Traditional Stochastic Resonance Research Articles

Asymmetric delay feedback stochastic resonance detection method based on prior knowledge particle swarm optimization

For the adjustable parameters stochastic resonance system, the selection of the structural parameters plays a decisive role in the performance of the detection method. The vibration signal of rotating machinery is non-linear and unstable, and its weak fault characteristics are easily concealed by noise. Under strong background noise interference, the detection of fault features is particularly challenging. Therefore, a type of weak fault feature extraction method, named knowledge-based particle swarm optimization algorithm for asymptotic delayed feedback stochastic resonance (abbreviated as KPSO-ADFSR) is proposed. Through deduction under adiabatic approximation, we observe that both the asymmetric parameters, the length of delay and the feedback strength, impact the potential function. After adjusting the asymmetric parameters of the system, the output signal-to-noise ratio (SNR) is used as the fitness function, and the setting of the relationship between the noise intensity and barrier height is used as the prior knowledge of the particle swarm algorithm. Through this algorithm, the delay length and the feedback strength are optimized. This method achieves global optimization of system parameters in a short time; it overcomes the shortcomings of the traditional stochastic resonance method, which has a long convergence time and tends to easily fall into local optimization. It can effectively improve the detection of weak fault features. In the bearing rolling body pitting corrosion failure experiment and steel field engineering experiment, the proposed method could extract the characteristics of a weak fault more effectively than the traditional stochastic resonance method based on the standard particle swarm algorithm.

A novel adaptive stochastic resonance method based on coupled bistable systems and its application in rolling bearing fault diagnosis

Abstract Stochastic resonance (SR), as a typical noise-assisted signal processing method, has been extensively studied in weak signal detection by virtue of the advantage of using noise to enhance the feature of periodic signal. And how to better apply the SR method in engineering signal processing has always been the research hotspot. In this paper, a novel adaptive SR method based on coupled bistable systems (ACBSR) is proposed to further improve the performance of SR method for weak signal detection. Compared with the cascaded bistable SR system, the suggested coupled bistable SR (CBSR) system can enhance the target signal while suppressing the low-frequency and high-frequency interferences, whose output behavior exhibits good bandpass filtering characteristic. In addition, a weighted spectral peak signal-to-noise ratio (WPSNR) index is constructed by using spectral peak SNR, spectral correlation coefficient and zero-crossing ratio to serve as the measurement index of SR for periodic signal detection. The constructed WPSNR index is simple in form and easy to calculate, which can quantitatively evaluate the resonance effect of periodic signal, even though the target signal frequency cannot be estimated accurately. And the combination of WPSNR index and the CBSR system is beneficial to improve the performance of SR method in rolling bearing fault diagnosis. Experiments and engineering application are performed to verify the effectiveness and superiority of the proposed ACBSR method in comparison with the traditional SR method.

A multiscale noise tuning stochastic resonance for fault diagnosis in rolling element bearings

Condition monitoring of rotating machinery is important to extend the mechanical system's reliability and operational life. However, in many cases, useful information is often overwhelmed by strong background noise and the defect frequency is difficult to be extracted. Stochastic resonance (SR) is used as a noise-assisted tool to amplify weak signals in nonlinear systems, which can detect weak signals of interest submerged in the noise. The multiscale noise tuning SR (MSTSR), which is originally based on discrete wavelet transform (DWT), has been applied to identify the fault characteristics and has also increased the signal-to-noise ratio (SNR) improvement of SR. Therefore, a novel tri-stable SR method with multiscale noise tuning (MST) is proposed to extract fault signatures for fault diagnosis of rotating machinery. The wavelet packets transform (WPT) based MST can obtain better denoising effect and higher SNR of resonance output compared with the traditional SR method. Thus the proposed method is well-suited for enhancement of rotating machine fault identification, whose effectiveness has been verified by means of practical vibration signals carrying fault information from bearings. Finally, it can be concluded that the proposed method has practical value in engineering.

Stochastic resonance energy harvesting for a rotating shaft subject to random and periodic vibrations: influence of potential function asymmetry and frequency sweep

Stochastic resonance is referred to as a physical phenomenon that is manifest in nonlinear systems whereby a weak periodic signal can be significantly amplified with the aid of inherent noise or vice versa. In this paper, stochastic resonance is considered to harvest energy from two typical vibrations in rotating shafts: random whirl vibration and periodic stick-slip vibration. Stick-slip vibrations impose a constant offset in centrifugal force and distort the potential function of the harvester, leading to potential function asymmetry. A numerical analysis based on a finite element method was conducted to investigate stochastic resonance with potential function asymmetry. Simulation results revealed that a harvester with symmetric potential function generates seven times higher power than that with asymmetric potential function. Furthermore, a frequency-sweep analysis also showed that stochastic resonance has hysteretic behavior, resulting in frequency difference between up-sweep and down-sweep excitations. An electromagnetic energy harvesting system was constructed to experimentally verify the numerical analysis. In contrast to traditional stochastic resonance harvesters, the proposed harvester uses magnetic force to compensate the offset in the centrifugal force. System identification was performed to obtain the parameters needed in the numerical analysis. With the identified parameters, the numerical simulations showed good agreement with the experiment results with around 10% error, which verified the effect of potential function asymmetry and frequency sweep excitation condition on stochastic resonance. Finally, attributed to compensating the centrifugal force offset, the proposed harvester generated nearly three times more open-circuit output voltage than its traditional counterpart.

Realizing the empirical mode decomposition by the adaptive stochastic resonance in a new periodical model and its application in bearing fault diagnosis

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.

Weak Signal Detection Based on Cascade Adaptive Stochastic Resonance

The gain of the output signal-to-noise ratio (SNR) is insufficient in traditional stochastic resonance (SR) method to detect weak signals. In order to obtaining a higher SNR gain, a kind of signal detection method of adaptive stochastic resonance that use cascade system is proposed. To achieve the optimal output, stochastic resonance parameters adjustment is transformed into the multi-parameter optimization of particle swarm optimization. The optimal result in weak signal detection can be reached by adjusting the parameters of two layers subsystem. The weak signal submerged in strong noise background can be extracted through this simple method that has a fast convergence speed. The threshold of the weak signal detection is lowered by this method, and the applicable scope of stochastic resonance can be enlarged.

An adaptive stochastic resonance method for weak fault characteristic extraction in planetary gearbox

Planetary gearbox is widely used in rotating machinery and prone to damage and failure due to heavy load and complex operating conditions. Furthermore, due to heavy background noise and complicated transmission path, the fault characteristics imbedded in the acquired signals is very weak and difficult to be extracted. Therefore, it is a challenge task for extracting fault characteristics of planetary gearboxes. To tackle this task, this paper proposes an adaptive stochastic resonance method for weak fault characteristic extraction of planetary gearbox, where a chaos ant colony algorithm characterized global optimization ability is employed to achieve adaptive matching between potential parameters and thereby overcoming the local optimization shortcoming of traditional stochastic resonance. Simulation and planetary gearbox experiments with a missing tooth and broken tooth validate the effectiveness of the proposed method, respectively. The results show that the proposed method is not only able to extract weak fault characteristics but also superior to singular value decomposition method.

Improving the bearing fault diagnosis efficiency by the adaptive stochastic resonance in a new nonlinear system

It is a challenging task to detect the weak character signal in the noisy background. The stochastic resonance (SR) method has been wildly adopted recently because it can not only reduce the noise, but also enhance the weak feature information simultaneously. However, the traditional bistable model for SR is not perfect. So, this paper presents a new model with periodic potential to induce the adaptive SR. In the new model, based on the adaptive SR theory, the system parameters are simultaneously optimized by the improved artificial fish swarm algorithm. Meanwhile, the improved signal-to-noise ratio (ISNR) is set as the evaluation index. When the ISNR reaches a maximum, the output is optimal. In order to eliminate interference to obtain more useful information, the signals are preprocessed by Hilbert transform and High-pass filter before being input to the adaptive SR system. To verify the effectiveness of the proposed method, both numerical simulation and the vibration signal of the rolling element bearing from the lab experimental are adopted. Both of the results indicate that the adaptive SR model proposed shows better performance in weak character signals detection than the traditional adaptive SR in the bistable model. Meanwhile, the experimental signals with different working conditions are also processed by the new method. The results show that the method proposed could be more widely applied.

Effects of the colored noise on the resonance at the subharmonic frequency in bistable systems

We investigate the colored noise induced resonance at the 1/3 subharmonic frequency in the overdamped and the underdamped bistable systems by numerical simulations. We find that the resonance at the 1/3 subharmonic frequency may be stronger than the traditional stochastic resonance that occurring at the excitation frequency in some cases. Moreover, we study the effects of the correlation time of the colored noises on the response in detail. If the colored noise is generated by the Ornstein–Uhlenbeck process, there are two major results discovered. Firstly, the critical noise intensity which induces the strongest resonance will increase with the increase of the correlation time. Secondly, when the noise intensity is large enough, the response amplitude at the considered frequency will also increase with the increase of the correlation time. If the colored noise is generated by the power-limited process, the corresponding results are contrary to those in the system under the colored noise excitation that is generated by the Ornstein-Uhlenbeck process. The results in this paper indicate that the type of the colored noise has important effects on the responses of the system.

An underdamped stochastic resonance method with stable-state matching for incipient fault diagnosis of rolling element bearings

Most traditional overdamped monostable, bistable and even tristable stochastic resonance (SR) methods have three shortcomings in weak characteristic extraction: (1) their potential structures characterized by single stable-state type are insufficient to match with the complicated and diverse mechanical vibration signals; (2) they vulnerably suffer the interference from multiscale noise and largely depend on the help of highpass filters whose parameters are selected subjectively, probably resulting in false detection; and (3) their rescaling factors are fixed as constants generally, thereby ignoring the synergistic effect among vibration signals, potential structures and rescaling factors. These three shortcomings have limited the enhancement ability of SR. To explore the SR potential, this paper initially investigates the SR in a multistable system by calculating its output spectral amplification, further analyzes its output frequency response numerically, then examines the effect of both damping and rescaling factors on output responses and finally presents a promising underdamped SR method with stable-state matching for incipient bearing fault diagnosis. This method has three advantages: (1) the diversity of stable-state types in a multistable potential makes it easy to match with various vibration signals; (2) the underdamped multistable SR, equivalent to a moving nonlinear bandpass filter that is dependent on the rescaling factors, is able to suppress the multiscale noise; and (3) the synergistic effect among vibration signals, potential structures and rescaling and damping factors is achieved using quantum genetic algorithms whose fitness functions are new weighted signal-to-noise ratio (WSNR) instead of SNR. Therefore, the proposed method is expected to possess good enhancement ability. Simulated and experimental data of rolling element bearings demonstrate its effectiveness. The comparison results show that the proposed method is able to obtain higher amplitude at target frequency and larger output WSNR, and performs better than traditional SR methods.

Rotating machine fault diagnosis through enhanced stochastic resonance by full-wave signal construction

This study proposes a full-wave signal construction (FSC) strategy for enhancing rotating machine fault diagnosis by exploiting stochastic resonance (SR). The FSC strategy is utilized to transform a half-wave signal (e.g., an envelope signal) into a full-wave one by conducting a Mirror–Cycle–Add (MCA) operation. The constructed full-wave signal evenly modulates the bistable potential and makes the potential tilt back and forth smoothly. This effect provides the equivalent transition probabilities of particle bounce between the two potential wells. A stable SR output signal with better periodicity, which is beneficial to periodic signal detection, can be obtained. In addition, the MCA operation can improve the input signal-to-noise ratio by enhancing the periodic component while attenuating the noise components. These two advantages make the proposed FSCSR method surpass the traditional SR method in fault signal processing. Performance evaluation is conducted by numerical analysis and experimental verification. The proposed MCA-based FSC strategy has the potential to be a universal signal pre-processing technique. Moreover, the proposed FSCSR method can be used in rotating machine fault diagnosis and other areas related to weak signal detection.

Periodic fault signal enhancement in rotating machine vibrations via stochastic resonance

This paper proposes a novel approach to periodic fault signal enhancement in rotating machine vibrations with a tristable mechanical vibration amplifier (TMVA) by exploiting stochastic resonance (SR). The TMVA is a nonlinear physical structure system that consists of a cantilever beam and a magnet system. Through the TMVA, the periodic weak signal can be amplified with the assistance of noise in the regime of SR. Benefitting from a wider interwell spacing and a smoother potential curve, the TMVA produces a more regular output waveform with lower noise in a wider operating bandwidth as compared to the monostable and bistable amplifiers. Different from the traditional signal enhancement approach which is based on digital signal processing (DSP) techniques, the designed physical structure can realize signal enhancement in a simple, intuitive, effective and adaptive way without too much complex operations. The effectiveness and efficiency of the proposed approach are validated by a simulated fault signal and the practical bearing and gearbox fault signals, in comparison with a traditional DSP-based SR method. The principle of the proposed approach shows potential applications on rotating machine fault diagnosis area and other areas related to weak periodic signal enhancement.

Nonstationary weak signal detection based on normalization stochastic resonance with varying parameters

The nonlinear stochastic resonance system possesses the ability of taking advantage of background noise to enhance the weak signal. It provides a new approach to detect the weak signal embedded with heavy noise. This study proposes a new varying parameter stochastic resonance employing the fourth-order Runge–Kutta numerical method as well as the normalized transformation of a bistable stochastic resonance system. The model performs well in the detection of a time-varying signal with background noise for denoising and signal recovery. We take the fitness coefficient and cross-correlation coefficient as the criteria and analyze the influence of different parameters. The simulating results indicate its availability, validity and that it generates a better performance than the traditional stochastic resonance. The method develops the area of time-varying signal detection with stochastic resonance and presents new strategy for detection and denoising of a time-varying signal. It can be expected to be widely used in the areas of aperiodic signal processing, radar communication, etc.

Enhanced Rotating Machine Fault Diagnosis Based on Time-Delayed Feedback Stochastic Resonance

The fault-induced impulses with uneven amplitudes and durations are always accompanied with amplitude modulation and (or) frequency modulation, which leads to that the acquired vibration/acoustic signals for rotating machine fault diagnosis always present nonlinear and nonstationary properties. Such an effect affects precise fault detection, especially when the impulses are submerged in heavy background noise. To address this issue, a nonstationary weak signal detection strategy is proposed based on a time-delayed feedback stochastic resonance (TFSR) model. The TFSR is a long-memory system that can utilize historical information to enhance the signal periodicity in the feedback process, and such an effect is beneficial to periodic signal detection. By selecting the proper parameters including time delay, feedback intensity, and calculation step in the regime of TFSR, the weak signal, the noise, and the potential can be matched with each other to an extreme, and consequently a regular output waveform with low-noise interference can be obtained with the assistant of the distinct band-pass filtering effect. Simulation study and experimental verification are performed to evaluate the effectiveness and superiority of the proposed TFSR method in comparison with a traditional stochastic resonance (SR) method. The proposed method is suitable for detecting signals with strong nonlinear and nonstationary properties and (or) being subjected to heavy multiscale noise interference.

Effects of underdamped step-varying second-order stochastic resonance for weak signal detection

Stochastic resonance (SR) has been proved to be an effective approach for weak signal detection. In this paper, an underdamped step-varying second-order SR (USSSR) method is proposed to further improve the output signal-to-noise ratio (SNR). In the method, by selecting a proper underdamped damping factor and a proper calculation step, the weak periodic signal, the noise and the potential can be matched with each other in the regime of second-order SR to generate an optimal dynamical system. The proposed method has three distinct merits as: 1) secondary filtering effect produces a low-noise output waveform; 2) good band-pass filtering effect attenuates the multiscale noise that locates in high- and (or) low-frequency domains; and 3) good anti-noise capability in detecting weak signal being submerged in heavy background noise. Numerical analysis and application verification are performed to confirm the effectiveness and efficiency of the proposed method in comparison with a traditional SR method.

Adaptive bistable stochastic resonance and its application in mechanical fault feature extraction

Stochastic resonance (SR) is an important approach to detect weak vibration signals from heavy background noise. In order to increase the calculation speed and improve the weak feature detection performance, a new bistable model has been built. With this model, an adaptive and fast SR method based on dyadic wavelet transform and least square system parameters solving is proposed in this paper. By adding the second-order differential item into the traditional bistable model, noise utilization can be increased and the quality of SR output signal can be improved. The iteration algorithm for implementing the adaptive SR is given. Compared with the traditional adaptive SR method, this algorithm does not need to set up the searching range and searching step size of the system parameters, but only requires a few iterations. The proposed method, discrete wavelet transform and the traditional adaptive SR method are applied to analyzing simulated vibration signals and extracting the fault feature of a rotor system. The contrastive results verify the superiority of the proposed method, and it can be effectively applied to weak mechanical fault feature extraction.

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

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.

Stochastic resonance with Woods–Saxon potential for rolling element bearing fault diagnosis

This paper proposes a weak signal detection strategy for rolling element bearing fault diagnosis by investigating a new mechanism to realize stochastic resonance (SR) based on the Woods–Saxon (WS) potential. The WS potential has the distinct structure with smooth potential bottom and steep potential wall, which guarantees a stable particle motion within the potential and avoids the unexpected noises for the SR system. In the Woods–Saxon SR (WSSR) model, the output signal-to-noise ratio (SNR) can be optimized just by tuning the WS potential's parameters, which delivers the most significant merit that the limitation of small parameter requirement of the classical bistable SR can be overcome, and thus a wide range of driving frequencies can be detected via the SR model. Furthermore, the proposed WSSR model is also insensitive to the noise, and can detect the weak signals with different noise levels. Additionally, the WS potential can be designed accurately due to its parameter independence, which implies that the proposed method can be matched to different input signals adaptively. With these properties, the proposed weak signal detection strategy is indicated to be beneficial to rolling element bearing fault diagnosis. Both the simulated and the practical bearing fault signals verify the effectiveness and efficiency of the proposed WSSR method in comparison with the traditional bistable SR method.

Under Sampling Stochastic Resonance for Detecting Weak Signal

For stochastic resonance can enhance the signal-to-noise ratio, it is widely applied to detect weak signal in a strong noise background. Aiming at the issue of the traditional stochastic resonance only applicable to deal with small parameters signals, a weak signal detection method based on under sampling stochastic resonance was proposed. Stochastic resonance was successfully expanded into the applications of the large parameters signals on the basis of scale-transformation and retrieve technology in the under sampling stochastic resonance. The improved stochastic resonance model was put forward and simulation results have proved the validity of the method. Large parameters weak signal mixed with strong noise is detected accurately. This method is effective for future application.

Multi-scale bistable stochastic resonance array: A novel weak signal detection method and application in machine fault diagnosis

Weak signal detection based on stochastic resonance (SR) can hardly succeed when noise intensity exceeds the optimal value of SR. This paper explores a novel parallel bistable SR array mechanism by decomposed multi-scale noises from input signal. A smoother output with lower noise is obtained from the combination of colored noise SR effect and parallel bistable SR array. The influence of noise intensity and array size on the SR effect and output noise intensity is analyzed through numerical simulation. A signal detection method based on the new SR mechanism and normalized scale transform is proposed for the case of heavy background noise. Simulation is conducted to confirm the effectiveness of parameter tuning and amplitude tuning of normalized scale transform on the proposed SR model. The proposed method has three advantages: the input noise intensity of each unit is reduced by wavelet decomposition; the output noise level decreases due to array ensemble average; the SR effect of each unit is optimized by normalized scale transform for high frequency signal. Experiment on bearing inner and outer race fault diagnosis has verified the effectiveness and advantages of the proposed SR model in comparison with traditional SR method and kurtogram.