Application of Artificial Neural Networks and Hybrid Methods in the Solution of Inverse Problems

Abstract

In this chapter Artificial Neural Networks are presented and used to solve different parameter estimation inverse problems, that is, Gas-liquid Adsorption Mass Transfer, Radiative Transfer Problems, and Simultaneous Heat and Mass Transfer. Besides, results obtained using hybrid methods are also presented, combining the Artificial Neural Network (ANN) method to other inverse problem solutions techniques, such as Simulated Annealing (SA) and Levenberg-Marquardt (LM). The first problem studied is the radiative transfer phenomenon, modeled with an integrodifferential equation known as Boltzmann equation. This equation describes mathematically the interaction of the radiation with the participating medium, i.e., a medium that may absorb, scatter and emit radiation. The inverse radiative transfer problem considered the simultaneous estimation of the absorption and scattering coefficients of a two-layer medium, using measured exit radiation intensities. In this sense, a study is presented regarding the estimation of radiative properties using ANN and hybrid methods combining ANN and LM. Then, the inverse problem of simultaneous heat and mass transfer modeled by Luikov equations is studied using a hybrid combination of the ANN, LM and SA. Direct and inverse problems are presented, formulated and solved. An ANN was used to generate the initial guess for the LM, another ANN to approximate the gradient needed by LM, and finally the global minimum was searched using the SA. The experimental data used was generated using the solution for the direct problem with the addition of artificial noise. The gas-liquid interface adsorption isotherm identification is also investigated using the same hybrid approach, that is, the combination of an ANN, LM and SA methods. The bubble and foam fractionation columns system works basically through the injection of a gas at the base of a column containing the solution. The gas bubbles formed in the