·Table of Contents ·Aeronautics and Aerospace | Automatic estimation of ultrasonic attenuation for porosity evaluation in composite materialsL.-K. Shark and C. YuDepartment of Engineering and Product Design University of Central Lancashire Preston, PR1 2HE, UK J. P. Smith BAE SYSTEMS Warton, Preston, PR4 1AX, UK Contact |
Ultrasonic signals are noisy in nature due to the back scattering phenomenon produced by the inherent microstructure of the material. From the previously published literature, the advantages of using the wavelet transform for signal restoration have been well-established [3]. The approach is based on thresholding the wavelet coefficients produced by the forward discrete wavelet transform (DWT) of the ultrasonic signal, thereby allowing only significant wavelet coefficients (with their magnitude values greater than the threshold) to be used in the inverse DWT (IDWT) to suppress noise. However, the quality of the ultrasonic echoes restored depends heavily on the choice of wavelet, its order and threshold value. Presented in Section 2 is a novel signal restoration method, whereby an automatic signal segmentation process is included before denoising to facilitate the optimisation of the wavelet order, and the dilemma in setting an appropriate threshold is solved by using a special fuzzy membership function [4]. Normally, the porosity level is evaluated based on the amplitude ratio of the second echo reflected from the bottom surface of the component with respect to the first echo reflected from the top surface of the component. Section 3 presents the validity of using the energy ratio as an additional measure to improve the reliability of porosity estimation. To demonstrate the effectiveness of the proposed method, some experimental results based on practical ultrasonic signals acquired from purpose-made samples are presented in Section 4 with some general conclusions given in Section 5.
2.1 Automatic Signal Segmentation
Figure 1 shows a typical ultrasonic record acquired from a particular point of a laminated composite material part. It is seen to consist of a transmitted signal followed by two echoes reflected from the top and bottom surfaces respectively. While the transmitted signal is seen to possess the strongest amplitude, the second echo is seen to be weaker than the first echo due to material attenuation of the ultrasonic energy. Furthermore, between these signals is noise due to back scattering.
Fig 1: A typical ultrasonic record |
The aim of automatic signal segmentation is to separate the transmitted signal and echoes from noise, and is achieved by exploiting the differences between noise and the transmitted signal/echoes in term of their statistical properties. Since echoes and the transmitted signal are likely to be strongly correlated due echoes being produced by the transmitted signal, and since noise caused by back scattering is likely to be random due to the irregularity of the material microstructure, the following steps are devised for the automatic signal segmentation:
Figure 2 shows a result of the start and the end of the first and second echoes estimated by of the proposed automatic signal segmentation method. Although the echo intervals estimated are not precise, they do contain the main peaks of each echo. Furthermore, it should be apparent that the accuracy and the execution time of the proposed method can be improved by incorporating additional information such as component thickness, approximate ultrasonic velocity in the component, and the sampling rate of the ultrasonic measurement system.
Fig 2: Echo intervals identified |
2.2 Wavelet based denoising
With the positions of the two echoes being identified by the automatic signal segmentation method, a region based error criterion can be established for the following denoising operation. If the denoised signal is required to be as similar to the original signal as possible in the two identified echo intervals and as near to zero as possible outside the two identified echo intervals, then the error criterion can be written as
(1) |
The minimisation of the error criterion by the wavelet based denoising method depends on the choice of wavelet, its order and threshold value. After experimenting with a number of different wavelets on ultrasonic signals, the symlet wavelet was found to outperform other wavelets based on visual comparison due to its linear phase property. To select the optimum order of the wavelet, a search operation is carried out to perform denoising based on the wavelet filter bank implemented using the 2nd symlet wavelet up to the maximum 8th order symlet wavelet. The optimum filter length corresponds to the minimum e value produced. Although the search of optimum wavelet order may be viewed as a time-consuming process, it may be only necessary to do it once at the start of a ultrasonic scan or the search range can be limited to the adjacent orders of the optimal order previously estimated.
A number of different methods for threshold value selection are available. One is based on the Stein's unbiased risk estimate (SURE) [5], and the other is a fixed form threshold with some asymptotic near-minimax properties [6]. While the latter is known as a conservative one as it tends to `overkill' the wavelet coefficients, the former tends to `underkill' the wavelet coefficients. Consequently, there is a problem in selecting between the SURE threshold and the fixed from threshold. By treating the SURE threshold and the fixed form threshold as the lower bound and the upper bound respectively, a possible compromise is use a fuzzy membership function to allow the wavelet coefficients lying between lower bound and the upper bound to contribute partially in the signal reconstruction according to their magnitude values. Let w_{ m,n} denote the nth wavelet coefficient at the mth decomposition stage with t_{m}^{sure} and t_{m}^{fixed} denoting the SURE threshold and the fixed form threshold respectively, an appropriate fuzzy threshold function proposed previously [4] is given by
(2) | |
where | (3) |
(4) | |
(5) |
For the original ultrasonic signal shown in dash line in Figures 3(a), the signal restored based on the proposed wavelet denoising method is shown in solid line and was obtained using the 8th order symlet wavelet (which was found to be the optimum order) with 5 decomposition stages. Compared with Figure 3(b) which shows the signal restored using the 3rd order symlet wavelet with the same number of decomposition stages and the fixed form threshold, the proposed denoising method is seen to offer better performance with the restored echoes fitting better to the original echoes and containing significantly less amplitude distortions.
Fig 3: (a) Proposed denoising, (b) Standard denoising |
(6) |
Fig 4: (a) Attenuation estimated, (b) Variance of attenuation estimated |
Grade | A | B | C | D | E | F |
Porosity | <0.2% | 0.2%~0.5% | 0.5%~1% | 1%~2% | 2%~5% | >5% |
Table 1 : |
Using the middle values of each porosity range as the nominal porosity level for each grade, except grade A and grade F which are denoted by 0.1% and 7% respectively, Figure 5 shows the relationship between the porosity level and the ultrasonic attenuation estimated by averaging the amplitude ratio and the energy ratio obtained over the scan area. From Figure 5, the ultrasonic attenuation is seen to increase as the porosity level increases. Furthermore, the strong agreement between the amplitude ratio and the energy ratio provides the confidence in the results obtained.
Fig 5: Attenuation versus porosity |
Figure 6 shows two images corresponding to the amplitude and energy attenuation distributions of a sample. The agreements between the two images are again apparent. Based on the histogram of the attenuation distribution showing the number of pixels per each attenuation interval defined according to the specified porosity ranges, an accurate and consistent porosity grade can be automatically derived for components manufactured using composite materials.
Fig 6: (a) Amplitude attenuation, (b) Energy attenuation |
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