Modelling of multivariable systems using advance fuzzy arithmetic

Abstract

Fuzzy arithmetic has received little attention among researchers regarding its ability to solve real world problem. However, in recent years, fuzzy arithmetic which is based on transformation method (TM) has been used to solve many optimization problems in engineering. In this study, state space modelling of several multivariable systems using fuzzy arithmetic based on the TM are presented. The TM is used to evaluate the state space model equations and to quantify the influence of each parameter of a given system. As a result, the value of its gain factors is calculated to allow the estimation of the relative measures of the uncertainty. A software, called, FAMOUS (Fuzzy Arithmetical Modelling of Uncertain Systems) is customized to illustrate the effectiveness of fuzzy arithmetic based on the TM. Moreover, the analytical solutions of state equations of these systems are obtained. The effectiveness of the method is shown by implementing it to the state space model of components in power plants (steam turbine and boiler) and nuclear power plants (steam generator and pressurizer). The computation time is reduced once the analytical solutions are determined for the systems. Furthermore, the influences of the uncertain parameters are obtained by simulations.