Cascaded Nonlinear Mass Fluctuation Stochastic Resonance System and Its Application in Bearing Fault Diagnosis

Stochastic resonance (SR) can realize bearing fault signal diagnosis by transferring noisy energy. In order to enhance the output response of the system and realize effective signal extraction, the nonlinear mass fluctuation SR system caused by nonlinear asymmetric dichotomous noise is cascaded to obtain the cascaded nonlinear mass fluctuation SR system. First, the output amplitude gain of the first-stage of the system is derived, and the influence of different parameters on it is explored; then the effects of different parameters of the cascaded system on the output amplitude gain and the output SNR are studied separately, which proves that the cascaded system can effectively double enhance the output response of the system; finally, the adaptive genetic algorithm is used to solve the difficulty of parameter adjustment, and the cascaded nonlinear mass fluctuation SR system is applied to the bearing fault diagnosis. The system proposed in this paper takes into account the effects of nonlinear asymmetric dichotomous noise and cascaded systems and performs waveform smoothing and double enhancement of the output signal. It can better extract fault signals and has effective engineering value.

Non-Maxwellian distribution in linear systems and its applications

Bimodality is a typical behavior of bistable nonlinear stochastic differential equations. In this work, we find an exact result for calculating the dynamical and stationary probability distribution function in a simple linear system driven by an asymmetric Markovian dichotomous noise. The results show that asymmetric dichotomous noise leads to a unimodal-bimodal distribution transition, exhibiting eight different non-Maxwellian stationary probability distribution profiles in the parameter space. The noise-induced transitions depend on the correlation time, which characterizes the asymmetric dichotomous noise. The calculations are performed using a linear configuration; but applications to other systems governed by nonlinear equations such as single species population growth models are discussed. In the proper limits, the symmetric case, including the Gaussian white noise limit, is recovered. Numerical simulations show good agreement with analytical results. Finally, a possible experimental setup is proposed.

The Stochastic Resonance Phenomenon of Different Noises in Underdamped Bistable System

In this paper, the stochastic resonance (SR) phenomenon of four kinds of noises (the white noise, the harmonic noise, the asymmetric dichotomous noise, and the Lévy noise) in underdamped bistable systems is studied. By applying theory of stochastic differential equations to the numerical simulation of stochastic resonance problem, we simulate and analyze the system responses and pay close attention to stochastic control in the proposed systems. Then, the factors of influence to the SR are investigated by the Euler-Maruyama algorithm, Milstein algorithm, and fourth-order Runge-Kutta algorithm, respectively. The results show that the SR phenomenon can be generated in the proposed system under certain conditions by adjusting the parameters of the control effect with different noises. We also found that the type of the noise has little effect on the resonance peak of the output power spectrum density, which is not observed in conventional harmonic systems driven by multiplicative noise with only an overdamped term. Therefore, the conclusion of this paper can provide experimental basis for the further study of stochastic resonance.

Disorder–order transitions in diluted and nondiluted direct transmission lines with asymmetric dichotomous noise

In this work we study the localization properties of diluted and nondiluted disordered direct transmission lines (TLs), when we distribute two values of inductances, LA and LB, according to an asymmetric dichotomous sequence. Using the scaling properties of the participation number D we study the localization properties in the thermodynamic limit. For certain τ and β parameter specific values, which characterize the dichotomous noise, we have found the following limit conditions: lim β→∞m(ω,τ,β) → 1.0 or lim τ→∞m(ω,τ,β) → 1.0, for the appearing of the disorder–order transitions. Here m(ω,τ,β) are the slopes of the linear relationships between ln (D) and ln (N). In addition, in each ωc resonance frequency generated by the dilution process we demonstrate the existence of extended intermediate states in the thermodynamic limit.

Damping Coefficient Induces Stochastic Multiresonance in Bistable System with Asymmetric Dichotomous Noise

Stochastic resonance (SR) and stochastic multiresonance (SMR) phenomena as a function of the underdamping and overdamping coefficients in bistable system with asymmetric dichotomous noise are investigated numerically. By the efficient numerical simulation of the asymmetric dichotomous noise and the fourth-order Runge-Kutta algorithm, we calculate the system responses, the averaged power spectrum, and the signal-noise-ratio (SNR) that can be a measure of the existence of SR and SMR phenomenon. And the effects of damping coefficients on the three characteristics are analyzed. Firstly, it is found that the periodic asymmetric distribution of the particle’s hopping between two potential wells in the system response is gradually weakened as underdamping coefficient is increased to overdamping coefficient. And it also displays the periodic asymmetric distribution under the circumstance of overdamping coefficient. Then the averaged power spectrum exhibits multiple sharp peaks, and the highest peak increases and decreases for underdamping coefficient which is added to overdamping coefficient. Finally, SNR versus the damping coefficient for the system parameters and the noise parameters are acquired and they show multiple peaks and valleys, which illustrates the obvious SMR phenomena in bistable system with asymmetric dichotomous noise.

Stochastic Resonance Enhanced by Colored Multiplicative and Additive Noises in a Time-Delayed Bistable System

The phenomenon of stochastic resonance (SR) in a time-delayed bistable system with square-wave signal, a constant force, with asymmetric dichotomous noise and multiplicative and additive colored noise is investigated. It is found that, the SR behavior can be observed on the signal-to-noise ratio (SNR) curves as a function of the intensity and asymmetry of the dichotomous noise, as a function of the amplitude of the square-wave, the constant force, as well as of the strength of the colored noises.