Detection of Weak Signal Based on Parameter Identification of Delay Differential System with Noise Disturbance

Abstract

Extraction of the weak signals is crucial for fault prognostics in which case features are often very weak and masked by noise. In the time domain, the detection of weak signals depends on the identification of nonlinear parameters. A new signal detection and estimation method based on the incremental harmonic balance (IHB) is developed from the stochastic Van der Pol–Duffing equation with delayed feedback under parametric excitation. This is the first time that the IHB has been applied for the identification of parameters in stochastic delay differential equations (SDDEs). Compared to the method of intermittency transition between order and chaos to detect weak signals, this new method is more direct and the calculation result is what we want to obtain. This new method is suitable for the generalization and application of SDDEs.

Automated weak signal frequency estimation method based on Duffing oscillator and particle swarm optimization

“…Yang et al [30] used a charge control memristor to replace the cubic nonlinear part of the VDPD oscillator, and established a chaotic synchronization system based on the drive-response principle to measure the amplitude of a weak signal. The literature [31,32] proposed the time-delay feedback structure of the Duffing oscillator to further improve the weak signal detection ability.…”

Automated system for weak periodic signal detection based on Duffing oscillator

“…The periodic or quasi‐periodic signals can be detected as the weak signals in the time series obtained from the measurable processes of dynamical systems such as electroencephalogram (EEG) signals in the brain [1–3] and seismic signals in earthquakes [4–6]. The weak periodic signals [7–10] have a very low signal‐to‐noise ratio (SNR), thus, have low amplitudes. The weak periodic signals that have predictable and deterministic characteristics are used in the analysis of the dynamical systems, especially in the processing of non‐stationary signals in various applications such as the development of biomedical device technology.…”