No abstract

This paper proposes the stiffness nonlinearities and asymmetric SD (smooth and discontinuous) oscillators under time-delay feedback control with a fractional damping. With the effect of displacement and velocity feedback, the oscillator can be adjusted to the desired vibration state and then the stochastic resonance (SR) is achieved. This article discusses the contribution of various system parameters and time-delay feedback to SR, especially which induced by fractional damping. It should be noted that this paper provides effective guidance for fault diagnosis and weak signal detection, energy harvesting, vibration isolation and vibration reduction.

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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.

This paper proposes the stiffness nonlinearities and asymmetric SD (smooth and discontinuous) oscillators under time-delay feedback control with a fractional damping. With the effect of displacement and velocity feedback, the oscillator is adjusted to the desired vibration state and then the stochastic resonance (SR) is achieved. This article discusses the contribution of various system parameters and time-delay feedback to SR, especially which induced by fractional damping. It should be noted that this paper provides effective guidance for fault diagnosis and weak signal detection, energy harvesting, vibration isolation and vibration reduction.