A sequential simulation method for probability box uncertainty analysis of structural responses

The key to hybrid uncertainty propagation of the structural response lies in solving the response probability box (P-box). To determine the bounds of the response CDFs, the computation is more complex and has more computational cost than probabilistic uncertainty propagation. Furthermore, the bounds of the CDFs are often determined by only a few CDF samples. This paper proposes a sequential simulation (SS) method for uncertainty analysis of structural response P-box. Using the sequential simulation method, we aim to iteratively find the samples that determine the CDF bounds. Firstly, initial global sampling of the outer-layer interval parameters and simulation are performed. Then, the contributive samples that determine the current upper or lower bound of the CDF are retained. In subsequent sequential simulations, local sampling in the neighborhoods of contributive samples and global sampling within the bounded space are conducted. In this way, the boundary of CDF can be sequentially extended until convergence. In each step of the simulation sequence, the inner-layer uses a univariate dimensionality reduction method (UDRM) with the Johnson distribution to acquire the CDF. Through examples and comparisons, it is demonstrated that the proposed method is more efficient than the direct simulation method in conducting structural response P-box analysis.