Deciphering Acoustic Emission with Machine Learning

TL;DR

A machine learning based method is proposed with which one can infer microscopic details of dislocation avalanches in micropillar compression tests from merely acoustic emission data and this approach is suitable for the prediction of the force-time response.

Abstract

Acoustic emission signals have been shown to accompany avalanche-like events in materials, such as dislocation avalanches in crystalline solids, collapse of voids in porous matter or domain wall movement in ferroics. The data provided by acoustic emission measurements is tremendously rich, but it is rather challenging to precisely connect it to the characteristics of the triggering avalanche. In our work we propose a machine learning based method with which one can infer microscopic details of dislocation avalanches in micropillar compression tests from merely acoustic emission data. As it is demonstrated in the paper, this approach is suitable for the prediction of the force-time response as it can provide outstanding prediction for the temporal location of avalanches and can also predict the magnitude of individual deformation events. Various descriptors (including frequency dependent and independent ones) are utilised in our machine learning approach and their importance in the prediction is analysed. The transferability of the method to other specimen sizes is also demonstrated and the possible application in more generic settings is discussed.

Figures (13)

• Figure 1: The workflow of the ML approach. Micropillar compression tests provide force and AE data which are, then, divided into equisized time windows. From the windows, frequency independent and dependent descriptors and force increments (ground truth) are extracted. These are utilised for the training of random forest ML models.
• Figure 2: Acoustic signals from compression tests of micropillars with a diameter of $\pmb{8\ \upmu}$m. (a): A representative AE signal that constitutes of a few characteristic frequencies. The noise have a mean frequency of $\sim$500 kHz. When an event occurs a short ($\sim$20 $\upmu$s long) signal with a frequency of $\sim$250 kHz emerges from the noise which is followed by a longer periodic pattern of frequency $\sim$100 kHz. (b): The absolute value of the Fourier transform $C_\mathcal{F}$ of the frequency $f$ averaged on several time windows centred on signals. The colour-coding is consistent with the legend of panel a) and it highlights the peaks corresponding to the characteristic frequencies. (c): Typical signals shifted with $t_0$ such that their starting points coincide at $t-t_0=0$. These curves demonstrate that the signals and the involved frequencies are rather similar despite their different amplitude/energy.
• Figure 3: Double-scale prediction of the force-time response of micropillars. (a): Predictions of fine-scale response of a micropillar of diameter of $8~\upmu\mathrm{m}$ using frequency independent features. The data points correspond to force increments in $\Delta t = 300$ ms wide time windows. $\Delta F_\mathrm{ground}$ and $\Delta F_\mathrm{pred}$ are the ground truth and the prediction of the force increment, respectively. (b): Prediction (using frequency independent features) of the coarse-scale behaviour of the same micropillar with a time-resolution of 50 s. (c): Comparison of the final prediction (obtained by combining the fine- and coarse-scale prediction) with the ground truth for an 8-micron specimen.
• Figure 4: Feature importance for $\pmb{d=8\upmu}$m samples. (a): The Pearson correlation of the frequency independent features (of form $\sqrt[k]{\left\langle|V|^k\right\rangle}$ where $V$ is the raw (voltage) signal from the piezo-sensors with the target variable (for increment) for individual 8-micron experiments (small markers) and the mean for the four experiments (large markers). $k\xrightarrow {}\infty$ corresponds to the maximum. (b): The $R^2$ score for prediction based on single features for with the same meaning of small and large markers as in (a). The features best-correlated with the target variable are typically the high-order moments, however, the best scores can be achieved using lower moments. (c): The $R^2$ score for prediction based on subsets of $n$ features. All combinations are shown (light point clouds) and the best scores are highlighted with the darker markers. The best score already saturates at around $n=3$. The subset of features corresponding to the best score for each $n$ is presented in (d). Clearly, the lowest moment is of the utmost importance, however, the subset performing the best usually combines lower and higher moments as well. (e): The Pearson correlation $C_\mathrm{Pearson}$ of the frequency dependent features with the target variable (force increment) averaged for all 8-micron experiments. Different colours correspond to features based on different order moments (mean, standard deviation, the fourth root of the kurtosis and maximum) of slices of the spectrograms of the AE data (see colourbar). (f): The mean $R^2$ score for predictions based on single features. The correlations and scores clearly show that information of lower frequencies (100-300 kHz, especially around 100 kHz) that are characteristic to acoustic events is the most important. (g): The $R^2$ score for prediction based on subsets of $n$ features. The features used are the moments of order $k=1,2,4,\infty$ at frequencies 100 kHz, 250 kHz and 500 kHz [marked with dashed lines in panel (e) and (f)]. All combinations are shown (violin plots) and the best scores are highlighted with the markers. The best score already saturates at around $n=4$. (h): The subset of features corresponding to the best score for each $n$. The optimal model compositions suggest that the combined use of 100 kHz and 250 kHz features is very beneficial.
• Figure 5: Transferability of the ML method across different sample sizes. The $R^2$ score for different combinations of 4-experiment of training sets and 1-experiment test sets. The combinations with the test set of the same micropillar diameter are arranged in the same panel the main colour of the panel indicating the diameter corresponding to the test set. The composition of the training sets are showed by the miniature pie charts. The striped slices denote a training experiment that is either of one diameter or of another. In each scenario two point clouds and violin plots indicate the performance for the frequency independent and frequency dependent approaches. The mean $R^2$ scores are indicated by the orange and purple markers in the two cases. Generally, it can be observed that, even though, the prediction score get better as the similarity of the training and the testing data increases, the model performs reasonably well even if it was not shown experiments of the same pillar size as in the test experiment. This observation holds regardless of the inclusion/exclusion of frequency information.