Abstract
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 short-term 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 double-layer Elman deep neural network recovery model (DEDR model) is proposed, which is based on the Elman deep learning network model and single-point 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.
Highlights
Weak signal is a weak amount that is difficult to detect
The Lorenz system is used to generate the chaotic noise background signal, the detection threshold is measured by the signal-to-interference ratio (SIR) [30, 31], and the mean square error (MSE) and ROC curve are used to measure the accuracy of the recovery result
4,000 points of the observed signal are selected as samples, and the signal is detected by the Elman deep learning adaptive detection model (EDAD) model and recovered by the double-layer Elman deep neural network recovery model (DEDR) model. e experimental results are shown in Table 3: It can be seen from the results shown in Table 3 that the ability of the DEDR model to recover signals changes with the gradual change of the pulse signal intensity
Summary
Weak signal is a weak amount that is difficult to detect. It is small amplitude compared to background noise and is a signal that is often annihilated by noise and has a low signalto-interference ratio [1, 2]. Li et al proposed a local linear-periodic detection-Kalman filtering hybrid algorithm to detect weak signal in strong chaotic backgrounds [19]. Leung and Lo used an RBF network predictor to introduce a detection technique for small sea targets based on this dynamic model [9] Chinese scholars He et al proposed a method for detecting signals submerged under chaotic background using neural networks and studied the antinoise interference of this method [22]. Our paper considers an adaptive detection and recovery of Elman deep learning network based on weak pulse signal in the background of chaotic noise. A double-layer Elman deep neural network recovery model is constructed based on pseudo-observation signal reconstruction, and parameters of the model are estimated by using the least squares method to recover the weak pulse signal. E structure of this paper is as follows: Section 2 describes weak signals for adaptive detection; Section 3 recovers weak pulse signals based on DEDR model; Section 4 presents simulation experiments and analysis; and Section 5 concludes the paper
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