Analysis of Acoustic Wave Frequency Spectrum Characters of Rock Mass under Blasting Damage Based on the HHT Method
International Journal of
Analysis of Acoustic Wave Frequency Spectrum Characters of Rock Mass under Blasting Damage Based on the HHT Method
Haiping Yuan 0 1
Xiaole Liu 0
Yan Liu 2
Hanbing Bian 3
Wen Chen 3
Pier Paolo Rossi
0 School of Civil Engineering, Hefei University of Technology , Hefei , China
1 Hunan Province Key Lab of Safety Coal Mining Technology, Hunan University of Science and Technology , Xiangtan , China
2 State Key Laboratory of Explosion Science and Technology, Beijing Institute of Technology , Beijing 100081 , China
3 LEM3 CNRS, Universite ? de Lorraine , Metz 57073 , France
Correspondence should be addressed to Yixian Wang; -e limitation associated with Fourier transform and wavelet analysis that they often fail to produce satisfactory resolution simultaneously in time and frequency when dealing with nonlinear and nonstationary signals is frequently encountered. -erefore, this paper aims at using the HHT (Hilbert-Huang transform) method, which is built on the basis of the EMD(empirical mode decomposition-) based wavelet threshold denoising technique and the Hilbert transform, to analyze the blasting vibration signals in a south China lead-zinc mine. -e analysis is conducted in terms of three-dimensional Hilbert spectrum, marginal spectrum, and instantaneous energy spectrum. -e results indicate that the frequencies of the blasting vibration signals lie mainly within 0?200 Hz, which consists of more than 90% of the total signal energy. At the onset of the blasting, the vibration frequency tends to be low, with the frequency that is less than 50 Hz being dominant. By using instantaneous energy spectrum, which can reveal the condition of energy release for detonator explosion, the initiation moments of detonators with 7 time-lag levels are accurately identified. -is accurate identification demonstrates the superiority of the HHT method in coping with nonlinear and nonstationary signals. Additionally, the HHT method that is characterized by adaptivity, completeness, strong reconfigurability, and high accuracy provides an opportunity for reflecting signals' change features with regard to time domain, frequency domain, and energy irrespective of the limitation of the Heisenberg uncertainty principle.
-e blasting technique has been widely applied to engineering
constructions of railway, mining, tunneling, and so on [
During blasting, the explosion energy will apply work to
surrounding rock mass, and then, part of them propagates
away in the form of wave [
]. Considering that abundant
information about blasting vibration is included in the
blasting vibration wave, the extraction and analysis of the
blasting vibration signals provide effective tools that can be
used in studying the blasting efficiency.
Since Fourier published the theory of heat conduction
analysis in 1822, the Fourier transform has been extensively
used as a tool of analysis in the signal processing field [
-is tool transforms signals from the time domain to the
frequency domain and describes the variation of signals in the
frequency domain by using the overall frequency components
that are included in the signals. Because of the inability to
account for the instantaneous variation in some signal
frequency, the tool possesses limitations in dealing with
nonlinear and nonstationary signals. Under the restriction of the
Heisenberg uncertainty principle [
], this tool also fails to
generate satisfactory resolution simultaneously in time and
On the contrary, since the introduction of the concept of
wavelet in the 1980s by Morlet, a French geophysicist, the
wavelet analysis theory has begun being gradually
]. At present, wavelet transform is serving as a tool
that is extensively used in the analysis of nonstationary
signals. In the effort to analyze vibration signals by using the
wavelet technique, Newland [
] extended the engineering
applications of this technique. Based on the usage of Mexican
hat wavelets, Zhou and Adeli [
] developed a method for the
analysis of time-frequency signals in earthquake records.
Sua?rez and Montejo [
] proposed a wavelet-based procedure
to produce an accelerogram with a response spectrum that
was compatible with the target spectrum. -is
procedure contributes to the application of wavelet technique in
the seismic wave analysis. Zhong et al. [
] analyzed the
wavelet packet energy spectra for blasting vibration signals
through utilizing the technique of the wavelet packet
analysis. -ey also investigated the characteristics of
attenuation of blasting vibration wave for various explosion
However, wavelet transform is still not free from the
Heisenberg uncertainty principle. Under certain scales,
wavelet transform cannot achieve high accuracy at both
time and frequency. In addition, the wavelet basis is
difficult to choose [
-e HHT method, which was proposed by Huang et al.
] in 1998, is a new alternative for dealing with nonlinear
and nonstationary signals. -is method can reveal accurate
time-frequency information for signals. Compared to
traditional methods of signal processing and failure testing
], the HHT method is more accurate [
Because of this, it seems preferable to introduce the HHT
method to the analysis of blasting vibration signals.
Consequently, the objective of this paper is to use the
HHT method to analyze the blasting vibration signals in
a south China lead-zinc mine in terms of three-dimensional
Hilbert spectrum, marginal spectrum, and instantaneous
2. Basic Principle
Taking into account the inherent characteristics of signals,
the HHT method decomposes signals into a series of
intrinsic mode functions (IMFs) using the empirical mode
decomposition (EMD) method. And then, Hilbert
transform is applied to these IMF components, leading to the
derivation of energy distribution spectrogram on the
timefrequency plane. -e derived energy distribution
spectrogram conveys accurately various information with
respect to time, frequency, and energy. It has been well
known that the HHT method is mainly composed of EMD
and Hilbert transform.
2.1. 3e EMD Method. -e EMD method hypothesizes that
a signal is a compound signal consisting of different IMFs.
Each of these IMF components must satisfy the following:
(1) over the entire time series, the number of extrema and
zero crossing point must be equal or differ at most by one;
and (2) at any point, the mean value of the envelope
defined by the local maxima and the envelope defined by
the local minima is zero. In this way, any signal can be
decomposed into the addition of a finite number of IMF
-e detailed implementation procedure of EMD can be
summarized as follows:
(1) Firstly, find out all the maximum and the minimum
points for the signal y(t). -ese points are then fitted
by using cubic spline functions to generate two
envelopes, which are defined, respectively, by the maxima
and the minima. Calculate the mean value of the two
envelopes, a1(t). -e subtraction of a1(t) from the
original series y(t) results in deriving a new series
without low frequency, v1:
y(t) ? a1(t)
(2) Repeat Step 1 k times, until v1(t) satisfying the
requirement defined for IMF: the derived mean value
approaches to zero. -us, the first IMF component
f1, which represents the highest frequency of signal
y(t), is obtained.
(3) Separate f1(t) from y(t) to derive a signal without
high-frequency component, r1(t):
y(t) ? f1(t).
(4) Treat r1(t) as the original data, and repeat the above
steps. -en, the second IMF component f2(t) is
derived. Continue repeating n times, leading to the
derivation of IMF components with a total number
of n. At the end of the repetition, the following
relationship is obtained:
fj(t) + rn(t),
where rn(t) is the residual function, representing the average
trend of the original signal. Note that the frequency bands
are varied for different IMF components. And the
sequence of f1(t), f2(t), . . . , fn(t) is ranked in the descending
2.2. Hilbert Transform. For the time series F(t), its Hilbert
?? t ? ?
where K is Cauchy?s principal value. When the relationship
of F(t) and G(t) is the complex conjugate, then the
following analytic signal is derived:
F(t) + iG(t)
where a(t) F2(t) + G2(t) and ?(t) arctan(G(t)/F(t)).
Meanwhile, it is requisite to define instantaneous
frequency as ? d?(t)/dt. -erefore, the Hilbert transform
13?S4# drawn sha
provides a specific function which can be used to calculate
the instantaneous frequency and the amplitude.
Applying the Hilbert transform to each of the IMF
components gives rise to the derivation of the Hilbert
where Re represents taking the real component. Equation (6)
indicates the distribution of amplitude on the
frequencytime plane. -e time-domain integral of the Hilbert
spectrum in (6) generates the marginal spectrum H(?):
Furthermore, the instantaneous energy spectrum is
3. Engineering Background and Data Sources
Field testing of blasting vibration signals was implemented
in the S5#S stope, middle section of SH-455m, a south
China lead-zinc deep mine. -e all-band wave velocity and
the vibration data that were collected during the 4th field
blasting have been chosen to analyze using the HHT
-e plane layout in field is shown in Figure 1, in which
point B represents blasting source, and points 1, 2, and 3 are
three vibration monitoring points (MP). Points 1 and 2
locate, respectively, on two sides of the chamber. Point 3
locates on one side of the roadway. -ese three MPs are
collinear which brings convenience to study the blasting
effect at different distances from the blasting source.
Connecting line ree-dimensional sensor
-e Blastmate III manufactured in the USA, a vibration
monitoring instrument as shown in Figure 2, has been used
to monitor the blasting vibration effect and to collect data.
-e detector was selected as the Triaxial Geophone, which
is capable of collecting the radial, the normal, and the
tangential wave velocities in rock mass during blasting. -e
component of the instrument includes microphones,
geophone, recorder, microcomputer, and microprinter, which
have various functions such as vibration signal acquisition,
signal analysis and processing, and report printing. -e main
parameters of the instrument are shown in Table 1. (-e
sampling rate of this experiment is 4026.)
-e blasting was triggered by a high-precision
millisecond detonator. -e time lag levels of the detonator and
the corresponding emulsion explosive weight for this
blasting are presented in Table 2.
4. Signal Processing and Analysis
-e preliminary analysis of the collected signal data has been
conducted by applying the Fourier transform. -e
Measuring range (mm/s) 254
Radial 2.0 2.0 49.5
comparisons among the three monitoring points in terms of
peak vibration velocities (PVV) and main vibration
frequencies (MVF) along different directions are presented in
Table 3. It is suggested from Table 3 that the peak vibration
velocities and the main vibration frequencies in the vertical
direction are almost consistently greater than that in radial
and tangential directions, so the vertical vibration signals
have been selected to analyze based on the HHT method.
For MP 2, its original vibration waveform in the vertical
direction is shown in Figure 3.
Since signal collection is often disturbed by numerous
factors associated with the complex mining environment,
noise signals inevitably exist in the original signals. However,
the noise signals can pollute the original vibration signals,
reducing greatly the accuracy of the signal analysis.
-erefore, denoising before the signal analysis is very
4.1. EMD-Based Wavelet 3reshold Denoising. -e
EMDbased wavelet threshold denoising technique has been
widely used in the signal denoising area, thanks to the
advantages it possesses [
]. -is technique is characterized
by the multiresolution analysis, good time-frequency
localization, and flexible threshold selection. It can also
detect the transient state of the normal signals. Considering
that the collected vibration signals are composed of
lowfrequency blasting vibration signals and high-frequency
noise signals, and that the EMD method is capable of
decomposing the blasting vibration wave into a series of IMF
components that are ranked in descending order of
frequency, in this paper, denoising has been conducted for the
high-frequency IMF components using this technique.
-e treatment of the vertical vibration signals at MP 2 by
using the EMD method produces 11 IMF components. -e
waveforms of these IMF components are presented in
Figure 4. It can be seen that the included frequencies are
varied for different IMF components. From IMF1 to IMF10,
the frequency and the amplitude decrease, while the time
period increases. For IMF11, because no complete period
is observed over the entire time-domain and the
amplitude is relatively small, this component is the residual
component representing the average trend of the original
signals. It can also be indicated that the EMD method can
analyze directly the signals taking considerably into
account the signal characteristics, while without introducing
any limitations. -is method decomposes adaptively the
signals into IMF components of finite number. And loss
or emitting of IMF components is not omission.
Consequently, the advantages of the EMD method, that is,
adaptivity, completeness, and strong reconfigurability, are
Among all the IMF components, the frequencies of
IMF1, IMF2, and IMF3 are distinctly greater, indicating that
high-frequency noise signals are included in them.
Meanwhile, the amplitudes of these three IMFs are relatively
greater than those of other IMF components. -is means
that they are the dominant components that take up most of
the total energy in the original signals. If wavelet-forced
denoising is applied to IMF1, IMF2, and IMF3, then the
valuable information included in the original signals is
possibly removed which may lead to distortion of signals. On
the contrary, the valuable information can be effectively
extracted if the EMD-based wavelet threshold denoising
technique is used. -e detailed procedure of denoising using
this technique is presented below.
Firstly, obtain the removed noise thresholds for IMF1,
IMF2, and IMF3 through the wavelet function. Secondly,
using the db4 wavelet basis function, decomposition of
5 levels is applied to the three IMFs to isolate the
highfrequency coefficients. -irdly, quantitative processing of
the high-frequency coefficients is performed using the
removed-noise thresholds. Fourthly, reconstruct the signal to
complete denoising of the IMF components. Finally, the IMF1,
IMF2, and IMF3 components after denoising are combined
with the remaining 8 IMF components to derive the signals
without noise. -e signals without noise and the removed
noise signals are shown in Figure 5. It can be seen that the
vibration curve of the signals after denoising is smoother, and
the trend of the vibration curve is clearer compared to that of
the original signals.
4.2. Analysis of 3ree-Dimensional Hilbert Spectrum.
Reapply the EMD method to the signals after denoising to
obtain new IMF components. -ese components are then
subjected to the Hilbert transform, leading to the derivation
of three-dimensional Hilbert spectrum, marginal spectrum,
and instantaneous energy spectrum for the signals after
Figure 6 shows the derived three-dimensional Hilbert
spectrum, which can reflect visually the instantaneous
characteristics of the vibration signals and reveal clearly the
distribution of signal energy on the frequency-time plane
]. In this figure, each of the bars of different colors
represents the normalized instantaneous energy at some
specific frequency and time. It is recognized that the bars
are mainly distributed within the range defined by the time
of 0.2?0.4 s and frequency of 0?200 Hz, while the energy
corresponding to frequency greater than 200 Hz can be
neglected. -is means that most of the frequencies of the
blasting vibration signals are less than 200 Hz. -e
published studies of blasting vibration signals are mainly
performed through either Fourier transform or wavelet
transform, with mere consideration of the influence of
frequency or amplitude while without analyzing the combining
effect of frequency, energy, and vibration duration [
However, this defect can be compensated by the introduction
of three-dimensional Hilbert spectrum.
4.3. Analysis of Marginal Spectrum. -e marginal spectrum
is the time-domain integral of the Hilbert spectrum and thus
represents the addition of the amplitude for each of the
frequencies over the time domain [
]. -erefore, marginal
spectrum can reflect the condition of energy concentration
for the frequencies. -e marginal spectrum of the signals is
shown in Figure 7. From this figure, it can be seen that the
energy is mainly located in the low-frequency band where
the frequency is less than 200 Hz. In particular, within the
band of 0?10 Hz, the accumulated amplitude is relatively
greater with a maximum of 1043 mm/s when compared to
other frequency bands. -e concentration of most of the
energy in this frequency band indicates that the frequency
tends to decay to the low-frequency band (less than 10 Hz)
during the blasting process. After reaching 10 Hz, the
amplitudes for the frequencies drop dramatically and then fluctuate
around 100 mm/s. When the frequency becomes greater than
200 Hz, the amplitude begins to decay to zero.
For the convenience of quantitative description of the
energy included in different frequency bands, 6 frequency
bands, that is, 0?50, 50?100, 100?200, 200?300, 300?400,
and >400 Hz, are selected. According to (8), the integrals of
frequency over these frequency bands are performed to
calculate the ratios of energy taken up by these frequency
bands. To ensure the accuracy of the calculated results, the
data for the three MPs are analyzed parallelly. -e ratios of
energy taken up by these frequency bands are listed in
Table 4. It is indicated from Table 4 that the energy taken up
by the frequency band of 0?50 Hz is the maximum, being
more than 50% of the total energy. -is also means that the
frequency band of 0?50 Hz is the dominant frequency band.
-e ratio of energy taken up by the <200 Hz frequency band
reaches 93.1%, which further indicates that the frequency of
the blasting vibration wave is almost totally within the range
of 0?200 Hz.
4.4. Analysis of Instantaneous Energy Spectrum. -e
instantaneous energy spectrum can reveal the accumulation
of blasting vibration energy over the time domain and its
variational characteristics. Figure 8 shows the waveform
and the instantaneous energy spectrum of the signals. It can
be seen that the distribution of instantaneous energy agrees
well with the vibration curve. And the peaks of the
instantaneous energy are reached when the mutations of
vibration waveform take place. -is further validates the
ability of the HHT method in recognizing signals and its
better resolution. For the instantaneous energy spectrum in
Figure 8, it is indicated that the energy begins to appear at
0.22 s and approximately disappears at 0.45 s, showing that
the blasting vibration at this MP keeps being observable
during this duration. Also, 7 peaks of instantaneous energy
are clearly observed during this duration. -ese peaks,
however, represent the release of energy brought by
emulsion explosive explosion. -erefore, the peaks in the
instantaneous energy spectrum can be used to determine the
initiation instant of time of the detonator and to check if
blasting initiates at the accurate instant of time for each of
the time-lag levels.
-e instant of time corresponding to these 7 peaks are
0.240, 0.266, 0.295, 0.326, 0.353, 0.426, and 0.450 s, which
represent, respectively, the initiation instant of time of
time-lag level 1, 2, 3, 4, 5, 6, 7, and 8. Note that the third
peak is the maximum, indicating that the explosive
quantity for the time-lag level 3 is relatively large. Similarly,
the magnitude of the sixth and the seventh peaks shows that
their explosive quantities are relatively small. -e
comparison between the theoretical and the measured time lags
for these time lag levels is presented in Table 5, which shows
that the measured time lags are all within the theoretical
ranges of time lag. If an assumption is made that the
timelag level 1 detonator explodes punctually at an instant of
time 0, then the real initiation instant of time for these
detonators of different time-lag levels can be determined
according to the measured time lags. It can be indicated
that the time-lag level 8 detonator explodes with 15 ms
earlier compared to the theoretical initiation instant of
time. Despite this, the overall blasting effect is
Based on the blasting (4 times) vibration data collected from
the S5#S stope, the middle section of SH-455m, a south
China lead-zinc mine, the HHT method has been used to
analyze the blasting vibration waves in terms of
timefrequency and energy characteristics. -e following
conclusions can be drawn:
(1) -e marginal spectrum shows that the accumulative
amplitude is relatively great in the frequency domain
of less than 10 Hz. In this domain, the maximum
amplitude is 1043 mm/s. -e fact that most of the
signal energy is concentrated in this frequency
domain indicates a direction to which the frequency
tends to develop when explosion initiates.
(2) Most of the blasting vibration frequencies are
concentrated within the range of 0?200 Hz. -is range
takes up over 90% of the total energy. Additionally,
in this range, half of the total energy is taken up by
the 0?50 Hz frequency band, demonstrating that the
0?50 Hz frequency band is the dominant frequency
(3) -e calculated initiation instant of time of the
detonators by recognition of the instantaneous energy
spectrum agrees well with the measured results,
demonstrating the feasibility of using this method in
recognizing delay blasting. Also, good resolution and
excellent recognition capability are validated for the
HHT method in signal processing.
Conflicts of Interest
-e authors declare that there are no conflicts of interest
regarding the publication of this paper.
-is research work was funded by Open Research Fund
Program of Hunan Province Key Laboratory of Safe Mining
Techniques of Coal Mines (Hunan University of Science and
Technology, Grant no. 201505), National Natural Science
Foundation of China (Grant nos. 51004007 and 51774107),
the Open Program of State Key Laboratory of Explosion Science
and Technology (Beijing Institute of Technology, KFJJ17-12M),
the Fundamental Research Funds for the Hefei Key Project
Construction Administration (2013CGAZ0771), and the
Fundamental Research Funds of the Housing and
Construction Department of Anhui Province (2013YF-27).
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