Stochastic Resonance Theory Research Articles

Effectiveness of bimodal stimulation of the auditory-somatosensory system in the treatment of tonal tinnitus

Background and objectivesThe dorsal cochlear nucleus (DCN) is the interaction site of auditory and somatosensory system inputs. According to the stochastic resonance theory, hearing loss increases the neural activity of the somatosensory system in the DCN and causes tinnitus. it is possible to modulate this neural hyperactivity by applying random noise through the auditory and somatosensory systems (bimodal stimulation). Therefore, this study aimed to investigate the effectiveness of the bimodal intervention based on the theory of stochastic resonance. MethodsThe study divided 34 participants into unimodal and bimodal groups with 17 subjects in each. The bimodal group received customized acoustic stimulation along with transcutaneous auricular vagus nerve stimulation (tAVNS) and the unimodal group received customized acoustic stimulation along with tAVNS as a sham. The treatment sessions in both groups were 6 sessions and each session lasted for 20 min. The participants were evaluated before, immediately after, and one month after the completion of the intervention sessions, using the Tinnitus Handicap Inventory (THI) questionnaire and the mismatch negativity (MMN) test. ResultsAfter the intervention sessions, the results indicated a statistically significant decrease in THI scores and a significant increase in the MMN amplitude in the bimodal group compared to the unimodal group. No significant changes in MMN latency were observed between the two groups. These changes were stable in the one-month follow-up visit. ConclusionsOur study showed that bimodal stimulation is a better intervention option compared to unimodal stimulation. Bimodal stimulation may be an effective intervention method for some subjects with tinnitus, especially people with hearing loss who have tonal tinnitus.

Enhanced Underwater Single Vector-Acoustic DOA Estimation via Linear Matched Stochastic Resonance Preprocessing

Underwater acoustic vector sensors (UAVSs) are increasingly utilized for remote passive sonar detection, but the accuracy of direction-of-arrival (DOA) estimation remains a challenging problem, particularly under low signal-to-noise ratio (SNR) conditions and complex background noise. In this paper, a comprehensive theoretical analysis is conducted on UAVS signal preprocessing subjected to gain-phase uncertainties for average acoustic intensity measurement (AAIM) and complex acoustic intensity measurement (CAIM)-based vector DOA estimation, aiming to explain the theoretical restrictions of intensity-based vector acoustic preprocessing approaches. On this basis, a generalized vector acoustic preprocessing optimization model is established in which the principle can be described as “maximizing the denoising performance under the constraints of an equivalent amplitude-gain response and phase-bias response”. A novel vector acoustic preprocessing method named linear matched stochastic resonance (LMSR) is proposed within the framework of matched stochastic resonance theory, which can naturally guarantee the linear gain-phase restrictions, as well achieving effective denoising performance. Numerical analyses demonstrate the superior vector DOA estimation performance of our proposed LMSR-AAIM and LMSR-CAIM methods in comparison to classical intensity-based AAIM and CAIM methods, especially under low-SNR conditions and non-Gaussian impulsive noise circumstances. Experimental verification conducted in the South China Sea further verifies its the effectiveness for practical application. This work can lay a solid foundation to break through the challenges of underwater remote vector acoustic DOA estimation under low-SNR conditions and complex ocean ambient noise and can provide important guidance for future research work.

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.

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.

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.

Noisy Low-Illumination Image Enhancement Based on Parallel Duffing Oscillator and IMOGOA

In complex environment, the captured images face several kinds of problems, including low illumination and intensive noise, which deteriorates image quality and has a great impact on the follow-up work. In this work, inspired by stochastic resonance theory, we design a model that considers the spatial characteristics of image and noise reduction and enhancement are simultaneously realized. The 8-neighborhood pixel extraction method and the Duffing oscillator model are used to parallel process the image, and then the image details are restored by homomorphic filter. In order to optimize the parameters of parallel Duffing oscillator model and homomorphic filter adaptively, multiobjective grasshopper optimization algorithm is introduced into the method. Sobol sequence and differential mutation operators are used to improve the optimization algorithm, and the fitness function is constructed by using peak signal-to-noise ratio and standard deviation. To verify the effectiveness of the proposed method, low-illumination image data with Gaussian noise is used for subjective and objective evaluation. The experimental results show that the proposed algorithm gives prominence to useful information, which has smaller color distortion and better visual quality.

Stochastic resonance in a high-dimensional space coupled bistable system and its application

As a noise-enhanced signal processing method, stochastic resonance has been widely applied in the field of condition detection and fault diagnosis. To further consummate the application of stochastic resonance in practical engineering, a high-dimensional space model based on coupled bistable stochastic resonance system is proposed in this paper. Firstly, taking the three-dimensional space coupled bistable stochastic resonance system as the research object, the influence of system parameters on the output signal-to-noise ratio is analyzed. Then, the output signal-to-noise ratio of the high-dimensional space coupled bistable stochastic resonance system are analyzed in different dimensions. It is found that the output signals of these coupling ends with the same system parameters are identical, and there is always an optimal dimension for a given input so that the output signal-to-noise ratio reaches the maximum. Moreover, simulation results indicate that the proposed model has good feature enhancement ability and anti-noise robustness. Finally, the proposed approach is employed to diagnose fault signals of two different bearing types. The optimal output of the system is determined by establishing the best dimension value. The bigger output signal-to-noise ratio demonstrates that the proposed method outperforms the one-dimensional bistable stochastic resonance and two-dimensional coupled bistable stochastic resonance in weak fault signal detection, which improves the engineering practicability of stochastic resonance theory.

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

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

Research on the Weak Signal Extraction Method with Adaptive Stochastic Resonance Based on the Time Grid Sensor for PMSM

Because the output signal of the time grid sensor is so weak and is easily affected by the disturbing noise, it is difficult to extract the induction signal containing the position information, when the time grid sensor is used to detect the rotor position of the permanent magnet synchronous motor (PMSM). In this paper, an adaptive monostable stochastic resonance method is proposed to realize the weak signal detection of the time grid sensor. The tunnel magnetoresistance effect sensor (TMR) is adopted to detect the change of the rotor magnetic field of the motor in this method, and the detection model of the time grid sensor about PMSM is constructed. The monostable stochastic resonance theory is applied to extract the induction signal of the time grid sensor. As to the problem of the tuning the parameters of the monostable stochastic resonance system, the genetic algorithm is adopted to optimize the parameters of the monostable stochastic resonance system. The experimental results show that the monostable stochastic resonance method based on the genetic algorithm can effectively detect the weak induction signal of the time grid sensor about PMSM. This method solves the problem of the weak signal extraction of the time grid sensor for PMSM, and the detection accuracy is also improved.

The mechanism for SMEs growth by applying stochastic dynamical approach

The purpose of this paper is to establish an interpretable framework to describe the growth mechanism of small and micro enterprises (SMEs) under the tech-economic paradigm and develop a new measurement method for growth performance. Based on stochastic resonance theory, as the inherent capital–product switches are applied with capital driving and risk incentive, SMEs’ growth might exhibit an optimal state subject to the implementation of different strategies. Simulation results verify these strategies from management orientation, specialization level, and environmental uncertainty to reveal some nonintuitive phenomena. These findings lead us to create useful decision rules in risk management, growth path optimization or SME loans. Finally we wish the framework established in this paper may provide another new mathematical way to explain Schumpter’s economic development theory based on SMEs growth with innovation.

Stochastic resonance at early visual cortex during figure orientation discrimination using transcranial magnetic stimulation

Visual noise usually reduces the visibility of stimuli. However, very low contrast or subliminal visual noise can sometimes enhance the visibility of low-contrast stimuli. It has been suggested that this enhancement occurs at the visual cortex. The aims of this study are to clarify the role of the early visual cortex (V1/V2) in the enhancement effect and to clarify the relationship of the SR characteristics among different experiments. Noise was added directly to the visual cortex by using transcranial magnetic stimulation (TMS) with randomly varying intensity. The location on the scalp and the timing (stimulus onset asynchrony, SOA) of TMS were specifically adjusted to target the early visual cortex. Contrast thresholds for figure orientation discrimination were measured as a function of TMS noise intensity. With increasing TMS noise intensity the contrast threshold for figure discrimination first decreased (enhancement) and then increased (impairment). These effects were clearly dependent both on scalp location and timing (SOA). The optimum SOA was around 60 ms, while the optimum location varied across participants. Outside the optimum location and SOA values, no TMS effects were found. The enhancement effect can be accounted for by the stochastic resonance (SR) theory based on a threshold device. In addition, we reveal similarity in characteristics of the SR phenomenon between different experiments.

Caracterização da magnitude da vibração imposta por plataformas vibratórias estocásticas de corpo inteiro utilizadas em reabilitação e treinamento: estudo preliminar

Abstract The use of devices that produce stochastic whole-body vibration as a resource for rehabilitation and training programs has been founded on the theory of stochastic resonance. However, the prescription of rehabilitation and training programs must be preceded by the verification of imposed-vibration magnitude and of how it can be affected by the presence of an individual on the devices. The aim of this research was to characterize and analyze the effect of an individual's mass on the vibratory stimulus provided by stochastic whole-body vibration (SWBV) devices. The sample consisted of 30 repetitions for each one of the 6 vibration levels of the SWBV device (level 02, 04, 06, 08, 10 and 12), performed in two experimental situations (Without Load; Load [70Kg]; ≈ 35 kg on the right and left surfaces of the platform). For the antero-posterior, latero-lateral, and vertical directions, all variables showed significant differences between treatments, levels and interaction between experimental factors (p<.05), except for the Disp variable between treatments (p=.075). To measure vibration magnitude, a triaxial accelerometer was attached at the center of the board of one of the platform surfaces. Load interferes with parameters of vibration imposed by SWBV platforms, increasing ARMS and APEAK in the latero-lateral and antero-posterior directions, reducing these same parameters in the vertical direction.

A New Index for Detecting Frequency of Unknown Underwater Weak Signals with Genetic Algorithm

In this paper, a new index is proposed for detecting the frequency of unknown underwater signals based on the stochastic resonance theory. When the received weak signal is input into the stochastic resonance system, first, by frequency analysis, the frequency with the highest amplitude Aₘ of the output signal spectrum is considered as the pre-detection fre-quency. Then a cosine signal with the pre-detection frequency and unit amplitude is constructed. Define the pre-signal-to-noise-ratio as the logarithm of the squared amplitude Aₘ over the mean of signal amplitudes in all other frequencies. The new index is defined as the product of the pre-signal-to-noise-ratio and the correlation coefficient between the received unknown signal and the constructed cosine signal. The new index is featured by taking into account the signal characteristics in both time and frequency domain, and it will yield better signal frequency detection performance. In addition, to improve the time efficiency of the frequency detection, a method to bound the searching range, keyed to the genetic algorithm, of the stochastic resonance system parameters is proposed. The method can be used to detect the frequency of both single frequency and frequency-hopping unknown signals. With the designed new index and system parameter bounding method, the simulations and experiments for the weak underwater unknown signals are conducted. Compared to the piecewise mean value index and weighted power spectral kurtosis index, the new index yields a higher detection probability at varied input signal-to-noise ratios and signal frequencies. With bounding system parameter searching ranges, the time efficiency is improved. The main purpose of this paper is to detect the frequency of unknown underwater weak signals by stochastic resonance system with genetic algorithm. The main contributions are summarized as follows. First, the detection probability of weak signals is improved by stochastic resonance system with the proposed signal detection index than some other indexes. Second, to improve the time efficiency of the signal frequency detection, a method to bound the searching range of system parameters is proposed.

Construction of weak signal's automatic capture model of mechanical equipment for intelligent manufacturing

Aiming at the problem that the existing weak signal automatic capture model fails to effectively separate the blind source signal, which leads to its poor signal capture performance, the paper designs a weak signal automatic capture model of mechanical equipment for intelligent manufacturing. On the basis of obtaining the instantaneous frequency of the equipment, the stochastic resonance theory is used to process the signal's singular value decomposition and noise reduction. By separating and detecting blind source signals, automatic capture of weak signals of mechanical equipment for intelligent manufacturing can be realised. The experimental results show that the accuracy of the designed models are all higher than 80%, the automatic capture time is less than three minutes, and the automatic capture cost is always less than 360 yuan, which shows that the model has certain practical application value.

A high dimensional stochastic resonance system and its application in signal processing

At present, the stochastic resonance (SR) theory based on the traditional model with periodic input signal has been extensively studied. To further investigate dynamic process and improve the universality of SR system, a high-dimensional SR model is proposed in this paper. By analyzing the dynamic characteristics, the SR phenomenon is explained from the perspective of equilibrium point which is driven by the input signal. The expression of some key parameters is derived, and the noise reduction of aperiodic image signal is studied. Experimental results show that the SR phenomenon can be induced by appropriate input signal, and the proposed high-dimensional SR system has obvious noise reduction effect on aperiodic image signals, which further widens the application of SR theory in signal processing.

Fault Diagnosis Using Cascaded Adaptive Second-Order Tristable Stochastic Resonance and Empirical Mode Decomposition

Aiming at the problems of poor decomposition quality and the extraction effect of a weak signal with strong noise by empirical mode decomposition (EMD), a novel fault diagnosis method based on cascaded adaptive second-order tristable stochastic resonance (CASTSR) and EMD is proposed in this paper. In the proposed method, low-frequency interference components are filtered by using high-pass filtering, and the restriction conditions of stochastic resonance theory are solved by using an ordinary variable-scale method. Then, a chaotic ant colony optimization algorithm with a global optimization ability is employed to adaptively adjust the parameters of the second-order tristable stochastic resonance system to obtain the optimal stochastic resonance, and noise reduction pretreatment technology based on CASTSR is developed to enhance the weak signal characteristics of low frequency. Next, the EMD is employed to decompose the denoising signal and extract the characteristic frequency from the intrinsic mode function (IMF), so as to realize the fault diagnosis of rolling bearings. Finally, the numerical simulation signal and actual bearing fault data are selected to prove the validity of the proposed method. The experiment results indicate that the proposed fault diagnosis method can enhance the decomposition quality of the EMD, effectively extract features of weak signals, and improve the accuracy of fault diagnosis. Therefore, the proposed fault diagnosis method is an effective fault diagnosis method for rotating machinery.

A multi-exposure fusion framework for contrast enhancement of hazy images employing dynamic stochastic resonance

Current imaging devices coupled with advanced hardware and software are smart enough to enhance low light images taken in clear weather. But in hazy or foggy environments, the captured images are of degraded quality. To address this issue, image processing algorithms are employed to enhance the degraded images to make useful for extracting meaningful features. In this study, we propose a haze removal algorithm to improve the color and contrast of images captured in hazy environments. The first step involves generation of images with various exposures using the theory of dynamic stochastic resonance. The images are then fused in a multi-scale fusion framework crafting weight maps viz. haze density, chromaticity, and luminance gradient. The fusion process focuses on uniformly enhancing the dark and bright regions of the image. However, it may overemphasize haze affected regions. Therefore, in the second step, the atmospheric scattering equation is referred and its modified version is applied that accomplishes the haze removal task. Quantitative and qualitative analyses demonstrate the effectiveness of the proposed method.

Stochastic resonance in coupled star-networks with power-law heterogeneity

In this paper, the power-law heterogeneity of the coupling coefficients is proved to have an important influence on the output signal-to-noise ratio (SNR) of the central oscillator in coupled star-network. The network is described by dimensionless Langevin equations subjected to periodic forces and additive noise in a symmetric bistable potential. Creatively, a random variable with power-law-like distribution is constructed to model the heterogeneity of coupling coefficients. It is revealed that the degree of heterogeneity of coupling coefficients can be measured by the entropy of random variables. In numerical simulation, the output SNR of the central oscillator is obtained to divide the two-dimensional parameter space into four regions of resonance, non-resonance, sub-resonance and super-resonance. In each region, the monotonicity of output SNR curves is discussed to determine the optimal SNR and the corresponding power exponent. At last, an explanation of physical mechanism is given based on the stochastic resonance (SR) theory.

Recovery and enhancement of unknown aperiodic binary signal by adaptive aperiodic stochastic resonance

In this study, the system with fractional power nonlinearity is introduced into the theory of aperiodic stochastic resonance (ASR). The fractional exponent is a key parameter and its effect on the ASR phenomenon excited by aperiodic binary signal is investigated in this system. Compared to the classical bistable system, the system with fractional power nonlinearity shows better performance. It can adjust not only the noise intensity but also the fractional exponent to enhance weak signal. In the field of signal transmission, pure aperiodic binary signal is usually submerged in the noise and the signal is unknown. Thus, an effective method is proposed based on ASR and moving average. By the method, the unknown aperiodic binary signal can be recovered in the noise background. To improve the efficiency of the signal recovery, the adaptive ASR is realised with the help of adaptive particle swarm optimisation (APSO) algorithm to optimise the parameters. The method may provide some reference to the engineering field.