Stochastic Substructural Response Reconstruction and Reliability Analysis of High-Dimensional Systems

Existing stochastic dynamic response analysis requires the probability distributions of all variables in the system. Some of them are difficult or even impossible to obtain, and assumed probability density functions are often adopted which may lead to potential unrealistic estimation. This error may accumulate with the dimension of the structural system. This paper proposed a strategy to address this problem in the response analysis of a high-dimensional stochastic system. Partial measurement and finite element model of the target substructure of the system are required. The stochastic responses at several unmeasured locations are reconstructed from the measured responses. Only the variability of the substructure is considered. Other parameters outside the substructure are represented by their mean values contributing to the measured responses. The proposed strategy is illustrated with the analysis of a seven-storey plane frame structure using the probability density evolution method integrated with the response reconstruction technique. Measurement noise is noted to have a large influence on stochastic dynamic responses as different from that in a deterministic analysis. The proposed stochastic substructural response analysis strategy is found more computational efficient than traditional approach and with more realistic information of the structure from the measured responses.