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Application of a Particle Filter to Flaw Identification for Ultrasonic Nondestructive Evaluation: Assimilation of Simulated and Measured Data

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Abstract

The assimilation of simulated and measured data is essential for advancing technology in NDE 4.0. In this study, a particle filter (PF) was applied to identify the geometry of flaws for ultrasonic nondestructive testing. A PF based on a probabilistic approach that allows errors in measurement and simulation models may be of great assistance for the data assimilation. In the PF, state variables are expressed by random data samples called particles, together with their associated weights. The PF estimates the probabilistic density function of the state variables by merging simulation data with measured data. Data types must be physically identical in the simulation and measurement to enhance the accuracy and to accelerate the convergence speed in the PF. Here, the scattering component, which is specific information related to the flaw geometry, was used for the likelihood evaluation in the PF. The simulation, which needed many particles, was conducted using the elastodynamic finite integration technique accelerated by parallel computing with graphics processing units. The proposed PF approach was demonstrated in ultrasonic measurement, and the geometries of artificial flaws in aluminum specimens were identified using only one pulse-echo signal at a single transducer.

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References

  1. Meyendorf, N.G., Bond, L.J., Curtis-Beard, J., Heilmann, S., Pal, S., Schallert, R., Scholz, H., Wunderlich, C.: NDE 4.0-NDE for the 21st century- the internet of things and cyber physical systems will revolutionize NDE, No. 117. In: Proceedings of the 15th Asia Pacific Conference for Nondestructive Testing (APCNDT2017), Singapore (2017)

  2. Vrana, J.: NDE perception and emerging reality: NDE 4.0 value extraction. Mater. Eval. 78(7), 835–851 (2020)

    Google Scholar 

  3. Drinkwater, B.W., Wilcox, P.D.: Ultrasonic arrays for non-destructive evaluation: a review. NDT E Int. 39, 525–541 (2006)

    Article  Google Scholar 

  4. Kouche, A.E., Hassanein, H.S.: Ultrasonic non-destructive testing (NDT) using wireless sensor networks. Procedia Comput. Sci. 10, 136–143 (2012)

    Article  Google Scholar 

  5. Zhong, C.H., Croxford, A.J., Wilcox, P.D.: Remote inspection system for impact damage in large composite structure. Proc. R. Soc. A 471(2173), 20140631 (2015)

    Article  Google Scholar 

  6. Liu, Z., Meyendorf, N.G., Mrad, N.: The role of data fusion in predictive maintenance using digital twin. In: Proceedings of 44th Annual Review of Progress in Quantitative Nondestructive Evaluation, AIP Conference Proceedings, Vol. 1949, 020023 (2018)

  7. Kalman, R.E.: A new approach to linear filtering and prediction problems. Trans. ASME 82(1), 35–45 (1960)

    Article  MathSciNet  Google Scholar 

  8. Dobie, G.: Ultrasonic Sensor Platforms for Non-Destructive Evaluation, Ph.D. thesis, University of Strathclyde (2010)

  9. Angrisani, L., Baccigalupi, A., Lo Moriello, R.S.: Ultrasonic time-of-flight estimation through unscented Kalman filter. IEEE Trans. Instrum. Meas. 55(4), 1077–1084 (2006)

    Article  Google Scholar 

  10. Yoon, M.-H.: New ultrasonic signal processing techniques for NDE applications, Ph.D. thesis, Iowa State University (1994)

  11. Engelhardt, M., Stavroulakis, G.E., Antes, H.: Crack and flaw identification in elastodynamics using Kalman filter techniques. Comput. Mech. 37(3), 249–265 (2006)

    Article  MATH  Google Scholar 

  12. Evensen, G.: Data Assimilation, The Ensemble Kalman Filter. Springer, New York (2009)

    MATH  Google Scholar 

  13. Gordon, N.J., Salmond, D.J., Smith, A.F.M.: Novel approach to nonlinear/non-Gaussian Bayesian state estimation. IEEE Proc. F 140(2), 107–113 (1993)

    Google Scholar 

  14. Emerick, A.A., Reynolds, A.C.: Ensemble smoother with multiple data assimilation. Comput. Geosci. 55, 3–15 (2013)

    Article  Google Scholar 

  15. Kitagawa, G.: Monte Carlo filter and smoother for non-Gaussian nonlinear state space models. J. Comput. Graph. Stat. 5(1), 1–25 (1996)

    MathSciNet  Google Scholar 

  16. Nakamura, K., Higuchi, T., Hirose, N.: Sequential data assimilation: information fusion of a numerical simulation and large scale observation data. J. Univ. Comput. Sci. 12(6), 608–626 (2006)

    Google Scholar 

  17. Muir, J.B., Tsai, V.C.: Geometric and level set tomography using ensemble Kalman inversion. Geophys. J. Int. 220, 967–980 (2020)

    Article  Google Scholar 

  18. Evensen, N.: The Ensemble Kalman Filter: theoretical formulation and practical implementation. Ocean Dyn. 53, 343–367 (2003)

    Article  Google Scholar 

  19. Potthast, R., Walter, A., Rhodin, A.: A localized adaptive particle filter within an operational NWP framework. Mon. Weather Rev. 147(1), 345–362 (2019)

    Article  Google Scholar 

  20. Schmerr, L.W.: Fundamentals of ultrasonic nondestructive evaluation. Plenum Press, New York (1998)

    Book  Google Scholar 

  21. Schmerr, L.W., Song, S.-J.: Ultrasonic Nondestructive Evaluation Systems. Models and Measurement. Springer, New York (2007)

    Book  Google Scholar 

  22. Dassios, G., Kiriaki, K., Polyzos, D.: On the scattering amplitudes for elastic waves. J. Appl. Math. Phys. 38, 856–873 (1987)

    MathSciNet  MATH  Google Scholar 

  23. Schafbuch, P.J.: Application of the boundary element method to elastic wave scattering problems in ultrasonic nondestructive evaluation, Ph.D. thesis, Iowa State University (1991)

  24. Fellinger, P., Marklein, R., Langenberg, K.J., Klaholz, S.: Numerical modeling of elastic wave propagation and scattering with EFIT-elastodynamic finite integration technique. Wave Motion 21, 47–66 (1995)

    Article  MATH  Google Scholar 

  25. Terada, K., Miura, T., Kikuchi, N.: Digital image-based modeling applied to the homogenization analysis of composite materials. Comput. Mech. 20, 331–346 (1997)

    Article  MATH  Google Scholar 

  26. Taheri, S.: A review on five key sensors for monitoring of concrete structures. Construct. Build. Mater. 204, 492–509 (2019)

    Article  Google Scholar 

  27. Nakahata, K., Chang, J., Takahashi, M., Ohira, K., Ogura, Y.: Finite integration technique for coupled acoustic and elastic wave simulation and its application to noncontact ultrasonic testing. Acoust. Sci. Technol. 35(5), 260–268 (2014)

    Article  Google Scholar 

  28. Murakami, A., Shuku, T., Nishimura, S., Fujisawa, K., Nakamura, K.: Data assimilation using the particle filter for identifying the elastoplastic material properties of geomaterials. Int. J. Numer. Anal. Methods Geomech. 37, 1642–1669 (2013)

    Article  Google Scholar 

  29. Myers, M.R.: Parameter estimation using extended Kalman filter and ultrasonic pulse time of flight to locate transient, concentrated heating sources, Ph.D. thesis, Vanderbilt University (2012)

  30. Courant, P., Friedrichs, K., Lewy, H.: On the partial difference equations of mathematical physics. IBM J. Res. Dev. 11(2), 215–234 (1967)

    Article  MathSciNet  MATH  Google Scholar 

  31. Schubert, F., Koehler, B.: Three-dimensional time domain modeling of ultrasonic wave propagation in concrete in explicit consideration of aggregates and porosity. J. Comput. Acoust. 9(4), 1543–1560 (2011)

    Article  Google Scholar 

  32. Ricker, N.: The computation of output disturbance from amplifiers for true wavelet inputs. Geophysics 10, 207–220 (1945)

    Article  Google Scholar 

  33. Collino, F., Tsogka, C.: Application of the PML absorbing layer model to the linear elastodynamic problem in anisotropic heterogeneous media, Rapport de Recherche. INRIA N3471 (1998)

  34. Li, T., Sun, S., Sattar, T.P., Corchado, J.M.: Fight sample degeneracy and impoverishment in particle filters: a review of intelligent approaches. Expert Syst. Appl. 41, 3944–3954 (2014)

    Article  Google Scholar 

  35. Nguyen, V.P., Anitescu, C., Bordas, S., Rabczuk, T.: Isogeometric analysis: an overview and computer implementation aspects. Math. Comput. Simul. 117, 89–116 (2015)

    Article  MathSciNet  MATH  Google Scholar 

  36. Jones, B., Johnson, R.T.: Design and analysis for the Gaussian process model. Qual. Reliab. Eng. Int. 25, 515–524 (2009)

    Article  Google Scholar 

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Acknowledgements

This work was supported by JSPS KAKENHI Grant Numbers 19K21987 and 20H02230.

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Authors and Affiliations

  1. Ehime University, 3 Bunkyo, Matsuyama, Ehime, 790-8577, Japan

    Kazuyuki Nakahata & Taizo Maruyama

  2. Tokyo Institute of Technology, W8-22, 2-12-1 O-okayama, Meguro-ku, Tokyo, 152-8552, Japan

    Sohichi Hirose

Authors
  1. Kazuyuki Nakahata
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  2. Taizo Maruyama
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  3. Sohichi Hirose
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Correspondence to Kazuyuki Nakahata.

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Nakahata, K., Maruyama, T. & Hirose, S. Application of a Particle Filter to Flaw Identification for Ultrasonic Nondestructive Evaluation: Assimilation of Simulated and Measured Data. J Nondestruct Eval 40, 34 (2021). https://doi.org/10.1007/s10921-021-00765-x

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