eliminated by using convolution methods. However, using this method - also addressed as moving averages filter - have some disadvantages, because the amplitude of the interesting part of the signal is also affected (i. e. reduced) by averaging effects. Additionally, frequency dependent phase shifting effects usually occur, what is somehow more important in AE analysis. The onset time determination is not reliable any more, what is demonstrated in Fig. 3. Artefacts are generated by the application of digital filters due to artificial "signals" (red part of the time series in the upper part of Fig. 3), which can be misinterpreted as AE signal parts. This can result in a completely wrong onset time.
|Fig 3: Artefacts generated by digital filtering of a seismic signal. UC: uncorrected time series; CO: corrected samples (right side same signal as left side but 30 times magnified). Example published by F. Scherbaum , Institute of Geoscience, University of Potsdam, Germany.|
Such artefacts can be eliminated using bi-directional filter techniques [Scherbaum 2001]. The filter is applied in forward direction of the time series and subsequently again backwards. However, a correction has to be applied using this forward-backward approach anyway to avoid artefacts generated by the symmetrical response of zero-phase FIR filters [Scherbaum 1997]. It should be stressed that the correction of artefacts using these techniques is time-consuming and ineffective concerning acoustic emission data recording.
Using Fourier transform techniques the spectral content of a signal can be determined accurately. Filter techniques depending on this transformation are manipulating the signal in frequency domain and transform the signal afterwards back into time domain by using an inverse Fourier transform. Unfortunately, the time information is somehow lost using inverse techniques, since the phase of the signal is usually not determined with the same precision [Hubbard 1998]. Dealing with acoustic emission signals the frequency content is time dependent what is usually difficult to be handled by these techniques.
One solution is the division of the time series into smaller units and the sequential application of Fourier transform techniques. This procedure is called Short Time Fourier Transform (STFT) or Windowed Fourier Transform [Gabor 1991]. Again, there are some disadvantages caused by the preset fixed time window necessary to apply the STFT. Broader window lengths are giving a better frequency resolution (especially for lower frequencies), while smaller windows enhances the time resolution. STFT has limited benefits, if a good frequency resolution is required together with a proper time resolution.
Wavelets are mathematical functions that cut up data into different frequency components, and then study each component with a resolution matched to its scale [Graps 1995]. Approximation using superposition of functions has existed since the early 1800's, when Joseph Fourier  discovered that he could superpose sines and cosines to represent other functions. The most interesting dissimilarity between these two kinds of transforms is that individual wavelet functions are localized in space. Fourier sine and cosine functions are not. One way to see the time-frequency resolution differences between the Fourier transform and the wavelet transform is to look at the basis function coverage of the time-frequency plane [Vetterli & Herley 1992]. Fig. 4 shows in the upper left part the resolution of a time series depending on the sampling interval. In frequency domain (upper right) the resolution is given by the number of points used for the discrete Fourier transform. In the lower part of Fig. 4 the resolution of a STFT is shown, where the window is simply a square. The square window truncates the wave function to fit a window of a particular width. Because a single window width is used for all frequencies in the STFT, the resolution of the analysis is the same at all locations in the time-frequency plane.
|Fig 4: Basis functions, time windows, and coverage of the time frequency plane.|
Wavelet algorithms process data at different scales or resolutions. If we look at a signal with a large window, we would notice gross features. Similarly, if we look at a signal with a small window, we would notice small features. The result in wavelet analysis is to see both (Fig. 4, lower right).
Wavelet transforms do not have a single set of basis functions like the Fourier transform, which utilizes just the sine and cosine functions. Instead, wavelet transforms have a very large (infinite) set of possible basis functions. Thus wavelet analysis provides immediate access to information that can be obscured by other time-frequency methods such as Fourier analysis.
Therefore, the wavelet transform is a subsequent advancement using an adaptive window length.
Wavelets are mathematical functions of short duration defining an orthogonal basis with the quality to be converted from the basic function by two simple parameters t and s:
The basic function is usually called mother wavelet and has to serve the following two conditions:
Functions meeting these requirements are showing symmetry of high order looking like small waves. Thats why the geophysicist Jean Morlet, who invented this technique in the early 1980s, called these groups of functions wavelets. Since there are many different mother wavelets nowadays used in science, some are well-known and have their own name because of their usefulness for different applications. The most important are shown in Fig. 5 along with their mathematical description.
|Fig 5: Several different families of mother wavelets with typical waveforms and mathematical representations.|
The data processing of many events during an AE test requires the automatic determination of arrival times. However, automatic "picking" is strongly dependent on the signal quality. Some picking techniques are based on frequency [Zang, Wagner, et al. 1997] and others are related to energy [Grosse & Reinhardt 1999; Grosse 2000].
The disadvantages of conventional filter techniques using analogue filters, band-pass digital filters or filters based on FFT or STFT algorithms were discussed in the previous sections. Wavelet techniques have been suggested [Ruzzante & Serrano 2000; Yoon, Weiss, et al. 2000, Zhao, Ma, et al. 2000, Grosse, Ruck et al. 2001] to enhance the signal-to-noise ratio, but most algorithms are not available to public or are not applicable to large data sets in acoustic emission analysis.
|Fig 6: Screenshot of the program WaveFilter.|
New software using wavelet algorithms in combination with a digital band-pass filter was written. This software was designed to work automatically with large data sets of up to several thousand acoustic emissions acting as a pre-processor followed by picking algorithms and an automatic onset time determination. A screenshot is shown in Fig. 6.
The raw data is transformed to the wavelet domain, where a threshold is automatically determined separating signal from noise. In this case a discrete wavelet transform is applied and after cutting off the noise the signal is transformed back to time domain using an inverse wavelet transform. Additionally, a band-pass filter can be applied and different mother wavelets can be tested. A detailed description of this procedure is given in Motz .
A typical signal with low signal-to-noise ratio obtained during an acoustic emission experiment is shown in Fig. 7. A Fourier transform proves that signal energy is partly in the noise band and so band-pass filtering alone is ineffective.
|Fig 7: Example of a typical acoustic emission signal. Broadband noise is interfering with the signal so that the onset time is difficult to determine automatically.|
Applying the described forward and inverse discrete wavelet transform algorithms the onset time of the signal is much easier to be detected as shown in Fig. 8. Even simple threshold algorithms commonly applied in AE technique for parameter-based systems can now be used to detect the arrival time of the signal. To use this filter technique in combination with more sophisticated picking algorithms is an issue of ongoing research.
|Fig 8: Original (upper) AE signal as shown in Fig. 7 and denoised (lower) AE signal using the wavelet algorithm WaveFilter. Both signals are shifted concerning the amplitude axis for better comparizion. Note that the left axis scale is valid for the upper and right axis for the lower signal.|
In comparison to conventional Fourier transform based filter techniques the advantages of wavelet based techniques were described. Transforming signals to the wavelet domain the time information included in the signals phase is conserved. This enables new ways of signal analysis and conditioning. One application is the design of sophisticated wavelet filters to enhance the signal-to-noise ratio in acoustic emission analysis.
Compared to the field of image compression and communication techniques wavelet algorithms for signal analysis applications in non-destructive testing are still rare. One promising application is the filtering of time series as described. Other examples in AE analysis are fracture mechanical interpretations or discrimination between noise and signals.
This work was financially supported by the Deutsche Forschungsgemeinschaft (DFG) via the collaborative research project "Sonderforschungsbereich" SFB381.
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