J. Cent. South Univ. (2012) 19: 2674-2680 

DOI: 10.1007/s11771-012-1326-5

Influence of explosion parameters on wavelet packet frequency band energy distribution of blast vibration

ZHONG Guo-sheng(中国生)^1,2,3, AO Li-ping(敖丽萍)^1,2, ZHAO Kui(赵奎)²

1. Department of Architecture and Civil Engineering, Huizhou University, Huizhou 516007, China

2. School of Resources and Environmental Engineering, Jiangxi University of Science and Technology, Ganzhou 341000, China;

3. School of Civil and Transportation, South China University of Technology, Guangzhou 510641, China

? Central South University Press and Springer-Verlag Berlin Heidelberg 2012

Abstract: Blast vibration analysis is one of the important foundations for studying the control technology of blast vibration damage. According to blast vibration live data that have been collected and the characteristics of short-time non-stationary random signals, the wavelet packet energy spectrum analysis for blast vibration signal has made by wavelet packet analysis technology and the signals were measured under different explosion parameters (the maximal section dose, the distance of blast source to measuring point and the section number of millisecond detonator). The results show that more than 95% frequency band energy of the signals s1-s8 concentrates at 0-200 Hz and the main vibration frequency bands of the signals s1-s8 are 70.313-125, 46.875-93.75, 15.625-93.75, 0-62.5, 42.969-125, 15.625-82.031, 7.813-62.5 and 0-62.5 Hz. Energy distributions for different frequency bands of blast vibration signal are obtained and the characteristics of energy distributions for blast vibration signal measured under different explosion parameters are analyzed. From blast vibration signal energy, the decreasing law of blast seismic waves measured under different explosion parameters was studied and the wavelet packet analysis is an effective means for studying seismic effect induced by blast.

Key words: blast vibration; wavelet packet analysis; explosion parameter; energy distribution

1 Introduction

The analysis of blast vibration is the base and premise technology for the study of blast vibration harm control. For a long time, under the limit of the development of the theory, the traditional analysis of blast vibration performance is based on the Fourier transformation, because blast vibration is a short and unstable random process. The blast vibration signal is characterized by the short duration and quick vibration, and it belongs to the typical unstable signal. The Fourier transformation based on the stable and random process cannot reflect the essential characteristics of blast vibration [1-5]. Recently, with the development and progress of science and technology, especially the emergence of new mathematical tools, the signal time-frequency analytic method has widely applied in the engineering. More and more research results have already obtained by using the wavelet transformation to process the unstable random signal. However, it is still in the exploring stage using the wavelet transformation for processing blast vibration signal, and many researchers make some beneficial attempts and exploration [6-7]. In recent years, LING et al [8-9] studied the influence of maximum decking charge on intensity of blast vibration, and explored the influence of distance from blasting center on frequency band energy distribution of blast vibration signals with wavelet packet technology. So far, little study was conducted on the energy distribution characteristic of the blast vibration signal under different blast parameters (the maximal section dose, the distance of blast source to measuring point and the section number of millisecond detonator).

According to the blast vibration monitor data, there are a lot of influencing factors of the blast seismic effects, such as the total dose of the blast, the maximal section dose, the distance of blast source to measuring point, the section number and delay-time interval of millisecond detonator, and the location condition of the blast, but under certain location condition of blast, the explosion parameters like the maximal section dose, the distance of blast source to measuring point, and the section number of millisecond detonator are the main influencing factors of the blast seismic effect [10-11]. Based on the measured data of the blast engineering, the wavelet packet energy spectrum was analyzed, the energy distribution characteristic of the blast vibration signal under different explosion parameters (the maximal section dose, the distance of blast source to measuring point and the section number of millisecond detonator) was studied, and the attenuation law of blast seismic waves under different blast parameters was explored from the perspective of blast vibration signal energy.

2 Wavelet packet analysis of blast vibration signal

2.1 Characteristics of wavelet packet

In wavelet analysis, the signal was decomposed into two parts, low and high frequencies. In the decomposition, the lost information in the low frequency part was acquired by the high frequency part. In the next layer of decomposition, the decomposed low-frequency turned into low and high frequencies. The lost information of the low-frequency was acquired by the high-frequency and so on. Then, a deeper level of decomposition was completed. According to the wavelet decomposition structure, the frequency resolution of the wavelet transformation decreased with increasing frequency, while the wavelet packet decomposition did not. It was decomposed into not only the low frequency part but also the high frequency part. In the wavelet packet decomposition, the appropriate matching of the frequency band and signal spectrum was selected according to the signal characteristics and analysis requirements, and it was a more precise decomposition way than the wavelet decomposition. The wavelet packet decomposition was based on a variety of rigorous mathematical theory and numerical method, and a lot of works were discussed in detail [12-13].

When using the wavelet packet analysis in analyzing the blast vibration signals, the number of decomposition layers depended on the specific signal and the working frequency of blasting vibration recorder. The IDTS3850 blast vibration recorder was used in the blast vibration test, and its minimum working frequency was 1 Hz, developed by the Chengdu Zhongke Dynamic Instrument Co. Ltd (China). The main frequency of blast vibration signal was less than 200 Hz. According to the sampling theorem [14], the sampling frequency was set at 2 000 Hz, so the Nyquist frequency was 1 000 Hz. Based on the wavelet packet decomposition, the analysis of the signal went to the 8th floor decomposition, and the corresponding lowest frequency band was 0-3.906 25 Hz. After wavelet packet decomposition, the   frequency band range of the blast vibration signal is seen in Table 1.

2.2  Theory of wavelet packet analysis for blast vibration signal

After the wavelet packet decomposition of the blast vibration signal s(t), 2ⁱ sub-bands are got in the i-th layer, so s(t) is expressed as

                    (1)

where is the reconstruction signal after the wavelet packet decomposition. If the lowest frequency of s(t) is 0 and the highest frequency is ω_m, the width of each frequency band in the i-th decomposition level is ω_m/2ⁱ.

According to signal spectral analysis in the Parseval theory [15], the energy spectrum of the blast vibration signal s(t) is got from Eq. (1) by using the wavelet packet analysis:

              (2)

where (; ;  m is the discrete sampling point of blast vibration signal) is the amplitude of the discrete points of the reconstruction signal. is the frequency band energy in the i-th layer and the j-th node of the blast vibration signal after the wavelet packet decomposition.

Table 1 Frequency band range of blast vibration signal after 8th floor wavelet packet decomposition

From Eq. (2), the total energy of blast vibration signal s(t) is

                              (3)

After the blast vibration signal s(t) is decomposed into the i-th layer by wavelet packet technology, the ratio of each frequency band energy to the total energy is

                               (4)

3 Influence of explosion parameters on energy distribution of blast vibration signals

3.1 Blast vibration measurement

In order to study the influence of different explosion parameters (the maximal section dose, the distance of blast source to measuring point, and the section number of millisecond detonator) on the energy distribution of the blast vibration signals, the signals were acquired in the same testing site. Therefore, the testing site was selected in 1 082 m excavating roadway of Changba Lead-Zinc Mining Co. Ltd in Gansu Province, China. The explosion source of excavating roadway was in short-delay blasting mode. The vertical vibration velocity of particle was selected as the monitoring physical quantity. The sensor of the testing site was arranged in bedrock.

In order to study the influence of the distance between the explosion centers on the energy distribution of the blast vibration signals, the influence of the largest section dose and the section number of the millisecond detonators on the blast seismic effect was excluded. Therefore, the blast vibration signals from different distances of blast source to measuring point were tested at the same explosion.

Similarly, when studying the maximal section dose and the section number of millisecond detonator on the energy distribution of the blast vibration signals, the influence of the distance between the explosion centers on the blast seismic effect was excluded.

Based on the above research target, explosion parameters and monitoring parameters of the testing site are listed in Table 2, and the velocity-time curves of blast vibration are shown in Fig. 1.

3.2 Wavelet packet energy spectrum analysis for blast vibration signal

To analyze the blast vibration signal by the wavelet packet technology, the choice of wavelet basis is a very important issue, because using different wavelet bases in analyzing the same signal produces different results [16]. Research shows that, db7 and sym8 wavelets with good compact support, smoothness and myopia symmetry, are the best wavelet bases in analyzing the non-stationary blast vibration signal.

There is a wavelet toolbox in Matlab 7.0, the blast vibration signals are analyzed using sym8 in the wavelet packet, and the signals are decomposed into the 8th layer. According to the Matlab language compiling computing program for Eqs. (1)-(4), the wavelet packet energy spectrum distribution of the signals is obtained, as shown in Fig. 2 (Because the energy of the signal is mainly in 0-200 Hz, the horizontal axis of the graph only gets to 200 Hz). For comparison, different frequency band energy distributions of eight signals are listed in Table 3.

Table 2 Explosion parameters and monitoring parameters of testing site

Fig. 1 Velocity-time curves of blast vibration signals

Fig. 2 Wavelet packet energy spectrum distributions for blast vibration signals

Table 3 Band energy distributions (%) for blast vibration signals at different wavelet packet frequencies

3.3  Influence of explosion parameters on energy distribution of blast vibration signal

1) From Fig. 2 and Table 3, the energy ratios of eight signals at 0-199.218 75 Hz accounting for total energy are 95.009 8%, 96.66%, 95.941%, 95.544 5%, 95.17%, 95.871 7%, 96.717 5% and 95.590 6%. The result shows that the energy of blast vibration signal is widely distributed in the frequency domain, but most energy concentrates at 0-200 Hz.

2) From Tables 3 and 4, the dominant energy of blasting vibration signal is mainly distributed in the main vibration frequency band. From Fig. 2, the main vibration frequency band is divided into several sub vibration frequency bands. Therefore, the influence of the different frequency components of original signal on the blast vibration is obtained by wavelet packet technology.

Table 4 Energy ratio of main vibration frequency band for blast vibration signal

3) From Table 3, Table 4 and the wavelet packet energy spectrum distribution of the signals s1-s4 in Fig. 2, when the distance of blast source to measuring point is smaller, the signal energy is mainly distributed in the middle and high frequency bands, and the frequency band energy distribution is wider. With the increase of the distance of blast source to measuring point, the signal energy distribution tends to the low frequency band. Therefore, destruction capacity of blast seismic wave in the process of transmission, although its vibration intensity declines, could increase. Because the natural frequency of surrounding building is commonly low, it always happens that the structure near explosion source is not destroyed and the distant structure is ruined.

4) From Table 3, Table 4 and the wavelet packet energy spectrum distribution of the signals s5-s8 in Fig. 2, when the maximal section dose is less, the signal energy is mainly distributed in the middle and high frequency bands, and the frequency band energy distribution is wider. With the increase of the maximal section dose, the signal energy distribution tends to the low frequency band. Therefore, it is obviously unfavorable to the building’s safety in the blast engineering because the natural frequency of surrounding building is commonly low.

5) According to Table 3, Table 4 and the wavelet packet energy spectrum distribution of the signals s5-s8 in Fig. 2, when the section number of millisecond detonator is smaller, the signal energy is mainly distributed in the middle and low frequency bands and the band energy distribution is more concentrated. With the increase of the section number of millisecond detonator, the signal energy distribution tends to the high frequency band. Research shows that the increase of the section number of millisecond detonator can really reduce blast vibration. Therefore, the millisecond blast should be implemented in the blast engineering.

4 Conclusions

1) The blast vibration signal can be decomposed into blast vibration components of different frequency bands by the wavelet packet technology. By obtaining the energy distribution of blast vibration components at different frequency bands, the influence of different frequency components of original signal on the blast vibration can be analyzed. Therefore, the wavelet packet analysis has more obvious advantage than the spectrum analysis based on the Fourier transform.

2) Different frequency band energy distributions of the blast vibration signal can be acquired by the wavelet packet analysis. The energy distribution characteristics of the blast vibration signal can be analyzed under different blast parameters (the maximal section dose, the distance of blast source to measuring point and the section number of millisecond detonator). The reducing laws of different blast parameters of the blast seismic wave can be explored from the view of signal energy, so it can provide a new practical analysis technology for the further study of blast seismic effect.

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(Edited by YANG Bing)

Foundation item: Project(51064009) supported by the National Natural Science Foundation of China; Project(201104356) supported by the China Postdoctoral Science Foundation; Project(20114BAB206030) supported by the Natural Science Foundation of Jiangxi Province, China

Received date: 2011-07-18; Accepted date: 2012-02-20

Corresponding author: ZHONG Guo-sheng, PhD, Professor; Tel: ＋86-20-87114038; E-mail: zgs1001@163.com