Frugal Wavelet Transform for detecting faults in non-stationary signals (with Matlab codes)

Published Aug 28, 2025
https://doi.org/10.46223/HCMCOUJS.acs.en.15.2.78.2025
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Received: 2025-08-07
Accepted: 2025-08-28
Published: 2025-08-28
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15(2)2025

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Morteza Saadatmorad - Eng.saadatmorad@gmail.com
Department of Civil, Chemical, Environmental and Materials Engineering, University of Bologna, Italy
https://orcid.org/0000-0001-6202-6132
Bochra Khatir
Polytechnic University of Marche, Ancona, Italy

Abstract

According to the literature, one of the most notable weaknesses of the Wavelet Transform (WT) is its dependence on the selection of the wavelet function, resulting in different wavelet functions yielding varying results. To overcome this weakness, this paper introduces a new transform called the FrugWT (FrugWT). The Frugal Wavelet Transform, a type of discrete wavelet transform, emphasizes the preservation and approximation of detail signals, especially when the detection of local abrupt changes in the signal is apparently not possible. This study demonstrates that the FrugWT mitigates the influence of wavelet function selection on fault detection and exhibits resilience to acceptable noise levels. The FrugWT outperforms both the WT and signal derivative methods. Its effectiveness is demonstrated in detecting subtle faults within arrhythmic heartbeats (ECG) and abnormal brainwaves (EEG) signals. Matlab code is available in the appendix.

Keywords

damage detection, fault detection, FrugWT, Frugal Wavelet Transform, signal processing, wavelet transform

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Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

How to Cite
Saadatmorad, M., & Khatir, B. (2025). Frugal Wavelet Transform for detecting faults in non-stationary signals (with Matlab codes). HCMCOU Journal of Science - Advances in Computational Structures, 15(2), 55–79. https://doi.org/10.46223/HCMCOUJS.acs.en.15.2.78.2025
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References

  1. Addison, P. S. (2018). Introduction to redundancy rules: The continuous Wavelet Transform comes of age. Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 376(2126), Article 20170258. https://doi.org/10.1098/rsta.2017.0258 DOI: https://doi.org/10.1098/rsta.2017.0258
  2. Daubechies, I. (1992). Ten lectures on wavelets. Society for Industrial and Applied Mathematics. DOI: https://doi.org/10.1137/1.9781611970104
  3. Debnath, L. (2012). A short biography of Joseph Fourier and historical development of Fourier series and Fourier transforms. International Journal of Mathematical Education in Science and Technology, 43(5), 589-612. https://doi.org/10.1080/0020739x.2011.633712 DOI: https://doi.org/10.1080/0020739X.2011.633712
  4. Farge, M. (1992). Wavelet Transforms and their applications to turbulence. Annual Review of Fluid Mechanics, 24(1), 395-458. https://doi.org/10.1146/annurev.fl.24.010192.002143 DOI: https://doi.org/10.1146/annurev.fl.24.010192.002143
  5. Gdeisat, M. A., Abid, A., Burton, D. R., Lalor, M. J., Lilley, F., Moore, C., & Qudeisat, M. (2009). Spatial and temporal carrier fringe pattern demodulation using the one-dimensional continuous Wavelet Transform: Recent progress, challenges, and suggested developments. Optics and Lasers in Engineering, 47(12), 1348-1361. https://doi.org/10.1016/j.optlaseng.2009.07.009 DOI: https://doi.org/10.1016/j.optlaseng.2009.07.009
  6.  Katunin, A. (2014). Vibration-based spatial damage identification in honeycomb-core sandwich composite structures using wavelet analysis. Composite Structures, 118, 385-391. https://doi.org/10.1016/j.compstruct.2014.08.010 DOI: https://doi.org/10.1016/j.compstruct.2014.08.010
  7. Li, X., Bi, G., & Li, S. (2012). On uncertainty principle of the local polynomial Fourier transform. EURASIP Journal on Advances in Signal Processing, 2012(1), Article 120. https://doi.org/10.1186/1687-6180-2012-120 DOI: https://doi.org/10.1186/1687-6180-2012-120
  8. Pirooz, R. M., & Homami, P. (2021). An improvement over Fourier transform to enhance its performance for frequency content evaluation of seismic signals. Computers & Structures, 243, Article 106422. https://doi.org/10.1016/j.compstruc.2020.106422 DOI: https://doi.org/10.1016/j.compstruc.2020.106422
  9. Saadatmorad, M., Jafari-Talookolaei, R. A., Ghandvar, H., Cuong-Le, T., & Khatir, S. (2025). Relative Frugal Wavelet Transform to detect damages in functionally graded tapered beams made of porous material. Multidiscipline Modeling in Materials and Structures, 21(3), 692-714. https://doi.org/10.1108/MMMS-08-2024-0248 DOI: https://doi.org/10.1108/MMMS-08-2024-0248
  10. Saadatmorad, M., Jafari-Talookolaei, R. A., Khatir, S., Ammar, A., Ghandvar, H., & Cuong-Le, T. (2025). Continuous Frugal Wavelet Transform for damage detection in frame structures. Applied Acoustics, 234, Article 110621. https://doi.org/10.1016/j.apacoust.2025.110621 DOI: https://doi.org/10.1016/j.apacoust.2025.110621
  11. Saadatmorad, M., Jafari-Talookolaei, R. A., Khatir, S., Fantuzzi, N., & Cuong-Le, T. (2025). Frugal Wavelet Transform for damage detection of laminated composite beams. Computers & Structures, 314, Article 107765. https://doi.org/10.1016/j.compstruc.2025.107765 DOI: https://doi.org/10.1016/j.compstruc.2025.107765
  12. Saadatmorad, M., Jafari-Talookolaei, R. A., Pashaei, M. H., & Khatir, S. (2021). Damage detection on rectangular laminated composite plates using wavelet based convolutional neural network technique. Composite Structures, 278, Article 114656. https://doi.org/10.1016/j.compstruct.2021.114656 DOI: https://doi.org/10.1016/j.compstruct.2021.114656
  13. Saadatmorad, M., Khatir, S., Cuong-Le, T., Benaissa, B., & Mahmoudi, S. (2024). Detecting damages in metallic beam structures using a novel wavelet selection criterion. Journal of Sound and Vibration, 578, Article 118297. https://doi.org/10.1016/j.jsv.2024.118297 DOI: https://doi.org/10.1016/j.jsv.2024.118297
  14. Saadatmorad, M., Sadripour, S., Gholipour, A., Jafari-Talookolaei, R. A., Khatir, S., Shahavi, M. H., & Thanh, C. L. (2025). A novel hybrid Wavelet Transform for detecting damages in laminated composite cylindrical panels. Advances in Engineering Software, 204, Article 103895. https://doi.org/10.1016/j.advengsoft.2025.103895 DOI: https://doi.org/10.1016/j.advengsoft.2025.103895
  15. Saadatmorad, M., Shahavi, M. H., & Gholipour, A. (2024). Damage detection in laminated composite beams reinforced with nano-particles using covariance of vibration mode shape and wavelet transform. Journal of Vibration Engineering & Technologies, 12(3), 2865-2875. https://doi.org/10.1007/s42417-023-01019-y DOI: https://doi.org/10.1007/s42417-023-01019-y
  16. Saadatmorad, M., Talookolaei, R. A. J., Pashaei, M. H., Khatir, S., & Wahab, M. A. (2022). Pearson correlation and discrete wavelet transform for crack identification in steel beams. Mathematics, 10(15), Article 2689. https://doi.org/10.3390/math10152689 DOI: https://doi.org/10.3390/math10152689
  17. Shi, J., Zheng, J., Liu, X., Xiang, W., & Zhang, Q. (2020). Novel short-time fractional Fourier transform: Theory, implementation, and applications. IEEE Transactions on Signal Processing, 68, 3280-3295. https://doi.org/10.1109/tsp.2020.2992865 DOI: https://doi.org/10.1109/TSP.2020.2992865
  18. Tu, G. J., & Karstoft, H. (2015). Logarithmic dyadic Wavelet Transform with its applications in edge detection and reconstruction. Applied Soft Computing, 26, 193-201. https://doi.org/10.1201/9781315372556 DOI: https://doi.org/10.1016/j.asoc.2014.09.044

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