A Bayesian-based approach for inversion of earth pressures on in-service underground structures

This paper presents a Bayesian inversion approach to identify earth pressures on in-service underground structures based on structural deformations. Ill-conditioning and non-uniqueness of solutions are major issues for load inversion problems. Traditional approaches are mostly based on an optimization framework where a smooth solution is uniquely determined using regularization techniques. However, these approaches require tuning of regularization factors that may be subjective and difficult to implement for pressure inversion on in-service underground structures. By contrast, the presented approach is based on a Bayesian framework. Instead of regularization techniques and corresponding tuning procedure, only physically plausible bounds are required for specifying constraints. The complete posterior distribution of feasible solutions is obtained based on Bayes' rules. By inferring the potential pressures with the complete posterior distribution, a natural regularization advantage can be shown. Specifically, this advantage is demonstrated in detail by a series of comparative tests: (1) the Bayesian posterior mean exhibits an inherent quality to smooth out ill-conditioned features of inversion solutions; (2) satisfactory inference of the pressures can be made even in the presence of non-uniqueness. These properties are valuable when observed data is noisy or limited. A recorded field example is also presented to show effectiveness of this approach in practical engineering. Finally, deficiencies and potential extensions are discussed.