Predictive Gaussian-Process Reconstruction and Anomaly Observability of Bridge Displacement Fields from Sparse Sensors

Sparse sensor measurements remain a major limitation in bridge structural health monitoring because dense instrumentation is often restricted by installation cost, access difficulties, sensor maintenance, and the limited duration of full-scale load tests. As a result, the structural response between measurement locations must usually be inferred rather than directly observed. This study presents a sequential Gaussian-process Bayesian framework for reconstructing bridge displacement fields and tracking structural response across progressive loading stages. The novelty of the approach lies in treating the load test as an evolving Bayesian inference problem rather than as a set of independent static reconstructions: posterior information from one loading stage is propagated to the next while measurement and process uncertainty are explicitly retained.

The method is applied to a full-scale prestressed concrete bridge tested under seven displacement-controlled loading stages ranging from 5 mm to 60 mm. Five laser displacement sensors distributed along the bridge span were used to estimate the spatial displacement response. Representative measurements were extracted from stable loading plateaus, and several Gaussian-process models with different covariance kernels and mean functions were compared using leave-one-sensor-out validation. The best-performing model, based on a squared-exponential kernel and constant mean, achieved a leave-one-sensor-out root-mean-square error of 14.04 mm and a 94.3% coverage rate for nominal 95% prediction intervals. It also reduced prediction error by approximately 45.1% compared with the best deterministic baseline.

The selected model was then embedded in a sequential Bayesian updating scheme. This provides an advantage over independent stage-by-stage reconstruction because it preserves accumulated information, improves uncertainty consistency across loading stages, and enables innovation-based assessment of whether newly observed responses remain compatible with the previously inferred structural state. The sequential model showed good uncertainty calibration, with a mean normalized innovation squared value of 4.99 for the five-sensor system. Controlled anomaly tests showed that detection depended strongly on anomaly severity, spatial width, and location relative to the sensors. The results demonstrate that sequential Gaussian-process inference can reconstruct displacement fields from sparse measurements, quantify uncertainty, and reveal practical limits in anomaly observability.