Reconstruction of Spatially Distributed Wind Loads from Partial Measurements via Gaussian Processes

Many environmental types of loads, such as wind loads or fluid pressures, are spatially distributed on structures and vary over time. In the absence of direct measurements, these loads are typically represented a priori using stochastic models that are physics-based or semi-empirical. Such characterizations correspond to a best statistical guess. However, in many practical situations, partial measurements can be obtained from a limited number of sensors, such as anemometers or pressure taps. These measurements are spatially incomplete, as they provide point-wise information. Assuming the loads follow a joint Gaussian distribution, Gaussian process regression provides a Bayesian framework for inferring the unmeasured full load field from available data while accounting for uncertainty. Through appropriate covariance modeling, the spatial correlations can be exploited to reconstruct distributed load fields from sparse sensor data. This contribution explores the Bayesian reconstruction of spatially varying wind fields from anemometer data and discusses its integration into digital-twin frameworks for instrumented structures, where the load estimates can also be combined with other sensor data such as response measurements. Particular attention is given to challenges related to the propagation of uncertainties, the role of turbulence coherence in defining effective correlations, and the influence of sensor density on reconstruction quality. This is demonstrated in a numerical example on a simple beam structure under distributed loading. Furthermore, the work discusses strategies for modeling kernels that are non-separable in time, space, and frequency. Herein, computationally efficient approximations that maintain sufficient accuracy for engineering applications are sought.