On a trust metric for stochastic multi-objective model-based damage localisation

Model-based structural health monitoring (SHM) is commonly applied to identify the position and extent of potential damage. This is achieved by updating damage parameters to match measured dynamic responses, such as modal properties. Local reductions in stiffness in the updated model can indicate the presence of damage. However, not every damage can be accurately localised, as uncertainties in both the input data and the structural model, along with ambiguities in the optimisation problem itself, may lead to inconclusive or false localisation results. This can result in an incorrect assessment of the risk of the damage or lead to incorrect maintenance decisions. In this work, inspired by the model-assisted probability of localisation, a metric is presented which quantifies the trust that can be placed in the obtained localisation results under known input uncertainties, termed trust of localisation (ToL). Identified uncertainties in the modal properties are quantified and propagated through the model-updating problem to evaluate their impact on the damage parameters. The ToL is derived by evaluating all optimal damage parameters identified and determining whether they can also be obtained in a model-to-model comparison under the prevailing uncertainties. It should be interpreted as a model-conditional trust metric, that is, robustness to uncertain input parameters under the adopted finite element model and objectives, rather than a model-independent reliability measure. Two case studies are considered: a laboratory steel cantilever beam with different mass positions and weights for verification, and an outdoor lattice tower with reversible damage mechanisms as a real-world application problem. The results indicate that the ToL generally distinguishes meaningful localisation results from those lacking informative value for most of the damage cases considered. This is reflected in the correlation between the ToL value and the localisation accuracy, highlighting the potential of the approach to act as a case-specific addition to reliability assessment in model-based SHM applications. Furthermore, the application of the ToL metric to the outdoor structure suggests its potential to improve damage localisation accuracy. While the ToL framework shows promise, further validation in challenging environments is needed, as its discriminative performance was limited in specific cases. In summary, the proposed ToL offers benefits for continuous monitoring and subsequent decision-making.