Artificial Neural Network (ANN) - Bayesian Probability Framework (BPF) based method of dynamic force reconstruction under multi-source uncertainties

In view of the universal existence of multi-source uncertainty factors in engineering structures, a novel method of dynamic force reconstruction is investigated based on Artificial Neural Network (ANN) and Bayesian probability framework (BPF). The deterministic force reconstruction is first solved by the back propagation (BP) ANN, in which the mapping relationship of external forces and displacement responses can be readily obtained through reiterative supervised learning rather than fussy formula deduction. The interval-set model is adopted to characterize uncertain variables and the most potential points in the interval domain (determine the boundaries of dynamic forces) are selected adaptively utilizing the BPF approach. Different from traditional uncertainty propagation methods, the present BPF strategy will construct a surrogate model of uncertain forces using the Bayesian theorem combined with two acquisition functions. The usage of the ANN-BPF based method is demonstrated with three numerical examples: a cantilever beam, a stiffened plate and a missile structure, in which some negative issues related to stiffness degradation, noise jamming and complicated boundary constraints, are discussed as well. In addition, some auxiliary indices are defined to evaluate the effects of reconstructed nominal forces and force boundaries of transient states and overall processes, like peak relative error (PRE), normalized mean squared error (NMSE), mean uncertain level (MUL), etc. The results indicate that the identified curves are all consistent with the real dynamic forces both in magnitude and regularity aspects, and the quantized data obtained by deterministic cases and uncertain cases is measured in reasonable ranges for engineering applications.