State Identification of Duffing Oscillator Based on Extreme Learning Machine

As an important weak target detection method, Duffing oscillator is very effective in detecting signals with very low signal-to-noise ratio. However, the accurate discrimination between chaotic and periodic states is a crucial problem and that is the prerequisite for using the Duffing oscillator. Conventionally, the Lyapunov exponent is used as an index to identify different states, but as this indicator has the problem of heavy computation cost, slow convergence rate, and requires a mass of data, its application becomes seriously limits. To solve this problem, a novel method for state identification of the Duffing oscillator based on extreme learning machine (ELM) is proposed. The feature data, as the input of ELM, are extracted from the phase diagram and the time series of the Duffing oscillator. Three effective features are extracted in this letter, i.e., ratio of points in and out of the closed region, average distance, and power spectrum. Computer simulations are presented to validate the proposed method and demonstrate that the state classification performance is superior to other related methods with higher computation efficiency, faster convergence rate, and better accuracy.