Probabilistic Identification of Multi-DOF Structures Subjected to Ground Motion Using Manifold-Constrained Gaussian Processes - Hao, Shuo; Ni, Yi-Qing; Wang, Su-Mei (Frontiers in Built Environment, 2022)
Bayesian uncertainty quantification has a pivotal role in structural identification, yet the posterior distribution estimation of unknown parameters and system responses is still a challenging task. This paper proposes a novel method, named manifold-constrained Gaussian Processes (GPs), for the probabilistic identification of multi-DOF structural dynamical systems, taking shear-type frames subjected to ground motion as a demonstrative paradigm. The key idea of the method is to restrict the GPs (priorly defined over system responses) on a manifold which satisfies the equation of motion of the structural system. In contrast to widely used Bayesian probabilistic model updating methods, the manifold-constrained GPs avoid the numerical integration when formulating the joint probability density function of unknown parameters and system responses, hence achieving an accurate and computationally efficient inference for the posterior distributions. An eight-story shear-type frame is analyzed as a case study to demonstrate the effectiveness of the manifold-constrained GPs. The results indicate the posterior distributions of system responses and unknown parameters can be successfully identified, and reliable probabilistic model updating can be achieved.