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.

Airborne magnetic anomaly detection based on Bi-stable stochastic resonance system

In order to address the problem with low signal-to-noise ratio (SNR) detection for airborne magnetic anomaly detection (MAD), an adaptive detection method based on bi-stable stochastic resonance (SR) system is proposed. The method adopts a series structure, S-SR, effectively improving detection speed. Allowing for the difficulty in parameter selection for the SR system, this method can achieve the adaptive selection of system parameters. On this basis, the effect of different sampling frequencies in the Runge–Kutta method on the numerical model of the SR system is investigated. Finally, the simulation and experiment analysis of MAD methods are performed to draw a comparison between the S-SR, orthogonal basis functions (OBF) decomposition, and high-order crossing (HOC) methods. According to the simulation and experiment results, the S-SR method outperforms the OBF and HOC methods in the outcome and range of detection under the same conditions.

Linearly-coupled sigmoid bistable stochastic resonance for weak signal detection

Abstract The paper focuses on developing a stochastic resonance (SR) system designed for the detection of weak signals under alpha-stable-distributed noises. Initially, in view of the strong impulsive characteristics of noises, a linearly-coupled sigmoid bistable stochastic resonance (LSBSR) system is proposed, which is constructed by potential function and sigmoid function. Through formula derivation, it is theoretically proved that the output signal-to-noise ratio (SNR) of the LSBSR system is superior to that of the classical bistable SR system. Then, a new signal processing strategy based on the LSBSR system is introduced. Simulation experiments have demonstrated that under the input SNR = −20 dB, the detection probability of the LSBSR system exceeds 95% for the alpha-stable-distributed noise with α= 1.5. When α is reduced to 0.1, the detection probability approaches 80%, significantly outperforming other detection methods. Finally, the LSBSR system is applied to detect sea-trial signals with an SNR improvement of 22.5 dB, which further validates the practicability of the proposed system.

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.

Multi-Type Stochastic Resonances for Noise-Enhanced Mechanical, Optical, and Acoustic Sensing.

Stochastic resonance (SR) typically manifests in nonlinear systems, wherein the detection of a weak signal is bolstered by the addition of noise. Since its first discovery in a study of ice ages on Earth, various types of SRs have been observed in biological and physical systems and have been implemented in sensors to benefit from noise. However, a universally designed sensor architecture capable of accommodating different types of SRs has not been proposed, and the widespread applications of SRs in daily environments have not yet been demonstrated. Here, we propose a sensor architecture to simultaneously realize multi-type SRs and demonstrate their wide applications in mechanical, optical, and acoustic sensing domains. In particular, we find the coexistence of excitable SR and bistable SR in a sensor architecture composed of wirelessly coupled inductor-capacitor resonators connected to a nonlinearly saturable amplifier. In both types of SRs, adding noise to the system leads to a characteristic noise-enhanced signal-to-noise ratio (SNR). We further validate our findings through mechanical, optical, and acoustic sensing experiments and obtain noise-enhanced SNR by 9 dB, 3 dB, and 7 dB, respectively, compared to the standard methods devoid of SR integration. Our findings provide a general strategy to design various types of SRs and pave the way for the development of a distinctive class of sensors leveraging environmental noise, with potential applications ranging from biomedical devices to ambient sensing.

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.

Adaptive bistable stochastic resonance based weak signal reception in additive Laplacian noise

Adaptive bistable stochastic resonance based weak signal reception in additive Laplacian noise

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 frequency weak signals detection based on under-sampling bistable stochastic resonance

Signal detection has a wide range of practical applications. Compared with traditional weak signal detection, the nonlinear effect of noise in the bistable system is typical and easy to extend, so bistable stochastic resonance detection technique has a wider applicability. In this paper, the multi-frequency weak signals detection based on under-sampling bistable stochastic resonance is studied. Based on the theory of bistable stochastic resonance, a simulation model is established to simultaneously detect multiple low-frequency weak signals. The spectrum of input and output signals is obtained through numerical simulation calculation, and the system characteristics are analyzed. When the large parameter signal does not meet the adiabatic approximation theory, the appropriate sampling coefficient can be selected to directly under-sample the input signal to make it conform to the conditions, and then the scale inverse transformation can be carried out. Finally, combined with the simulation analysis, the correctness of the under-sampling bistable stochastic resonance system to detect the multi-frequency weak signals is verified, the sampling rate is reduced, and the complexity is effectively decreased.

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.

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.

Single acoustic vector sensor DOA enhanced by unsaturated bistable stochastic resonance with linear amplitude response constrained

Acoustic vector sensors (AVS) are increasingly utilized for remote target passive perception, but accurate direction-of-arrival (DOA) estimation remains a formidable challenge, particularly in the presence of heavy background noise. In this paper, we propose a novel DOA estimation method that utilizes complex acoustic intensity measurements (CAIM) and unsaturated bistable stochastic resonance with linear amplitude response constrained (LAR-UBSR). The proposed method aims to exploit the excellent denoising performance of stochastic resonance (SR) to enhance the accuracy of DOA estimation. The proposed LAR-UBSR method is based on the theoretical analysis of the signal pre-processing requirements of CAIM, which determines the linear amplitude response and fixed phase shift. LAR-UBSR achieves a stable phase shift and linear amplitude response by utilizing the unsaturated potential well and limited potential parameters adjustment method of SR. We analyze the amplitude response linearity of LAR-UBSR under different signal-to-noise ratios (SNRs) and a wide range of frequencies, demonstrating a larger linear amplitude response interval that meets the signal pre-processing requirements of CAIM. Numerical analysis and application verification show that the proposed DOA method outperforms existing methods, particularly under low SNR conditions. The results suggest the potential for high-accuracy DOA estimation using nonlinear signal processing strategies in the presence of heavy background noise.

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.

Novel Piecewise Normalized Bistable Stochastic Resonance Strengthened Cooperative Spectrum Sensing

A novel piecewise normalized bistable stochastic resonance (PNBSR) strengthened cooperative spectrum sensing is established by the PNBSR, residual covariance matrices, credibility weighted matrix fusion and a convolutional neural network (CNN) classification at low signal-to-noise ratios (SNRs). First, the PNBSR based on the traditional bistable stochastic resonance (TBSR) is proposed to improve the SNRs of received signals. Second, the output of the PNBSR is demodulated to obtain in-phase (I) and quadrature-phase (Q) covariance matrices. Third, the I/Q covariance matrices from different secondary users (SUs) are Cholesky decomposed to construct residual covariance matrices in a fusion center (FC). Subsequently, a new credibility weighted coefficient is proposed to fuse residual covariance matrices of the SUs. Finally, both training and test samples of the fusion detection statistics are fed into the CNN to train a high-performance classification model of cooperative spectrum sensing. The main innovations include the PNBSR, optimization index, Cholesky decomposition-based matrix cancellation to construct residual covariance matrices and credibility weighted matrix fusion. Simulation results show that the SNR of received signals strengthened by the PNBSR is improved by 3.36 dB other than received signals on average, which is 0.22dB larger than that of the TBSR. The detection probability of the proposed scheme also outperforms those of the support vector machine (SVM) and CNN schemes by 77% and 75% at -15 dB, respectively.

Adaptive bistable stochastic resonance based blind watermark extraction in discrete cosine transform domain

AbstractBlind watermark extraction in discrete cosine transform (DCT) domain has a wide application prospect as well as a challenging subject. The imperceptibility of watermark signal makes watermark extraction a weak signal reception issue in essence. For DCT coefficients of host image generally disobey Gaussian distribution, at which the performance of linear correlated reception is no longer optimal. Aiming at this, a novel blind watermark extraction scheme combining the uncorrelated reception with adaptive bistable stochastic resonance (ABSR) technique is proposed. First, by block DCT transformation for host image, an additive watermark embedding algorithm is introduced, in which the watermarked image can be converted to one dimensional time domain weak signal (binary watermark image) reception under additive Laplacian noise (selected DCT coefficients). On this basis, through the key technology research on quantitatively cooperative resonance relationship under Laplacian noise, the ABSR system can be implemented by bistable system parameters self‐adaptive adjustment, in which the ABSR system output signal will be enhanced rather than be weakened by random noise. Finally, the ABSR‐based watermark extraction scheme is investigated, and both the visual effect, bit error ratio performance and robustness of proposed scheme are testified to be superior to that of traditional uncorrelated extraction.

Extracting weak electromagnetic signals based on RMPSO-SPBSR in virtual anechoic chamber

To enhance the signal extraction performance at weak noise intensity in virtual anechoic chamber, this study investigates the correlation between the generation conditions of a stochastic resonance (SR) system and its output performance. To achieve optimal resonance effects, an adaptive system called symmetric piecewise bistable SR (SPBSR) is proposed. This system improves its structure by modifying the potential function to facilitate the occurrence of SR. Meanwhile, it combines a regional multi-role strategy and particle swarm optimization algorithm to determine the optimal structural parameters. The adaptive optimization process utilizes update rules that balance global and local optimal solutions, thereby mitigating the tendency to quickly converge to a local optimum. Experimental results demonstrate that the proposed system exhibits excellent performance within a noise intensity range of 0–10 dB, with a correlation coefficient of over 0.75, which can effectively suppress noise interference. In practical signal processing, the system excels at accurately extracting signal characteristics, resulting in improved similarity and smoothness of the detected signal. Both simulation and experimental results validate this algorithm’s strong practical relevance.

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.

Research and Application of Wavelet Transform-Based Two-Dimensional Pinning Potential Stochastic Resonant System

In stochastic resonance (SR) weak signal detection, there is no literature currently report on the study and comparison of one-dimensional (1D) and 2D pinning potential worldwide which has potential research necessity. A one (ODPPBSR) and a 2D pinning potential bistable SR (TDPPBSR) are proposed. The expressions for MFPT, SPD and SNR are derived based on adiabatic approximation theory. To investigate the correctness of the theoretical results, numerical simulations are carried out with the Runge–Kutta algorithm and the genetic algorithm (GA) is used to optimize the system. The system has exceptional ability to restore signal periodicity and amplitude amplification at low frequency, high frequency and multi-frequency. The two systems are compared of the detection capabilities on weak signals through wavelet transform denoising and applied to the 6205-2RS JEM SKF and HRB 6205-2Z for bearing fault detection. The experimental results show that the 2D system is superior to the 1D system.