Statistical Detection of Weak Pulse Signal under Chaotic Noise Based on Elman Neural Network Weak signal detection is a significant problem in modern detection such as mechanical fault diagnosis. The uniqueness of chaos and good learning ability of neural networks provide new ideas and framework for weak signal detection field. In this paper, Elman neural network is applied to detect and recover weak pulse signal in chaotic noise. For detection problem of weak pulse signal under chaotic noise, based on shortterm predictability of chaotic observations, phase space reconstruction for observed signals is carried out. And Elman deep learning adaptive detection model (EDAD model) is established for weak pulse signal detection, and a hypothesis test is used to detect weak pulse signal from the prediction error. For the recovery of weak pulse signal under chaotic noise, a doublelayer Elman deep neural network recovery model (DEDR model) is proposed, which is based on the Elman deep learning network model and singlepoint jump model for weak pulse signal, and it is optimized with goal of minimizing mean square prediction error of the Elman model. The profile least squares method is applied to estimate parameters of the DEDR model for difficult recovery of weak pulse signal because the DEDR model is essentially a semiparametric model with parametric and nonparametric parts. In the end, simulation experiments show that the model built in this paper can effectively detect and recover weak pulse signal in the background of chaotic noise.

A recallingenhanced recurrent neural network: conjugate gradient learning algorithm and its convergence analysis Abstract   Elman network is a classical recurrent neural network with an internal delay feedback. In this paper, we propose a recallingenhanced recurrent neural network (RERNN) which has a selective memory property. In addition, an improved conjugate algorithm with generalized Armijo search technique that speeds up the convergence rate is used to train the RERNN model. Further enhancement performance is achieved with adaptive learning coefficients. Finally, we prove weak and strong convergence of the presented algorithm. In other words, as the number of training steps increases, the following has been established for RERNN: (1) the gradient norm of the error function with respect to the weight vectors converges to zero, (2) the weight sequence approaches a fixed optimal point. We have carried out a number of simulations to illustrate and verify the theoretical results that demonstrate the efficiency of the proposed algorithm.