Artificial neural networks applied to the estimation of random variables associated to a two-mass model for the vocal folds

Abstract

The aim of this article is to use artificial neural networks (ANNs) to solve a stochastic inverse problem related to a model for voice production. Three parameters of the model are considered uncertain and random variables are associated to these parameters. For each random variable, a probability density function is constructed using the Maximum Entropy Principle. Substituting the three uncertain parameters for the associated random variables, the new model constructed is stochastic and its output is a stochastic process consisting of realizations of voice signals. The proposed inverse problem consists in mapping the three random variables from the voice signals and the use of ANNs to construct the solution of the inverse problem. Features are extracted from the output voice signals and taken as inputs of the designed ANN, whose outputs are random variables. The probability density functions of these random outputs are estimated and compared with the original ones. Two kinds of problems are discussed. At first, the same probability distribution is used to generate the voice signals and to solve the corresponding inverse stochastic problem. In this case, the actual probability density functions are very well fitted by the simulated ones. Then, different probability density functions are used to generate the voice signals to be used to train the ANN, and to solve the corresponding inverse problem. A good surprise appears: the quality of the estimation is almost unchanged, except for one of the random variables.