Meta-models for transfer learning in source localisation

TL;DR

This work looks to capture the interdependencies between acoustic emission experiments (as meta-models) and then use the resulting functions to predict the model hyperparameters for previously unobserved systems.

Abstract

In practice, non-destructive testing (NDT) procedures tend to consider experiments (and their respective models) as distinct, conducted in isolation and associated with independent data. In contrast, this work looks to capture the interdependencies between acoustic emission (AE) experiments (as meta-models) and then use the resulting functions to predict the model hyperparameters for previously unobserved systems. We utilise a Bayesian multilevel approach (similar to deep Gaussian Processes) where a higher level meta-model captures the inter-task relationships. Our key contribution is how knowledge of the experimental campaign can be encoded between tasks as well as within tasks. We present an example of AE time-of-arrival mapping for source localisation, to illustrate how multilevel models naturally lend themselves to representing aggregate systems in engineering. We constrain the meta-model based on domain knowledge, then use the inter-task functions for transfer learning, predicting hyperparameters for models of previously unobserved experiments (for a specific design).

Figures (10)

• Figure 1: A visual example of multilevel models for multitask learning: predictive tasks $f_k$ are parametrised by $\theta_k = \{\theta^\prime_k, \theta^{\prime\prime}_k\}$ or $\theta_k =\{\theta^\prime_k, \theta^{\prime\prime\prime}_k\}$; in turn, $\theta_k$ is generated by shared intertask functions $\{g^\prime, g^{\prime\prime}\}$ or $\{g^\prime, g^{\prime\prime\prime}\}$. The notation $g \rightarrow \theta$ shows a function $g$ that predicts a parameter $\theta$.
• Figure 2: Image of plate used in the AE experiments.
• Figure 3: Left: all source locations (blue $\bullet$) and sensor locations (black $\bullet$). Right: heatmap of the $\Delta$ToA (response $y_i$) given locations (inputs $\mathbf{x}_i = \{x^{(1)}_i, x^{(2)}_i\}$) for experiment $k=15$, sensor pair (3, 5).
• Figure 4: Heatmaps of the measured $\Delta$ToA ($y_i$) with respect to locations ($\mathbf{x}_i$) for all sensor combinations. Large black markers plot sensor pairs, while small black markers plot training observations. The remaining data are used to test out-of-sample performance. The number in the bottom right is the experiment index $k \in \{1,2, ...28\}$.
• Figure 5: The inferred sensor pair (3,5) for experiment $k=15$ (left) and a length-wise slice to visualise the heteroscedastic noise (right).