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Maximum fraction cross-correlation spectrum for time of arrival estimation of ultrasonic echoes

  • Acoustic Methods
  • Published:
Russian Journal of Nondestructive Testing Aims and scope Submit manuscript

Abstract

In this paper, a maximum fractional cross-correlation spectrum (FCCS) parameter estimation method is proposed to estimate the time of arrival (TOA) and/or time of flight (TOF) of the ultrasonic echoes with a high resolution. The FCCS is the integration of the fractional cross-correlation of a matched filter and the truncation function of the ultrasonic signal with respect to each time delay, and the range of the integration is limited in the essential-bandwidth which is the bandwidth of the fractional autocorrelation of the ultrasonic echo. If the matched filter matched the truncation function of the ultrasound signal, a local maximum magnitude of the FCCS can be obtained. It can simultaneously produce a measure of TOA of the ultrasonic echoes. The use of FCCS in estimate the TOA or/and TOF of the ultrasonic echoes can eliminate/reduce the noise in an effective manner, even under the very noisy condition, the curve of the FCCS is still smooth with the prominent local extremums. The maximum FCCS parameter estimation method can be repeated with different fractional Fourier transform (FRFT) in order to obtain multiple estimates of TOA of the ultrasonic echoes. These multiple estimates can further be averaged to obtain more robust estimates of the TOA. Numerical simulations and experimental results make evidence the good performance of the proposed approach which has good effect of noise suppression and results in much improved accuracy in the estimation of echo arrival time.

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References

  1. Song, S.P. and Que, P.W., Wavelet based noise suppression technique and its application to ultrasonic flaw detection, Ultrasonics, 2006, vol. 44, no. 2, pp. 188–193.

    Article  Google Scholar 

  2. Honarvar, F., Sheikhzadeh, H., and Moles, M., Improving the time-resolution and signal-to-noise ratio of ultrasonic NDT signals, Ultrasonics, 2004, vol. 41, no. 9, pp. 755–763.

    Article  Google Scholar 

  3. Grennberg, A. and Sandell, M., Estimation of subsample time delay differences in narrowband ultrasonic echoes using the Hilbert transform correlation, IEEE Trans. Ultrasonics, Ferroelectrics, Frequency Control, 1994, vol. 41, no. 5, pp. 588–595.

    Article  Google Scholar 

  4. Nandi, A.K., On the subsample time delay estimation of narrowband ultrasonic echoes, IEEE Trans. Ultrasonics, Ferroelectrics, Frequency Control, 1995, vol. 42, no. 6, pp. 993–1001.

    Article  Google Scholar 

  5. Maskell, D.L. and Woods, G.S., The discrete-time quadrature subsample estimation of delay, IEEE Trans. Instrum. Measurement, 2002, vol. 51, no. 1, pp. 133–137.

    Article  Google Scholar 

  6. Maskell, D.L. and Woods, G.S., The estimation of subsample time delay of arrival in the discrete-time measurement of phase delay, IEEE Trans. Instrum. Measurement, 1999, vol. 48, no. 6, pp. 1227–1231.

    Article  Google Scholar 

  7. Pei, S.C. and Ding, J.J., Closed-form discrete fractional and affine Fourier transforms, IEEE Trans. Signal Processing, 2000, vol. 48, no. 5, pp. 1338–1353.

    Article  Google Scholar 

  8. Sharma, K.K. and Joshi, S.D., Time delay estimation using fractional Fourier transform, Signal Processing, 2007, vol. 87, no. 5, pp. 853–865.

    Article  Google Scholar 

  9. Tao, R., Li, X.M., and Li, Y.L., Time-delay estimation of chirp signals in the fractional Fourier domain, IEEE Trans. Signal Processing, 2009, vol. 57, no. 7, pp. 2852–2855.

    Article  Google Scholar 

  10. Almeida, L.B., The fractional Fourier transform and time-frequency representations, IEEE Trans. Signal Processing, 1994, vol. 42, no. 11, pp. 3084–3091.

    Article  Google Scholar 

  11. Demirli, R. and Saniie, J., Model-based estimation of ultrasonic echoes, Part I: Analysis and algorithms, IEEE Trans. Ultrasonics, Ferroelectrics, Frequency Control, 2001, vol. 48, no. 3, pp. 787–802.

    Article  Google Scholar 

  12. Ozaktas, H., Arikan, O., and Kutay, M.A., Digital computation of the fractional Fourier transform, IEEE Trans. Signal Processing, 1995, vol. 44, no. 9, pp. 2141–2150.

    Article  Google Scholar 

  13. Akay, O. and Boudreaux-Bartels, G.F., Fractional convolution and correlation via operator methods and an application to detection of linear FM signals, IEEE Trans. Signal Processing, 2001, vol. 49, no. 5, pp. 979–993.

    Article  Google Scholar 

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Authors and Affiliations

  1. School of Mechatronics Engineering, University of Electronic Science and Technology of China, Chengdu, 611731, P.R. China

    Wei Liang, Liang Chen, Zhi-Hua Ge & Guo Ding

  2. School of Information Science and Engineering, Wuhan University of Science and Technology, Wuhan, 430081, P.R. China

    Feng-xing Zhou

Authors
  1. Wei Liang
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  2. Liang Chen
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  3. Feng-xing Zhou
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  4. Zhi-Hua Ge
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  5. Guo Ding
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Correspondence to Wei Liang.

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Liang, W., Chen, L., Zhou, Fx. et al. Maximum fraction cross-correlation spectrum for time of arrival estimation of ultrasonic echoes. Russ J Nondestruct Test 51, 120–130 (2015). https://doi.org/10.1134/S1061830915020096

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  • DOI: https://doi.org/10.1134/S1061830915020096

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