[en] We investigate a multi-frequency signal that cannot be decomposed by empirical mode decomposition directly. Moreover, this kind of signal in the noisy background cannot be decomposed successfully by the traditional stochastic resonance with bistable system yet. We propose a new method which using the empirical mode decomposition combined the adaptive stochastic resonance in a new periodical model to solve this problem. The results show that the proposed method decomposes the multi-frequency signal perfectly. Meanwhile, the general scale transformation and random particle swarm optimization algorithm are used to help obtain a better result in the process of optimization. Through using this new method, the simulation results are satisfactory. More importantly, this new method also shows good performance in the application of bearing fault diagnosis.

[en] A method is proposed to induce strong aperiodic resonance in a linear frequency modulated signal excited nonlinear system. The phenomenon has application value in weak linear frequency modulated signal enhancement. The spectral amplification factor is used to measure the aperiodic resonance performance. By piece-wise analysis, appropriate system parameters are found. Then, a strong resonance output is achieved. The cross-correlation coefficient between the input and the output is another measurement of aperiodic resonance. However, there is a weakness in analysis of the linear frequency modulated signal. To overcome the shortness, a modified cross-correlation coefficient is proposed. As a result, the error of the cross-correlation coefficient induced by the phase difference of the excited signal is eliminated. In addition, by adding another much faster excitation, aperiodic resonance is further enhanced by vibrational resonance. (paper)

[en] We propose a fractional-order system resonance method for enhancing the weak characteristics of raw signals. The system response amplitude is used as the evaluation index. Based on this, the optimal value of a fractional order is found to achieve the system resonance. By analyzing the system responses, weak low-frequency signals can apparently be enhanced. Both numerical and approximate analytical solutions are used to certify the accuracy and validity of the method. However, if an excitation is a high-frequency signal, the signal cannot usually be favorably enhanced by the system with small system parameters. Nevertheless, a re-scaled method allows us to seek appropriate matching parameters to achieve the enhancement of the high-frequency signal. Two intuitional studies on the high-frequency harmonic signal and bearing fault simulated signal are performed to verify the effectiveness of the re-scaled method. By processing the experimental bearing fault signals, the results indicate that the amplitude at the fault frequency is greatly amplified and those at other frequencies are obviously suppressed simultaneously. It shows excellent performances in the bearing fault recognition. In addition, we compare the fractional-order system resonance with stochastic resonance (SR) and vibrational resonance (VR), respectively. The excellent performance of the proposed new method is shown. (paper)

[en] Rolling bearings often run under variable speed condition, in addition to constant speed condition. How to achieve the bearing fault diagnosis under variable speed condition has been an important and hot issue. Nevertheless, there are few works on bearing fault diagnosis under variable speed condition especially for the feature extraction of unknown fault. Thus, this paper proposes a method based on fractional Fourier transform (FRFT) and stochastic resonance (SR) to extract bearing fault features. First, we use FRFT filtering algorithm to extract fault formation from the original signal. Next, we apply zero centering and high pass filtering to the signal which contains the fault information. Since the separated fault information is usually relatively weak and is not easy to identify, SR is used to enhance the weak fault feature information. Finally, bearing fault is diagnosed by observing the fault characteristic frequency in the time-frequency distribution plane. The method can achieve the extraction of the bearing fault characteristic frequency in the unknown situation and meanwhile remove a lot of noise interference. The method has been validated by numerical simulations and experimental analyses, where the scratches on both outer race and rolling element can be diagnosed successfully. By comparison with previous methods, fast kurtogram and variable mode decomposition, fault features extracted by the proposed method are much clearer and more accurate. The method may provide reference for the application of fault diagnosis in engineering occasions. (paper)

[en] We investigate logical stochastic resonance (LSR) in a nonlinear fractional-order system with an asymmetric bistable potential function. We use the success probability of the logical output to measure the logical operation ability of the system. If the success probability is 1, the logical output presents reliable LSR completely. When there are only two logical signals existing in the excitation, LSR can be realized by varying the value of the fractional order or the bias of the potential function. If the fractional order is relatively large, the system performs correct logical operations more easily. With the increase in the bias, the interval of the fractional order corresponding to LSR increases first and then decreases. When both logical signals and Gaussian white noise exist in the excitation, the intervals of the fractional order and the bias corresponding to LSR decrease with the increase in the noise intensity. In addition, with the increase in the value of the fractional order, the maximal value of the success probability also increases. Further, the system usually performs more accurate logical operations when the value of the fractional order lies in the interval [1, 1.5]. The results expand the achievements of LSR. They also provide a reference in choosing an optimal system of LSR.

[en] The stochastic resonance phenomenon in overdamped systems with fractional power nonlinearity is thoroughly investigated. The first kind of nonlinearity is a general fractional power function. The second kind of nonlinearity is a fractional power function with deflection. For the first case, the response is clearly divergent for some fractional exponent values. The curve of the spectral amplification factor versus the fractional exponent presents some discrete regions. For the second case, the response will not be divergent for any fractional exponent value. The spectral amplification factor decreases with the increase in the fractional exponent. For both cases, the nonlinearity is the necessary ingredient to induce stochastic resonance. However, it is not the sufficient cause to amplify the weak signal. On the one hand, the noise cannot induce stochastic resonance in the corresponding linear system. On the other hand, the spectral amplification factor of the nonlinear system is lower than that of the corresponding linear system. Through the analysis carried out in this paper, we are able to find that the system with fractional deflection nonlinearity is a better stochastic resonance system, especially when an appropriate exponent value is chosen. The results in this paper might have a certain reference value for signal processing problems in relation with the stochastic resonance method.