ADAPTIVE STOCHASTIC RESONANCE

This paper shows how adaptive systems can learn to add an optimal amou nt of noise to some nonlinear feedback systems. Noise can improve the signal-to-noise ratio of many nonlinear dynamical systems. This ''stoc hastic resonance'' (SR) effect occurs in a wide range of physical and biological systems. The SR effect may also occur in engineering system s 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 oth er 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 stoc hastic learning system should try to achieve. The adaptive system lear ns the SR effect as the system performs a stochastic gradient ascent o n the signal-to-noise ratio. The stochastic learning scheme does not d epend on a fuzzy system or any other adaptive system. The learning pro cess 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 learnin g 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 fu zzy techniques and perhaps other adaptive ''black box'' or ''intellige nt'' techniques can induce SR in many cases when users cannot state th e exact form of the dynamical systems. The appendixes derive the basic additive fuzzy system and the neural-like learning laws that tune it.