Stochastic Resonance Research Articles

Low-light Image Enhancement Method Based on Illumination Curve Adjustment

This paper presents an advanced low-light image enhancement approach based on Zero-Reference Deep Curve Estimation. The technique enhances images through: (1) the integration of the Dynamic Stochastic Resonance equation for enhanced contrast and brightness, leveraging adjustable parameters for optimal image quality, and (2) application of an Anisotropic Diffusion function for image denoising and smoothing, preserving edges and texture details while effectively removing noise. This adaptive algorithm tailors diffusion intensity to local image features, further refining the resulting image quality. Experimental results confirm the efficacy of our approach in improving visual quality and noise removal in low-light images.

Entropic stochastic resonance of a fractional confined system driven by bounded noise

Entropic stochastic resonance of a fractional confined system driven by bounded noise

Embedding phase reduction for fast-slow systems with noise-induced stochastic quasiperiodic orbits

Noise is ubiquitous in natural systems and can induce coherent stochastic oscillations which cannot occur in the absence of noise, or stochastic quasiperiodic orbits which are markedly different from the deterministic limit cycle. For fast-slow systems, noise acting on the fast subsystem can induce quasi-periodic orbits tuned by the slow variable, which were termed as self-induced stochastic resonance (SISR). In our previous work [Zhu et al., 2022 [46]], we proposed a phase reduction framework on the SISR-oscillator by the hybrid approximation on the stochastic quasiperiodic orbit and the estimation of the effective noise. In this work, we remove the restriction of the additive Gaussian form assumption on the effective noise, and propose a more natural dimensionality-reduction method which we refer to as embedding phase reduction. Different SISR-oscillators induced by varying noise intensities, which can be embedded into a limit cycle, can have a unified form of the reduced phase equation. The efficiency of the embedding phase reduction is validated by Monte Carlo simulations of the case of periodic forcing, where excellent agreement is achieved for the entrainment and phase drifting dynamics. The simplicity and generality of the proposed embedding phase reduction approach indicate its potential applications in practical experiments and relevance in biological systems.

The inverse stochastic resonance in a small-world neuronal network under electromagnetic stimulation

Electromagnetic stimulation is an important neuromodulation technique that modulates the electrical activity of neurons and affects cortical excitability for the purpose of modulating the nervous system. The phenomenon of inverse stochastic resonance is a response mechanism of the biological nervous system to external signals and plays an important role in the signal processing of the nervous system. In this paper, a small-world neural network with electrical synaptic connections was constructed, and the inverse stochastic resonance of the small-world neural network under electromagnetic stimulation was investigated by analyzing the dynamics of the neural network. The results showed that: the Levy channel noise under electromagnetic stimulation could cause the occurrence of inverse stochastic resonance in small-world neural networks; the characteristic index and location parameter of the noise had significant effects on the intensity and duration of the inverse stochastic resonance in neural networks; the larger the probability of randomly adding edges and the number of nearest neighbor nodes in small-world networks, the more favorable the anti-stochastic resonance was; by adjusting the electromagnetic stimulation parameters, a dual regulation of the inverse stochastic resonance of the neural network can be achieved. The results of this study provide some theoretical support for exploring the regulation mechanism of electromagnetic nerve stimulation technology and the signal processing mechanism of nervous system.

Characterising modulatory effects of high-intensity high frequency transcranial random noise stimulation using the perceptual template model

Neural noise is an inherent property of all nervous systems. However, our understanding of the mechanisms by which noise influences perception is still limited. To elucidate this relationship, we require techniques that can safely modulate noise in humans. Transcranial random noise stimulation (tRNS) has been proposed to induce noise into cortical processing areas according to the principles of stochastic resonance (SR). Specifically, it has been demonstrated that small to moderate intensities of noise improve performance. To date, however, high intensity tRNS effects on neural noise levels have not been directly quantified, nor have the detrimental effects proposed by SR been demonstrated in early visual function. Here, we applied 3 mA high-frequency tRNS to primary visual cortex during an orientation-discrimination task across increasing external noise levels and used the Perceptual Template Model to quantify the mechanisms by which noise changes perceptual performance in healthy observers. Results show that, at a group level, high-intensity tRNS worsened perceptual performance. Our computational analysis reveals that this change in performance was underpinned by an increased amount of additive noise and a reduced ability to filter external noise compared to sham stimulation. Interestingly, while most observers experienced detrimental effects, a subset of participants demonstrated improved performance. Preliminary evidence suggests that differences in baseline internal noise levels might account for these individual differences. Together, these results refine our understanding of the mechanisms underlying the influence of neural noise on perception and have important implications for the application of tRNS as a research tool.

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.

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).

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.

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.

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.

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.

Impact of Non-Gaussian Noise and Time Delay on Stability and Stochastic Resonance for a FitzHugh-Nagumo Neural System Subjected to a Multiplicative Periodic Signal

In this paper, we focus on the investigations on the stochastic stability and the stochastic resonance (SR) phenomena for a FitzHugh-Nagumo system with time delay induced by a multiplicative non-Gaussian colored noise and an additive Gaussian colored noise. By use of the fast descent method, the unified colored noise approximation and the two-state theory for the SR, the stationary probability density function (SPDF) and the signal-to-noise ratio (SNR) caused by different noise terms and time delay are explored. The investigation results indicate that the two noise intensities, time delay and the departure parameter from the Gaussian noise can all reduce the probability density around the two stable states and destroy the stability of the neural system; while the two noise correlation times [Formula: see text] and [Formula: see text] can both improve the probability density around both stable states and reinforce the biological stability of the neural system. As regards the SNR, it is found that the two noise intensities and the departure coefficient can all weaken the SR effect, while time delay [Formula: see text] and the correlation time [Formula: see text] of the multiplicative noise will always magnify the SR phenomenon. It is worth to mention that the correlation time [Formula: see text] of the additive noise can stimulate the SR effect, but not alter the maximum of the SNR.

Autoregression, First Order Phase Transition, and Stochastic Resonance: A Comparison of Three Models for Forest Insect Outbreaks

Three models of abundance dynamics for forest insects that depict the development of outbreak populations were analyzed. We studied populations of the Siberian silkmoth Dendrolimus sibiricus Tschetv. in Siberia and the Far East of Russia, as well as a population of the pine looper Bupalus piniarius L. in Thuringia, Germany. The first model (autoregression) characterizes the mechanism where current population density is dependent on population densities in previous k years. The second model considers an outbreak as analogous to a first-order phase transition in physical systems and characterizes the outbreak as a transition through a potential barrier from a low-density state to a high-density state. The third model treats an outbreak as an effect of stochastic resonance influenced by a cyclical factor such as solar activity and the “noise” of weather parameters. The discussion focuses on the prediction effectiveness of abundance dynamics and outbreak development for each model.

Control of stochastic and inverse stochastic resonances in a liquid-crystal electroconvection system using amplitude and phase noises

Stochastic and inverse stochastic resonances are counterintuitive phenomena, where noise plays a pivotal role in the dynamics of various biological and engineering systems. Even though these resonances have been identified in various systems, a transition between them has never been observed before. The present study demonstrates the presence of both resonances in a liquid crystal electroconvection system using combined amplitude and phase noises, which correspond to colored noises with appropriate cutoff frequencies (i.e., finite correlation times). We established the emergence of both resonances and their transition through systematic control of the electroconvection threshold voltage using these two noise sources. Our numerical simulations were experimentally confirmed and revealed how the output performance of the system could be controlled by combining the intensity and cutoff frequency of the two noises. Furthermore, we suggested the crucial contribution of a usually overlooked additional phase noise to the advancements in various noise-related fields.

A novel untrained SSVEP-EEG feature enhancement method using canonical correlation analysis and underdamped second-order stochastic resonance.

Compared with the light-flashing paradigm, the ring-shaped motion checkerboard patterns avoid uncomfortable flicker or brightness modulation, improving the practical interactivity of brain-computer interface (BCI) applications. However, due to fewer harmonic responses and more concentrated frequency energy elicited by the ring-shaped checkerboard patterns, the mainstream untrained algorithms such as canonical correlation analysis (CCA) and filter bank canonical correlation analysis (FBCCA) methods have poor recognition performance and low information transmission rate (ITR). To address this issue, a novel untrained SSVEP-EEG feature enhancement method using CCA and underdamped second-order stochastic resonance (USSR) is proposed to extract electroencephalogram (EEG) features. In contrast to typical unsupervised dimensionality reduction methods such as common average reference (CAR), principal component analysis (PCA), multidimensional scaling (MDS), and locally linear embedding (LLE), CCA exhibits higher adaptability for SSVEP rhythm components. This study recruits 42 subjects to evaluate the proposed method and experimental results show that the untrained method can achieve higher detection accuracy and robustness. This untrained method provides the possibility of applying a nonlinear model from one-dimensional signals to multi-dimensional signals.

Additive Sensory Noise Effects on Operator Performance in a Lunar Landing Simulation.

INTRODUCTION: Adding noise to a system to improve a weak signal's detectability is known as stochastic resonance (SR). SR has been shown to improve sensory perception and cognitive performance in certain individuals, but it is unknown whether this performance improvement can translate to meaningful macrocognitive enhancements in performance for complex, operational tasks.OBJECTIVE: We investigated human operator performance in a lunar landing simulation while applying auditory white noise and/or noisy galvanic vestibular stimulation.METHODS: We measured performance (N = 16 subjects) while completing simulation trials in our Aerospace Research Simulator. Trials were completed with and without the influence of auditory white noise, noisy galvanic vestibular stimulation, and both simultaneously in a multimodal fashion. Performance was observed holistically and across subdimensions of the task, which included flight skill and perception. Subjective mental workload was collected after completing four trials in each treatment.RESULTS: We did not find broad operator improvement under the influence of noise, but a significant interaction was identified between subject and noise treatment, indicating that some subjects were impacted by additive noise. We also found significant interactions between subject and noise treatment in performance subdimensions of flight skill and perception. We found no significant main effects on mental workload.CONCLUSIONS: This study investigated the utility of using additive sensory noise to induce SR for complex tasks. While SR has been shown to improve aspects of performance, our results suggest additive noise does not yield operational performance changes for a broad population, but specific individuals may be affected.Sherman SO, Shen Y-Y, Gutierrez-Mendoza D, Schlittenhart M, Watson C, Clark TK, Anderson AP. Additive sensory noise effects on operator performance in a lunar landing simulation. Aerosp Med Hum Perform. 2023; 94(10):770-779.

Зависимость стохастического резонанса в нелинейной системе от характеристик каждого слагаемого аддитивной смеси

A nonlinear system was investigated using a modeling approach, constructed based on the scheme of a digital filter using the Lyapunov characteristic function. The phenomenon of stochastic resonance was observed in the nonlinear system when there was an additive mixture of a quasi-deterministic signal and noise at the system input. Stochastic resonance improves the signal-to-noise ratio at the system output by more than 15400 times compared to its value at the system input. The recorded number may vary and represents the main characteristic of the resonance. The dependence of the stochastic resonance characteristic on the variations of the probabilistic characteristics of the quasi-deterministic signal and noise was studied. An analysis of experimental data describing the values of the characteristic and the peculiarities of the stochastic resonance effect in the nonlinear system was performed. Additionally, a connection between the value of the resonance characteristic and the total energy of the periodic signal was discovered for the first time.

Зависимость стохастического резонанса в нелинейной системе от характеристик каждого слагаемого аддитивной смеси

A nonlinear system was investigated using a modeling approach, constructed based on the scheme of a digital filter using the Lyapunov characteristic function. The phenomenon of stochastic resonance was observed in the nonlinear system when there was an additive mixture of a quasi-deterministic signal and noise at the system input. Stochastic resonance improves the signal-to-noise ratio at the system output by more than 15400 times compared to its value at the system input. The recorded number may vary and represents the main characteristic of the resonance. The dependence of the stochastic resonance characteristic on the variations of the probabilistic characteristics of the quasi-deterministic signal and noise was studied. An analysis of experimental data describing the values of the characteristic and the peculiarities of the stochastic resonance effect in the nonlinear system was performed. Additionally, a connection between the value of the resonance characteristic and the total energy of the periodic signal was discovered for the first time.

Langevin’s Equation of Motion: Dynamical States and Stochastic Resonance

In this present work, we numerically observe the existence of two dynamical states of trajectories in the underdamped motion of a particle in an inhomogeneous periodic bistable potential with high friction coefficient driven by a periodic force. The system is inhomogeneous in the sense that the coefficient of friction is periodic in space and with phase difference 'ϕ' with respect to the periodic bistable potential. Just like in sinusoidal potentials, the occurrence of stochastic resonance (SR) in the periodic bistable potential is due to the transitions between the dynamical states at an optimal (thermal) noise strength.

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.