Hilbert spectrum analysis method of blast vibration signal based on HHT instantaneous phase optimization

Compared with wavelet analysis method of signal data, HHT (Hilbert-Huang Transform) method is widely used for the local signal data analysis in the time–frequency domain associated with adaptable capacity, which has been recognized as one of the most efficient method to address the non-stationary signals. In this study, Matlab software was used as the calculation code and field millisecond delay blasting data was collected as the research objects, the Hilbert time–frequency spectrum, marginal spectrum, instantaneous energy spectrum and Hilbert energy spectrum scatter were obtained for the signal IMF components under the standard instfreq.m function (as shown in Section 3.3) frequency modulation with the identified bandwidth of 1 Hz. The reasons of negative frequency for digital signals were discussed based on the theoretical analysis and the digitial signals were then summarized as two types of negative frequency according to the instantaneous phase characteristics. The field collected blasting vibration signals were used to illustrate the features of the negative frequency points such as large number, correlated relation between the signal amplitude extent and frequency band, and non-negligible of the total vibration energy. In addition, a theoretical equation was proposed for the instantaneous phase optimization function based on the HHT method, and a triple identification approach of millisecond time was proposed based on instantaneous phase optimization method. The process of Hilbert spectrum analysis based on HHT instantaneous phase optimization was implemented using Matlab, which was used to analyze Hilbert spectrum characteristics. Further, a theoretical comparison and analysis between the standard instfreq.m time–frequency modulation and the proposed phase optimized HHT spectrum were performed, and the results shows that the optimized HHT spectrum analysis improves the accuracy of time–frequency spectrum and Hilbert spectrum calculation, besides, the frequency domain recognition width is about 2∙r times of that from the standard solution. Finally, the phase optimization was used to analyze the amplitude spectrum, instantaneous velocity energy spectrum and 3D time–frequency seismic velocity energy spectrum features, application of HHT-based instantaneous phase optimization method is given for the accurate recognition application of multi-segment detonation millisecond time in underground blasting.