  Locks and dams are critical pieces of inland waterways. However, many
components of existing locks have been in operation past their designed
lifetime. To ensure safe and cost effective operations, it is therefore
important to monitor the structural health of locks. To support lock gate
monitoring, this work considers a high dimensional Bayesian inference problem
that combines noisy real time strain observations with a detailed finite
element model. To solve this problem, we develop a new technique that combines
Karhunen-Lo\`eve decompositions, stochastic differential equation
representations of Gaussian processes, and Kalman smoothing that scales
linearly with the number of observations and could be used for near real-time
monitoring. We use quasi-periodic Gaussian processes to model thermal
influences on the strain and infer spatially distributed boundary conditions in
the model, which are also characterized with Gaussian process prior
distributions. The power of this approach is demonstrated on a small synthetic
example and then with real observations of Mississippi River Lock 27, which is
located near St. Louis, MO USA. The results show that our approach is able to
probabilistically characterize the posterior distribution over nearly 1.4
million parameters in under an hour on a standard desktop computer.
