Stochastic Resonance Model Research Articles

A novel exponential unsaturated bistable stochastic resonance-boosted incipient fault identification in rotating machineries

Abstract Stochastic resonance (SR) for weak fault detection stands as a significant constructive methodology leveraging noise in nonlinear information systems processing. In virtue of the SR technique in conjunction with coupled non-saturated nonlinear systems, an exponential unsaturated bistable stochastic resonance (EUBSR) model is developed to enhance output levels. By integrating the exponential monostable stochastic resonance system (ESR) and the unsaturated bistable stochastic resonance (UBSR) system through coupling coefficients, this model offers a broader spectrum of resonance characteristics. The performance of the EUBSR is evaluated based on the relevant indicators signal-to-noise ratio (SNR) and residence time distribution ratio. These indicators are treated as multi-objective functions, with the coati optimization algorithm employed to optimize both the parameters and coupling coefficients of the EUBSR model simultaneously. Moreover, the paper takes into account the interdependence of nonlinear systems and their interactions by considering both cascade and parallel models of the ESR and UBSR systems. Fault diagnosis is carried out on simulation signals and bearings to validate the effectiveness of the proposed EUBSR model. The results demonstrate that the EUBSR model surpasses not only its individual component models but also cascade and parallel models.

Two-dimensional quad-stable Gaussian potential stochastic resonance model for enhanced bearing fault diagnosis

In this study, a two-dimensional quad-stable Gaussian potential stochastic resonance model is explored for the first time. First, the structure of the proposed model is analyzed to have a broader potential field and verified to break through the severe output saturation inherent in the classical two-dimensional quad-stable stochastic resonance model. Then, we analyze the relationship between the structure and parameters of the model and derive the steady-state probability density and the mean first-passage time using adiabatic approximation theory to describe the specific process of the Brownian particle transitions. By combining the adiabatic approximation theory and the probability flow equation, the spectral amplification factor of the model is derived, and the effects of different parameters on the model performance are investigated. Further, a fourth-order Runge-Kutta algorithm was applied to evaluate the model performance in multiple dimensions. Finally, the model parameters were optimized using an adaptive genetic algorithm and applied to complex practical engineering detection. The experimental results show that the proposed model is superior and universal in fault diagnosis. Overall, this study provides important mathematical support for solving various engineering problems and demonstrates a wide range of practical applications.

Dynamic potential stochastic resonance for weak signal detection

To suppress the low-frequency interference noise, a dynamic potential stochastic resonance (DPSR) model is proposed in this paper for weak signal detection. The DPSR model introduces a single dynamic parameter k that simplifies parameter optimization. Its dynamic potential function can adaptively adjust to match noisy input signals. This model provides a new nonlinear model for triggering the SR phenomenon. Experimental results indicate that compared to the traditional methods that rely on clear interference frequency distributions to filter low-frequency components directly, the SR model offers greater flexibility and convenience. Unlike classical SR models, the proposed DPSR model demonstrates a 1.5 dB improvement in output performance for suppressing low-frequency interference. Therefore, the DPSR model not only robustly suppresses interference but also effectively enhances and detects characteristic signals in variant-noise environments. Application to sea trial signals highlights the superior performance of the DPSR model in significantly reducing low-frequency interference and improving target signal recognizability compared to other models.

A novel comprehensive method for weak signal blind detection based on adaptive quasi-periodic potential stochastic resonance and its application in bearing fault detection

In order to solve the common output saturation of stochastic resonance systems and the limitation of classical index SNR for blind detection, a novel adaptive quasi-periodic potential stochastic resonance blind detection method is proposed. First, a model of quasi-periodic potential stochastic resonance (QPPSR) possessing infinite steady state is constructed and analyzed for its structure change pattern. The superior performance of the model is verified by using the fourth-order Runge–Kutta algorithm. Secondly, the mechanism of QPPSR is analyzed using the probability flow method, which reveals the relationship between system parameters and performance. Again, a novel comprehensive blind detection index (CBDI) is exquisitely constructed to make up for the shortcomings of each indicator. Finally, CBDI and QPPSR are constructed into an adaptive blind detection system and applied to bearing fault detection. The results analyzed by experiments verify the good engineering application prospect of CBDI-QPPSR.

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.

Dual-channel two-dimensional stochastic resonance and its application in bearing fault detection under alpha-stable noise

Coupled two-dimensional stochastic resonance (CTDSR) systems exhibit a higher quantity of steady-states and hold significant theoretical and practical value. However, the coupling between nonlinear systems generates multiplicative noise, which impairs signal transmission. In this paper, a novel dual-channel two-dimensional stochastic resonance (DCTDSR) model is proposed to harness multiplicative noise for enhancing system output. It is evident from the potential well analysis that multiplicative noise causes variations in the properties and amounts (from 2 to 4) of resonance peaks in the DCTDSR system. The steady-state probability density (SPD) of the novel system is derived by implementing the adiabatic approximation theory. In the background of alpha-stable noise, simulation results indicate that the DCTDSR system exhibits heightened detection capabilities for weak signals that are immersed in severe impulsive and heavy-tailed noise. Based on the stability of alpha-stable noise, an adaptive stochastic resonance fault diagnosis method that adjusts both parameters and multiplicative noise is designed to overcome the issue of insufficient single energy regulation. Experimental results have demonstrated that the DCTDSR system boosts noise energy transmission and offers improved bearing fault detection accuracy. Thus, effectively utilizing multiplicative alpha-stable noise can further enhance the practical applicability of stochastic resonance theory in engineering.

Stochastic resonance induced weak signal enhancement in a second-order tri-stable system with single-parameter adjusting

Weak signal detection methods based on stochastic resonance (SR) have been extensively studied due to their capability to utilize noise energy for enhancing weak signals. Among various SR models, the second-order tri-stable SR models have demonstrated their superiority in weak-signal detection with better output performance compared to other SR models. To optimize the output performance of the second-order tri-stable systems, a variety of parameter optimization methods have been proposed to optimize the parameters of the system. However, these optimization methods often require to optimize multiple parameters, which leads to an increase in computational costs and reduces the real-time processing efficiency of signal processing. Such multi-parameter optimization methods cannot meet the demands for timely signal processing in the context of big data. To address this challenge, this paper proposes two single-parameter-adjusting SR models. The proposed models can attain an ideal output performance by adjusting a single parameter in the SR system. The spectral amplification as an indicator is derived to quantitatively analyze the effects of the proposed models on SR output. On this basis, the influences of the proposed models on the SR output under different potential well parameters, noise intensities, signal frequency, and damping ratio are fully investigated through numerical simulations. At last, the proposed models are employed to process an experimental signal with a weak fault feature, and the experimental results verify the feasibility of the proposed models in optimizing the SR output. The research results can guide the design of tri-stable SR models and support the application of the SR-based signal processing model in the context of big data.

Magnetic Anomaly Detection Based on a Compound Tri-Stable Stochastic Resonance System.

In the case of strong background noise, a tri-stable stochastic resonance model has higher noise utilization than a bi-stable stochastic resonance (BSR) model for weak signal detection. However, the problem of severe system parameter coupling in a conventional tri-stable stochastic resonance model leads to difficulty in potential function regulation. In this paper, a new compound tri-stable stochastic resonance (CTSR) model is proposed to address this problem by combining a Gaussian Potential model and the mixed bi-stable model. The weak magnetic anomaly signal detection system consists of the CTSR system and judgment system based on statistical analysis. The system parameters are adjusted by using a quantum genetic algorithm (QGA) to optimize the output signal-to-noise ratio (SNR). The experimental results show that the CTSR system performs better than the traditional tri-stable stochastic resonance (TTSR) system and BSR system. When the input SNR is -8 dB, the detection probability of the CTSR system approaches 80%. Moreover, this detection system not only detects the magnetic anomaly signal but also retains information on the relative motion (heading) of the ferromagnetic target and the magnetic detection device.

Stochastic resonance impact signal detection method based on a novel single potential well model

Our research introduces a novel stochastic resonance (SR) model featuring a single potential well and develops a dedicated detection system designed to address the challenging problem of detecting impact signals within a highly noisy background. We begin by examining the limitations of conventional metrics, such as the cross-correlation coefficient and kurtosis index, in identifying nonperiodic impact signals, and subsequently introduce an improved metric. By harnessing parameter-adjusted SR, this innovative potential well model and metric is integrated to formulate an adaptive detection method for nonperiodic impact signals. This method automatically adjusts system parameters in response to the input signal. Subsequently, numerical simulations of the system is conducted so as to perform a comparative analysis with experimental results obtained from both asymmetric single potential well and periodic potential systems. Our findings conclusively demonstrate the enhanced effectiveness of our proposed method in detecting impact signals within a high-noise environment. Furthermore, the method provides more accurate estimates of both the intensity and precise location of the input impact signal from the output results.

Caputo-Fabrizio fractional order derivative stochastic resonance enhanced by ADOF and its application in fault diagnosis of wind turbine drivetrain

Fault diagnosis of wind turbine drivetrains is vital to maintain the reliability of wind turbines and stochastic resonance (SR) is regarded as a powerful method to amplify the fault-induced weak characteristics of vibration signals. However, without considering the high dependence between current and previous values of vibration signals, integer-order SR may not be effective enough to amplify the weak characteristics. Moreover, non-Gaussian noise originating from severe working condition generally reduce the efficiency of amplification. To address these issues, a Caputo-Fabrizio fractional order derivative (CF) SR improved by ascending density outlier factor (ADOF) for fault diagnosis of wind turbine drivetrains is proposed in this paper. First, ADOF is constructed to remove the large impulsive noise of vibration signals. Second, CF is discretized into the second-order SR model, then the weak characteristics of vibration signal are amplified by the established CF second-order SR model (CF-SR). The effectiveness is validated by a simulation and two experimentations based on two real vibration signals collected from the key components of wind turbines. Compared with traditional diagnosis methods such as deconvolution and Kurtogram, the proposed method is superior for fault diagnosis of wind turbines working in severe environments.

Research and application of composite stochastic resonance in enhancement detection

Aiming at the problem that the intermediate potential part of the traditional bistable stochastic resonance model cannot be adjusted independently, a new composite stochastic resonance (NCSR) model is proposed by combining the Woods–Saxon (WS) model and the improved piecewise bistable model. The model retains the characteristics of the independent parameters of WS model and the improved piecewise model has no output saturation, all the parameters in the new model have no coupling characteristics. Under α stable noise environment, the new model is used to detect periodic signal and aperiodic signal, the detection results indicate that the new model has higher noise utilization and better detection effect. Finally, the new model is applied to image denoising, the results showed that under the same conditions, the output peak signal-to-noise ratio (PSNR) and the correlation number of NCSR method is higher than that of other commonly used linear denoising methods and improved piecewise SR methods, the effectiveness of the new model is verified.

Fractional Order Derivative and Time-Delay Feedback Enabled Stochastic Resonance for Bearing Fault Diagnosis

The benefits of noise can be found in nonlinear systems where a type of resonances can inject the noise into systems to enhance weak signals of interest, including stochastic resonance, vibrational resonance, and chaotic resonance. Such benefits of noise can be improved further by adding some items into the nonlinear systems. Considering the time-dependent memory of fractional-order derivative and time-delay feedback which makes the nonlinear systems take advantage of their historical information and makes the output of nonlinear systems affect the input by feedback control, therefore, we attempt to design the model of stochastic resonance (SR) enhanced by both fractional-order derivative and time-delay feedback. Among them, fractional-order derivative and time delay would reinforce the memory of nonlinear systems for historical information and feedback would use the output of systems to control the systems precisely. Therefore, we hope that their advantages would be fused to improve the weak signal detection performance of SR further. Then, it would be applied to bearing fault diagnosis and compared with that without fractional-order derivative and time-delay feedback and even other diagnostic methods. The experimental results indicate that the SR enhanced by fractional-order derivative and time-delay feedback where a local signal-to-noise ratio is designed as the objective function to optimize these tuning parameters of the proposed method could enhance early fault signature of bearings and outperform that without fractional-order derivative and time-delay feedback and even infogram method.

Typical stochastic resonance models and their applications in steady-state visual evoked potential detection technology

Typical stochastic resonance models and their applications in steady-state visual evoked potential detection technology

Analysis of a class of Lorenz-like stochastic resonance model and its application in induction motor fault diagnosis

Analysis of a class of Lorenz-like stochastic resonance model and its application in induction motor fault diagnosis

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 adaptive weak fault diagnosis method based on modulation periodic stochastic pooling networks

Stochastic resonance, known for its strong capability to amplify weak signals, has been widely applied in rotating machinery fault diagnosis. However, the increasing intelligence of mechanical equipment and the harsh service environment leads to new challenges for stochastic resonance method. Moreover, the adaptive stochastic resonance system relying on the signal-to-noise ratio (SNR) as the loss function requires extensive prior knowledge of the signal to be measured, limiting its application in engineering. Therefore, this paper presents a modulation periodic stochastic pooling networks (MPSPN) with integral modulation factor. By using the normalized least-mean-square (NLMS)algorithm, an adaptive bearing fault diagnosis method based on MPSPN under unknown faults is developed. The study first proposes a modulated periodic stochastic resonance (MPSR) model and investigates its stochastic resonance characteristics through the steady-state probability density. Then, it introduces a modulation signal detection index (IMBF) and derives an adaptive weight allocation scheme under NLMS optimization. Finally, the superiority of the MPSPN system is demonstrated through simulations and the analysis of bearing fault data obtained from two distinct experimental platforms. The results indicate that, in comparison to the conventional periodic stochastic resonance (PSR) system, the MPSPN system is capable of effectively diagnosing unknown faults in bearings and significantly improving the SNR of the diagnostic output.

Controlled Symmetry with Woods-Saxon Stochastic Resonance Enabled Weak Fault Detection.

Weak fault detection with stochastic resonance (SR) is distinct from conventional approaches in that it is a nonlinear optimal signal processing to transfer noise into the signal, resulting in a higher output SNR. Owing to this special characteristic of SR, this study develops a controlled symmetry with Woods-Saxon stochastic resonance (CSwWSSR) model based on the Woods-Saxon stochastic resonance (WSSR), where each parameter of the model may be modified to vary the potential structure. Then, the potential structure of the model is investigated in this paper, along with the mathematical analysis and experimental comparison to clarify the effect of each parameter on it. The CSwWSSR is a tri-stable stochastic resonance, but differs from others in that each of its three potential wells is controlled by different parameters. Moreover, the particle swarm optimization (PSO), which can quickly find the ideal parameter matching, is introduced to attain the optimal parameters of the CSwWSSR model. Fault diagnosis of simulation signals and bearings was carried out to confirm the viability of the proposed CSwWSSR model, and the results revealed that the CSwWSSR model is superior to its constituent models.

Is phase locking crucial to improve hearing thresholds in tinnitus patients?

Temporal processing of auditory data plays a crucial role in our proposed model of tinnitus development through stochastic resonance (SR). The model assumes a physiological mechanism optimizing auditory information transmission (as quantified by autocorrelation [AC] analysis) into the brain by adding the optimal amount of neuronal noise to otherwise subthreshold signals. We hypothesize that this takes place at the second synapse of the auditory pathway in the dorsal cochlear nucleus (DCN). We propose that after hearing loss, this neuronal noise is increased in the affected frequency band to improve hearing thresholds at the cost of upward propagation of this added noise, which finally may be perceived as tinnitus. We already showed the improvement of hearing thresholds in a large population of patients. Until now, we did not investigate the differences in hearing thresholds based on the biological constraints of early auditory temporal processing (phase locking) that is only possible up to frequencies of 5kHz. In this report, we grouped our patient database (N= 47,986) according to tinnitus pitch (TP) of below (TP<5kHz ) or above (TP>5kHz ) the 5kHz limit or having no tinnitus (NT) and compared their mean audiograms. We found that TP<5kHz patients showed significantly better hearing thresholds than all other patient groups independent of age. No improvement was seen for TP>5kHz patients who even showed worse thresholds than NT patients for high frequencies. These results are further evidence for our SR model of tinnitus development and the existence of AC analysis at the level of the DCN.

Nonlinear dynamics analysis of enhancing energy harvesting from intense vibration based on improved asymmetric bistable stochastic resonance model

While the improved bistable energy harvesting (IBEH) system is excellent at harvesting energy from weak excitation signals, it is still inadequate at harvesting energy from intense excitation signals. Due to the strict resonance problem, energy harvesting strategies for intense excitation modes are not yet mature. Stochastic resonance seems to be a suitable solution for intense excitation vibration energy harvesting. An asymmetric improved bistable energy harvesting (AIBEH) system is proposed to address this issue by varying the position of the fixed-end magnet. Combining the AIBEH system with stochastic resonance theory and simulation results demonstrate that by simultaneously moving the fixed-end magnet up or down, the depth of a single potential well can be reduced while maintaining two stable state points, decreasing the slope of the potential wall on one side and increasing the dynamic output of the system under intense excitation signals. The research develops a mathematical model of the AIBEH system and numerically solves the electromechanical coupling control equations. The potential energy of three systems is analyzed: IBEH, AIBEH, and ABEH (asymmetric bistable energy harvesting). The Kramers rate and signal-to-noise ratio are derived for an asymmetric bistable system under a harmonic excitation signal and Gaussian white noise. In addition, the effects of harmonic excitation and additional noise on the AIBEH capture performance are investigated. The simulation results indicate that the harvesting performance of AIBEH is superior to that of IBEH at intense excitation.

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.