Parameter Optimization Algorithm for Bistable Stochastic Resonance

In bistable stochastic resonance systems, optimization of parameters a and b is crucial for system performance. Parameter optimization typically employs a stepwise strategy: first fixing one parameter while optimizing the other.

When parameter b is fixed, the optimization process for parameter a proceeds as follows: Set b to a reasonable initial value (typically selected based on system characteristics) Generate a series of discrete points within the possible value range of a Calculate the signal-to-noise ratio (SNR) gain of system output for each value of a Plot the curve of SNR gain versus a values Select the a value that maximizes the SNR gain as the optimal parameter In code implementation, this can be achieved using a for-loop or vectorized operations to iterate through a values, with SNR calculation functions incorporating system dynamics equations and noise modeling.

The characteristics of SNR gain curves typically exhibit nonlinear behavior: When a values are small, gain increases rapidly with increasing a After reaching peak values, gain may slowly decrease or stabilize The curve shape is influenced by noise intensity and input signal characteristics The optimization algorithm should account for these nonlinearities through appropriate sampling density and peak detection methods, potentially using gradient-based or interpolation techniques for refined searches.

This stepwise parameter optimization method effectively reduces the complexity of multidimensional searches, making it suitable for rapid parameter tuning in engineering applications of bistable systems. Subsequent optimization can be performed on parameter b using similar methods based on the optimized a value, achieving coordinated parameter optimization. The complete algorithm can be structured as nested optimization loops with convergence criteria to ensure parameter stability.