scholarly journals The Effect of Fractional Damping and Time-delayed Feedback on the Stochastic Resonance of Asymmetric SD Oscillator

2021 ◽  
Author(s):  
Qiubao Wang ◽  
Hao Wu ◽  
Yuejuan Yang
Keyword(s):  
Time Delay ◽  
Stochastic Resonance ◽  
Vibration Isolation ◽  
Weak Signal Detection ◽  
Fractional Damping ◽  
System Parameters ◽  
Sd Oscillator ◽  
Delay Feedback Control ◽  
Detection Energy ◽  
Time Delayed Feedback

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 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.

Influence of Fractional Damping and Time Delay on Maxwell-Voigt Model for Vibration Isolation

2016 ◽  
Author(s):  
Sudhir Kaul
Keyword(s):  
Time Delay ◽  
Dynamic Characteristics ◽  
Vibration Isolation ◽  
Model Parameters ◽  
Fractional Damping ◽  
Vibration Isolators ◽  
Multiple Parameters ◽  
Realistic Representation ◽  
Voigt Model ◽  
Isolation Systems

Models of vibration isolators are very commonly used for the design and analysis of isolation systems. Accurate isolator modeling is critical for a successful prediction of the dynamic characteristics of isolated systems. Isolators exhibit a complex behavior that depends on multiple parameters such as frequency, displacement amplitude, temperature and loading conditions. Therefore, it is important to choose a model that is accurate while adequately representing the relationships with relevant parameters. Recent literature has indicated some inherent advantages of fractional derivatives that can be exploited in the modeling of elastomeric isolators. Furthermore, time delay of damping is also seen to provide a realistic representation of damping. This paper examines the Maxwell-Voigt model with fractional damping and a time delay. This model is compared with the conventional Maxwell-Voigt model (without time delay or fractional damping) and the Voigt model in order to comprehend the influence of fractional damping and time delay on dynamic characteristics. Multiple simulations are performed after identifying model parameters from the data collected for a passive elastomeric isolator. The analysis results are compared and it is observed that the Voigt model is highly sensitive to fractional damping as well as time delay.

Stochastic resonance in asymmetric time-delayed bistable system under multiplicative and additive noise and its applications in bearing fault detection

2019 ◽  
Vol 33 (28) ◽  
pp. 1950341 ◽  
Author(s):  
Lifang He ◽  
Dayun Hu ◽  
Gang Zhang ◽  
Siliang Lu
Keyword(s):  
Time Delay ◽  
Stochastic Resonance ◽  
Additive Noise ◽  
Random Force ◽  
Small Time ◽  
Delayed Feedback ◽  
Bistable System ◽  
Bearing Fault ◽  
Strength Formula ◽  
Time Delayed Feedback

The asymmetric bistable system with time delays in the feedback force and random force under multiplicative and additive Gaussian noise is studied. Using the small time delay approximation approach and time-delayed Fokker–Planck equations (FPE), the signal-to-noise ratio (SNR) of the proposed stochastic system is obtained. The stochastic resonance (SR) phenomena influenced by parameters — including system parameters [Formula: see text], [Formula: see text], asymmetry parameter [Formula: see text], time delay [Formula: see text], strength [Formula: see text] of the time-delayed feedback, noise intensities [Formula: see text] and [Formula: see text] of multiplicative and additive noise, and correlation strength [Formula: see text] between two noises, are also analyzed by numerical simulations. Results demonstrate that the SR performance of the asymmetric bistable system is superior to one symmetric bistable system. Besides, both time delay and strength of time-delayed feedback could enhance the SR to some extent. Then, the asymmetric time-delayed bistable SR (ATDBSR) method is used to the bearing fault diagnosis. The engineering applications of the ATDBSR method are realized and the value of the method is verified by effective experimental results.

Maxwell-Voigt and Voigt Models for Vibration Isolation: Influence of Fractional Damping and Time Delay

2018 ◽  
Author(s):  
Sudhir Kaul
Keyword(s):  
Time Delay ◽  
Frequency Response ◽  
Fractional Order ◽  
Vibration Isolation ◽  
Damping Ratio ◽  
Maximum Amplitude ◽  
Damping Force ◽  
Fractional Damping ◽  
Integer Order ◽  
Voigt Model

This paper presents results from a follow-up study of fractional damping and time delay. Fractional damping has been used in the literature to demonstrate certain advantages over integer-order damping in many applications involving viscoelastic characteristics. It is observed that fractional damping can be used to influence stability boundaries, natural frequencies and vibration amplitudes, thus providing modeling flexibility in predicting the response of an isolated system during preliminary design. Additionally, time delay or lag is known to be inherent in a damped system, therefore a direct representation of time delay in modeling the damping force is expected to enhance model fidelity. This paper investigates the use of Voigt and Maxwell-Voigt models that incorporate fractional damping and time delay. In this paper, fractional damping has been particularly introduced to investigate possible improvements in the frequency response. Results indicate that fractional damping can be used to significantly enhance the capability of the Voigt model. The influence of the fractional order is found to be analogous to the damping ratio in an integer-order model. Fractional order is seen to exhibit a somewhat limited influence on the Maxwell-Voigt model. However, attributes such as the peak frequency and maximum amplitude are seen to be directly influenced by the fractional order. Although time delay is seen to exhibit an influence on the frequency response, it needs to be limited within useful bounds. Overall, it is observed that fractional order and time delay can be used to improve the accuracy of the Voigt and Maxwell-Voigt models. These enhanced models can be used for the design and development of elastomeric isolators and vibration isolation systems.

Stochastic resonance in deformable potential with time-delayed feedback

2021 ◽  
Vol 379 (2192) ◽  
pp. 20200234 ◽  
Author(s):  
Y. J. Wadop Ngouongo ◽  
M. Djolieu Funaye ◽  
G. Djuidjé Kenmoé ◽  
T. C. Kofané
Keyword(s):  
Time Delay ◽  
Stochastic Resonance ◽  
Brownian Particle ◽  
Delayed Feedback ◽  
Memory Effects ◽  
Loop Area ◽  
Feedback Strength ◽  
Hysteresis Loop Area ◽  
Time Delayed Feedback ◽  
With Memory

This paper reports the stochastic resonance (SR) phenomenon with memory effects for a Brownian particle in a potential whose shape is subjected to deformation. We model the deformation in the system by the Remoissenet–Peyrard potential and the memory effects by the time-delayed feedback. The question of the possible influence of time-delayed feedback on the occurrence of SR is then of our interest. We examine numerically the effect of feedback strength as well as time delay on SR phenomenon in terms of hysteresis loop area. It is found that time-delayed feedback has a significant effect on SR and can induce double resonances in the system. We show that the properties of SR are varying, depending on interdependence between feedback strength, time delay and shape parameter. This article is part of the theme issue ‘Vibrational and stochastic resonance in driven nonlinear systems (part 1)’.

Study on Heterodyne Stochastic Resonance System for Weak Signal Detection

2011 ◽  
Vol 88-89 ◽  
pp. 341-345
Author(s):  
Jun Jun Yao ◽  
Yong Mei Huang ◽  
Li Qing Hu ◽  
Min Lin
Keyword(s):  
Signal Detection ◽  
Stochastic Resonance ◽  
Frequency Measurement ◽  
Periodic Signal ◽  
Weak Signal ◽  
Weak Signal Detection ◽  
Resonance System ◽  
Resonance Theory ◽  
System Parameters ◽  
Simulation Results

The method based on stochastic resonance is a newly developed signal processing technology. Different from other methods by restraining the noise, it takes full advantage of the noises to strengthen the weak signal to improve SNR of the system. Based on stochastic resonance theory, a heterodyne system is presented in the paper to detect the frequency of the weak periodic signal. The simulation results manifest that the method is effective and the system parameters have extensive influence for frequency measurement. The parameters of the system are investigated for optimizing system design and weak signal detection.

Stochastic resonance in a time-delayed tumor cell growth system driven by additive and multiplicative noises

2018 ◽  
Vol 32 (22) ◽  
pp. 1850259 ◽  
Author(s):  
Gang Zhang ◽  
Jiabei Shi ◽  
Tianqi Zhang
Keyword(s):  
Time Delay ◽  
Cell Growth ◽  
Tumor Cell ◽  
Stochastic Resonance ◽  
Additive Noise ◽  
State Theory ◽  
Periodic Signal ◽  
Tumor Cell Growth ◽  
System Parameters ◽  
Growth System

In this paper, the stochastic resonance (SR) phenomenon in a time-delayed tumor cell growth system subjected to a multiplicative periodic signal, the multiplicative and additive noise is investigated. By applying the small time-delay method and two-state theory, the expressions of the mean first-passage time (MFPT) and signal-to-noise ratio (SNR) are obtained, then, the impacts of time delay, noise intensities and system parameters on the MFPT and SNR are discussed. Simulation results show that the multiplicative and additive noise always weaken the SR effect; while time delay plays a key role in motivating the SR phenomenon when noise intensities take a small value, it will restrain SR phenomenon when noise intensities take a large value; the cycle radiation amplitude always plays a positive role in stimulating the SR phenomenon, while, system parameters play different roles in motivating or suppressing SR under the different conditions of noise intensities.

scholarly journals Stochastic Resonance with a Joint Woods-Saxon and Gaussian Potential for Bearing Fault Diagnosis

2014 ◽  
Vol 2014 ◽  
pp. 1-17 ◽  
Author(s):  
Haibin Zhang ◽  
Qingbo He ◽  
Siliang Lu ◽  
Fanrang Kong
Keyword(s):  
Fault Diagnosis ◽  
Stochastic Resonance ◽  
Potential Model ◽  
Signal To Noise Ratio ◽  
Weak Signal Detection ◽  
Gaussian Potential ◽  
System Parameters ◽  
Bearing Fault ◽  
Bearing Fault Diagnosis ◽  
Proposed Model

This work aims for a new stochastic resonance (SR) model which performs well in bearing fault diagnosis. Different from the traditional bistable SR system, we realize the SR based on the joint of Woods-Saxon potential (WSP) and Gaussian potential (GP) instead of a reflection-symmetric quartic potential. With this potential model, all the parameters in the Woods-Saxon and Gaussian SR (WSGSR) system are not coupled when compared to the traditional one, so the output signal-to-noise ratio (SNR) can be optimized much more easily by tuning the system parameters. Besides, a smoother potential bottom and steeper potential wall lead to a stable particle motion within each potential well and avoid the unexpected noise. Different from the SR with only WSP which is a monostable system, we improve it into a bistable one as a general form offering a higher SNR and a wider bandwidth. Finally, the proposed model is verified to be outstanding in weak signal detection for bearing fault diagnosis and the strategy offers us a more effective and feasible diagnosis conclusion.

CHAOTIFICATION OF A NONLINEAR VIBRATION ISOLATION SYSTEM BY DUAL TIME DELAYED FEEDBACK CONTROL

2013 ◽  
Vol 23 (06) ◽  
pp. 1350096 ◽  
Author(s):  
YINGLI LI ◽  
DAOLIN XU ◽  
YIMING FU ◽  
JIAXI ZHOU
Keyword(s):  
Time Delay ◽  
Feedback Control ◽  
Vibration Isolation ◽  
Delayed Feedback ◽  
Delayed Feedback Control ◽  
Stable Region ◽  
Control Parameters ◽  
Isolation System ◽  
Vibration Isolation System ◽  
Time Delayed Feedback

Line spectrum of noise radiated from machinery vibrations of underwater vehicles is one of the most harmful signals that expose the characteristics of vehicles and locations. In order to distort the features and restrain the intensity of the line spectra, we attempt to chaotify the vibration system by time delay control. To avoid blindly numerical testing of the control parameters, stability of a two-dimensional vibration isolation floating raft system with two time-delayed feedback control is studied in this paper, aiming to provide guidance for chaotification. The system with dual equal time delay is investigated by the generalized strum method and the polynomial eigenvalues are adopted to analyze the stability of the controlled vibration isolation system with two unequal time delays. The critical control gains and delays for stability switches are obtained. By adjusting the control parameters beyond stable region, it is feasible to chaotify the system. Numerical simulations are conducted to compare the effect of two time delay with different control parameters and different control scheme to complicate the vibration isolation system.

Sign in / Sign up

Export Citation Format

Share Document