Detection of Weak Pulse Signal in Chaotic Noise Based on Improved Brain Emotional Learning Model and PSO-AGA

Abstract

A model for detecting weak pulse signals in chaotic noise was proposed. Firstly, based on the short-term predictability of chaotic signals, according to Takens’s theorem, the phase space of observed signal was reconstructed. Then, an improved brain emotional learning (BEL) model combined with PSO-AGA was proposed to predict chaotic signals, and the one-step prediction error was obtained. In order to optimize the parameters of the BEL model, an algorithm named PSO-AGA combined with particle swarm optimization and adaptive genetic algorithm was adopted to achieve the balance of global search and local search capabilities. Finally, the hypothesis testing method was used to detect whether there existed the pulse signal from the one-step prediction error. The experiments simulated the Lorenz system and the magnetic storm loop current system. In the Lorenz system, the MAD of BEL-PSO-AGA, BP-NN-PSO-AGA, and Wavelet-NN-PSO-AGA were 0.0022, 0.0142, and 0.0076; the MSE were $8.95\times 10^{-6}$ , 0.00034, and 0.00016; the RMSE were 0.0029, 0.0187, and 0.0128; the running times were 410 s, 792 s, and 721 s; the ACC were 0.999, 0.972, and 0.997; the F1 were 0.984, 0.423, and 0.878. It could be seen that the BEL model had better performance, shorter running time and higher values of the ACC and F1, indicated that the BEL model ran faster and had a better predictive effect. The MAD of BEL-PSO-AGA, BEL-WOA, BEL-AGA, and BEL-PSO were 0.0022, 0.0065, 0.0135, and 0.0071; the MSE were $8.95\times 10^{-6}$ , 0.00013, 0.00029, and 0.00014; the RMSE were 0.0029, 0.0115, 0.0173, and 0.0119; the ACC were 0.999, 0.992, 0.990, and 0.997; the F1 were 0.984, 0.733, 0.451, and 0.878. This indicated that the PSO-AGA also had better performance and higher prediction accuracy. In the magnetic storm loop current system, the experimental results were similar to the Lorenz experiment, which also indicated that the BEL-PSO-AGA model was better. To sum up, the detection results of simulations showed that the proposed model and algorithm could effectively detect weak pulse signals from the chaotic noise.