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This paper shows how 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 (SR) 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 learning terms. Simulations test this SR learning scheme on the popular quartic-bistable dynamical system and on other dynamical systems. The driving noise types range fram Gaussian white noise to impulsive noise to chaotic noise. Simulations suggest that fuzzy techniques and perhaps other adaptive black box or intelligent techniques can induce SR in many cases when users cannot state the exact form of the dynamical systems. The appendixes derive the basic additive fuzzy system and the neural-like learning laws that tune it.
Keyword:
adaptive signal processing
dynamical systems
fuzzy systems
neural networks
noise processing
robust statistics
stochastic resonance
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