Enhancement of Stochastic Resonance Using Optimization Theory∗

The traditional stochastic resonance is realized by adding an optimal amount of noise, while the parameter-tuning stochastic resonance is realized by optimally tuning the system parameters. This paper reveals the possibility to further enhance the stochastic resonance effect by tuning system parameters and adding noise at the same time using optimization theory. The further improvement of the maximal normalized power norm of the bistable double-well dynamic system with white Gaussian noise input can be converted to an optimization problem with constraints on system parameters and noise intensity, which is proven to have one and only one local maximum for the Gaussian-distributed weak input signal. This result is then extended to the arbitrary weak input signal case. For the purpose of practical implementation, a fast-converging optimization algorithm to search the optimal system parameters and noise intensity is also proposed. Finally, computer simulations are performed to verify its validity and demonstrate its potential applications in signal processing.