Estimation of Structural Displacements from Measured Accelerations via Gaussian Process Regression

In the context of Structural Health Monitoring, displacement responses can be informative on the structural performance when combined with virtual sensing techniques or when compared to numerical analyses. Unfortunately, traditional displacement sensors are often expensive, limited in sampling frequency, and prone to low signal-to-noise ratios. In contrast, accelerometers are cost-effective, capable of high-rate sampling, and generally associated with higher signal-to-noise ratios, and can therefore be used for estimating displacements. However, estimating displacements from acceleration measurements through numerical double integration presents significant challenges: measurement noise in the low-frequency range becomes amplified, causing drift and distortion that can render displacement estimates unreliable. This can be particularly problematic for structures exhibiting low-frequency responses. This study presents a methodology for estimating structural displacements from noisy acceleration measurements using Gaussian Process (GP) regression in state space form. GP regression enables Bayesian inference with physically informed priors in the form of displacement magnitude and zero-mean assumptions. Additionally, uncertainty in the estimated displacements is quantified, providing not only point estimates but also credible intervals given the specified kernel hyperparameters. The method is validated through numerical examples of offshore structures subjected to wave loads.