Probabilistic analysis of tunnels: A hybrid polynomial correlated function expansion based approach

This paper presents a novel approach for the analysis of tunnels in the presence of uncertainties. The proposed approach, referred to here as hybrid polynomial correlated function expansion (H-PCFE), performs a bi-level approximation: first on global scale via polynomial correlated function expansion (PCFE) and second on local scale via Kriging. While PCFE approximates the overall trend of the output response by using extended bases, Kriging utilizes covariance function to track the local variations. Additionally, a novel homotopy algorithm is utilized for estimating the unknown coefficients associated with the bases. The proposed approach has been utilized for analysis of two benchmark tunnel problems. In order to demonstrate the superior performance of the proposed approach, results obtained have been compared with those obtained using radial basis function (RBF) and Kriging. For both the problems, the proposed H-PCFE based approach yields highly accurate results outperforming both RBF and Kriging. Additionally, the proposed approach is computationally efficient as indicated by the convergence plots that illustrate the rapid decrease in prediction error with the increase in number of training points.