Method of estimation of cusp catastrophe occurrence possibility based on limited statistical information

Abstract

This paper deals with the improvement of probabilistic methods of design by using the catastrophe theory and the possibility theory application. A brief description of the catastrophe theory is presented, the cusp catastrophe is considered, control parameters are viewed as fuzzy variables with unknown distribution laws in the first part of the paper. The definition of the possibility measure of the cusp catastrophe occurrence is given in the second part of the paper. The condition of the cusp catastrophe occurrence is formulated according to Zadeh’s extension principle. The proposed method can be applied to solve the problems of the technical systems reliability and to give recommendations for engineering of forest machine and equipment elements in the case of limited statistical information.