- Email: [email protected]
Ultrasonic inspection of composite hydrogen reservoirs using frequency diversity techniques
Ultrasonics 39 (2001) 203±209
www.elsevier.nl/locate/ultras
Ultrasonic inspection of composite hydrogen reservoirs using frequency diversity techniques D. Zellouf *, J. Goyette, D. Massicotte, T.K. Bose Institut de recherches sur l'Hydrog ene, Universit e du Qu ebec a Trois-Rivi eres, C.P. 500, Trois-Rivi eres, Qu ebec, Canada G9A5H7 Received 1 March 2000; received in revised form 1 September 2000
Abstract The use of the signal processing techniques based on the principle of quasi-frequency diversity can be a suitable solution for the ultrasonic inspection of liquid hydrogen tanks manufactured out of composite materials. Nevertheless, the algorithms developed up to now suer from limitations that restrict their large-scale use. The split-spectrum processing requires preliminary adjustments that are not always accessible to the user, while the cut-spectrum processing is not sensitive enough to eliminate the noise. We have thus developed an interesting alternative to these two ®lters. Based on the use of progressive low-pass ®lters, this algorithm, called lowspectrum processing, takes into account the physical characteristics of the ultrasonic wave propagation in a composite material. Its use in the inspection of tanks made in composites showed better performances. Ó 2001 Elsevier Science B.V. All rights reserved. PACS: 81.70; 81.05.Q/ Keywords: C-scan; Composite materials; Quasi-frequency diversity; Signal processing; Ultrasonic imaging; Ultrasonic testing
1. Introduction Composite materials are used more and more in the manufacture of liquid hydrogen reservoirs. These tanks are subjected during their service to both hydrostatic and hygrothermic stresses. This can have as consequence the initiation or the propagation of cracks within the structure of material. Therefore, there is a need to inspect these tanks when they are manufactured as well as during their service. The ultrasonic techniques are used quite extensively in the non-destructive evaluation of materials. Nevertheless, the analysis of ultrasonic signals collected during the inspection of composite materials must be dealt with carefully because of the presence of a strong background noise due to the reinforcement. The most widely used techniques for the elimination of this noise are all based on the principle of quasi-frequency diversity (QFD) [1,2]. Several algorithms based on this principle exist, the better known being the split-spectrum processing (SSP) [2,3]. Its expansion phase consists in generating a set of narrow band signals from
*
Corresponding author. Tel.: +1-819-376-5011-4458; fax: +1-819376-5164. E-mail address: [email protected] (D. Zellouf).
the multiplication of the measured signal spectrum by a collection of regularly distributed bandpass ®lters having the same bandwidth. Although this algorithm is fast, it requires an a priori knowledge of the target echo spectrum and an optimal adjustment of many parameters, e.g. the number of ®lters and the ®lter parameters [4]. Another algorithm developed more recently is the cut-spectrum processing (CSP), [5]. Based on the application of stop-band ®lters, instead of bandpass ®lters, this technique is more robust than the SSP, since the expansion can be performed successfully even though the spectral location of the target echo is not known. Nevertheless, the CSP is less powerful to decorrelate the noise. Another expansion algorithm, known as the fragment-split-processing (FSP), gathering the advantages of the last two techniques without their disadvantages, has been developed lately by Stepinski [6]. This algorithm produces signals from a set of irregular comb ®lters that have a frequency response consisting of alternating pass- and stop-band windows. Although more robust and more sensitive than the two preceding algorithms, the FSP is nevertheless more complex. These expansion algorithms can be coupled with some extraction algorithms, such as minimization [7], polarity thresholding [2,3] and median interval [5] to detect coherent information.
0041-624X/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 4 1 - 6 2 4 X ( 0 0 ) 0 0 0 6 5 - 2
204
D. Zellouf et al. / Ultrasonics 39 (2001) 203±209
Our work consists in developing an algorithm more robust and eective than the SSP and the CSP algorithms while being simple to use. This approach is based on the physical properties of the pulse propagation within composite materials. The result is an algorithm called the low-spectrum processing (LSP), since the expansion phase is performed by applying a low-pass ®lter bank to the measured signal. This algorithm is as robust as the CSP, but is more powerful to remove noise information. In this paper, we brie¯y review how the most used QFD techniques (SSP and CSP) work. In Section 3, we present the principle of the LSP algorithm and how it can improve the detectability of the target echo. In Section 4, we report on an ultrasonic inspection performed on liquid hydrogen reservoir and show image obtained after ®ltration of signals by the LSP. Also, the performances of the LSP with regard to imaging the inner structure of these reservoirs are compared with those of the two other QFD algorithms and some practical considerations are then discussed. Last, we present our conclusion in Section 5 to show how the LSP algorithm improves the imaging of the inner structure of glass/epoxy reservoirs designed mainly to store liquid hydrogen.
2. Quasi-frequency diversity techniques An ultrasonic echo re¯ected from a target within a composite material can be dicult to detect. This results mostly from the background noise caused by the interferences between the waves that are diracted on the reinforcement (®bres, spherical particles, etc.). Since the target echo and noise in which it is embedded have the same frequency bandwidth, we cannot use conventional linear ®lters, e.g. pass- and stop-band ®lters, to improve the signal-to-noise ratio. Indeed, let us suppose we have a pulse echo set-up; the noisy signal that is re¯ected from the material can be written as: e t rf t rt t b t
to produce a set of diverse-frequency signals that all contain both coherent and incoherent information and from which the noise can be decorrelated. 2.1. The split-spectrum processing 2.1.1. Expansion algorithm The principle of this algorithm consists in creating a collection of narrow bandwidth signals by multiplying the noisy signal spectrum by a ®lterbank of identical and regularly distributed gaussian windows (Fig. 1). The result of the multiplication by each ®lter is called a split spectrum. The set of split spectrums obtained this way is then normalized in amplitude. The inverse Fourier transform of each of those produces a split signal. Since the echo re¯ected by a target is the result of a physical interaction, it must present invariable properties relative to the frequency and should therefore be detected at the same time in each split signal contained within the bandwidth of this echo. At the opposite, the background noise results from interferences between the scattered waves, and its amplitude depends strongly on the frequency. By comparing the split signals at the same moment, one should be able to identify which information corresponds to the target echo. However, this depends on how the expansion is performed. Any decomposition of the measured signal spectrum outside the frequency limits of the target echo means that this echo will be lost from at least one split signal. Consequently, the coherence between split signals decreases at this instant and this echo will be identi®ed as noise. The gaussian windows must then be optimized in such a way that the target echo information is present in each of them. To ensure this, a solution is to have an a priori knowledge of the frequency bandwidth of the target echo, which is feasible if the echo spectrum is identical to the one of the emitted signal. Nevertheless,
1
where rf is the signal re¯ected by the material front surface, rt is target echo (coming from the back surface or/and a defect) and b the background noise. The Fourier transform of this noisy signal becomes: E x Rf x Rt x B x
2
The last equation shows that the spectral amplitude at a given frequency is the sum of the contributions of both echoes and noise. This means that noise information may exist in all frequency bands of the spectrum. Yet, the behaviour of noise vary with the frequency. Therefore, studying the behaviour of the measured signal at a given instant in dierent bands of the spectrum can reveal which information behaves dierently from a band to another. This is precisely how the QFD works; it aims
Fig. 1. The split-spectrum processing principle.
D. Zellouf et al. / Ultrasonics 39 (2001) 203±209
this is seldom true in the case of highly attenuative composite materials, where the attenuation becomes more important as the frequency increases. Moreover, optimizing the gaussian window parameters is as important
s ti
8 < :
Pm
e ti
if
0
otherwise
j1
aj ti > qm
where aj ti
as the knowledge of the frequency bandwidth [4]. Indeed, the shape of a gaussian window imposes a choice of a bandwidth allowing a sucient overlapping between the adjacent split spectrums. Hence, the optimal jth gaussian window must have a frequency bandwidth bx j 4=T and be centred at a frequency fj such as fj1 fj 1=T , T being the total signal time duration [4]. 2.1.2. Extraction Once the expansion phase has been completed, it is necessary to investigate the coherence between split signals; this statistical process is usually known as extraction. This operation consists in eliminating or minimizing any information that presents a variable behaviour according to the frequency at an instant ti . This operation can be performed by means of several algorithms. 2.1.2.1. Minimization algorithm. The main characteristic of this technique is to reduce the background noise instead of entirely removing it [8]. Coupled with this algorithm, the output of the SSP ®lter becomes: s ti minbabs e1 ti ; . . . ; abs ej ti ; . . . ; abs em ti c 3 where ej t is the value of amplitude of the jth split signal at instant ti , m being the number of split signals. This algorithm is not able to reconstruct the target echo when this echo is absent from only one split signal. 2.1.2.2. Polarity thresholding. At the opposite of the minimization algorithm, this one is built so that any non-coherent information can be removed entirely [2,3]. Nevertheless, it is less robust as soon as the coherent information is lost from at least one split signal. The result of ®ltering using this algorithm leads to: s ti
e ti 0
if sign ej ti cte 8 j 1; 2; . . . ; m else 4
2.1.2.3. Median interval. This algorithm can tolerate a lack of target echo information in a few split signals.
205
Indeed, an echo at instant ti is considered as coherent since its amplitude is contained within an interval centred at a median value (med) of the amplitudes of split signals at this moment. The output of this ®lter is:
1 0
if 1 kmed ti < e ti < 1 kmed ti otherwise
5
where m is the number of split signals. However, its major drawback lies in the number of parameters that needs to be adjusted (q and k). 2.2. Cut-spectrum processing A serious alternative, which permits to improve the robustness of SSP, is the expansion technique known as CSP [5]. This algorithm was designed to produce a set of signals that all contain the target echo. As in the case of the SSP technique, the CSP is designed according to a two-step process. 2.2.1. Expansion Although the frequency limits of the target echo are not known, one can be sure that they are located at frequencies lower than the Nyquist frequency. If one decomposes this frequency domain by applying SSP ®lters, one cannot know whether the target echo information is present in a given split signal or not; however, one can be sure that the sum of the other split signals will contain this echo. In the CSP process, the diverse frequency signal sj t is the result of the inverse Fourier transform of the sum of the split signals excluding the jth. In other words, while the SSP produces a set of signals by applying a bandpass ®lterbank, the CSP acts through a collection of band stop ®lters (Fig. 2). It is obvious that the amplitude of the coherent echo is but slightly aected by the removal of only one split spectrum. This provides a better robustness to this algorithm. But noise could also behave the same way, since it could happen that its amplitude at instant t does not vary enough to consider it as non-coherent. Moreover, the handling of a great number of spectra requires much more computation time than the SSP. The expansion procedure can be described as follows: ! m X sk t iff t Ej x with Ek x 0 6 1
2.2.2. Extraction The extraction technique proposed by Ericsson and Stepinski [5] takes into account the lesser sensitivity of the CSP algorithm to decorrelate the noise. This
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D. Zellouf et al. / Ultrasonics 39 (2001) 203±209
The attenuation evolves as the square of frequency a f x2 [9]. 2. The scattering of waves by the reinforcement, this mechanism being much more sensitive to the frequency than the absorption a f x4 [10].
Fig. 2. The cut-spectrum processing principle.
algorithm has only one adjustable parameter q, and a suitable value may be chosen by visual examination. The output of this ®lter becomes: e ti if emin ti > qemax ti 0 < q < 1 s ti 7 0 otherwise where emin (ti ) and emax (ti ) are respectively the minimum and the maximum of the split signals at instant ti and q is a tunable parameter. 3. The low-spectrum processing Compared to the SSP, the major disadvantage of the CSP algorithm lies in its lesser capacity to decorrelate the noise. This limitation arises from the smallness of the ratio of the surfaces under the removed split spectrum to the remained spectrum. This problem may be solved by increasing as much as possible the bandwidth of the removed frequency band while the target echo information remains contained within the kept band. This is particularly true if the spectral removal is performed in the upper part of spectrum, where spectral energy is mostly due to the noise. Taking into account these considerations, we built a robust expansion algorithm that allows to decorrelate noise information. 3.1. Expansion The expansion algorithm that we propose is simple, robust and takes into account the physical properties of the propagation of pulses within composite materials. Indeed, in a heterogeneous polymeric material, the acoustic attenuation results from two phenomena. 1. The absorption of part of the acoustic energy, related to the viscoelastic properties of the polymeric matrix.
As far as one can observe, the higher the frequency, the stronger the attenuation. In other words, the spectrum of the echo re¯ected from the bottom edge of material is shifted towards the lower parts of the measured signal spectrum. Indeed, Karpur et al. [11] showed the importance of knowing the optimal bandwidth of the bandpass ®lterbank over which the expansion is performed. They proved that the spectrum of the emitted signal is dierent from the one of the measured signal, because the attenuative materials ®lter out the higher frequencies. On the other hand, it is known that the spectrum of the noise evolves according to whether the interference is constructive or destructive. The probability of localizing coherent information within the re¯ected signal coming back from the bottom is much more important in the lower bands of spectrum. We can then reasonably suppose that the echo information from the back surface is still conserved even when we remove the higher parts of spectrum. Furthermore, removing an important part of the spectrum of the measured signal could increase the capacity to decorrelate noise information. Taking these considerations into account, the expansion algorithm we propose, called the LSP, consists in gradually eliminating the higher frequency regions of the measured signal spectrum, frequency after frequency according to: sj t iff t E x where E x E x if x < xj where x 6 dB j 1dx 0 xj 6 x < xnyq where xj < xmax 8 Hence, the ®rst step of the expansion operation consists in resetting the band between the frequency at which the spectral amplitude is at 6 dB and the Nyquist frequency xj xnyq . The width of the removed band increases as the expansion process evolves (Fig. 3). Therefore, the step j consists in removing the spectrum parts that are located at frequencies higher than xj x 6 dB j 1 dx. In the last operation, we eliminate all the frequencies beyond xmax (xmax being the frequency at which the spectral amplitude reaches its maximum). In this way, the LSP algorithm produces a set of diverse frequency signals that all should contain the target echo. Moreover, the large number of signals produced this way permit to have a higher sensitivity to decorrelate the noise than with the CSP algorithm. Its robustness and sensitivity are such that we could use this
D. Zellouf et al. / Ultrasonics 39 (2001) 203±209
Fig. 3. The low-spectrum processing principle.
algorithm with the polarity thresholding. Yet, we prefer also to design an extraction technique that can improve its robustness. 3.2. Extraction As a measure of security, we need a statistical process that can tolerate the lack of target echo in a few diverse frequency signals. We therefore need to de®ne a threshold value corresponding to the number of split signals that are coherent at the same moment and underneath of which the information can be considered as noise. Meanwhile, instead of comparing the frequency diversity signals between them, we compare each split signal with the measured signal e t. The output of this ®lter becomes: 8 m < e t if Pk t > q f fmax 1 i j i j s ti 1 : 0 otherwise 9 where 1 when sign e ti sign sj ti kj ti 0 otherwise
4. Experimental In this section, we study the performances of the LSP algorithm as a suitable ®ltration technique for the ultrasonic inspection composite reservoirs designed to store liquid hydrogen. The signals resulting from this inspection are often strongly noisy. Results obtained after ®ltration of these signals by the LSP are then compared with those obtained by using the other QFD techniques presented in this paper.
207
To do this, ultrasonic measurements are performed on parts of a cylindrical reservoir made of glass/epoxy composites. The reservoir shell is 3 mm thick. Reinforcement is glass ®bres at 68% volumic rate. Ultrasonic inspection is carried-out by scanning above a region that contains arti®cial defects. These defects were made on the back surface of the reservoir shell so that they do not emerge to the external surface. They consist of three equally shaped circular holes of 4-mm diameter. The ultrasonic investigation is done by means of a wide-band transducer that can deliver a short pulse of 5 MHz central frequency. This transducer is spherical shape and is focused at a distance of 50 mm from the centre of the emitting surface. This property allows us to focus the acoustic inside the reservoir shell. The transducer is moved by a six axis robot that permits us to have all the displacements needed to investigate the cylindrical reservoirs. The received signal re¯ected from the shell is sampled at a frequency of 100 MHz. This signal consists in the sum of signals originating from the front surface, the one re¯ected from the bottom, and eventually a defect echo, in addition to the background noise. After applying the diversity frequency ®lter to the measured signal, we ®rst identify the echo coming from the back surface; we can do that easily since we approximately know the time that the signal takes to return from the inner surface. The structural inspection of the reservoir shell has been performed according to a two-dimensional C-scan mode. The ®rst axis of displacement is along the axis of the cylinder. The second axis is provided by the rotation of reservoir around its axis. The combination of these two displacements allows a complete scan of the shell. The emitting surface of the transducer remains parallel to inspected surface and is separated from this one by a distance such as the ultrasonic beam is focused at the bottom of the shell. The results obtained by processing the measured ultrasonic signal by means of the QFD techniques presented previously are shown in Fig. 4. This ®gure exhibits the ®ltration capabilities of each ®lter studied in this paper. As far as we can see, it con®rms the fact that the median interval is the most suitable extraction algorithm as an output of the SSP. The back surface signal is well de®ned and fully restored. When one knows approximately the frequency bandwidth, the PT algorithm behaves as well. But these performances have been reached after several adjustments of the number of gaussian windows. In our case, the CSP removes entirely the noise, with a tunable parameter q ®xed to 0.88. This algorithm has been used without needing to know the frequency limits of the target echo. But in that case, the computation time was about ®ve times longer than the one required while using SSP coupled with a PT algorithm. The LSP algorithm is as powerful as the CSP to restore the target echo and to remove noise. Meanwhile,
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D. Zellouf et al. / Ultrasonics 39 (2001) 203±209
Fig. 4. The ®ltering capabilities of the QFD techniques. (a) The measured signal, (b) SSP minimization, (c) SSP polarity thresholding, (d) SSP median interval, (e) CSP, (f) LSP.
the LSP ®ltration of one signal requires about half the computation time of the CSP. The assumption that the target echo is contained at least in the lower part of the measured signal spectrum seems to be veri®ed in this case. This algorithm is so robust that the tunable parameter q has been ®xed to one, which means that all the QFD signals produced during the expansion contain the target echo information. The images were obtained from the result of ®ltering signals digitized over of a restricted zone containing
the arti®cial defects. We thus limit our visualization to a region of about 3 3 cm2 . The results are shown below (Fig. 5). Using the SSP, the defects are better imaged when we use the median interval instead of the minimization algorithm (Fig. 5a and b). Although it is slower, the CSP builds an image that presents a good contrast so that the defects are easy to identify (Fig. 5c). Lastly, the quality of the image obtained with the LSP is comparable with that provided by the CSP (Fig. 5d). Yet, the defect three only appears very slightly even in
Fig. 5. C-scan of the surface of the reservoir using the ®ltered signals. (a) SSP minimization, (b) SSP median interval, (c) CSP, (d) LSP.
D. Zellouf et al. / Ultrasonics 39 (2001) 203±209
the best case; this is due to the fact that it is located beneath a surface which is not perfectly plane, from where a signi®cant loss of energy.
5. Conclusion In this paper, we have presented an alternative to the CSP and SSP algorithms that could improve their effectiveness without decreasing their robustness. The solution we designed consists in applying a set of lowpass ®lters that have dierent frequency responses, being sure that the target echo is always contained in the kept part of the spectrum. Furthermore, this algorithm is easily tuned since it requires only one parameter, which, in addition, is close to the unity. Finally, this algorithm allows a decrease of the computation time. Setting the single parameter to 1, this technique has shown a good ability to remove the background noise and image the defects in composite materials. The SSP algorithm is the better known of the pseudofrequency diversity techniques. Its use in the non-destructive inspection of composite materials is however restricted by the requirement that the frequency bandwidth of the target echo has to be known beforehand. The lack of this information could lead to a failure of the SSP to detect defects. The CSP technique brings some improvements since the coherent echo information is always contained within the frequency range of the diverse frequency signals. Nevertheless, this algorithm is far from being satisfying due to the important amount of computations it requires. Moreover, it often happens that there is not enough sensitivity to decorrelate the noise; this is due to the small frequency range that is removed from the summation during the expansion. This work has shown that the QFD techniques are well adapted to control the quality and integrity of complex composite structures on the condition of providing some improvements that make these algorithms robust, fast and easy to use.
209
Acknowledgements The authors thank Dr. Mohammed Chibani, 2CI Technology, for his help and support to this work. The ®nancial help of Ministere de l'industrie et du Commerce of the Quebec government given to us from the Fonds des Priorites Gouvernementales en Sciences et Technologies is gratefully acknowledged.
References [1] V.L. Newhouse, N.M. Bilgutay, J. Saniie, E.S. Furgason, Flawto-grain echo enhancement by split-spectrum processing, Ultrasonics 20 (2) (1982) 59±68. [2] P.M. Shankar, P. Karpur, V.L. Newhouse, J.L. Rose, Splitspectrum processing: analysis of polarity thresholding algorithm for improvement of signal-to-noise ratio and detectabil ity in ultrasonic signals, IEEE Trans. UFFC 36 (1) (1989) 101± 108. [3] N.M. Bilgutay, U. Bencharit, R. Murthy, J. Saniie, Analysis of a non-linear frequency diverse clutter suppression algorithm, Ultrasonics 28 (2) (1990) 90±96. [4] J.D. Aussel, Split-spectrum processing with ®nite impulse response ®lters of constant frequency-to-bandwidth ratio, Ultrasonics 28 (4) (1990) 229±239. [5] L. Ericsson, T. Stepinski, Cut spectrum processing: a novel signal processing algorithm for ultrasonic ¯aw detection, NDT & E Int. 25 (2) (1992) 59±64. [6] X. Maldague, Advances in Signal Processing for Nondestructive Evaluation of Materials, Kluwer Academic, Dordrecht, 1994. [7] P. Karpur, P.M. Shankar, J.L. Rose, V.L. Newhouse, Splitspectrum processing: optimizing the processing parameters using minimization, Ultrasonics 25 (4) (1987) 204±208. [8] J.L. Rose, P. Karpur, V.L. Newhouse, Utility of split-spectrum processing in ultrasonic nondestructive evaluation, Materials evaluation 46 (1) (1988) 114±122. [9] P. Papadakis, Ultrasonic attenuation caused by scattering in polycristalline media, Physical Acoustic Mason Thriston 4 (1967) 269. [10] M. O'Donnell, E.T. Jaynes, J.G. Miller, J. Acoust. Soc. Am. 69 (1981) 696±705. [11] P. Karpur, P.M. Shankar, J.L. Rose, V.L. Newhouse, Determination of the available bandwidth for spectral splitting, Ultrasonics 26 (4) (1988) 204±209.
www.elsevier.nl/locate/ultras
Ultrasonic inspection of composite hydrogen reservoirs using frequency diversity techniques D. Zellouf *, J. Goyette, D. Massicotte, T.K. Bose Institut de recherches sur l'Hydrog ene, Universit e du Qu ebec a Trois-Rivi eres, C.P. 500, Trois-Rivi eres, Qu ebec, Canada G9A5H7 Received 1 March 2000; received in revised form 1 September 2000
Abstract The use of the signal processing techniques based on the principle of quasi-frequency diversity can be a suitable solution for the ultrasonic inspection of liquid hydrogen tanks manufactured out of composite materials. Nevertheless, the algorithms developed up to now suer from limitations that restrict their large-scale use. The split-spectrum processing requires preliminary adjustments that are not always accessible to the user, while the cut-spectrum processing is not sensitive enough to eliminate the noise. We have thus developed an interesting alternative to these two ®lters. Based on the use of progressive low-pass ®lters, this algorithm, called lowspectrum processing, takes into account the physical characteristics of the ultrasonic wave propagation in a composite material. Its use in the inspection of tanks made in composites showed better performances. Ó 2001 Elsevier Science B.V. All rights reserved. PACS: 81.70; 81.05.Q/ Keywords: C-scan; Composite materials; Quasi-frequency diversity; Signal processing; Ultrasonic imaging; Ultrasonic testing
1. Introduction Composite materials are used more and more in the manufacture of liquid hydrogen reservoirs. These tanks are subjected during their service to both hydrostatic and hygrothermic stresses. This can have as consequence the initiation or the propagation of cracks within the structure of material. Therefore, there is a need to inspect these tanks when they are manufactured as well as during their service. The ultrasonic techniques are used quite extensively in the non-destructive evaluation of materials. Nevertheless, the analysis of ultrasonic signals collected during the inspection of composite materials must be dealt with carefully because of the presence of a strong background noise due to the reinforcement. The most widely used techniques for the elimination of this noise are all based on the principle of quasi-frequency diversity (QFD) [1,2]. Several algorithms based on this principle exist, the better known being the split-spectrum processing (SSP) [2,3]. Its expansion phase consists in generating a set of narrow band signals from
*
Corresponding author. Tel.: +1-819-376-5011-4458; fax: +1-819376-5164. E-mail address: [email protected] (D. Zellouf).
the multiplication of the measured signal spectrum by a collection of regularly distributed bandpass ®lters having the same bandwidth. Although this algorithm is fast, it requires an a priori knowledge of the target echo spectrum and an optimal adjustment of many parameters, e.g. the number of ®lters and the ®lter parameters [4]. Another algorithm developed more recently is the cut-spectrum processing (CSP), [5]. Based on the application of stop-band ®lters, instead of bandpass ®lters, this technique is more robust than the SSP, since the expansion can be performed successfully even though the spectral location of the target echo is not known. Nevertheless, the CSP is less powerful to decorrelate the noise. Another expansion algorithm, known as the fragment-split-processing (FSP), gathering the advantages of the last two techniques without their disadvantages, has been developed lately by Stepinski [6]. This algorithm produces signals from a set of irregular comb ®lters that have a frequency response consisting of alternating pass- and stop-band windows. Although more robust and more sensitive than the two preceding algorithms, the FSP is nevertheless more complex. These expansion algorithms can be coupled with some extraction algorithms, such as minimization [7], polarity thresholding [2,3] and median interval [5] to detect coherent information.
0041-624X/01/$ - see front matter Ó 2001 Elsevier Science B.V. All rights reserved. PII: S 0 0 4 1 - 6 2 4 X ( 0 0 ) 0 0 0 6 5 - 2
204
D. Zellouf et al. / Ultrasonics 39 (2001) 203±209
Our work consists in developing an algorithm more robust and eective than the SSP and the CSP algorithms while being simple to use. This approach is based on the physical properties of the pulse propagation within composite materials. The result is an algorithm called the low-spectrum processing (LSP), since the expansion phase is performed by applying a low-pass ®lter bank to the measured signal. This algorithm is as robust as the CSP, but is more powerful to remove noise information. In this paper, we brie¯y review how the most used QFD techniques (SSP and CSP) work. In Section 3, we present the principle of the LSP algorithm and how it can improve the detectability of the target echo. In Section 4, we report on an ultrasonic inspection performed on liquid hydrogen reservoir and show image obtained after ®ltration of signals by the LSP. Also, the performances of the LSP with regard to imaging the inner structure of these reservoirs are compared with those of the two other QFD algorithms and some practical considerations are then discussed. Last, we present our conclusion in Section 5 to show how the LSP algorithm improves the imaging of the inner structure of glass/epoxy reservoirs designed mainly to store liquid hydrogen.
2. Quasi-frequency diversity techniques An ultrasonic echo re¯ected from a target within a composite material can be dicult to detect. This results mostly from the background noise caused by the interferences between the waves that are diracted on the reinforcement (®bres, spherical particles, etc.). Since the target echo and noise in which it is embedded have the same frequency bandwidth, we cannot use conventional linear ®lters, e.g. pass- and stop-band ®lters, to improve the signal-to-noise ratio. Indeed, let us suppose we have a pulse echo set-up; the noisy signal that is re¯ected from the material can be written as: e t rf t rt t b t
to produce a set of diverse-frequency signals that all contain both coherent and incoherent information and from which the noise can be decorrelated. 2.1. The split-spectrum processing 2.1.1. Expansion algorithm The principle of this algorithm consists in creating a collection of narrow bandwidth signals by multiplying the noisy signal spectrum by a ®lterbank of identical and regularly distributed gaussian windows (Fig. 1). The result of the multiplication by each ®lter is called a split spectrum. The set of split spectrums obtained this way is then normalized in amplitude. The inverse Fourier transform of each of those produces a split signal. Since the echo re¯ected by a target is the result of a physical interaction, it must present invariable properties relative to the frequency and should therefore be detected at the same time in each split signal contained within the bandwidth of this echo. At the opposite, the background noise results from interferences between the scattered waves, and its amplitude depends strongly on the frequency. By comparing the split signals at the same moment, one should be able to identify which information corresponds to the target echo. However, this depends on how the expansion is performed. Any decomposition of the measured signal spectrum outside the frequency limits of the target echo means that this echo will be lost from at least one split signal. Consequently, the coherence between split signals decreases at this instant and this echo will be identi®ed as noise. The gaussian windows must then be optimized in such a way that the target echo information is present in each of them. To ensure this, a solution is to have an a priori knowledge of the frequency bandwidth of the target echo, which is feasible if the echo spectrum is identical to the one of the emitted signal. Nevertheless,
1
where rf is the signal re¯ected by the material front surface, rt is target echo (coming from the back surface or/and a defect) and b the background noise. The Fourier transform of this noisy signal becomes: E x Rf x Rt x B x
2
The last equation shows that the spectral amplitude at a given frequency is the sum of the contributions of both echoes and noise. This means that noise information may exist in all frequency bands of the spectrum. Yet, the behaviour of noise vary with the frequency. Therefore, studying the behaviour of the measured signal at a given instant in dierent bands of the spectrum can reveal which information behaves dierently from a band to another. This is precisely how the QFD works; it aims
Fig. 1. The split-spectrum processing principle.
D. Zellouf et al. / Ultrasonics 39 (2001) 203±209
this is seldom true in the case of highly attenuative composite materials, where the attenuation becomes more important as the frequency increases. Moreover, optimizing the gaussian window parameters is as important
s ti
8 < :
Pm
e ti
if
0
otherwise
j1
aj ti > qm
where aj ti
as the knowledge of the frequency bandwidth [4]. Indeed, the shape of a gaussian window imposes a choice of a bandwidth allowing a sucient overlapping between the adjacent split spectrums. Hence, the optimal jth gaussian window must have a frequency bandwidth bx j 4=T and be centred at a frequency fj such as fj1 fj 1=T , T being the total signal time duration [4]. 2.1.2. Extraction Once the expansion phase has been completed, it is necessary to investigate the coherence between split signals; this statistical process is usually known as extraction. This operation consists in eliminating or minimizing any information that presents a variable behaviour according to the frequency at an instant ti . This operation can be performed by means of several algorithms. 2.1.2.1. Minimization algorithm. The main characteristic of this technique is to reduce the background noise instead of entirely removing it [8]. Coupled with this algorithm, the output of the SSP ®lter becomes: s ti minbabs e1 ti ; . . . ; abs ej ti ; . . . ; abs em ti c 3 where ej t is the value of amplitude of the jth split signal at instant ti , m being the number of split signals. This algorithm is not able to reconstruct the target echo when this echo is absent from only one split signal. 2.1.2.2. Polarity thresholding. At the opposite of the minimization algorithm, this one is built so that any non-coherent information can be removed entirely [2,3]. Nevertheless, it is less robust as soon as the coherent information is lost from at least one split signal. The result of ®ltering using this algorithm leads to: s ti
e ti 0
if sign ej ti cte 8 j 1; 2; . . . ; m else 4
2.1.2.3. Median interval. This algorithm can tolerate a lack of target echo information in a few split signals.
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Indeed, an echo at instant ti is considered as coherent since its amplitude is contained within an interval centred at a median value (med) of the amplitudes of split signals at this moment. The output of this ®lter is:
1 0
if 1 kmed ti < e ti < 1 kmed ti otherwise
5
where m is the number of split signals. However, its major drawback lies in the number of parameters that needs to be adjusted (q and k). 2.2. Cut-spectrum processing A serious alternative, which permits to improve the robustness of SSP, is the expansion technique known as CSP [5]. This algorithm was designed to produce a set of signals that all contain the target echo. As in the case of the SSP technique, the CSP is designed according to a two-step process. 2.2.1. Expansion Although the frequency limits of the target echo are not known, one can be sure that they are located at frequencies lower than the Nyquist frequency. If one decomposes this frequency domain by applying SSP ®lters, one cannot know whether the target echo information is present in a given split signal or not; however, one can be sure that the sum of the other split signals will contain this echo. In the CSP process, the diverse frequency signal sj t is the result of the inverse Fourier transform of the sum of the split signals excluding the jth. In other words, while the SSP produces a set of signals by applying a bandpass ®lterbank, the CSP acts through a collection of band stop ®lters (Fig. 2). It is obvious that the amplitude of the coherent echo is but slightly aected by the removal of only one split spectrum. This provides a better robustness to this algorithm. But noise could also behave the same way, since it could happen that its amplitude at instant t does not vary enough to consider it as non-coherent. Moreover, the handling of a great number of spectra requires much more computation time than the SSP. The expansion procedure can be described as follows: ! m X sk t iff t Ej x with Ek x 0 6 1
2.2.2. Extraction The extraction technique proposed by Ericsson and Stepinski [5] takes into account the lesser sensitivity of the CSP algorithm to decorrelate the noise. This
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The attenuation evolves as the square of frequency a f x2 [9]. 2. The scattering of waves by the reinforcement, this mechanism being much more sensitive to the frequency than the absorption a f x4 [10].
Fig. 2. The cut-spectrum processing principle.
algorithm has only one adjustable parameter q, and a suitable value may be chosen by visual examination. The output of this ®lter becomes: e ti if emin ti > qemax ti 0 < q < 1 s ti 7 0 otherwise where emin (ti ) and emax (ti ) are respectively the minimum and the maximum of the split signals at instant ti and q is a tunable parameter. 3. The low-spectrum processing Compared to the SSP, the major disadvantage of the CSP algorithm lies in its lesser capacity to decorrelate the noise. This limitation arises from the smallness of the ratio of the surfaces under the removed split spectrum to the remained spectrum. This problem may be solved by increasing as much as possible the bandwidth of the removed frequency band while the target echo information remains contained within the kept band. This is particularly true if the spectral removal is performed in the upper part of spectrum, where spectral energy is mostly due to the noise. Taking into account these considerations, we built a robust expansion algorithm that allows to decorrelate noise information. 3.1. Expansion The expansion algorithm that we propose is simple, robust and takes into account the physical properties of the propagation of pulses within composite materials. Indeed, in a heterogeneous polymeric material, the acoustic attenuation results from two phenomena. 1. The absorption of part of the acoustic energy, related to the viscoelastic properties of the polymeric matrix.
As far as one can observe, the higher the frequency, the stronger the attenuation. In other words, the spectrum of the echo re¯ected from the bottom edge of material is shifted towards the lower parts of the measured signal spectrum. Indeed, Karpur et al. [11] showed the importance of knowing the optimal bandwidth of the bandpass ®lterbank over which the expansion is performed. They proved that the spectrum of the emitted signal is dierent from the one of the measured signal, because the attenuative materials ®lter out the higher frequencies. On the other hand, it is known that the spectrum of the noise evolves according to whether the interference is constructive or destructive. The probability of localizing coherent information within the re¯ected signal coming back from the bottom is much more important in the lower bands of spectrum. We can then reasonably suppose that the echo information from the back surface is still conserved even when we remove the higher parts of spectrum. Furthermore, removing an important part of the spectrum of the measured signal could increase the capacity to decorrelate noise information. Taking these considerations into account, the expansion algorithm we propose, called the LSP, consists in gradually eliminating the higher frequency regions of the measured signal spectrum, frequency after frequency according to: sj t iff t E x where E x E x if x < xj where x 6 dB j 1dx 0 xj 6 x < xnyq where xj < xmax 8 Hence, the ®rst step of the expansion operation consists in resetting the band between the frequency at which the spectral amplitude is at 6 dB and the Nyquist frequency xj xnyq . The width of the removed band increases as the expansion process evolves (Fig. 3). Therefore, the step j consists in removing the spectrum parts that are located at frequencies higher than xj x 6 dB j 1 dx. In the last operation, we eliminate all the frequencies beyond xmax (xmax being the frequency at which the spectral amplitude reaches its maximum). In this way, the LSP algorithm produces a set of diverse frequency signals that all should contain the target echo. Moreover, the large number of signals produced this way permit to have a higher sensitivity to decorrelate the noise than with the CSP algorithm. Its robustness and sensitivity are such that we could use this
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Fig. 3. The low-spectrum processing principle.
algorithm with the polarity thresholding. Yet, we prefer also to design an extraction technique that can improve its robustness. 3.2. Extraction As a measure of security, we need a statistical process that can tolerate the lack of target echo in a few diverse frequency signals. We therefore need to de®ne a threshold value corresponding to the number of split signals that are coherent at the same moment and underneath of which the information can be considered as noise. Meanwhile, instead of comparing the frequency diversity signals between them, we compare each split signal with the measured signal e t. The output of this ®lter becomes: 8 m < e t if Pk t > q f fmax 1 i j i j s ti 1 : 0 otherwise 9 where 1 when sign e ti sign sj ti kj ti 0 otherwise
4. Experimental In this section, we study the performances of the LSP algorithm as a suitable ®ltration technique for the ultrasonic inspection composite reservoirs designed to store liquid hydrogen. The signals resulting from this inspection are often strongly noisy. Results obtained after ®ltration of these signals by the LSP are then compared with those obtained by using the other QFD techniques presented in this paper.
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To do this, ultrasonic measurements are performed on parts of a cylindrical reservoir made of glass/epoxy composites. The reservoir shell is 3 mm thick. Reinforcement is glass ®bres at 68% volumic rate. Ultrasonic inspection is carried-out by scanning above a region that contains arti®cial defects. These defects were made on the back surface of the reservoir shell so that they do not emerge to the external surface. They consist of three equally shaped circular holes of 4-mm diameter. The ultrasonic investigation is done by means of a wide-band transducer that can deliver a short pulse of 5 MHz central frequency. This transducer is spherical shape and is focused at a distance of 50 mm from the centre of the emitting surface. This property allows us to focus the acoustic inside the reservoir shell. The transducer is moved by a six axis robot that permits us to have all the displacements needed to investigate the cylindrical reservoirs. The received signal re¯ected from the shell is sampled at a frequency of 100 MHz. This signal consists in the sum of signals originating from the front surface, the one re¯ected from the bottom, and eventually a defect echo, in addition to the background noise. After applying the diversity frequency ®lter to the measured signal, we ®rst identify the echo coming from the back surface; we can do that easily since we approximately know the time that the signal takes to return from the inner surface. The structural inspection of the reservoir shell has been performed according to a two-dimensional C-scan mode. The ®rst axis of displacement is along the axis of the cylinder. The second axis is provided by the rotation of reservoir around its axis. The combination of these two displacements allows a complete scan of the shell. The emitting surface of the transducer remains parallel to inspected surface and is separated from this one by a distance such as the ultrasonic beam is focused at the bottom of the shell. The results obtained by processing the measured ultrasonic signal by means of the QFD techniques presented previously are shown in Fig. 4. This ®gure exhibits the ®ltration capabilities of each ®lter studied in this paper. As far as we can see, it con®rms the fact that the median interval is the most suitable extraction algorithm as an output of the SSP. The back surface signal is well de®ned and fully restored. When one knows approximately the frequency bandwidth, the PT algorithm behaves as well. But these performances have been reached after several adjustments of the number of gaussian windows. In our case, the CSP removes entirely the noise, with a tunable parameter q ®xed to 0.88. This algorithm has been used without needing to know the frequency limits of the target echo. But in that case, the computation time was about ®ve times longer than the one required while using SSP coupled with a PT algorithm. The LSP algorithm is as powerful as the CSP to restore the target echo and to remove noise. Meanwhile,
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Fig. 4. The ®ltering capabilities of the QFD techniques. (a) The measured signal, (b) SSP minimization, (c) SSP polarity thresholding, (d) SSP median interval, (e) CSP, (f) LSP.
the LSP ®ltration of one signal requires about half the computation time of the CSP. The assumption that the target echo is contained at least in the lower part of the measured signal spectrum seems to be veri®ed in this case. This algorithm is so robust that the tunable parameter q has been ®xed to one, which means that all the QFD signals produced during the expansion contain the target echo information. The images were obtained from the result of ®ltering signals digitized over of a restricted zone containing
the arti®cial defects. We thus limit our visualization to a region of about 3 3 cm2 . The results are shown below (Fig. 5). Using the SSP, the defects are better imaged when we use the median interval instead of the minimization algorithm (Fig. 5a and b). Although it is slower, the CSP builds an image that presents a good contrast so that the defects are easy to identify (Fig. 5c). Lastly, the quality of the image obtained with the LSP is comparable with that provided by the CSP (Fig. 5d). Yet, the defect three only appears very slightly even in
Fig. 5. C-scan of the surface of the reservoir using the ®ltered signals. (a) SSP minimization, (b) SSP median interval, (c) CSP, (d) LSP.
D. Zellouf et al. / Ultrasonics 39 (2001) 203±209
the best case; this is due to the fact that it is located beneath a surface which is not perfectly plane, from where a signi®cant loss of energy.
5. Conclusion In this paper, we have presented an alternative to the CSP and SSP algorithms that could improve their effectiveness without decreasing their robustness. The solution we designed consists in applying a set of lowpass ®lters that have dierent frequency responses, being sure that the target echo is always contained in the kept part of the spectrum. Furthermore, this algorithm is easily tuned since it requires only one parameter, which, in addition, is close to the unity. Finally, this algorithm allows a decrease of the computation time. Setting the single parameter to 1, this technique has shown a good ability to remove the background noise and image the defects in composite materials. The SSP algorithm is the better known of the pseudofrequency diversity techniques. Its use in the non-destructive inspection of composite materials is however restricted by the requirement that the frequency bandwidth of the target echo has to be known beforehand. The lack of this information could lead to a failure of the SSP to detect defects. The CSP technique brings some improvements since the coherent echo information is always contained within the frequency range of the diverse frequency signals. Nevertheless, this algorithm is far from being satisfying due to the important amount of computations it requires. Moreover, it often happens that there is not enough sensitivity to decorrelate the noise; this is due to the small frequency range that is removed from the summation during the expansion. This work has shown that the QFD techniques are well adapted to control the quality and integrity of complex composite structures on the condition of providing some improvements that make these algorithms robust, fast and easy to use.
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Acknowledgements The authors thank Dr. Mohammed Chibani, 2CI Technology, for his help and support to this work. The ®nancial help of Ministere de l'industrie et du Commerce of the Quebec government given to us from the Fonds des Priorites Gouvernementales en Sciences et Technologies is gratefully acknowledged.
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