Fuzzy parametric uncertainty analysis of linear dynamical systems: A surrogate modeling approach

Uncertainty propagation engineering systems possess significant computational challenges. This paper explores the possibility of using correlated function expansion based metamodelling approach when uncertain system parameters are modeled using Fuzzy variables. In particular, the application of High-Dimensional Model Representation (HDMR) is proposed for fuzzy finite element analysis of dynamical systems. The HDMR expansion is a set of quantitative model assessment and analysis tools for capturing high-dimensional input–output system behavior based on a hierarchy of functions of increasing dimensions. The input variables may be either finite-dimensional (i.e., a vector of parameters chosen from the Euclidean space RMRM) or may be infinite-dimensional as in the function space CM[0,1]CM[0,1]. The computational effort to determine the expansion functions using the alpha cut method scales polynomially with the number of variables rather than exponentially. This logic is based on the fundamental assumption underlying the HDMR representation that only low-order correlations among the input variables are likely to have significant impacts upon the outputs for most high-dimensional complex systems. The proposed method is integrated with a commercial Finite Element software. Modal analysis of a simplified aircraft wing with Fuzzy parameters has been used to illustrate the generality of the proposed approach. In the numerical examples, triangular membership functions have been used and the results have been validated against direct Monte Carlo simulations.

► Random Sampling High-Dimensional Model Representation (RS-HDMR) is proposed for fuzzy structural dynamics.
► For different α-cutsα-cuts, the surrogate model obtained using RS-HDMR is used to calculate response bounds.
► The method is integrated with a commercial finite element software.
► Proposed approach yields accurate estimates of the response bounds.