Modeling tunnel profile in the presence of coordinate errors: A Gaussian process-based approach
提出一种基于高斯过程的方法，利用地面激光扫描仪的高频传感数据建模隧道内表面轮廓，通过重复测量和泰勒近似处理坐标误差，数值实验和案例表明该方法比传统方法更准确，适用于变形监测。
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.