基于完全贝叶斯估计的在役地下结构荷载随机反演方法

Stochastic Inversion Method for In-service Underground Structure Load Based on Full Bayesian Inference

摘要:

提出一种在役地下结构荷载随机反演方法。采用样条函数，将结构上的未知荷载参数化为一系列插值变量；基于贝叶斯框架，融入结构变形观测数据，并构建荷载参数的后验概率分布（PDF）；引入高效采样算法DREAM（differential evolution adaptive metropolis）实现对未知荷载的完全贝叶斯估计。实际案例结果表明：传统确定性反演方法表现出解不稳定的“病态反演”问题，而本方法的荷载期望值则与实测结果吻合较好；本方法得到了未知荷载的完整后验分布，体现出处理反演结果不唯一的优势。

Abstract:

A stochastic inversion method for in-service underground structure load was proposed. Firstly， based on spline function， the disorderly distributed load was parameterized into a set of interpolation unknowns. Secondly， on Bayesian framework， the posterior probability density function （PDF） of the unknowns was built by incorporating the measured deformation data. Lastly， the full Bayesian inference of the corresponding unknown load was carried out based on an efficient sampling method of DREAM（differential evolution adaptive metropolis）. Testing results from a field case indicated that the expectation load obtained from the proposed method fits well with the actual recorded pressures while the ill-conditioning is encountered by traditional deterministic inversion method. Apart from the expectation load， complete PDFs of the inversion load are obtained， which presents the natural advantage of the proposed method to deal with non-uniqueness.