Uncertainty Propagation Analysis of TBM Performance Based on Sparse Polynomial Chaos Expansion Combined with Kernel Density Estimation and Bayesian Model Average

Investigating the impacts of uncertain geological parameters on the performance of tunneling boring machines (TBMs) via uncertainty propagation method is of great importance for reliable analysis of TBM. However, the geological data collected during TBM excavation process are very limited, which challenges the accuracy of uncertainty propagation analysis. In this study, an uncertainty propagation analysis framework (KBPCE) that combines kernel density estimation (KDE), Bayesian model averaging (BMA) and polynomial chaos expansion (PCE) method is developed for analyzing the effects of uncertain geological parameters on the TBM performance using limited data. Specifically, KDE is used to estimate the probability function of the geological parameters in a nonparametric way, while BMA is used in combination with PCE to construct sparse PCE model with limited sample data. The proposed uncertainty propagation method is validated for uncertainty propagation analysis of TBM specific energy. In addition, the developed KBPCE method is compared to PCE-LASSO and PCE-ElasticNet models that integrate PCE with compressive sensing techniques, i.e., LASSO and ElasticNet regression method. Research results demonstrate that the KBPCE method performs better than the PCE-LASSO and PCE-ElasticNet models by selecting the most important polynomial basis through Bayesian model selection. Our study demonstrates that the proposed KBPCE-based uncertainty propagation method has significant potential for reliable analysis of TBM performance in real applications with complex geological conditions.