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Locks and dams are critical pieces of inland waterways. However, manycomponents of existing locks have been in operation past their designedlifetime. To ensure safe and cost effective operations, it is thereforeimportant to monitor the structural health of locks. To support lock gatemonitoring, this work considers a high dimensional Bayesian inference problemthat combines noisy real time strain observations with a detailed finiteelement model. To solve this problem, we develop a new technique that combinesKarhunen-Lo\`eve decompositions, stochastic differential equationrepresentations of Gaussian processes, and Kalman smoothing that scaleslinearly with the number of observations and could be used for near real-timemonitoring. We use quasi-periodic Gaussian processes to model thermalinfluences on the strain and infer spatially distributed boundary conditions inthe model, which are also characterized with Gaussian process priordistributions. The power of this approach is demonstrated on a small syntheticexample and then with real observations of Mississippi River Lock 27, which islocated near St. Louis, MO USA. The results show that our approach is able toprobabilistically characterize the posterior distribution over nearly 1.4million parameters in under an hour on a standard desktop computer.

High dimensional inference for the structural health monitoring of lock gates