Tristable Stochastic Resonance Research Articles

Research and application of two-dimensional time-delayed tri-stable stochastic resonance system for bearing fault detection

Research and application of two-dimensional time-delayed tri-stable stochastic resonance system for bearing fault detection

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.

Principle and application of variable-scale tristable stochastic resonance for fractional power systems

Principle and application of variable-scale tristable stochastic resonance for fractional power systems

Parametric study and multi-parameter optimization of a generalized second-order tri-stable stochastic resonance system

Parametric study and multi-parameter optimization of a generalized second-order tri-stable stochastic resonance system

A cascaded piecewise unsaturated asymmetric under-damped tri-stable stochastic resonance system and its application in bearing fault diagnosis

A cascaded piecewise unsaturated asymmetric under-damped tri-stable stochastic resonance system and its application in bearing fault diagnosis

4FSK signal processing based on adaptive tristable stochastic resonance under levy noise

Aiming at the problem of low quality of coherent demodulation transmission signal of digital signal in the background of Levy noise, this paper proposes a new method of 4FSK signal reception based on adaptive tristable stochastic resonance (SR) system. The bit error rate (BER) of output signals of adaptive tristable SR system model and the traditional modulation model are compared by simulation. The numerical simulation results show that compared with the traditional model, the output BER of the 4FSK signal after demodulation of the adaptive tristable SR system model is reduced by 4% compared with the traditional model. The time domain image of 4FSK signal is clearer, the burrs are significantly reduced and the spectral amplitude of 4FSK signal is greatly improved. The success of this experiment suggests a strong promise of SR systems for digital signal detection in impact noise.

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.

Adaptive detection of impact signals with two-dimensional piecewise tri-stable stochastic resonance and its application in bearing fault diagnosis

In this paper, we introduce an innovative method known as Adaptive Two-Dimensional Piecewise Tri-Stable Stochastic Resonance (TDPTSR) and discuss its applicability in extracting weak fault features. Initially, addressing the saturation issue of the Standard Tri-Stable Stochastic Resonance (STSR) system, we construct a novel piecewise tri-stable potential function. This function independently adjusts the depth and width of potential wells. We explore the particle output characteristics of the Piecewise Tri-Stable Stochastic Resonance (PTSR) system using the fourth-order Runge-Kutta algorithm. Subsequently, we delve into the performance analysis of the TDPTSR system. Leveraging adiabatic approximation theory, we derive the equivalent potential function, steady-state probability density (SPD), mean first-pass time (MFPT), and output signal-to-noise ratio (SNR) of the TDPTSR. We also investigate the impact of changes in system parameters on these metrics. Additionally, drawing from kurtosis and cosine similarity properties, we introduce a Modified Kurtosis Index (MKC) as a measurement index for impact signal detection. We propose a method for impact signal feature extraction by integrating MKC with the TDPTSR system. Simulation analysis demonstrates the suitability of MKC as an index for quantifying Stochastic Resonance and the superior detection capability of the TDPTSR system. Finally, we apply TDPTSR to the fault diagnosis of two types of bearings, optimizing system parameters using a genetic algorithm (GA). Comparative analysis with STSR and PTSR confirms that our proposed method in this paper yields further improvements in Signal-to-Noise Ratio Improvement (SNRI), higher spectral peak magnitude (Amout) at characteristic frequencies, and increased recognition quantity (Δ).

An underdamped and delayed tri-stable model-based stochastic resonance

Stochastic resonance (SR) is investigated in an underdamped tri-stable potential system driven by Gaussian colored noise and a periodic excitation, where both displacement and velocity time-delayed states feedback are considered. It is challenging to study SR in a second-order delayed multi-stable system analytically. In this paper, the improved energy envelope stochastic average method is developed to derive the analytical expressions of stationary probability density (SPD) and spectral amplification. The effects of noise intensity, damping coefficient, and time delay on SR are analyzed. The results show that the shapes of joint SPD can be adjusted to the desired structure by choosing the time delay and feedback gains. For fixed time delay, the SR peak is increased for negative displacement or velocity feedback gain. Meanwhile, the SR peak is decreased while the optimal noise intensity increases with increasing correlation time of noise. The Monte Carlo simulations (MCS) confirm the effectiveness of the theoretical results.

Piecewise time-delay tri-stable stochastic resonance system and its application in bearing fault diagnosis

Current studies of time-delay based systems are compared to classical tri-stable stochastic resonance (CTSR) system and do not reflect the effect of adding a delay term on unsaturated systems. In this paper, a piecewise delayed tri-stable stochastic resonance (PTTSR) system is proposed. Firstly, the equivalent Langevin for PTTSR system is derived and compared with the output of CTSR and piecewise tri-stable stochastic resonance (PTSR) systems, where the addition of the time-delay term can further improve the output amplitude. Secondly, mean first pass time (MFPT) and output signal-to-noise ratio (SNR) are derived, and the effects of different parameters on MFPT and SNR are investigated. increasing the feedback intensity and time-delay length improved the output SNR. Then, the input period signal is then numerically simulated using the signal-to-noise ratio gain (SNRG) as a measurement, which increases by 2.75 dB for PTTSR system compared to PTSR system. Finally, the three systems are used for bearing fault detection and the system parameters are optimized by genetic algorithm. The results showed that the output amplitude of PTTSR system is more than 12 times that of PTSR system and the SNRG increased by more than 2 dB. This demonstrates the superior performance of PTTSR system in detecting weak signals and provides good feasibility in engineering applications.

Two combination methods of piecewise unsaturated tri-stable stochastic resonance system and bearing fault detection under different noise

In this paper, a piecewise unsaturated tri-stable stochastic resonance (PUTSR) system is proposed to address the issue of output saturation. Firstly, the unsaturated characteristics of the PUTSR system are verified, followed by a discussion on the system performance of PUTSR under two different combinations of coupled and cascaded systems. The two-dimensional coupled piecewise unsaturated tri-stable stochastic resonance (TCPUTSR) system and cascaded piecewise unsaturated tri-stable stochastic resonance (CPUTSR) system are proposed. By implementing the adiabatic approximation theory, the steady-state probability density (SPD) of TCPUTSR system and spectral amplification (SA) coefficient of TCPUTSR and CPUTSR systems are derived respectively. The impact of different system parameters on the SPD and SA are also investigated. Finally, PUTSR, TCPUTSR and CPUTSR systems are applied to detection on the fault signal of bearing. Gaussian white noise and color noise are used to simulate actual noise environments in the experiments, while the adaptive genetic algorithm (AGA) is used to optimize the parameters and measure the system performance via signal-to-noise ratio improvement (SNRI). Results indicate that both coupled and cascaded systems demonstrate better detection capabilities than individual systems, with the CPUTSR system offering better enhancement and detection of bearing fault signals. Under Gaussian white noise, the SNRI of the CPUTSR system is 1.449 dB ~ 3.198 dB higher than that of the PUTSR and TCPUTSR systems, while under color noise it is 1.566 dB ~ 2.849 dB higher. This paper mainly compares the spectral amplification capability and fault signal detection capability of the same system under two different combinations of coupled and cascaded. The theoretical and numerical simulations further verify that the designed cascaded system outperforms the coupled system and proves the great superiority of CPUTSR system. These findings provide crucial theoretical support and practical application prospects for engineering purposes.

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.

Characteristic frequency detection of steady-state visual evoked potentials based on filter bank second-order underdamped tristable stochastic resonance

Brain computer interface (BCI) system based on steady-state visual evoked potentials (SSVEP) has great potential for communication and control applications. The actual intention of the user is determined by detecting the characteristic frequency of the SSVEP signals. However, the artifacts and spontaneous electroencephalogram (EEG) signals in SSVEP signals will degrade the performance of characteristic frequency detection. How to improve detection performance is a hot research topic. In this study, an innovative filter bank second-order underdamped tristable stochastic resonance (FBSUTSR) method is proposed and evaluated to enhance the characteristic frequency detection of SSVEP signals. FBSUTSR method uses noise to enhance signal detection and effectively utilizes the harmonic components contained in the signal. At the same time, the second-order underdamping characteristic makes the system form a unique filtering effect. In this study, the performance of SSVEP signals characteristic frequency detection with FBSUTSR, second-order underdamped tristable stochastic resonance (SUTSR), underdamped second-order stochastic resonance (USSR) and canonical coefficient analysis (CCA) is compared and analyzed using the public dataset of 40 types of stimulation targets of 35 subjects. When the stimulus data length is 5 s, FBSUTSR method achieves excellent performance with an average accuracy of 97.35±3.97% and an average information transmission rate (ITR) of 60.58±4.76bit·min-1, which is significantly higher than the performance of other three methods. This study verifies that the proposed FBSUTSR method has prominent performance advantages in implementing SSVEP signals characteristic frequency detection. The BCI system based on SSVEP using FBSUTSR method has great development potential in communication and control.

Second-order coupled tristable stochastic resonance and its application in bearing fault detection under different noises

Second-order coupled tristable stochastic resonance and its application in bearing fault detection under different noises

Feature Extraction and Signal Enhancement Based on Unsaturation Piecewise Tri-Stable Stochastic Resonance Driven by Lévy Noise

As science advances and machines become larger and more sophisticated, it is vital to determine whether there is a mechanical failure without damaging the device. Stochastic resonance (SR), as a widely used method, can effectively extract the periodic signal in the noise and then realize the identification of mechanical faults, which is very important for safety and property protection. Most studies on SR are based on additive white Gaussian noise (AWGN) as the driving source; however, there are many kinds of noise in reality. In this paper, based on the previously proposed piecewise tri-stable SR (PTSR) model, the influence of parameters on the mean of signal-to-noise ratio gain (SNR-GM) of the system driven by Lévy noise is studied. It is also verified by simulation signals and actual signals that PTSR can also achieve feature extraction and signal enhancement with Lévy noise as the driving source, which proves that PTSR can be applied in a wider range of conditions.

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.

A Novel Piecewise Tri-Stable Stochastic Resonance System Driven by Dichotomous Noise.

Stochastic resonance (SR) has been widely studied as a means of signal processing since its conception. Since SR is different from other denoising methods in nature, it can be used for not only feature extraction but also signal enhancement. Additive white Gaussian noise (AWGN) is often used as a driving source in SR research due to its convenience in numerical simulation and uniform distribution, but as a special noise, it is of great significance to study the SR principle of dichotomous noise as a driving source for nonlinear dynamics. In this paper, the method of piecewise tri-stable SR (PTSR) driven by dichotomous noise is studied, and it is verified that signal enhancement can still be achieved in the PTSR system. At the same time, the influence of the parameters of the PTSR system, periodic signal, and dichotomous noise on the mean of signal-to-noise ratio gain (SNR-GM) is analyzed. Finally, dichotomous noise and AWGN are used as the driving sources of the PTSR system, and the signal enhancement ability and noise resistance ability of the two drivers are compared.

Mechanical Fault Feature Extraction under Underdamped Conditions Based on Unsaturated Piecewise Tri-Stable Stochastic Resonance

In the case of the rapid development of large machinery, the research of mechanical fault signal feature extraction is of great significance, it can not only ensure the development of the economy but also ensure safety. Stochastic resonance (SR) is of widespread use in feature extraction of mechanical fault signals due to its excellent signal extraction capability. Compared with an overdamped state, SR in an underdamped state is equivalent to one more filtering of the signal, so the signal-to-noise ratio (SNR) of the output signal will be further improved. In this article, based on the piecewise tri-stable SR (PTSR) obtained from previous studies, the feature extraction of mechanical fault signals is carried out under underdamped conditions, and it is found that the SNR of the output signal is further improved. The simulation signals and experimental signals are used to verify that PTSR has better output performance under underdamped conditions.

A Cascaded Piecewise Unsaturated Asymmetric Under-Damped Tri-Stable Stochastic Resonance System and its Application in Bearing Fault Diagnosis

A Cascaded Piecewise Unsaturated Asymmetric Under-Damped Tri-Stable Stochastic Resonance System and its Application in Bearing Fault Diagnosis