Active learning for regression in engineering populations: A risk-informed approach

TL;DR

Data scarcity in engineering regression tasks hinders traditional supervised learning; the paper advances a risk-informed online active-learning framework built on hierarchical Bayesian modelling to enable population-level learning across similar assets. It introduces three components: (i) hierarchical regression with partial pooling, (ii) decision-theoretic action selection using expected utility $EU(a)$ and maximum expected utility $MEU$, and (iii) risk-based active learning for online inspection planning. A case study on a population of machining tools demonstrates improved predictive accuracy from partial pooling and substantial reductions in inspection costs compared with periodic inspection, while maintaining alignment with a gold-standard fully informed policy. The approach offers cost-efficient, scalable SHM and population-wide decision support for engineering applications, with potential extensions to value-of-information analyses and real-time inference.

Abstract

Regression is a fundamental prediction task common in data-centric engineering applications that involves learning mappings between continuous variables. In many engineering applications (e.g.\ structural health monitoring), feature-label pairs used to learn such mappings are of limited availability which hinders the effectiveness of traditional supervised machine learning approaches. The current paper proposes a methodology for overcoming the issue of data scarcity by combining active learning with hierarchical Bayesian modelling. Active learning is an approach for preferentially acquiring feature-label pairs in a resource-efficient manner. In particular, the current work adopts a risk-informed approach that leverages contextual information associated with regression-based engineering decision-making tasks (e.g.\ inspection and maintenance). Hierarchical Bayesian modelling allow multiple related regression tasks to be learned over a population, capturing local and global effects. The information sharing facilitated by this modelling approach means that information acquired for one engineering system can improve predictive performance across the population. The proposed methodology is demonstrated using an experimental case study. Specifically, multiple regressions are performed over a population of machining tools, where the quantity of interest is the surface roughness of the workpieces. An inspection and maintenance decision process is defined using these regression tasks which is in turn used to construct the active-learning algorithm. The novel methodology proposed is benchmarked against an uninformed approach to label acquisition and independent modelling of the regression tasks. It is shown that the proposed approach has superior performance in terms of expected cost -- maintaining predictive performance while reducing the number of inspections required.

Figures (12)

• Figure 1: A graphical model representing the linear mixed model with partial pooling.
• Figure 2: An active learning heuristic adapted from bullProbabilisticActiveLearning2019a
• Figure 3: Schematic showing the experimental set-up used for data acquisition wickramarachchiAutomatedTestingAdvanced2019a
• Figure 4: Experimental surface roughness measurements
• Figure 5: A graphical model representing the linear mixed model with partial pooling