Empirical Mode Decomposition Analysis of Continuous Acoustic Emission (AE) Data from Laboratory Rock Deformation Experiments

Abstract:

Continuous acoustic emission (AE) data recorded during rock deformation tests facilitates the monitoring of fracture initiation and propagation due to applied stress changes. Changes in the frequency and energy content of AE waveforms have been previously observed associated with microcrack coalescence and the induction or mobilisation of large fractures which are naturally associated with larger amplitude AE events and lower frequency components. The shift from high to low dominant frequency components during the late stages of the deformation experiment, as the rate of AE events increases and the sample approaches failure, indicates a transition from the micro-cracking to macro-cracking regime, where large cracks generated result in material failure.

To analyse and characterise these changes, a detailed time-frequency analysis of the continuous waveform data is required. Fourier-based techniques (e.g. STFT) and the Wavelet Transform have several drawbacks such as fixed window size (STFT), poor time-frequency resolution and some general assumption of linearity and/or stationarity. These techniques are not suitable for the detailed analysis of AE data which are generally nonstationary and nonlinear.

The Empirical Mode Decomposition (EMD) method is suitable for non-stationary and non-linear time-series analysis, with the ability to identify intrinsic features in the data. EMD adaptively decomposes a time-varying signal into a finite set of functions called intrinsic mode functions (IMFs), where each IMF represents an oscillatory term in the original signal in a different frequency band. The instantaneous frequency and amplitude of each IMF is derived by applying the Hilbert Transform (HT) to the IMFs which provides a high resolution time-frequency distribution of the data.

This paper proposes the use of the combined EMD and HT method to analyse the continuous AE data recorded during a laboratory triaxial deformation experiment on a cylindrical sample of Westerly Granite. The objectives of this study are to identify and extract the observed frequency changes which can be used to characterise the fracture process, particularly around failure where the fast occurrence of AE events does not allow the identification of individual AE events and phase arrivals.