Generalization of probabilistic transformation method for solving random differential equations

摘要

The probabilistic transformation method with the finite element analysis is a new technique to solve random differential equations. The advantage of this technique is finding the expression in an "exact" form of the probability density function of the solution when the probability density function of the input is known. The disadvantage is that it is limited to some special cases and it depends on the characteristics (geometry and materials) of the analysed structure, which is included in the random differential equation. In this paper, a developed formula is used to generalize this technique by obtaining the "exact" joint probability density function of the solution in any situation. Also, a technique for the non-linear case is proposed.