Sarah Bee

S. C. Bee, E. Papatheou, M Haywood-Alexander et al.

There have been recent efforts to move to population-based structural health monitoring (PBSHM) systems. One area of PBSHM which has been recognised for potential development is the use of multi-task learning (MTL); algorithms which differ from traditional independent learning algorithms. Presented here is the use of the MTL, ''Joint Feature Selection with LASSO'', to provide automatic feature selection for a structural dataset. The classification task is to differentiate between the port and starboard side of a tailplane, for samples from two aircraft of the same model. The independent learner produced perfect F1 scores but had poor engineering insight; whereas the MTL results were interpretable, highlighting structural differences as opposed to differences in experimental set-up.

S C Bee, N Dervilis, K Worden et al.

Equation discovery provides a grey-box approach to system identification by uncovering governing dynamics directly from observed data. However, a persistent challenge lies in ensuring that identified models generalise across operating conditions rather than over-fitting to specific datasets. This work investigates this issue by applying a Bayesian relevance vector machine (RVM) within a multi-task learning (MTL) framework for simultaneous parameter identification across multiple datasets. In this formulation, responses from the same structure under different excitation levels are treated as related tasks that share model parameters but retain task-specific noise characteristics. A simulated single degree-of-freedom oscillator with linear and cubic stiffness provided the case study, with datasets generated under three excitation regimes. Standard single-task RVM models were able to reproduce system responses but often failed to recover the true governing terms when excitations insufficiently stimulated non-linear dynamics. By contrast, the MTL-RVM combined information across tasks, improving parameter recovery for weakly and moderately excited datasets, while maintaining strong performance under high excitation. These findings demonstrate that multi-task Bayesian inference can mitigate over-fitting and promote generalisation in equation discovery. The approach is particularly relevant to structural health monitoring, where varying load conditions reveal complementary aspects of system physics.

Sarah Bee, Lawrence Bull, Nikolaos Dervilis et al.

A Nonlinear Auto-Regressive with eXogenous inputs (NARX) model can be used to describe time-varying processes; where the output depends on both previous outputs and current/previous external input variables. One limitation of NARX models is their propensity to overfit and result in poor generalisation for future predictions. The proposed method to help to overcome the issue of overfitting is a NARX model which predicts outputs at both the current time and several lead times into the future. This is a form of multi-task learner (MTL); whereby the lead time outputs will regularise the current time output. This work shows that for high noise level, MTL can be used to regularise NARX with a lower Normalised Mean Square Error (NMSE) compared to the NMSE of the independent learner counterpart.

Sarah Bee, Lawrence Bull, Nikolas Dervilis et al.

Multi-task neural networks learn tasks simultaneously to improve individual task performance. There are three mechanisms of multi-task learning (MTL) which are explored here for the context of structural health monitoring (SHM): (i) the natural occurrence of multiple tasks; (ii) using outputs as inputs (both linked to the recent research in population-based SHM (PBSHM)); and, (iii) additional loss functions to provide different insights. Each of these problem settings for MTL is detailed and an example is given.