A equação da onda acústica com parâmetro fuzzy do tipo 1 e do tipo 2 intervalar

Abstract

The human hearing system is responsible for several important bodily functions, highlighting balance, geolocation and communication. The cochlea plays a central role in hearing, being responsible for converting sounds into nervous impulses, through dynamics between the movement of fluids present in its cavities and internal membranes. In this work, the approach chosen for formulating the model is the acoustic wave equation, which has the speed of sound as a parameter. According to the literature, two factors that change the speed of sound in the air are temperature and absolute humidity. The uncertainty generated by these factors is treated through two Fuzzy Rule-Based Systems (FRBS) type-1 and interval type-2, with temperature and humidity being the input variables, and having the speed of sound as the output. To build the type-1 FRBS, the Adaptive Neuro-Fuzzy Inference System (ANFIS) neuro-fuzzy network is used, with data about the speed of sound, depending on the air temperature and humidity, obtained through the free thermodynamics toolbox CANTERA. The inference method for this system is Takagi-Sugeno. The interval type-2 FRBS is constructed through the flexibility of the parameters that make up the pertinence functions of the input and output variables. The aim of this work is to mathematically treat the uncertainty that can influence the behavior of acoustic pressure as a function of time, considering air as a fluid. The approximations of the solution of the wave equation are solved through the Finite Difference Method, for the one-dimensional case, and the Finite Element Method for bidimensional models with regular and irregular domains. The measures of the domains of each model are taken from previous scientific works related to the topic. The results obtained show how much considering the speed of sound as a fuzzy parameter, depending on temperature and humidity, influences the acoustic pressure, generating differences in the mechanical behavior of the fluid at a given point within the domain.