Energy spectrum analysis of blast waves based on an improved Hilbert–Huang transform

Abstract

Using the improved Hilbert–Huang transform (HHT), this paper investigates the problems of analysis and interpretation of the energy spectrum of a blast wave. It has been previously established that the energy spectrum is an effective feature by which to characterize a blast wave. In fact, the higher the energy spectra in a frequency band of a blast wave, the greater the damage to a target in the same frequency band. However, most current research focuses on analyzing wave signals in the time domain or frequency domain rather than considering the energy spectrum. We propose here an improved HHT method combined with a wavelet packet to extract the energy spectrum feature of a blast wave. When applying the HHT, the signal is first roughly decomposed into a series of intrinsic mode functions (IMFs) by empirical mode decomposition. The wavelet packet method is then performed on each IMF to eliminate noise on the energy spectrum. Second, a coefficient is introduced to remove unrelated IMFs. The energy of each instantaneous frequency can be derived through the Hilbert transform. The energy spectrum can then be obtained by adding up all the components after the wavelet packet filters and screens them through a coefficient to obtain the effective IMFs. The effectiveness of the proposed method is demonstrated by 12 groups of experimental data, and an energy attenuation model is established based on the experimental data. The improved HHT is a precise method for blast wave signal analysis. For other shock wave signals from blasting experiments, an energy frequency time distribution and energy spectrum can also be obtained through this method, allowing for more practical applications.