Efficient Algorithm for Frequency Estimation Used in Structural Damage Detection

Conference paper
Part of the Lecture Notes in Mechanical Engineering book series (LNME)


In damage detection processes, the accuracy of estimating the eigenfrequencies of structures is crucial because the frequencies are not highly sensitive to damage. This paper analyses the accuracy of the Discrete Fourier Transform when estimating the frequency and amplitude of sine waves, identifies its limitations and proposes an algorithm to significantly improve the attained results. Standard methods used to evaluate the eigenfrequencies fail because the results depend on the position of the spectral lines, which are related to the acquisition time. Frequently, interpolation involving the amplitude peaks displayed on several spectral lines located around the maximizer is employed to improve the frequency readability. The estimated results are improved indeed, but the achieved precision still depends on the acquisition time. We develop an algorithm that uses the maximizer of signals with different time lengths, which are obtained from the original acquired signal by cropping. The three selected maximizer are used for parabolic interpolation input data. The maximum of the regression curve represents a precise estimate of the amplitude, associated with the true frequency of the targeted harmonic component. The efficiency of the algorithm is demonstrated for harmonic and multi-harmonic signals.


Signal processing Accurate frequency estimation Discrete Fourier Transform Interpolation Excel VBA 


  1. 1.
    Ostachowicz, W.M., Krawczuk, M.: Vibration analysis of a cracked beam. Comput. Struct. 36(2), 245–250 (1990)CrossRefGoogle Scholar
  2. 2.
    Zenzen, R., Belaidi, I., Khatir, S., Wahab, M.A.: A damage identification technique for beam-like and truss structures based on FRF and bat algorithm. Comptes Rendus Mécanique 346(12), 1253–1266 (2018)CrossRefGoogle Scholar
  3. 3.
    Sakaris, C.S., Sakellariou, J.S., Fassois, S.D.: Vibration-based multi-site damage precise localization via the functional model based method. Procedia Eng. 199, 2072–2077 (2017)CrossRefGoogle Scholar
  4. 4.
    Dahak, M., Touat, N., Kharoubi, M.: Damage detection in beam through change in measured frequency and undamaged curvature mode shape. Inverse Prob. Sci. Eng. 27(1), 89–114 (2019)MathSciNetCrossRefGoogle Scholar
  5. 5.
    Zhou, Y.L., Abdel Wahab, M.: Cosine based and extended transmissibility damage indicators for structural damage detection. Eng. Struct. 141, 175–183 (2017)CrossRefGoogle Scholar
  6. 6.
    Zhao, J., DeWolf, J.T.: Sensitivity study for vibrational parameters used in damage detection. J. Struct. Eng. 125(4), 401–416 (1999)CrossRefGoogle Scholar
  7. 7.
    Gillich, G.R., Maia, N., Mituletu, I.C., Praisach, Z.I., Tufoi, M., Negru, I.: Early structural damage assessment by using an improved frequency evaluation algorithm. Lat. Am. J. Solids Struct. 12(12), 2311–2329 (2015)CrossRefGoogle Scholar
  8. 8.
    Gillich, G.R., Mituletu, I.C., Negru, I., Tufoi, M., Iancu, V., Muntean, F.: A method to enhance frequency readability for early damage detection. J. Vibr. Eng. Technol. 3(5), 637–652 (2015)Google Scholar
  9. 9.
    Mituletu, I.C., Gillich, G.R., Maia, N.M.M.: A method for an accurate estimation of natural frequencies using swept-sine acoustic excitation. Mech. Syst. Signal Process. 116, 693–709 (2019)CrossRefGoogle Scholar
  10. 10.
    Smith, W.S.: The scientist and engineer’s guide to digital signal processing. California Technical Publishing, San Diego (1997)Google Scholar
  11. 11.
    Gillich, G.R., Praisach, Z.I.: Modal identification and damage detection in beam-like structures using the power spectrum and time-frequency analysis. Signal Process. 96(PART A), 29–44 (2014)CrossRefGoogle Scholar
  12. 12.
    Gillich, G.R., Mituletu, I.C.: Signal post-processing for accurate evaluation of the natural frequencies. In: Yan, R., Chen, X., Mukhopadhyay, S. (eds.) Structural Health Monitoring, Measurement and Instrumentation, vol. 26, pp. 13–37. Springer, Cham (2017)Google Scholar
  13. 13.
    Gillich, N., Mituletu, I.C., Gillich, G.R., Chioncel, C.P., Hatiegan, C.: Frequency and magnitude estimation in voltage unbalanced power systems. In: Proceedings of the 10th International Symposium on Advanced Topics in Electrical Engineering (ATEE), pp. 1–4. IEEE, Bucharest (2017)Google Scholar
  14. 14.
    Grandke, T.: Interpolation algorithms for discrete Fourier transforms of weighted signals. IEEE Trans. Instrum. Meas. 32, 350–355 (1983)CrossRefGoogle Scholar
  15. 15.
    Quinn, B.G.: Estimating frequency by interpolation using fourier coefficients. IEEE Trans. Signal Process. 42, 1264–1268 (1994)CrossRefGoogle Scholar
  16. 16.
    Jain, V.K., Collins, W.L., Davis, D.C.: High-accuracy analog measurements via interpolated FFT. IEEE Trans. Instrum. Meas. 28, 113–122 (1979)CrossRefGoogle Scholar
  17. 17.
    Ding, K., Zheng, C., Yang, Z.: Frequency estimation accuracy analysis and improvement of energy barycenter correction method for discrete spectrum. J. Mech. Eng. 46(05), 43–48 (2010)CrossRefGoogle Scholar
  18. 18.
    Voglewede, P.: Parabola approximation for peak determination. Global DSP Mag. 3(5), 13–17 (2004)Google Scholar
  19. 19.
    Jacobsen, E., Kootsookos, P.: Fast, accurate frequency estimators. IEEE Signal Process. Mag. 24(3), 123–125 (2007)CrossRefGoogle Scholar
  20. 20.
    Gillich, G.R., Mituletu, I.C., Praisach, Z.I., Negru, I., Tufoi., M.: Method to enhance the frequency readability for detecting incipient structural damage. Iranian J. Sci. Technol. Trans. Mech. Eng. 41(3), 233–242 (2017)CrossRefGoogle Scholar
  21. 21.
    Minda, A.A., Gillich, G.R.: Sinc function based interpolation method to accurate evaluate the natural frequencies. Analele Universitatii Eftimie Murgu. Fascicula de Inginerie 24(1), 211–218 (2017)Google Scholar
  22. 22.
    Gillich, G.R., Praisach, Z.I., Negru, I.: Damages influence on dynamic behaviour of composite structures reinforced with continuous fibers. Mater. Plast. 49(3), 186–191 (2012)Google Scholar
  23. 23.
    Gillich, G.R., Minda, P.F., Praisach, Z.I., Minda, A.A.: Natural frequencies of damaged beams - a new approach. Rom. J. Acoust. Vibr. 9(2), 101–108 (2012)Google Scholar
  24. 24.
    Gillich, G.R., Abdel Wahab, M., Praisach, Z.I., Ntakpe J.L.: The influence of transversal crack geometry on the frequency changes of beams. In: Proceedings of International Conference on Noise and Vibration Engineering (ISMA2014) and International Conference on Uncertainty in Structural Dynamics (USD2014), pp. 485–498. Leuven (2014)Google Scholar
  25. 25.
    Gillich, G.R., Praisach, Z.I., Iancu, V., Furdui, H., Negru, I.: Natural frequency changes due to severe corrosion in metallic structures. Strojniški vestnik – J. Mech. Eng. 61(12), 721–730 (2015)CrossRefGoogle Scholar

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© Springer Nature Singapore Pte Ltd. 2020

Authors and Affiliations

  1. 1.Department of Mechanical Engineering“Eftimie Murgu” University of ResitaResitaRomania
  2. 2.Faculty of EngineeringUniversity of SzegedSzegedHungary
  3. 3.Soete Laboratory, Faculty of Engineering and ArchitectureGhent UniversityZwijnaardeBelgium

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