Towards an active-learning approach to resource allocation for population-based damage prognosis

Abstract

Damage prognosis is, arguably, one of the most difficult tasks of structural health monitoring (SHM). To address common problems of damage prognosis, a population-based SHM (PBSHM) approach is adopted in the current work. In this approach the prognosis problem is considered as an information-sharing problem where data from past structures are exploited to make more accurate inferences regarding currently-degrading structures. For a given population, there may exist restrictions on the resources available to conduct monitoring; thus, the current work studies the problem of allocating such resources within a population of degrading structures with a view to maximising the damage-prognosis accuracy. The challenges of the current framework are mainly associated with the inference of outliers on the level of damage evolution, given partial data from the damage-evolution phenomenon. The current approach considers an initial population of structures for which damage evolution is extensively observed. Subsequently, a second population of structures with evolving damage is considered for which two monitoring systems are available, a low-availability and high-fidelity (low-uncertainty) one, and a widely-available and low-fidelity (high-uncertainty) one. The task of the current work is to follow an active-learning approach to identify the structures to which the high-fidelity system should be assigned in order to enhance the predictive capabilities of the machine-learning model throughout the population.

Figures (6)

• Figure 1: The high-fidelity data of the initial population used to build the first instance of the prognosis model (left), and the corresponding projections on the principal component axis (coloured stars on the right-hand side) and the Gaussian distribution prior defined based on these principal components.
• Figure 2: The high-fidelity crack-growth data of the first testing population (left) and the corresponding low-fidelity crack-growth curves (right).
• Figure 3: Histograms of the error metrics of equation (\ref{['eq:error_metric']}) for different number of available samples $M$. The colours correspond to the same-colour curves of Figure \ref{['fig:first_testing_pop']} and the vertical lines correspond to the mean values of the errors.
• Figure 4: The high-fidelity crack-growth data of the second testing population (left) and the corresponding low-fidelity crack-growth curves (right).
• Figure 5: Probability density functions of the scaled errors of the prediction at the highest number of cycles. The black curve corresponds to the errors of the non-updated model. The coloured curves correspond to models updated using the corresponding curve from Figure \ref{['fig:first_testing_pop']}, the dashed-dotted curve corresponds to the expected error using random structure selection for the updating and the errors are provided for an increasing number of observations.