Multilevel Decomposition Framework for Reliability Assessment of Assembled Stochastic Linear Structural Systems

Abstract

To reduce the computational cost of assembled stochastic linear structural dynamic systems, a three-staged reduced order model-based framework for forward uncertainty propagation was developed. First, the physical domain was decomposed by constructing an equivalent reduced order numerical model that limited the cost of a single deterministic simulation. This was done in two phases: (1) reducing the system matrices of the subcomponents using component mode synthesis and (2) solving the resulting reduced system with the help of domain decomposition in an efficient manner. Second, functional decomposition was carried out in the stochastic space by employing a multioutput machine learning model that reduced the number of eigenvalue analyses to be performed. Thus, a multilevel framework was developed that propagated the dynamic response from the subcomponent level to the assembled global system level efficiently. Subsequently, reliability analysis was performed to assess the safety level and failure probability of linear stochastic dynamic systems. The results achieved by solving a two-dimensional (2D) building frame and a three-dimensional (3D) transmission tower model illustrated good performance of the proposed methodology, highlighting its potential for complex problems.