Search

Identifying earth pressures on in-service transportation tunnel linings is essential for their health monitoring and performance prediction, particularly in structures that exhibit poor performance. Due to the high costs associated with pressure gauges, pressure inversion based on easily observed structural responses, such as deformations, is preferred. A significant challenge lies in the non-uniqueness of inversion results, where various pressures can yield similar structural responses. Existing approaches often overlook detailed discussions on this critical issue. In addressing this gap, this study introduces a Bayesian approach. The proposed statistical framework effectively quantifies the uncertainty induced by non-uniqueness. Further analysis identifies the uniform component in distributed pressures as the primary source of non-uniqueness. Insights into mitigation strategies are provided, including increasing the quantity of deformation data or incorporating an observation of internal normal force within the tunnel lining -- the latter proving to be notably more effective. A practical application in a numerical case study demonstrates the effectiveness of this approach. In addition, our investigation recommends maintaining deformation measurement accuracy within the range of [-1, 1] mm to ensure satisfactory outcomes. Finally, deficiencies and potential future extensions of this approach are discussed., Comment: This paper has been accepted for publication in Transportation Geotechnics. Please find the published version at https://doi.org/10.1016/j.trgeo.2024.101344

Bayesian curve fitting plays an important role in inverse problems, and is often addressed using the Reversible Jump Markov Chain Monte Carlo (RJMCMC) algorithm. However, this algorithm can be computationally inefficient without appropriately tuned proposals. As a remedy, we present an adaptive RJMCMC algorithm for the curve fitting problems by extending the Adaptive Metropolis sampler from a fixed-dimensional to a trans-dimensional case. In this presented algorithm, both the size and orientation of the proposal function can be automatically adjusted in the sampling process. Specifically, the curve fitting setting allows for the approximation of the posterior covariance of the a priori unknown function on a representative grid of points. This approximation facilitates the definition of efficient proposals. In addition, we introduce an auxiliary-tempered version of this algorithm via non-reversible parallel tempering. To evaluate the algorithms, we conduct numerical tests involving a series of controlled experiments. The results demonstrate that the adaptive algorithms exhibit significantly higher efficiency compared to the conventional ones. Even in cases where the posterior distribution is highly complex, leading to ineffective convergence in the auxiliary-tempered conventional RJMCMC, the proposed auxiliary-tempered adaptive RJMCMC performs satisfactorily. Furthermore, we present a realistic inverse example to test the algorithms. The successful application of the adaptive algorithm distinguishes it again from the conventional one that fails to converge effectively even after millions of iterations., Comment: This paper has been accepted for publication in Inverse Problems. Please find the published version at https://doi.org/10.1088/1361-6420/ad2cf7