Spectral characteristics of Acoustic Emission of rock based on Singular point of HHT Analysis

. The sandstone test of uniaxial compression acoustic emission (AE) test has been studied, the HHT analysis is applied to AE signal processing, and through the analysis of AE signal to reveal the process of rock fracture. The results show that HHT is a method that based on principal component analysis of time-frequency analysis. The method of HHT can very convenient to deal the singular signal; it can be determine the main composition of singular signal. The instantaneous frequency can be used to describe precisely the time-frequency characteristics of singular signal. The method has a very important significance to reveal the frequency characteristics of AE signal. The EMD signal is decomposed into 8 IMF components in the failure process of rock sound. The component of IMF1 ~ IMF4 is the main component, and the IMF5 ~ IMF8 for low frequency noise signal. Through the EMD of AE signal frequency, the rock fracture has been decomposition into three stages: the initial zone, wave zone, quiet zone. This shows that in the analysis of rupture must eliminate noise interference signal characteristics of AE.


Introduction
As we known, there is a process from quantitative change to qualitative change in the occurrence of any damage. Various size of energy will be produced by rock damage; also the phenomenon of AE will generated. Based on the research of the AE signal, the internal condition change and the inversion of the rock failure mechanism can be concluded [1] .
In recent years, with the development of AE technology, and its application in rock mechanics, many scholars use the AE testing technology for rock failure process carried on the thorough analysis and research, including: Mansurov and Rudajev predict rock damage types by the AE measurement [2][3] . Nomikos studied on uniaxial compression under Mourinho Dionysus marble, and found that the AE activity and the energy release were increased significantly when the crack damage maximum phase [4] . Ganne studied the peak before the brittle failure of rock by using the AE technology, 4 process of AE accumulated energy could be taken [5] . Wang have took an AE positioning research on the rotor friction united the wavelet transform and correlation analysis, and a conclusion that a higher position precision than directly related to positioning [6] . Ishida through the AE signal inversion location of rock failure [7] . Moriya have taken an study on broken evolution process in Bain salt mine in Germany, and found that the distribution of AE signal changes over principal stress rotation direction and depth [8] .
The main research is from parameter analysis, just only from qualitative to description the rock failure process. This is very limited to reflect the rock failure nature from the angle of AE.

The test system
The experimental system is composed of loading system and AE system. The loading system used the TAW-3000 microcomputer controlled electro-hydraulic servo process, the AE system used the PCI-2 AE system produced on America acoustic physical company. In order to avoid the noise of contacting, using the axial loading control and pre-loading to 1.5kN, and followed by 0.2mm/min to failure. The threshold value of AE instrument set 40dB, the waveform settings in the sampling rate is 1MSPS, the pre-trigger is 256 and the length is 2K. The sensor is the R6α resonant type high sensitivity sensor, whose operating frequency is 35~100 kHz.Using the rock cutting mechanism to get the size of 50 mm 50 mm 100 mm (length width height), and the AE sensor probe directly fixed on the specimen surface. The stress-time curve of sandstone under uniaxial compression experiment was shown in figure 1. In order to use the AE to characterize the whole rupture process of rock, according to the mechanical curve of rock, select several signal point, represented by A, B, C, D and 1-7. According to point of A, B and D, the curve can divide into the following stages [12]: (1) the nonlinear compressive stage of OA, take point 1 to make an analysis; (2) the stage of linear elastic deformation, represented as AB, take point 2 and 3 to make an analysis; (3) the stage of nonlinear deformation stage, represented as BC, it can be further divided into following stage: The stage of stable crack growth (BB 0 ), take the point 5 to analysis.
Non-elastic deformation stage (B 0 C), take the point 6 and 7 to analysis, C point is called the peak stress (σ c =34.36 MPa); (4) the strain softening stage of CD segment, C 0 is the sample completely failure point.

AE signal processing
Step 1: take the curve of AE signal under the MATLAB program.
Step 2: the original signal of AE is decomposed into a series of different characteristic time scales of intrinsic mode function (IMF) by EMD decomposition of HHT and formula (1) and (2). Step 3: to calculate the contribution rate and the coefficient of original signal of each IMF component, and determine the advantages of the weight of IMF by principal component analysis and correlation analysis.
Step 4: the advantage of the IMF component type (4) is used to calculate the Hilbert spectrum, type (5) is used to calculate the marginal spectrum, the graphics of Hilbert spectrum and marginal spectrum can be draw by these analyses.

Principal component analysis
In principal component analysis, the variance contribution rate was used to measure the information content of someone factor. The IMF component was received by EMD decomposition, different components represent different factor, and the original signal component of main ingredients of the IMF can be determine by calculation of variance contribution ratio of the component. From the Figure 2 can be seen that at the same stress level, the IMF1 ~IMF4 variance rate is relatively large by EMD decomposition, and it can reach more than 98%. The IMF1 and IMF2 variance contribution rate changed with the stress obvious, the contribution rate of IMF3 and IMF4 components is very small.

Correlation analysis
The

Discussion
The marginal spectrum is integral of the timeline of the Hilbert spectrum, and is also an overall measure of each frequency component amplitude (or energy). Its accumulated amplitude of signal in probability sense, and it reflects the signal amplitude with the frequency in the whole frequency. When certain frequency energy appeared, it means there must be a vibration wave [14] . The bigger marginal spectrum amplitude makes the bigger energy. We can explore the evolution of the AE signal frequency in the process of rock failure by peak frequency changes in each frequency band.Analysis by above knowable, the AE signal frequency of siltstone in the rupture process of 0 ~ 120 kHz, and noise frequency band is 0 ~ 20 kHz. The AE signal of rock and noise frequency has overlap part, it means that when analyzing the characteristic of the failure process of the AE signal, we should eliminate noise interference first, and make an important theoretical basis to choose the corresponding resonance frequency of the AE sensor provides.

Summary
1 The analysis of the EMD decomposition of HHT is a kind of adaptive decomposition method based on principal component analysis. The primary and secondary components can be determined by analysis the AE signal singularity in the process of loading.
2 The AE signal of siltstone can be divided into 8 IMF components by the EMD decomposition. The IMF1 ~ IMF 4 components are the main ingredient, and are the main part of the AE source. The IMF5 ~ IMF8 for low frequency noise signal, and it should be removed in the AE signal analysis.
3 The Frequency of AE rupture process can be divided into three main frequencies. The frequency band of 0 ~ 20 kHz, the second band of 20kHz ~ 60 kHz, and the third band of 60kHz ~ 120 kHz. The firstly band is overlap with noise frequency, it's greatly influenced by the noise, so the secondly and thirdly can be seen as the effective frequency.