Chosen Possibilities of e-Fuzzy Boundary Elements Method Application in the Analysis of Conductivity Problems with Uncertainties

Abstract

The paper presents a methodology of solving boundary problems with uncertainty parameters based on the use of interval perturbation numbers. This methodology allows for the analysis of very complex problems with different uncertain parameters. Fuzzy Boundary Element Method (FBEM) using - number will be called  e-Fuzzy Boundary Element Method (e-FBEM). Detailed discussion of the problems of computing and applications will be presented on the example of the fuzzy boundary integral equation arising from the boundary problem for the potential problems with heterogeneous, fuzzy boundary conditions of Dirichlet and Neumann type, fuzzy internal sources, fuzzy boundary and fuzzy fundamental solution.
The presented methodology can be used to solve various engineering problems (e.g. in civil engineering, power engineering and others) – e.g. to analyze the temperature distribution in structural elements or elements located in the vicinity of objects or devices. In the latter case the increased temperature may be a symptom of a severe failure (e.g. power transformer overload, overexcitation or a fault) which cannot be tolerated due to the threat to the object and to the entire power system. Proposed method maybe used for electrical equipment diagnosis and in consequence as a power system failure prevention.
In this paper calculation methodology is illustrated on the example of an area bounded by a square, on the left boundary of which a certain temperature is set, while on the rest of the boundaries the conditions are equal to zero. A dedicated computer program allows for the calculation of both temperature and temperature derivative for any number of boundary elements using e-FBEM.