Enhancing the Weak Signal With Arbitrary High-Frequency by Vibrational Resonance in Fractional-Order Duffing Oscillators

2017 ◽  
Vol 12 (5) ◽  
Author(s):  
J. H. Yang ◽  
Miguel A. F. Sanjuán ◽  
H. G. Liu
Keyword(s):  
Fractional Order ◽  
High Frequency ◽  
Low Frequency ◽  
Original System ◽  
Scale Transformation ◽  
Weak Signal ◽  
Vibrational Resonance ◽  
High Frequency Signal ◽  
System A ◽  
Auxiliary Signal

When the traditional vibrational resonance (VR) occurs in a nonlinear system, a weak character signal is enhanced by an appropriate high-frequency auxiliary signal. Here, for the harmonic character signal case, the frequency of the character signal is usually smaller than 1 rad/s. The frequency of the auxiliary signal is dozens of times of the frequency of the character signal. Moreover, in the real world, the characteristic information is usually indicated by a weak signal with a frequency in the range from several to thousands rad/s. For this case, the weak high-frequency signal cannot be enhanced by the traditional mechanism of VR, and as such, the application of VR in the engineering field could be restricted. In this work, by introducing a scale transformation, we transform high-frequency excitations in the original system to low-frequency excitations in a rescaled system. Then, we make VR to occur at the low frequency in the rescaled system, as usual. Meanwhile, the VR also occurs at the frequency of the character signal in the original system. As a result, the weak character signal with arbitrary high-frequency can be enhanced. To make the rescaled system in a general form, the VR is investigated in fractional-order Duffing oscillators. The form of the potential function, the fractional order, and the reduction scale are important factors for the strength of VR.

Vibrational resonance in a discrete neuronal model with time delay

2014 ◽  
Vol 28 (16) ◽  
pp. 1450103 ◽  
Author(s):  
Canjun Wang ◽  
Keli Yang ◽  
Shixian Qu
Keyword(s):  
Time Delay ◽  
Input Signal ◽  
High Frequency ◽  
Phase Synchronization ◽  
Low Frequency ◽  
Neuronal Model ◽  
Vibrational Resonance ◽  
Frequency Signal ◽  
High Frequency Signal ◽  
Neuron System

The effects of time delay on the vibrational resonance (VR) in a discrete neuron system with a low-frequency signal and a high-frequency signal are investigated by numerical simulations. The results show that there exists a delay time that optimizes the phase synchronization between the low-frequency input signal and the output signal. VR is induced by the time delay. Furthermore, the time delay can improve the response to a low-frequency input signal. Therefore, the time delay plays a constructive role in the transmission of a low-frequency signal by inducing and enhancing VR.

On the Weak Signal Amplification by Twice Sampling Vibrational Resonance Method in Fractional Duffing Oscillators

2018 ◽  
Vol 13 (3) ◽  
Author(s):  
Jin-Rong Yang ◽  
Cheng-Jin Wu ◽  
Jian-Hua Yang ◽  
Hou-Guang Liu
Keyword(s):  
Fractional Order ◽  
High Frequency ◽  
Signal Amplification ◽  
Resonance Method ◽  
Weak Signal ◽  
Physical Processes ◽  
Vibrational Resonance ◽  
External Signals

In our former work developed by Yang et al. (2017, “Enhancing the Weak Signal With Arbitrary High-Frequency by Vibrational Resonance in Fractional-Order Duffing Oscillators,” ASME J. Comput. Nonlinear Dyn., 12(5), p. 051011), we put forward the rescaled vibrational resonance (VR) method in fractional duffing oscillators to amplify a weak signal with arbitrary high frequency. In the present work, we propose another method named as twice sampling VR to achieve the same goal. Although physical processes of two discussed methods are different, the results obtained by them are identical completely. Besides the two external signals excitation case, the validity of the new proposed method is also verified in the system that is excited by an amplitude modulated signal. Further, the dynamics of the system reveals that the resonance performance, i.e., the strength and the pattern, depends on the fractional order closely.

Optimum Vibrational Resonance in a Time-Delay Bistable System Driven by Biharmonic Signals

2014 ◽  
Vol 651-653 ◽  
pp. 2172-2176
Author(s):  
Yun Liang Meng ◽  
Chang Xing Pei ◽  
Dong Wu Li
Keyword(s):  
Time Delay ◽  
High Frequency ◽  
Low Frequency ◽  
Signal Amplitude ◽  
Resonance Peak ◽  
Response Amplitude ◽  
Bistable System ◽  
Vibrational Resonance ◽  
Frequency Signal ◽  
High Frequency Signal

The optimum vibrational resonance in a time-delay bistable system driven by bihiarmonic signals is discussed in this paper. The theoretically expression for the response amplitude gain of low frequency signal in the time-delay bistable system is deduced, and the effects of time delay parameter on the optimum vibrational resonance peak and the required amplitude of high frequency signal are investigated. It is shown that the optimum vibrational resonance can be achieved by adjusting the high frequency signal amplitude and time delay parameter jointly. Meanwhile, the optimum vibrational resonance appeared periodically with time delay parameter and the period is equal to the period of low-frequency signal. The amplitude of high-frequency signal required for the optimum vibrational resonance can be fixed or varied with different time delay parameter depending on the ratio of the frequencies between biharmonic signals.

scholarly journals An Investigation into Error Source Identification of Machine Tools Based on Time-Frequency Feature Extraction

2016 ◽  
Vol 2016 ◽  
pp. 1-10 ◽  
Author(s):  
Dongju Chen ◽  
Shuai Zhou ◽  
Lihua Dong ◽  
Jinwei Fan
Keyword(s):  
Machine Tool ◽  
Frequency Domain ◽  
Surface Topography ◽  
High Frequency ◽  
Low Frequency ◽  
Frequency Signal ◽  
High Frequency Signal ◽  
Time Frequency ◽  
Cross Correlation Analysis ◽  
Correlation Analysis Method

This paper presents a new identification method to identify the main errors of the machine tool in time-frequency domain. The low- and high-frequency signals of the workpiece surface are decomposed based on the Daubechies wavelet transform. With power spectral density analysis, the main features of the high-frequency signal corresponding to the imbalance of the spindle system are extracted from the surface topography of the workpiece in the frequency domain. With the cross-correlation analysis method, the relationship between the guideway error of the machine tool and the low-frequency signal of the surface topography is calculated in the time domain.

Vibrational Resonance in an Overdamped System with a Fractional Order Potential Nonlinearity

2018 ◽  
Vol 28 (07) ◽  
pp. 1850082 ◽  
Author(s):  
Jianhua Yang ◽  
Dawen Huang ◽  
Miguel A. F. Sanjuán ◽  
Houguang Liu
Keyword(s):  
Numerical Simulation ◽  
Nonlinear System ◽  
Theoretical Analysis ◽  
Fractional Order ◽  
Low Frequency ◽  
Response Amplitude ◽  
Resonance Phenomenon ◽  
Vibrational Resonance ◽  
Frequency Excitation ◽  
Overdamped System

We investigate the vibrational resonance by the numerical simulation and theoretical analysis in an overdamped system with fractional order potential nonlinearities. The nonlinearity is a fractional power function with deflection, in which the response amplitude presents vibrational resonance phenomenon for any value of the fractional exponent. The response amplitude of vibrational resonance at low-frequency is deduced by the method of direct separation of slow and fast motions. The results derived from the theoretical analysis are in good agreement with those of numerical simulation. The response amplitude decreases with the increase of the fractional exponent for weak excitations. The amplitude of the high-frequency excitation can induce the vibrational resonance to achieve the optimal response amplitude. For the overdamped systems, the nonlinearity is the crucial and necessary condition to induce vibrational resonance. The response amplitude in the nonlinear system is usually not larger than that in the corresponding linear system. Hence, the nonlinearity is not a sufficient factor to amplify the response to the low-frequency excitation. Furthermore, the resonance may be also induced by only a single excitation acting on the nonlinear system. The theoretical analysis further proves the correctness of the numerical simulation. The results might be valuable in weak signal processing.

Wavelet De-Noising Algorithm Based on OpenCV for Images Edge Detection

2014 ◽  
Vol 989-994 ◽  
pp. 3973-3976
Author(s):  
Yi Fan Ma ◽  
Shu Gui Liu
Keyword(s):  
Edge Detection ◽  
High Frequency ◽  
Low Frequency ◽  
Frequency Signal ◽  
High Frequency Signal ◽  
Canny Edge Detection ◽  
Image Edge Detection ◽  
Canny Edge ◽  
Image Edge ◽  
Wavelet Algorithm

Image edge detection is easily affected by noise. Wavelet algorithm can divide the image into low frequency and high frequency. By the processing of high frequency signal and the reconstruction of wavelet coefficients, the purpose of removing noise can be achieved. In the environment of VC++6.0, an image de-noising algorithm based on the wavelet combined with the Canny edge detection is proposed, which obtains a good result. The above algorithms are implemented based on OpenCV, which is more efficient, providing the conditions for subsequent image analysis and recognition. Experiments are carried out and the results show that the proposed algorithm is available and has a good performance.

An improved adaptive stochastic resonance with general scale transformation to extract high-frequency characteristics in strong noise

2018 ◽  
Vol 32 (15) ◽  
pp. 1850185 ◽  
Author(s):  
Dawen Huang ◽  
Jianhua Yang ◽  
Jingling Zhang ◽  
Houguang Liu
Keyword(s):  
Stochastic Resonance ◽  
High Frequency ◽  
Signal To Noise Ratio ◽  
Scale Transformation ◽  
Weak Signal ◽  
Signal Features ◽  
Signal Characteristics ◽  
Periodic Signals ◽  
Sr Method ◽  
General Scale

The idea of general scale transformation is introduced in detail. Based on this idea, an improved adaptive stochastic resonance (SR) method is proposed to extract weak signal features. Different periodic signals are considered to verify the proposed method. Compared with the normalized scale transformation, the output signal-to-noise ratio (SNR) of the proposed method is increased to a greater extent. Further, the influences of some key parameters on the responses of the two methods are discussed minutely. Results show that the improved adaptive SR method with general scale transformation is obviously superior to the traditional normalized scale transformation that is used in the former literatures. For different noise intensities and time scales, the proposed approach can always obtain the optimal response of SR to enhance the weak signal characteristics.

Optimizing the Electrical Power in an Energy Harvesting System

2015 ◽  
Vol 25 (12) ◽  
pp. 1550171 ◽  
Author(s):  
Mattia Coccolo ◽  
Grzegorz Litak ◽  
Jesús M. Seoane ◽  
Miguel A. F. Sanjuán
Keyword(s):  
Energy Harvesting ◽  
Kinetic Energy ◽  
High Frequency ◽  
Energy Harvester ◽  
Electrical Power ◽  
Low Frequency ◽  
Electrical Energy ◽  
Resonance Phenomenon ◽  
Vibrational Resonance ◽  
Energy Harvesting System

In this paper, we study the vibrational resonance (VR) phenomenon as a useful mechanism for energy harvesting purposes. A system, driven by a low frequency and a high frequency forcing, can give birth to the vibrational resonance phenomenon, when the two forcing amplitudes resonate and a maximum in amplitude is reached. We apply this idea to a bistable oscillator that can convert environmental kinetic energy into electrical energy, that is, an energy harvester. Normally, the VR phenomenon is studied in terms of the forcing amplitudes or of the frequencies, that are not always easy to adjust and change. Here, we study the VR generated by tuning another parameter that is possible to manipulate when the forcing values depend on the environmental conditions. We have investigated the dependence of the maximum response due to the VR for small and large variations in the forcing amplitudes and frequencies. Besides, we have plotted color coded figures in the space of the two forcing amplitudes, in which it is possible to appreciate different patterns in the electrical power generated by the system. These patterns provide useful information on the forcing amplitudes in order to produce the optimal electrical power.

Reduction Methods of Structure Models for Control System Purposes

2016 ◽  
Vol 248 ◽  
pp. 119-126 ◽  
Author(s):  
Andrzej Koszewnik ◽  
Zdzisław Gosiewski
Keyword(s):  
Control System ◽  
High Frequency ◽  
Closed Loop ◽  
Flexible Structures ◽  
Low Frequency ◽  
Point Of View ◽  
Closed Loop Systems ◽  
System A ◽  
Reduction Methods ◽  
The Stability

To design vibration control system for flexible structures their mathematical model should be reduced. In the paper we consider the influence of the model reduction on the dynamics of the real closed-loop system. A simply cantilever beam is an object of consideration since we are able to formulate the exact analytical model of such structure. As a result of reduction the model with low frequency resonances is usually separated from the high frequency dynamics because high frequency part of the model is naturally strong damped. In order to estimate dynamical system for control purposes in the paper we applied a few orthogonal methods such as: modal, Rayleigh-Ritz and Schur decompositions. As it is shown all methods well calculate resonances frequencies but generate different anti-resonances frequencies. From control strategy in point of view of the flexible structures these anti-resonances have significantly influence on the stability and dynamics of the closed-loop systems.

DIELECTRIC EVIDENCE FOR ACETONE HYDRATE

1963 ◽  
Vol 41 (2) ◽  
pp. 264-273 ◽  
Author(s):  
G. J. Wilson ◽  
D. W. Davidson
Keyword(s):  
Activation Energy ◽  
Dielectric Constant ◽  
High Frequency ◽  
Water System ◽  
Low Frequency ◽  
Water Molecules ◽  
Incongruent Melting ◽  
High Frequency Dielectric Constant ◽  
System A ◽  
Acetone Water

The phase diagram of the acetone–water system shows that acetone hydrate decomposes at an incongruent melting point. The existence of acetone hydrate is confirmed by a study of the low-frequency dielectric properties of this system. A dispersion region, related to the relaxation of water molecules in the clathrate structure, is characterized by a "static" dielectric constant and an activation energy about half as large as the corresponding values for ice, and by a limiting high-frequency dielectric constant of about 7 at 200° K. The magnitude of the latter is attributed to orientation of acetone molecules within the larger cavities of the hydrate structure.

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