Machine Learning for Failure Analysis: A Mathematical Modelling Perspective

Abstract

Failure analysis is an interdisciplinary and exciting research area that lies at the interface between mathematics, physics, and materials science. In this context, from the mathematical perspective, failure is a gradual or sudden loss of the ability to operate. Failure analysis leads to many interesting mathematical challenges spanning from model development to mathematical foundations including simulations and machine learning approaches. From a mathematical modelling viewpoint, there exists a variety of approaches that involve predicting whether failure will occur, computing the time until failure takes place, classifying failure modes, detecting anomalous behaviour, assessing the extent of deviation or degradation from an expected normal operating condition, among others. The data era has brought about approaches that employ machine learning (ML) methods to not only detect failure but also make predictions about the reliability (i.e., the ability to function without failure) of devices. They constitute a wide spectrum of models, ranging from survival models to investigate components ageing to Bayesian networks for anomaly detection, including generative neural networks to detect for example the degradation of a material. In this chapter, we give a description and illustration of the assumptions and basic models of ML and present a range of applications.