On Taylor series expansion for statistical moments of functions of correlated random variables

The paper is focused on reliability analysis of time-consuming mathematical models utilizing approximation in form of Taylor series expansion. Statistical analysis is crucial part of reliability analysis of structures but it is still challenging to analyze time-consuming mathematical models, e.g. represented by finite element method in implicit form. Efficient alternative is an approximation of original model by explicit function in specific form. The paper is focused on approximation by Taylor series expansion for statistical analysis of functions of random variables. Although it is common to use Taylor series expansion for functions of uncorrelated random variables, it is challenging to utilize Taylor series for correlated variables and highly non-linear functions. Therefore, possibilities and pitfalls of such approach are herein discussed from engineers point of view.