Multi-stable Stochastic Resonance Research Articles

Novel compound multistable stochastic resonance weak signal detection

Abstract The research on stochastic resonance (SR) which is used to extract weak signals from noisy backgrounds is of great theoretical significance and promising application. To address the shortcomings of the classical tristable SR model, this article proposes a novel compound multistable stochastic resonance (NCMSR) model by combining the Woods–Saxon (WS) and tristable models. The influence of the parameters of the NCMSR systems on the output response performance is studied under different α stable noises. Meanwhile, the adaptive synchronization optimization algorithm based on the proposed model is employed to achieve periodic and non-periodic signal identifications in α stable noise environments. The results show that the proposed system model outperforms the tristable system in terms of detection performance. Finally, the NCMSR model is applied to 2D image processing, which achieves great noise reduction and image recovery effects.

Bearing Fault-Detection Method Based on Improved Grey Wolf Algorithm to Optimize Parameters of Multistable Stochastic Resonance.

In an effort to overcome the problem that the traditional stochastic resonance system cannot adjust the structural parameters adaptively in bearing fault-signal detection, this article proposes an adaptive-parameter bearing fault-detection method. First of all, the four strategies of Sobol sequence initialization, exponential convergence factor, adaptive position update, and Cauchy-Gaussian hybrid variation are used to improve the basic grey wolf optimization algorithm, which effectively improves the optimization performance of the algorithm. Then, based on the multistable stochastic resonance model, the structure parameters of the multistable stochastic resonance are optimized through improving the grey wolf algorithm, so as to enhance the fault signal and realize the effective detection of the bearing fault signal. Finally, the proposed bearing fault-detection method is used to analyze and diagnose two open-source bearing data sets, and comparative experiments are conducted with the optimization results of other improved algorithms. Meanwhile, the method proposed in this paper is used to diagnose the fault of the bearing in the lifting device of a single-crystal furnace. The experimental results show that the fault frequency of the inner ring of the first bearing data set diagnosed using the proposed method was 158 Hz, and the fault frequency of the outer ring of the second bearing data set diagnosed using the proposed method was 162 Hz. The fault-diagnosis results of the two bearings were equal to the results derived from the theory. Compared with the optimization results of other improved algorithms, the proposed method has a faster convergence speed and a higher output signal-to-noise ratio. At the same time, the fault frequency of the bearing of the lifting device of the single-crystal furnace was effectively diagnosed as 35 Hz, and the bearing fault signal was effectively detected.

A novel coupled array of multi-stable stochastic resonance under asymmetric trichotomous noise and its application in rolling bearing compound fault diagnosis

Rolling bearings are often subject to various types of damage in actual industrial operations. However, the early fault information is weak and completely overwhelmed by interference from noise, which is difficult to detect. In this paper, a novel coupled array of multi-stable stochastic resonance (NCAMSR) driven by asymmetric trichotomous noise is proposed for compound fault diagnosis. The Multipoint Optimal Minimum Entropy Deconvolution Adjusted (MOMEDA) is used to separate the information of different fault features in the compound fault signal, and the outputs of the coupled array system are weighted to find the best effect. The spectral mean signal-to-noise ratio (SMSNR) is designed and the system parameters and weights are optimized using the particle swarm algorithm (PSO). To alleviate the problem of output saturation, the NCAMSR potential model based on the improved Gaussian potential is proposed, and the superior unsaturation of the NCAMSR potential function model is proven by theoretical analysis and experiments. Finally, the excellent performance of NCAMSR in compound fault detection is further verified by using engineering experiments with bearing data from Machinery Faults & Rotor Dynamics Simulator and real damage samples generated from accelerated life tests at Paderborn University, Germany.

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.

Stochastic resonance of a multi-stable system and its application in bearing fault diagnosis

This paper investigates the stochastic resonance and mean-first passage time of a quad-stable potential in the presence of Gaussian white noise and periodic forcing. The analytical expressions of mean-first passage time and spectral amplification are obtained, respectively. It is found that even small noise intensity can lead to noise-assisted hopping between two adjacent potential wells for the case of small damping coefficient. For large noise intensity, the escape process of Brownian particles is accelerated in an underdamped nonlinear system. Moreover, the curve of spectral amplification displays a typical resonant peak at an optimal noise intensity, suggesting the onset of stochastic resonance. Meanwhile, with the decrease of periodic signal frequency, the peak value of spectral amplification is enhanced. Especially, an optimal quad-stable potential structure exists to maximize the stochastic resonance effect. The proposed multi-stable stochastic resonance method is applied to the fault diagnosis of inner and outer race bearing, and the quantum particle swarm optimization algorithm is used to optimize the system parameters and damping coefficient. The good agreement between fault frequency and theoretical value validates efficiency of the proposed method. Compared with the overdamped tri-stable stochastic resonance method, the performance of fault diagnosis is enhanced substantially by the proposed method.

Weak signal detection method based on novel composite multistable stochastic resonance

The weak signal detection method based on stochastic resonance is usually used to extract and identify the weak characteristic signal submerged in strong noise by using the noise energy transfer mechanism. We propose a novel composite multistable stochastic-resonance (NCMSR) model combining the Gaussian potential model and an improved bistable model. Compared with the traditional multistable stochastic resonance method, all the parameters in the novel model have no symmetry, the output signal-to-noise ratio can be optimized and the output amplitude can be improved by adjusting the system parameters. The model retains the advantages of continuity and constraint of the Gaussian potential model and the advantages of the improved bistable model without output saturation, the NCMSR model has a higher utilization of noise. Taking the output signal-to-noise ratio as the index, weak periodic signal is detected based on the NCMSR model in Gaussian noise and α noise environment respectively, and the detection effect is good. The application of NCMSR to the actual detection of bearing fault signals can realize the fault detection of bearing inner race and outer race. The outstanding advantages of this method in weak signal detection are verified, which provides a theoretical basis for industrial practical applications.

Weak signal detection of composite multistable stochastic resonance with Woods–Saxon potential

Abstract Weak signal detection under strong noise is a common problem in many engineering fields. The research on the detection theory and method of stochastic resonance (SR) has very important theoretical significance and application value for the realization of early weak fault diagnosis. In order to further enhance the weak signal processing capability of SR, an improved novel composite multistable potential well model is proposed by combining the tristable model and the Woods–Saxon model. The switching mechanism of the novel model constructed with the fusion of the tristable model and the Woods–Saxon model between different steady states is studied, the output response performance of SR system with the novel composite multistable model is analyzed. The adaptive synchronization optimization method of multiple system parameters adopts the differential brainstorming algorithm to realize the adaptive selection of multiple parameters. Simulation experiments are carried out on single and multiple low-frequency periodic signals and single and multiple high-frequency periodic signals under the Gaussian noise environment, simulation results indicate that the novel composite multistable SR system performs better. On the basis of this model, the composite multistable SR system is applied to the fault detection of rolling bearings, which has a good detection effect.

Weak signal enhancement for small drill condition monitoring in PCB drilling process by using adaptive multistable stochastic resonance

The online tool condition monitoring is demanded to detect the tool wear and to ensure the hole drilling process of printed circuit boards (PCB) goes on smoothly. However, due to the impact of ambient noise caused by the limited size of the small drill and the laminated material of PCB, the tool wear signal features are too weak to extract. The stochastic resonance (SR) method has been proven to be effective in enhancing weak signals among various weak signal extractions. In this paper, an adaptive multistable stochastic resonance is presented to improve the performance of the SR method and process the tool wear signals for PCB drilling. The differential evolution (DE) algorithm is applied to adaptively optimize potential parameters and compensation factor, which makes the SR method suitable for high-frequency signals. Moreover, tool wear experiments with different drill wear are carried out to verify the effectiveness of the proposed method. The results indicate that the proposed method improves the signal-to-noise ratio and has great potential in enhancing weak signals for small drill condition monitoring in the PCB drilling process.

Piecewise unsaturated multi-stable stochastic resonance under trichotomous noise and its application in bearing fault diagnosis

The classical tri-stable stochastic resonance (CTSR) has the weakness of output saturation, which restricts the ability to enhance weak signal detection. To overcome the limitation of output saturation, a piecewise unsaturated multi-stable stochastic resonance (PUMSR) method is proposed. Due to the presence of trichotomous noise in practical application, this paper explores the PUMSR under a trichotomous noise environment. The performance of PUMSR is evaluated by means of an index, mean signal-to-noise ratio increase (MSNRI). In order to meet the adiabatic approximation conditions, the signal is secondary sampled and a genetic algorithm (GA) is implemented to optimize the system parameters. Simulation experiments demonstrate that the proposed PUMSR system is superior to the CTSR system in terms of its ability to extract signals at multi-frequency. The PUMSR is then applied to the diagnosis of bearing faults. It is further proved that the PUMSR system has good performance in bearing fault diagnosis and has great feasibility in real engineering application.

A Novel Advancing Signal Processing Method Based on Coupled Multi-Stable Stochastic Resonance for Fault Detection

In recent years, methods for detecting motor bearing faults have attracted increasing attention. However, it is very difficult to detect the faults from weak motor bearing signals under the strong noise. Stochastic resonance (SR) is a popular signal processing method, which can process weak signals with the noise, but the traditional SR is burdensome in determining its parameters. Therefore, in this paper, a new advancing coupled multi-stable stochastic resonance method, with two first-order multi-stable stochastic resonance systems, namely CMSR, is proposed to detect motor bearing faults. Firstly, the effects of the output signal-to-noise ratio (SNR) for system parameters and coupling coefficients are analyzed in-depth by numerical simulation technology. Then, the SNR is considered as the fitness function for the seeker optimization algorithm (SOA), which can adaptively optimize and determine the system parameters of the SR by using the subsampling technique. An advancing coupled multi-stable stochastic resonance method is realized, and the pre-processed signal is input into the CMSR to detect the faults of motor bearings by using Fourier transform. The faults of motor bearings are determined according to the output signal. Finally, the actual vibration data of induction motor bearings are used to prove the effectiveness of the proposed CMSR. The comparison results with the MSR show that the CMSR can obtain a higher output SNR, which is more beneficial to extract weak signal features and realize fault detection. At the same time, this method also has practical application value for engineering rotating machinery.

Study on the mean first-passage time and stochastic resonance of a multi-stable system with colored correlated noises

The mean first-passage time (MFPT) and the weak signal detection method of stochastic resonance (SR) on multi-stable nonlinear system under color correlated noise are studied. Using the uniform color noise approximation method, the Fokker-Planck equation of the system is obtained, and the steady-state probability density function of the multi-stable system driven by the multiplicative noise and additive noise is derived. On the basis of this, the formula of MFPT is derived, and the influence of parameters on the MFPT is analyzed. The problem of weak signal detection under color noise background is studied based on multi-stable SR. The results of simulation and experiment show that the method can effectively extract the frequency feature of weak signal in the background of color noise.

A novel parameter-induced adaptive stochastic resonance system based on composite multi-stable potential model

Stochastic resonance (SR) is used widely as a weak signal detection method by using noise in many fields. In order to improve the weak signal processing capability of SR, a novel composite multi-stable model is proposed, which is constructed by the joint of the tristable model and the Gaussian Potential (GP) model. The SR system based on this model is constructed and the signal-to-noise ratio (SNR) is regarded as the index to measure the SR effect. The differential brain storm optimization (DBSO) algorithm is used to optimize the system parameters collaboratively to achieve parameter-induced adaptive SR. The influences of the system parameters V and R and the noise intensity D on the output response of SR system are analyzed under Gaussian white noise and α stable noise environments, and the advantages of the composite multi-stable SR system over the traditional tristable system are verified. For different levels of weak signals, the output performances of SR systems based on composite multi-stable model, traditional tristable model, composite tristable model are compared and analyzed. The results prove that the proposed model has better performance. Meanwhile, the adaptive detection of the multiple high-frequency weak signal is realized using the composite multi-stable SR system. The simulation results show that the proposed system has strong weak signal processing capability and good immunity to noise types, which widens the application range of SR in practical engineering.

A new weak fault diagnosis method based on multi-scale wavelet noise tuning cascaded multi-stable stochastic resonance

For detecting the weak fault diagnosis submerged in heavy noise, a new method called multi-scale cascaded multi-stable stochastic resonance (MCMSR) is studied. The method can effectively extract weak fault diagnosis from noise background using multi-scale wavelet noise tuning stochastic resonance (SR). Firstly, input signal with noise is decomposed by multi-scale wavelets transformation, and each scale signal is adjusted by scaling factor, then the decomposed signal is used as the input of cascaded multi-stable systems to achieve the detection of fault diagnosis. If the input signal is a large parameter signal, to conform to the conditions of SR, the decomposed signal must be processed by twice sampling. The simulation and experimental signals are carried out to test the feasibility of the method. From the signal to noise ratio (SNR) comparison curves of original signal, SR output signal and MCMSR output signal plotted together, we can find that the useful signal can be enhanced by MCMSR method than SR method. The experimental results indicate that the MCMSR can extract fault diagnosis from heavy background noise.

Weak Fault Signal Detection of Rotating Machinery Based on Multistable Stochastic Resonance and VMD-AMD

For solving detection problems of multifrequency weak signals in noisy background, a novel weak signal detection method based on variational mode decomposition (VMD) and rescaling frequency-shifted multistable stochastic resonance (RFMSR) with analytical mode decomposition (AMD) is proposed. In this method, different signal frequency bands are processed by rescaling subsampling compression to make each frequency band meet the conditions of stochastic resonance. Before the enhanced signal components are synthesized, they are processed to achieve the enhanced signal by means of AMD, leaving only the enhanced sections of the signal. The processed signal is decomposed into intrinsic mode functions (IMF) by VMD, in order to require the detection of weak multifrequency signals. The experimental analysis of the rolling bearing inner ring fault and gear fault diagnosis demonstrate that the proposed method can not only enhance signal amplitude, reduce false components, and improve the VMD algorithm’s accuracy, but also effectively detect weak multifrequency signals submerged by noise.

Optimized Multistable Stochastic Resonance for the Enhancement of Pituitary Microadenoma in MRI.

Magnetic resonance imaging (MRI) is the modality of choice as far as imaging diagnosis of pathologies in the pituitary gland is concerned. Furthermore, the advent of dynamic contrast enhanced (DCE) has enhanced the capability of this modality in detecting minute benign but endocrinologically significant tumors called microadenoma. These lesions are visible with difficulty and a low confidence level in routine MRI sequences, even after administration of intravenous gadolinium. Techniques to enhance the visualization of such foci would be an asset in improving the overall accuracy of DCE-MRI for detection of pituitary microadenomas. The present study proposes an algorithm for postprocessing DCE-MRI data using multistable stochastic resonance (MSSR) technique. Multiobjective ant lion optimization optimizes the contrast enhancement factor (CEF) and anisotropy of an image by varying the parameters associated with the dynamics of MSSR. The marked regions of interest (ROIs) are labeled as normal and microadenoma of pituitary obtained with increased level of accuracy and confidence using proposed algorithm. The increased difference between the mean intensity curves obtained using these ROIs validated the obtained subjective results. Furthermore, the proposed MSSR-based algorithm has been evaluated on standard T1 and T2 weighted BrainWeb dataset images and quantified in terms of CEF, peak signal to noise ratio (PSNR), structure similarity index measure (SSIM), and universal quality index (UQI). The obtained mean values of CEF 1.22, PSNR 27.68, SSIM 0.75, UQI 0.83 for twenty dataset images were highest among considered contrast enhancement algorithms for the comparison.

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.

Multi-Stable Stochastic Resonance Based Protection Scheme for Parallel Transmission Lines with UPFC

This paper presents a multi-stable stochastic resonance (MSR) based on complex wavelet transform (CWT) for protecting a double line transmission system with unified power flow controller (UPFC) in one line. The fault detection at the sending end is recognized by the collective sum technique (CST) using the current signals of all the three-phases with heavy background noise. The noisy signal is processed by parameter compensation and the processed signal is decomposed by CWT with different scale frequencies. The spectral energies of each phase can be used to identify the faulty phases. The CWT is used to compute the spectral energies of each phase current. The proposed scheme has been studied for wide variation of operating parameters and compared with two other fault extraction methods such as EMD-based spectral analysis and wavelet transform with post spectral analysis. The test results of the proposed CWT based MSR algorithm indicates that it can accurately detect and classify the fault with in one cycle from fault inception.

Signal feature extraction based on cascaded multi-stable stochastic resonance denoising and EMD method

On the basis of cascaded multi-stable stochastic resonance system (CMSRS) theoretical studies, for the empirical mode decomposition (EMD) in heavy noisy mixtures, a method of EMD based on CMSRS denoising is presented. First, CMSRS is employed as the pretreatment to remove noise by virtue of its good effect in denoising performance, and the energy gradually is shifted from high to low frequency, then the denoised signal is decomposed by EMD. In simulated experiment, EMD is used to decompose the original and CMSRS output signals respectively. The result from the comparison shows that this method, not only removes high-frequency noise efficiently, but also reduces the decomposition layers and lets them have more reality meanings. At last, a diagnosis on the fault of inner race of rolling bearing confirms that this method removes high-frequency noise step by step, improves low-frequency signal’s energy, and can effectively identify characteristic signals.

Stochastic Resonance in a Multistable System Driven by Gaussian Noise

Stochastic resonance (SR) is investigated in a multistable system driven by Gaussian white noise. Using adiabatic elimination theory and three-state theory, the signal-to-noise ratio (SNR) is derived. We find the effects of the noise intensity and the resonance system parametersb,c, anddon the SNR; the results show that SNR is a nonmonotonic function of the noise intensity; therefore, a multistable SR is found in this system, and the value of the peak changes with changing the system parameters.

Multi-frequency weak signal detection based on wavelet transform and parameter compensation band-pass multi-stable stochastic resonance

In actual fault diagnosis, useful information is often submerged in heavy noise, and the feature information is difficult to extract. A novel weak signal detection method aimed at the problem of detecting multi-frequency signals buried under heavy background noise is proposed based on wavelet transform and parameter compensation band-pass multi-stable stochastic resonance (SR). First, the noisy signal is processed by parameter compensation, with the noise and system parameters expanded 10 times to counteract the effect of the damping term. The processed signal is decomposed into multiple signals of different scale frequencies by wavelet transform. Following this, we adjust the size of the scaled signals' amplitudes and reconstruct the signals; the weak signal frequency components are then enhanced by multi-stable stochastic resonance. The enhanced components of the signal are processed through a band-pass filter, leaving the enhanced sections of the signal. The processed signal is analyzed by FFT to achieve detection of the multi-frequency weak signals. The simulation and experimental results show that the proposed method can enhance the signal amplitude, can effectively detect multi-frequency weak signals buried under heavy noise and is valuable and usable for bearing fault signal analysis.