Interpretable Embedding of Laboratory Stick-Slip Acoustic Emission Time Series

Laboratory stick-slip experiments are a simple analogue for the earthquake cycle. The acoustic emissions (AE) of these experiments have been shown to contain hidden patterns. Machine Learning (ML) can extract these patterns and information on the fault state can be inferred (e.g. shear stress and time to failure). Two different ML approaches have been used in the past: 1) ensemble tree models, which are relatively easy to evaluate why they made a certain prediction, but only look at a snapshot in time and 2) deep neural networks using Long Short-Term Memory (LSTM), which have the ability to find patterns in the temporal changes in the signal, but act more as a black-box model, so the final predictions are hard to evaluate. Here we introduce an additional step in the workflow that can be used to allow the ensemble tree models information about the temporal changes of the input features. Furthermore, it is able to quantify and visualize whether a pattern is repetitive or not. Like earlier studies we start by calculating (statistical) features using a rolling window on the AE. The features are not directly used as the input of the model, but are placed in a larger Hankel matrix, where the consecutive time windows are the rows of the matrix. Using Principal Component Analysis (PCA) and Uniform Manifold Approximation and Projection (UMAP) we create an embedded version of this array that holds temporal information of features calculated in the previous step. Visual inspection of these embeddings shows that some features map to very distinct patterns that are repetitive over the majority of the stick-slip cycles. The advantage of this method is that an inverse mapping is easily available, allowing for an interpretable embedding of the data.