Demodulation-derived damage metrics for nonlinear wave modulation-based health monitoring of structures

Mohammad Ehsani, Naserodin Sepehry, Mahnaz Shamshirsaz, Mojtaba Sadighi*, Richard Loendersloot

*Corresponding author for this work

Research output: Contribution to journalArticleAcademicpeer-review

2 Citations (Scopus)
5 Downloads (Pure)


Nonlinear wave modulation (NWM) is a promising technique for structural health monitoring and contact-type damage detection. In NWM, the severity of the damage is proportional to the intensity of the modulation. Spectral analysis is often employed to calculate the Modulation Index (MI), and the damage intensity. According to some recent studies, damage metrics obtained by demodulation of the sensory signal can provide more information about the damage than spectral MIs. The Hilbert Transform (HT), Synchronous Demodulation (SD), Short-Time Fourier Transform (STFT), and more recently, In-Phase/Quadrature Homodyne Separation (IQHS) have been used to demodulate the sensory signal and extract effective damage metrics in the NWM technique. The objective of this work is to investigate demodulation methods to obtain reliable amplitude and frequency modulation damage indicators. The drawbacks of the HT and original IQHS methods are discussed, and a Modified-IQHS (M-IQHS) method is proposed to address them. The M-IQHS is validated analytically and experimentally, with the latter taking place in a sandwich panel setup with a loose bolt as the damage, and the results are compared to their HT and original IQHS-derived counterparts. The results show that the M-IQHS can improve NWM damage detection by providing precise modulation metrics for any range of pump frequency, including ultrasonics. It can also provide information about the MI distribution for signals with multiple sidebands. Furthermore, of the demodulation algorithms developed for NWM so far, M-IQHS is the most noise-resistant.

Original languageEnglish
Article number110749
Number of pages18
JournalMechanical systems and signal processing
Early online date12 Sept 2023
Publication statusPublished - 1 Dec 2023


  • Hilbert transform
  • In-phase/quadrature homodyne separation
  • Modulation index
  • Nonlinear ultrasonic modulation
  • Structural health monitoring
  • Vibro-acoustic modulation
  • 2024 OA procedure


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