ELLIPSE PERIMETER ESTIMATION USING NON- PARAMETRIC REGRESSION OF RBF NEURAL NETWORK BASED ON ELLIPTIC INTEGRAL OF THE SECOND TYPE

Abstract

Methods for calculating the ellipse perimeter provided so far, including Kepler equation, Euler, Ramanujan, Lindner, Gauss Kumar, do not have acceptable accuracy in some cases. In this study, calculation of ellipse perimeter was done using non- parametric regression of RBF neural network. To train the neural network, the data from the numerical calculation of second type elliptic integral was used. We used the least squares and gradient descent optimization methods to train the neural network and the deviation of the output of these two methods from the accurate method was calculated, using generalization error and learning error measures. Studies show that after the training phase, the network as an individual model, can estimate the ellipse perimeter for different values of eccentricity and major diameter with great accuracy.