Neural Net Gains Estimation Based on an Equivalent Model

Abstract

A model of an Equivalent Artificial Neural Net (EANN) describes the gains set, viewed as parameters in a layer, and this consideration is a reproducible process, applicable to a neuron in a neural net (NN). The EANN helps to estimate the NN gains or parameters, so we propose two methods to determine them. The first considers a fuzzy inference combined with the traditional Kalman filter, obtaining the equivalent model and estimating in a fuzzy sense the gains matrix A and the proper gain K into the traditional filter identification. The second develops a direct estimation in state space, describing an EANN using the expected value and the recursive description of the gains estimation. Finally, a comparison of both descriptions is performed; highlighting the analytical method describes the neural net coefficients in a direct form, whereas the other technique requires selecting into the Knowledge Base (KB) the factors based on the functional error and the reference signal built with the past information of the system.

Equivalent Neural Network Optimal Coefficients Using Forgetting Factor with Sliding Modes

“…The comparisons give us the idea of how the new estimation technique improves the original estimation presented in [7] for the EANN. In graphics, the estimation named as “optimum” is made using (5) while the “EFF” estimation includes the implementation of (7).…”

“…The Equivalent Artificial Neural Network (EANN), developed in [7], is a representation that considers the linearization of a multiple input-single output (MISO) system and is useful for cases where time is an important factor, applying different techniques to adjust their gains according to a reference, even with difficulty in modelling external perturbations. In general, any ANN could be reduced to a simpler equivalent model (EANN) integrated by multiple inputs that interact with a set of weights combined in some sense giving a final output [7, 8].…”

“…In general, any ANN could be reduced to a simpler equivalent model (EANN) integrated by multiple inputs that interact with a set of weights combined in some sense giving a final output [7, 8]. …”