ICML-98 Submission #195

Stochastic Resonance with Adaptive Fuzzy Systems

		   Sanya Mitaim and Bart Kosko 
		Signal and Image Processing Institute 
 	   Department of Electrical Engineering---Systems 
	        University of Southern California 
                Los Angeles, California 90089-2564


			    Abstract

Adaptive systems can learn to add an optimal amount of noise to some
nonlinear feedback systems.  Noise can improve the signal-to-noise
ratio of many nonlinear dynamical systems.  This ``stochastic
resonance'' effect occurs in a wide range of physical and biological
systems.  The SR effect may also occur in engineering systems in
signal processing, communications, and control.  The noise energy can
enhance the faint periodic signals or faint broadband signals that
force the dynamical systems.  Most SR studies assume full knowledge of
a system's dynamics and its noise and signal structure.  Fuzzy and
other adaptive systems can learn to induce SR based only on samples
from the process.  These samples can tune a fuzzy system's if-then
rules so that the fuzzy system approximates the dynamical system and
its noise response.  The paper derives the SR optimality conditions
that any stochastic learning system should try to achieve.  The
adaptive system learns the SR effect as the system performs a
stochastic gradient ascent on the signal-to-noise ratio.  The
stochastic learning scheme does not depend on a fuzzy system or any
other adaptive system.  The learning process is slow and noisy and can
require heavy computation.  Robust noise suppressors can improve the
learning process when we can estimate the impulsiveness of the noise
or of other learning terms.  Simulations test this SR learning scheme
on the popular quartic-bistable dynamical system and on other
dynamical systems for many types of noise.  Simulations suggest that
fuzzy techniques and perhaps other ``intelligent'' techniques can
induce SR in many cases when users cannot state the exact form of the
dynamical systems.

Keywords:  Stochastic resonance, Adaptation, Fuzzy function
approximation. 

E-mail address of contact author: kosko@sipi.usc.edu

Phone number of contact author: (213) 740-6242 (voice)
				(213) 740-4651 (fax)