Independent component analysis-based arbitrary polynomial chaos method for stochastic analysis of structures under limited observations

Reasonable modelling of non-Gaussian structural inputs from limited observations as well as efficient propagation of system response are of paramount importance in the uncertain analysis of real engineering problems. In this paper, we develop an independent component analysis-based (ICA-based) arbitrary polynomial chaos (aPC) method for the construction of non-Gaussian random model and associated propagation of response under limited observations. Our method firstly introduces the ICA in the context of Karhunen-Loeve (KL) representation of observations of uncertain parameters. By further implementing the aPC expansion on ICA variables, the associated aPC-based response propagation is developed. Since the ICA variables exhibit minimized dependence in all of the orthogonal transformation of KL coefficients, the curse of dimensionality and the inaccurate modelling encountered in the existing PC-based methods can be overcome in the developed ICA-based input model. Also, since the aPC expansion enables to directly construct PC representation with respect to arbitrary probability measure, the convergence of conventional PC-based response propagation is significantly accelerated, resulting an efficient aPC-based response analysis. In this way, the current work provides an effective framework for the reasonable stochastic modelling and efficient response propagation of real-life engineering systems with limited observations. Two numerical examples are presented, including the stochastic analysis of structures subjected to random seismic ground motion, highlighting the effectiveness of the proposed method.

Automated summary

This paper develops an independent component analysis-based arbitrary polynomial chaos method for constructing non-Gaussian random models and propagating responses under limited observations. The method overcomes the curse of dimensionality and inaccurate modeling issues encountered in existing methods, and significantly accelerates the convergence of traditional response propagation. It provides an effective framework for reasonable stochastic modeling and efficient response propagation in real-life engineering systems with limited observations.