On the use of Statistical Learning Theory for model selection in Structural Health Monitoring

TL;DR

This paper applies Statistical Learning Theory to improve model selection in Structural Health Monitoring, demonstrating that domain knowledge integration enhances model generalisation and reduces risk.

Contribution

It introduces a rigorous SLT-based approach for model selection in SHM, emphasizing the benefits of incorporating domain knowledge into the regression process.

Findings

SLT bounds can effectively guide model selection in SHM.

Incorporating domain knowledge reduces the guaranteed risk.

Kernel smoothing models can be optimized using SLT principles.

Abstract

Whenever data-based systems are employed in engineering applications, defining an optimal statistical representation is subject to the problem of model selection. This paper focusses on how well models can generalise in Structural Health Monitoring (SHM). Although statistical model validation in this field is often performed heuristically, it is possible to estimate generalisation more rigorously using the bounds provided by Statistical Learning Theory (SLT). Therefore, this paper explores the selection process of a kernel smoother for modelling the impulse response of a linear oscillator from the perspective of SLT. It is demonstrated that incorporating domain knowledge into the regression problem yields a lower guaranteed risk, thereby enhancing generalisation.