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Chapter 12.2.2 - Learning Algorithm Using Local Model Information

12.2.2.   Learning Algorithm Using Local Model Information

The learning algorithm employs both structure learning and parameter
learning to determine the premise part structure and the appropriate
premise / consequent parameters of a fuzzy neural network. Structure learning
determines the appropriate fuzzy neural structure by performing membership
function insertion and parameter setting of initial premiser / consequent parameters
of newly established rules. Parameter learning updates consequent weights via a
local least-squares estimation technique [22].

Parameter learning involves the computation of N locally weighted least-squares
regressions, one for each rule, using only the training data within the
rule’s receptive field. The consequent weights are not updated for rules
having zero training data within their receptive field.

The learning procedure follows the steps below:

  1. Use a subset of the training data set to perform network initialization.
    This network initialization is conducted offline using structure learning.
  2. Perform structure learning if necessary.
  3. Perform parameter learning.
  4. Repeat steps 2 and 3 for all training data entries.

12.2.3.   FNN Linear Incremental Model

A linear incremental model is derived, as a basis for the offline design of
mode transition controllers, by considering first-order input-output sensitivity
terms of the original FNN model. For each fuzzy rule, the input-output
relation is expressed as a function of the firing strength of the rule premise
and consequent parameters, the latter being denoted as the mean and
standard deviation of Gaussian functions.

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