A new method for stochastic analysis of structures under limited observations

Reasonable modeling of non-Gaussian system inputs from limited observations and efficient propagation of system response are of great significance in uncertain analysis of real engineering problems. In this paper, we develop a new method for the construction of non-Gaussian random model and associated propagation of response under limited observations. Our method firstly develops a new kernel density estimation-based (KDE-based) random model based on Karhunen-Loeve (KL) expansion of observations of uncertain parameters. By further implementing the arbitrary polynomial chaos (aPC) formulation on KL vector with dependent measure, the associated aPC-based response propagation is then developed. In our method, the developed KDE-based model can accurately represent the input parameters from limited observations as the new KDE of KL vector can incorporate the inherent relation between marginals of input parameters and distribution of univariate KL variables. In addition, the aPC formulation can be effectively determined for uncertain analysis by virtue of the mixture representation of the developed KDE of KL vector. Furthermore, the system response can be propagated in a stable and accurate way with the developed D-optimal weighted regression method by the equivalence between the distribution of underlying aPC variables and that of KL vector. In this way, the current work provides an effective framework for the reasonable stochastic modeling and efficient response propagation of real-life engineering systems with limited observations. Two numerical examples, including the analysis of structures subjected to random seismic ground motion, are presented to highlight the effectiveness of the proposed method.