Fuzzy finite element analysis based on the transformation between fuzzy and random variables

Tuan Hung Nguyen^1*, Huynh Xuan Le²

¹Faculty of Civil Engineering, Thuyloi University

²Hanoi University of Civil Engineering

Received 17 March 2021; accepted 15 June 2021

Abstract:

In this paper, a fuzzy finite element method for determining the responses of structures is proposed by using the transformation between fuzzy and random variables. Firstly, the formulae for establishing normal random variables equivalent to symmetric triangular fuzzy numbers are presented based on the combination of the principle of insufficient reason and that of maximum specificity. As a result, fuzzy finite element analysis is transferred into stochastic finite element analysis. To solve this problem, the response surface method with the aid of standard normal random variables is utilized to approximate the real responses of structures. Then, the errors between the training and test sets are estimated to select a suitable response surface model amongst the regression models.  Lastly, the formulae for determining the mean and the standard deviation values of the responses of structures are established. The accuracy and effectiveness of the proposed method are verified via an illustrative example.

Keywords: fuzzy sets theory, fuzzy finite element, surrogate model, stochastic finite element, response surface method, possibility-probability transformations.

Classification number: 2.3