Classical Bistable Stochastic Resonance Research Articles

Mechanism analysis and application of multi-dimensional single potential well stochastic resonance system

Currently, the focus of stochastic resonance (SR) research is primarily on bistable systems, and classical bistable SR systems have the problems of low dimension, inconvenient parameter adjustment, and high threshold for SR effects. In this paper, based on the classic bistable system, a class of multi-dimensional single potential well SR systems without transition threshold is proposed and applied to signal processing. Firstly, the mechanism of double potential well SR and single potential well SR is studied. On this basis, a kind of multi-dimensional single potential well SR system is defined and its theoretical conditions are analyzed. Then a specific four-dimensional single potential well SR system is constructed, and the dynamics of the system is analyzed. The gain range and the approximate relationship between the system input and the four-dimensional output are derived. Finally, the four-dimensional single potential well SR system is applied to the processing of various signals. The experimental results show that the constructed system has good noise reduction and feature amplification effects on noisy signals through the advantages of multi-dimensional output, and can be used to highlight the fault feature frequency in bearing fault signals.

Power System Signal-Detection Method Based on the Accelerated Unsaturated Stochastic Resonance Principle

The classical bistable stochastic resonance algorithm has an inherent output saturation defect that restricts the amplitude of the output signal. This paper examines the causes of this phenomenon and its negative impact on the detection of weak signals. Proposing the Unsaturated Bistable Stochastic Resonance (UBSR) detection algorithm involves constructing a segmented potential function using a linear function to eliminate the effect of higher-order terms in the classical stochastic resonance algorithm. A new type of segmented potential function has been created by combining exponential and linear functions. This new function helps to eliminate the impact of higher-order terms in classical algorithms while also improving the noise immunity of the stochastic resonance system. This results in the development of the accelerated stochastic resonance (ASR) detection algorithm. In this paper, the Kramers escape rate and output signal-to-noise ratio of two improved stochastic resonance algorithms are theoretically derived and compared with the classical bistable stochastic resonance algorithms, and the proposed algorithms are able to effectively avoid the output saturation phenomenon and have more excellent detection performance under strong background noise.

Bearing fault feature extraction based on MOMEDA and CS-Wood–Saxon stochastic resonance

Since rolling bearing is of great significance to ensure the safe and stable operation of rotating machinery, bearing fault feature extraction then demonstrates a hot topic of general interest in industry. In this work, we applied Multipoint Optimal Minimum Entroy Deconvolution Adjusted preprocessing algorithm to deal with the large amount of background noise containing in the collected bearing fault original signal. Then, the Wood–Saxon stochastic resonance nonlinear system model is adopted to solve the bearing fault feature extraction problem, which avoids the frequency interval and system parameters disadvantages in bistable stochastic resonance system. Furthermore, the parameter step and scale transform factor in the Wood–Saxon stochastic resonance nonlinear system is optimized adaptively by Cuckoo Search algorithm, in which way the output signal-to-noise of bearing fault signal is improved significantly. Therefore, the bearing fault feature can be extracted more effectively compared with the classical bistable stochastic resonance system model. Simulation and examples demonstrated that the proposed method can effectively reduce the noise in the signal and enhance the weak feature in bearing fault signal, so as to realize the accurate early bearing fault diagnosis.

Enhanced fault diagnosis via stochastic resonance in a piecewise asymmetric bistable system.

Weak fault signals are often overwhelmed by strong noise or interference. The key issue in fault diagnosis is to accurately extract useful fault characteristics. Stochastic resonance is an important signal processing method that utilizes noise to enhance weak signals. In this paper, to address the issues of output saturation and imperfect optimization of potential structure models in classical bistable stochastic resonance (CBSR), we propose a piecewise asymmetric stochastic resonance system. A two-state model is used to theoretically derive the output signal-to-noise ratio (SNR) of the bistable system under harmonic excitations, which is compared with the SNR of CBSR to demonstrate the superiority of the method. The method is then applied to fault data. The results indicate that it can achieve a higher output SNR and higher spectral peaks at fault characteristic frequencies/orders, regardless of whether the system operates under fixed or time-varying speed conditions. This study provides new ideas and theoretical guidance for improving the accuracy and reliability of fault diagnosis technology.

Stochastic resonance in Hindmarsh-Rose neural model driven by multiplicative and additive Gaussian noise

This paper investigates the occurrence of stochastic resonance in the three-dimensional Hindmarsh-Rose (HR) neural model driven by both multiplicative and additive Gaussian noise. Firstly, the three-dimensional HR neural model is transformed into the one-dimensional Langevin equation of the HR neural model using the adiabatic elimination method, and the effects of HR neural model parameters on the potential function are analyzed. Secondly the Steady-state Probability Density (SPD), the Mean First-Passage Time (MFPT), and the Signal-to-Noise Ratio (SNR) of the HR neural model are derived, based on two-state theory. Then, the effects of different parameters (a, b, c, s), noise intensity, and the signal amplitude on these metrics are analyzed through theoretical simulations, and the behavior of particles in a potential well is used to analyze how to choose the right parameters to achieve high-performance stochastic resonance. Finally, numerical simulations conducted with the fourth-order Runge–Kutta algorithm demonstrate the superiority of the HR neural model over the classical bistable stochastic resonance (CBSR) in terms of performance. The peak SNR of the HR neural model is 0.63 dB higher than that of the CBSR system. Simulation results indicate that the occurrence of stochastic resonance occur happens in HR neural model under different values of parameters. Furthermore, under certain conditions, there is a ‘suppress’ phenomenon that can be produced by changes in noise, which provides great feasibilities and practical value for engineering application.

Fault feature extraction method of rolling bearings based on coupled resonance system with vibrational resonance-assisted enhanced stochastic resonance

Stochastic resonance (SR), as a signal processing method that is able to use noise to enhance weak periodic signals, provides effective technical support for the detection of weak signals. However, due to the constraints of potential functions or control means, the detection results of a single SR system on weak signals often fails to achieve the desired effect. Through the interaction between different subsystems, SR under the action of multiple systems can obtain rich dynamic response characteristics and improve the detection ability of weak signals. Therefore, this paper proposes a fault feature extraction method of rolling bearings based on a coupled resonance system with vibrational resonance (VR)-assisted enhanced SR. First, a SR system based on a matched steady-state potential model is constructed, which has the ability to alleviate the phenomenon of output saturation to some extent compared with the classical bistable SR. Second, inspired by the synergy of multiple systems, a coupled resonance system with VR-assisted enhanced SR is constructed by combining VR control and SR control, which has the dual advantages of VR and SR and performs well in weak signal detection. Finally, simulation experiment and fault data of rolling bearings are adopted to analyze the suggested method, and the comparison results with other SR methods verify its practicality and superiority.

Multi-dimensional hybrid potential stochastic resonance and application of bearing fault diagnosis

Stochastic resonance is a method to enhance weak signal by using noise, which has a wide range of applications in weak signal detection. In order to further investigate the application of multi-dimensional coupling stochastic resonance in practical engineering, a Multi-dimensional Double connection coupling Hybrid Potential Stochastic Resonance (MDHPSR) system is proposed in this paper. Firstly, the potential functions of bi-stable and tri-stable are briefly described, and the tri-stable system having a higher output amplitude. Secondly, the effect of different coupling methods on the output of the central and adjacent coupling ends are studied, and the output amplitude of double connection coupling is higher. Then, the double connection coupling of different potential functions is studied, and MDHPSR system effect is the best. Compared with Multi-dimensional Double connection Classical Bi-stable Stochastic Resonance (MDCBSR) system, MDHPSR system has better anti-noise performance. Finally, applying the two multi-dimensional coupling systems to bearing fault diagnosis, MDHPSR system output amplitude is higher and the Signal-to-Noise Ratio (SNR) is improved by more than 3 dB. This demonstrates the superior performance of MDHPSR system for weak signal detection and the value of the multi-dimensional coupling system for practical engineering applications.

A novel image noise reduction method for composite multistable stochastic resonance systems

In the field of digital signal processing, image denoising is an more and more significant research direction. For the traditional noise reduction theory, noise is considered to be harmful, and the image quality can be improved by analyzing noise characteristics and filtering noise. The appearance of stochastic resonance theory proves that noise can be used to enhance signal, which brings new inspiration to image processing. The classical bistable stochastic resonance model has the problems of high potential barrier and easy saturation, which is not conducive to the improvement of image denoising effect. In this paper, a novel type of stochastic resonance potential well model is quoted, which solves the above shortcomings of the bistable stochastic resonance model, and then combines it with the Gaussian model to propose a composite multistable stochastic resonance model. The dynamic principle of the model in signal detection is described, and the influence of system parameters on image noise reduction is analyzed. The whale optimization algorithm is used to optimize the model parameters, and an adaptive compound multistable stochastic resonance system is established to process pictures and measured radar images under different noise backgrounds. The simulation experiment and engineering application show that the model proposed in this paper solves the problem of high potential barrier and easy saturation of the bistable model, and has better image noise reduction ability compared with Wiener filter, median filter, classical bistable stochastic resonance system and novel type of stochastic resonance potential well system.

Combined Underdamped Bistatic Stochastic Resonance for Weak Signal Detection and Fault Diagnosis under Wavelet Transform

A novel combined underdamped bistable stochastic resonance (CUBSR) is proposed in this paper. Under the noise-free condition, the output amplitude is used as a measurement index of classical bistable stochastic resonance (CBSR) and CUBSR, which demonstrate CUBSR does not have output saturation characteristics and has a more prominent signal enhancement capability. Then, the expressions of mean first-pass time (MFPT), steady-state probability density (SPD) and signal-to-noise ratio (SNR) are derived. Combined with the fourth-order Runge–Kutta algorithm and genetic algorithm (GA) for numerical simulations, the comparison of the theoretical derivation and numerical simulation of CUBSR can be verified. Then, the two systems are applied to the engineering application of bearing fault diagnosis. Finally, the multi-scale noise-modulated SR method based on wavelet packet transform is studied to overcome the limitation of traditional parameter modulation and to achieve SR detection at multiple frequencies. Simulation analysis and bearing fault diagnosis show that the method can effectively detect the multi-frequency weak signal submerged in noise, resulting in a significant enhancement in signal amplitude.

A novel two-dimensional exponential potential bi-stable stochastic resonance system and its application in bearing fault diagnosis

It is difficult for classical stochastic resonance systems to extract weak signals under strong noise environment, therefore a novel two-dimensional exponential potential bi-stable stochastic resonance system (NTBSR) is proposed. First, the equivalent potential function, the mean first-pass time (MFPT) and the output signal-to-noise ratio (SNR) of NTBSR are derived under the adiabatic approximation theory. At the same time, the influence of different system parameters on them is explored. Then, NTBSR, the one-dimensional bi-stable stochastic resonance system (OBSR) and the two-dimensional classical bi-stable stochastic resonance system (TCBSR) are respectively simulated numerically, based on the fourth-order Runge–Kutta algorithm. It is found that the output SNR of NTBSR is the best. Finally, the NTBSR is applied to the fault signal diagnosis of different types of bearings, and the parameters are optimized through the adaptive genetic algorithm (AGA). The test results are compared with wavelet transform method, and TCBSR. The detection results on two sets of bearing fault data show that the NTBSR system has better effects on the enhancement and detection of bearing fault signals, and it is verified that the stochastic resonance method is superior to the traditional wavelet transform method in terms of signal detection and noise utilization. This provides good theoretical support and application value for practical engineering application.

Structural damage detection of adaptive tangent-based unsaturated bistable stochastic resonance

The output saturation of classical bistable stochastic resonance (CBSR) limits its ability to enhance weak signal characteristics. To solve this problem, an adaptive tangent-based unsaturated bistable stochastic resonance (TUBSR) method is proposed. We construct a tangent-based piecewise unsaturated bistable potential model, and select the optimal system parameters with genetic algorithm (GA) to adaptively adjust the structure of potential model, so as to improve the output saturation and obtain a larger output signal-to-noise ratio (SNR). The simulated signals are used to verify that the TUBSR method can effectively improve the detection ability of weak signals. Finally, the method is applied to the damage detection of bearing inner race and the crack detection of curved plate. The results demonstrate that compared with CBSR and other improved bistable SR method, the TUBSR method has better detection ability for weak signals.

A New Piecewise Nonlinear Asymmetry Bistable Stochastic Resonance Model for Weak Fault Extraction

In order to solve output saturation problems found in traditional stochastic resonance methods and to improve the diagnosis ability of weak faults, a new piecewise nonlinear asymmetric bistable stochastic resonance (PNABSR) method is proposed. This model uses a left and right potential function with an asymmetrical shape, which makes it easier to induce stochastic resonance phenomena. Based on the PNABSR model, the expression of the signal-to-noise ratio (SNR) is derived, and the changes in the SNR with different parameters in the PNABSR model are analyzed. Then, the parameters in the PNABSR model are optimized using the adaptive intelligent algorithm to enhance the diagnostic ability. The diagnosis properties of the weak fault are compared between the PNABSR model and the classical bistable stochastic resonance model (CBSR). The experimental results prove that the PNABSR model can effectively extract the weak fault characteristic frequency under a strong noise background, verifying the effectiveness of this method.

Weak signal enhancement for machinery fault diagnosis based on a novel adaptive multi-parameter unsaturated stochastic resonance

The output saturation problem limits the application of classical bistable stochastic resonance (CBSR) in weak fault diagnosis. Furthermore, the adjustment of system parameters is essential to generate stochastic resonance (SR) for achieving the optimal output. In this paper, a novel adaptive multi-parameter unsaturation bistable stochastic resonance (AMUBSR) system based on piecewise linearization of potential function is proposed. The beetle antennae search (BAS) is adopted to optimize the system parameters, and the output signal-to-noise ratio (SNR) is selected as the objective function. The optimization results of the simulation signal prove that the validity and superiority of BAS algorithm in parameter matching compared with particle swarm optimization (PSO) algorithm and ant colony optimization (ACO) algorithm. Finally, the proposed method obtains the further improvement of the output SNR, higher spectrum peak value at characteristic frequency and bigger recognition quantity than the CBSR method from the diagnosis results of bearing inner ring and outer ring fault signals.

Double Gaussian potential stochastic resonance method and its application in centrifugal fan blade crack detection

Stochastic resonance (SR) has been extensively utilized in the field of weak fault signal detection for its characteristic of enhancing weak signals by transferring the noise energy. Aiming at solving the output saturation problem of the classical bistable stochastic resonance (CBSR) system, a double Gaussian potential stochastic resonance (DGSR) system is proposed. Moreover, the output signal-to-noise ratio (SNR) of the DGSR method is derived based on the adiabatic approximation theory to analyze the effect of system parameters on the DGSR method. At the same time, for the purpose of overcoming the drawback that the traditional SNR index needs to know the fault characteristic frequency (FCF), the weighted local signal-to-noise ratio (WLSNR) index is constructed. The DGSR with WLSNR can obtain optimal parameters adaptively, thereby establishing the DGSR system. Ultimately, a DGSR method is proposed and applied in centrifugal fan blade crack detection. Through simulations and experiments, the effectiveness and superiority of the DGSR method are verified.

A novel underdamped continuous unsaturation bistable stochastic resonance method and its application

In view of the saturation problem of classical bistable stochastic resonance (CBSR) system, an underdamped continuous unsaturation bistable stochastic resonance (UCUBSR) system is investigated and the feasibility of the system for weak fault feature extraction is discussed. Firstly, based on the reason of saturation phenomenon, a new potential function is constructed, which can independently adjust the steepness of the potential walls. The signal to noise ratio (SNR) of the system is derived. Secondly, a modified unsaturation index, amplitude gain, is proposed, and the influence of the steepness on SR based on SNR and amplitude gain is analyzed. The simulation analysis shows that the amplitude gain can be considered as an appropriate index to quantify SR and has a certain compensation effect on the SNR applied to evaluate unsaturation performance. Finally, from the simulation and experiment, a larger amplitude gain indicates that the proposed system has better unsaturation and weak fault detection ability compared with unsaturation bistable stochastic resonance (UBSR), and a higher amplitude of the output signal at the characteristic frequency proves that the amplitude gain as an indicator can further guide the parameter adjustment of SR and facilitate faint fault signature identification.

An adaptive improved unsaturated bistable stochastic resonance method based on weak signal detection

AbstractStochastic resonance can detect weak periodic signals from strong background noise without loss of signal energy. However, the classical bistable stochastic resonance has the inherent output saturation defect, which limits the detection performance of system. And it is more difficult to detect signal with strong background noise. In this article, we constructed improved unsaturated bistable stochastic resonance to overcome this shortcoming. The improved bistable potential function makes the output signal more easily oscillate in two potential wells. To improve the stability and the accuracy of the method, we further propose an adaptive improved unsaturated bistable stochastic resonance (AIUBSR) by constructing a synthetic index (SI). The SI combines zero‐crossing ratio and structural correlation coefficient, which can measure the periodicity of output signal and the accuracy of detective frequency at the same time. Theoretical analysis and numerical simulations show that the proposed AIUBSR can have good weak signal detection capability in strong background noise.

Stochastic resonance in cascaded monostable systems with double feedback and its application in rolling bearing fault feature extraction

Stochastic resonance (SR) has been widely concerned and studied in the field of mechanical fault detection due to the capability of weak signal detection. However, research focused on how to improve the performance of SR system and enable it to process large-parameter signals in engineering practice better. Therefore, from the perspective of feedback control and multi-system synergy, this paper presents a double-feedback cascaded monostable SR (CMSR) system and analyzes the SR phenomenon in the system by using the signal-to-noise ratio as the measurement index. It investigates specifically influence of the coefficients on the system performance. Introducing feedback control and serial structure to a monostable system, consisting of a symmetric quartic potential function, not only alters the response characteristics of the monostable system but also significantly improve the system performance. Compared with the classical bistable SR system with low-pass filtering characteristics, the proposed system can exhibit low-pass filtering or band-pass filtering behavior through different combinations of feedback coefficients, which can better match the frequency characteristic of target signal. Finally, the proposed double-feedback CMSR system is used for extraction of the weak signal features in rolling bearing fault detection, and its superiority and feasibility are verified by comparison with other SR systems.

A new method for weak fault feature extraction based on piecewise mixed stochastic resonance

In a continuous bistable system, when the input signal is continuously increased, the output signal tends to be stable and no longer increases. At this time, the weak signal under strong background noise is difficult to be extracted, which means saturation occurs. Aiming at the saturation characteristics of stochastic resonance (SR), the proposed piecewise nonlinear bistable system (PNBSR) model has achieved certain results. However, the potential barrier in the middle of the PNBSR method still completely uses the potential function of classical bistable stochastic resonance (CBSR). There is no fundamental solution to the fourth-order limitation. This paper explores an improved piecewise mixed stochastic resonance (PMSR) potential model. The fourth-order potential function that restricts particle motion in CBSR is improved to a piecewise second-order potential function. This potential function subverts the shape of the traditional potential function and presents a symmetrical double-hook shape. Based on PMSR model, this paper uses particle swarm optimization (PSO) to select system parameters and elaborates the characteristics of the potential function curve in detail. Under the same conditions, the output signal-to-noise ratio (SNR) curve of the improved system is generally higher than that of the CBSR and PNBSR systems. Experiments on bearings and gears show that the proposed method can accurately extract weak fault features, and the effect is better than the PNBSR method.

A novel mechanical fault signal feature extraction method based on unsaturated piecewise tri-stable stochastic resonance

Stochastic resonance (SR) is widely studied in signal feature extraction. The standard tri-stable SR (STSR) method possesses superior performance than the classical bistable SR (CBSR) method in signal feature extraction, but it still has output saturation phenomenon, which will reduce the signal-to-noise ratio (SNR) of the output signal and the signal amplitude of the characteristic frequency as the CBSR method. For the purpose of avoiding the influence of output saturation on the STSR method, a piecewise tri-stable stochastic resonance (PTSR) method is proposed and applied in fault feature signal extraction. Firstly, the simulation signals are processed using the PTSR method and the STSR method separately, then the comparison shows that the output signal has larger signal amplitude and a higher SNR. Ultimately, the devised PTSR method is utilized for extracting fault characteristics of two groups of actual signals, which also has better output characteristics compared with the STSR method.

Stochastic resonance in a single-well potential and its application in rolling bearing fault diagnosis.

In this paper, a single-well model based on the piecewise function and classical bistable stochastic resonance (CBSR) is proposed. The steady state probability density of particles and mean first passage time in the model are calculated. The output characteristics and performance of the proposed model are analyzed through numerical simulation. On the basis of CBSR and the proposed model, an adaptive system is established (ACSSR) to generate the highest gain of signal-to-noise ratio (SNRg). Finally, the effectiveness of ACSSR in weak signal detection is verified with both simulated and experimental input signals. The results indicate that the ACSSR could detect the defect signal correctly and improve the SNRg.