Modeling tunnel profile in the presence of coordinate errors: A Gaussian process-based approach

This article presents a Gaussian process (GP)-based approach to model a tunnel’s inner surface profile with high frequency sensing data provided by a Terrestrial Laser Scanner (TLS). We introduce a reading-surface profile that uniquely determines a three-dimensional tunnel in a Cartesian coordinate system. This reading-surface transforms the cylindrical tunnel to a two-dimensional surface profile, hence allowing us to model the tunnel profile by GP. To account for coordinate errors induced by TLS, we take repeated measurements at designed coordinates. We apply a Taylor approximation to extract mean and gradient estimations from the repeated measurements and then fit the GP model with both estimations to obtain a more robust reconstruction of the tunnel profile. We validate our method through numerical examples. The simulation results show that with the help of derivative estimations, our method outperforms the conventional GP regression with noisy observations in terms of mean-squared prediction error. We also present a case study to demonstrate that our method provides a more accurate result than the existing cylinder-fitting approach and has great potential for deformation monitoring in the presence of coordinate errors.