Reconstructing the bending moments time history of wind turbine tower from acceleration measurements using Gaussian processes

The proper estimation of the fatigue damage accumulated over time for a given wind turbine is a key information when evaluating the remaining lifetime of the structure. While the most obvious way to do so is to instrument the structure with strain gauges, not only this is a demanding task, it also only provides information about the sections that are being monitored. In this work we propose a new methodology to estimate the fatigue damage in any section of the tower based on the accelerations time series and a single instrumented section with strain gauges. We argue that accelerations and displacements of a linear structure under stochastic loading share a well defined covariance structure. This conclusion allow us to define a Monte Carlo Markov Chain (MCMC) algorithm to constrain the parameters that best describe this structure, as well as to use all the machinery associated with gaussian processes to convert accelerations into displacements, and these into bending moments. Using artificial experimental data obtained from a previously validated numerical model as input to our method, we obtained a good agreement between the simulated and reconstructed response. The results concerning fatigue damage were also in reasonable agreement, although presenting higher deviations that must be analysed in future studies.