A Gated Multi-Objective Learning-to-Optimize Framework for Fault-Tolerant Sensor Placement in Bridge Structural Health Monitoring

Structural Health Monitoring (SHM) relies on sensor placement to collect structurally relevant data, which are then interpreted according to the monitoring objective. Optimal Sensor Placement is therefore an essential step for collecting useful information for the monitoring task. However, conventional SHM design often separates the OSP and interpretation steps. Additionally, OSP approaches generally require a separate optimization process for each structural case. This study proposes L2O-OSP, a learning-to-optimize framework that learns sensor placement decisions across a population of bridge configurations. The architecture contains three components: a gating network that determines the sensor budget and the relative weights of the placement objectives; a selector network that ranks candidate response locations and retains the top-k candidates; and a prediction network that estimates severity from the selected structural responses. The placement objective combines prediction error, spatial coverage, sensor count, and a robustness-related term. The framework is evaluated using 2000 parametrically generated bridge configurations and three numerical loading cases per configuration. The model trained without sensor failures selected an average of 74.40 sensors from 180 candidate locations, a reduction of 58.67%, and achieved a severity MAE of 0.02389 with all selected sensors available. At 50% test sensor failure, its MAE increased to 0.03557 without retraining. We compare global severity-oriented ranking with L2O-OSP at matched sensor count; both methods achieved similar prediction errors, but L2O-OSP reduced the mean largest uncovered interval from 9.56% to 3.09% of the bridge span. Additional evaluations examined Gaussian measurement noise, candidate-count sensitivity, and generalization to bridge lengths outside the training range. These findings support the proposed multi-objective approach within the evaluated numerical setting.