Abstract
Detecting damage in the early state is crucial in assessing structural integrity. Most current vibration-based damage detection methods use frequency shifts to assess the damage, observed as a change of the positions on which the peaks in the spectrum are located. However, accurate estimation of the natural frequencies can be challenging due to the raw frequency resolution obtained for short signals. We propose in this paper a signal post-processing algorithm that permits obtaining a spectrum with significantly enhanced resolution, without being necessary to increase the length of the signal. The super-resolution is obtained by overlapping numerous spectra calculated for the signal cropped iteratively. The spectral peaks are distributed in accordance with a pseudosinc function, which is asymmetrical, but the estimated frequencies are close to the real one. By interpolation, we improve the estimate. Moreover, by applying a correction term we find the true frequency. The algorithm is implemented in a Python application that can be linked to any virtual instrument developed in LabVIEW. The algorithm is tested for signals with known frequencies, in the absence and presence of noise and for real-world signals. It provides accurate results that permit observing the occurrence of damage in the very early state.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Doebling, S.W., Farrar, C.R., Prime, M.B.: A summary review of vibration-based damage identification methods. Shock Vibr. Digest 30, 91–105 (1998)
Khatir, S., Dekemele, K., Loccufier, M., Khatir, T., Wahab, M.A.: Crack identification method in beam-like structures using changes in experimentally measured frequencies and particle swarm optimization. C. R. Méc. 346(2), 110–120 (2018)
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)
He, K., Zhu, W.D.: Structural damage detection using changes in natural frequencies: theory and applications. J. Phys: Conf. Ser. 305, 012054 (2011)
Chioncel, C.P., Gillich, N., Tirian, G.O., Ntakpe, J.L.: Limits of the discrete fourier transform in exact identifying of the vibrations frequency. Rom. J. Acoust. Vibr. 12(1), 16–19 (2015)
Gillich, G.R., Mituletu, I.C.: Signal post-processing for accurate evaluation of the natural frequencies. In: Yan, R., Chen, X., Mukhopadhyay, S.C. (eds.) Structural Health Monitoring. SSMI, vol. 26, pp. 13–37. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-56126-4_2
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. 13(8), 2311–2329 (2015)
Gillich, G.R., Maia, N.N.N., Mituletu, I.C.: Problem of detecting damage through natural frequency changes. Comput. Exp. Methods Struct. 10, 105–139 (2018)
Djukanović, S., Popović, T., Mitrović, A.: Precise sinusoid frequency estimation based on parabolic interpolation. In: Proceedings of the 24th Telecommunications Forum TELFOR, pp. 1–4. IEEE, Belgrade (2016)
Grandke, T.: Interpolation algorithms for discrete fourier transforms of weighted signals. IEEE Trans. Instrum. Measur. 32, 350–355 (1983)
Quinn, B.G.: Estimating frequency by interpolation using fourier coefficients. IEEE Trans. Signal Process. 42, 1264–1268 (1994)
Jain, V.K., Collins, W.L., Davis, D.C.: High-accuracy analog measurements via interpolated FFT. IEEE Trans. Instrum. Measur. 28, 113–122 (1979)
Ding, K., Zheng, C., Yang, Z.: Frequency estimation accuracy analysis and improvement of energy barycenter correction method for discrete spectrum. J.Mech. Eng. 46(5), 43–48 (2010)
Voglewede, P.: Parabola approximation for peak determination. Glob. DSP Mag. 3(5), 13–17 (2004)
Jacobsen, E., Kootsookos, P.: Fast, accurate frequency estimators. IEEE Signal Process. Mag. 24(3), 123–125 (2007)
Minda, A.A., Gillich, N., Mituletu, I.C., Ntakpe, J.L., Manescu, T., Negru, I.: Accurate frequency evaluation of vibration signals by multi-windowing analysis. Appl. Mech. Mater. 801, 328–332 (2015)
Gillich, G.R., Nedelcu, D., Malin, C.T., Biro, I., Wahab M.A.: Efficient algorithm for frequency estimation used in structural damage detection. In: Proceedings of the 13th International Conference on Damage Assessment of Structures, pp. 283–300. Springer, Porto (2020)
Gillich, G.R., Nedelcu, D., Barbinta, C.I., Gillich, N.: A versatile algorithm for estimating natural frequencies with high accuracy. Vibroeng. Procedia 27, 37–42 (2020)
Tufisi, C: Detection of branched cracks in beam-like structures, Ph.D. thesis, Universitatea “Eftimie Murgu” Resita, Romania (2020)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this paper
Cite this paper
Gillich, N., Lupu, D., Hamat, C., Gillich, GR., Nedelcu, D. (2021). Improving the Capability of Detecting Damages in the Early State by Advanced Frequency Estimation. In: Rizzo, P., Milazzo, A. (eds) European Workshop on Structural Health Monitoring. EWSHM 2020. Lecture Notes in Civil Engineering, vol 127. Springer, Cham. https://doi.org/10.1007/978-3-030-64594-6_45
Download citation
DOI: https://doi.org/10.1007/978-3-030-64594-6_45
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-64593-9
Online ISBN: 978-3-030-64594-6
eBook Packages: EngineeringEngineering (R0)