Stochastic analysis of structures under limited observations using kernel density estimation and arbitrary polynomial chaos expansion

Over the past decades there has been considerable interest among the scientific community in modeling random system inputs from limited observations and propagating the system responses. In this paper, we develop a novel method for the reasonable modeling of system inputs and efficient propagation of response. Our method firstly constructs the random model of system inputs from observations by developing a novel kernel density estimator (KDE) for Karhunen-Loeve (KL) variables. By further implementing the arbitrary polynomial chaos (aPC) formulation on dependent non-Gaussian KL variables, the associated aPC-based response propagation is then developed. In our method, the developed random model can accurately represent the input parameters from limited observations as the developed KDE of KL variables can incorporate the inherent relation between marginals of input parameters and KL variables, while empowering the input model to preserve the second -order correlations. Furthermore, since the statistical moments of KL variables can be analytically evaluated, the aPC formulation for achieving optimal convergence of system responses can be accurately determined. In addition, the system response can be accurately propagated in an efficient way by developing an aPC-based regression method using space-filling design, in which the conditional distributions in Rosenblatt transformation of aPC variables can be efficiently determined without evaluations of multi-dimensional integrations. 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 are presented to highlight the effectiveness of the developed method.(c) 2022 Elsevier B.V. All rights reserved.

Automated summary

Over the past decades, there has been considerable interest in modeling random system inputs and propagating system responses from limited observations. This paper proposed a novel method that constructs a random model of system inputs using a kernel density estimator for Karhunen-Loeve variables and propagates the response using the arbitrary polynomial chaos formulation. The developed method accurately represents input parameters and efficiently propagates system responses, providing an effective framework for stochastic modeling and response propagation in engineering systems with limited observations.