Nataf transformation based point estimate method

Abstract

Structural probabilistic analysis quantifies the effect of input random variables, such as material properties, geometrical parameters and loading conditions, on the structural responses. The point estimate method (PEM) is a direct and easy-used way to perform the structural probabilistic analysis in practice. In this paper, a novel and efficient point estimate method is proposed for computing the first four statistical moments of structural response which is a function of input random variables. The method adopts Nataf transformation to replace Rosenblatt transformation in conventional point estimate method. Because of the nature of engineering problems and limited statistical data, the joint probability density function (PDF) of all input random variables is hard to acquire, but it must be known in Rosenblatt transformation. A more common case is that the marginal PDF of each random variable and the correlation matrix are available, which just satisfy the service condition of Nataf transformation. Hence the Nataf transformation based point estimate method is particularly suitable for engineering applications. The comparison between the proposed method and the conventional point estimate method shows that (1) they are equivalent when all random variables are mutually independent; (2) if the marginal PDFs and the correlation matrix are known, the conventional PEM cannot be applicable, but the proposed method can give a rational approximation. Finally, the procedure is demonstrated in detail through a simple illustration.