Aperiodic Stochastic Resonance Research Articles

Mutual information measure of visual perception based on noisy spiking neural networks.

Note that images of low-illumination are weak aperiodic signals, while mutual information can be used as an effective measure for the shared information between the input stimulus and the output response of nonlinear systems, thus it is possible to develop novel visual perception algorithm based on the principle of aperiodic stochastic resonance within the frame of information theory. To confirm this, we reveal this phenomenon using the integrate-and-fire neural networks of neurons with noisy binary random signal as input first. And then, we propose an improved visual perception algorithm with the image mutual information as assessment index. The numerical experiences show that the target image can be picked up with more easiness by the maximal mutual information than by the minimum of natural image quality evaluation (NIQE), which is one of the most frequently used indexes. Moreover, the advantage of choosing quantile as spike threshold has also been confirmed. The improvement of this research should provide large convenience for potential applications including video tracking in environments of low illumination.

Aperiodic stochastic resonance in a biased monostable system excited by different weak aperiodic pulse signals and strong noise

Aperiodic stochastic resonance in a biased monostable system excited by different weak aperiodic pulse signals and strong noise

The Novel Method of Magnetic Anomaly Recognition Based on the Fourth Order Aperiodic Stochastic Resonance

In the background of strong interference noise, it is one of the crucial technologies of magnetic anomaly detection system to effectively detect and identify weak magnetic anomaly signals (MAS) gene- rated by targets. The detection and recognition of target signal under very low signal-to-noise ratio(SNR)below −10dB have not been achieved in the existing magnetic anomaly detection technology. To tackle these challenges, this paper proposes a magnetic anomaly recognition method based on fourth-order aperiodic stochastic resonance with the aid of sto- chastic resonance theory. The main nature of new algorithm is a four-layer fusion of single potential well stochastic resonance and has real-time recognition ability for MAS without prior information. When simulated magnetic anomaly signal of single object and mutil-targets were assumed in different condition, effect of parameters of algorithm was analyzed and range of optimal parameters was obtained. Through simulation and experimental verification of targets data, the new algorithm could realize target signal recognition in complex interference environment with SNR lower than −15dB,which demonstrates the efficacy of our proposed method and offer some useful design insights to practical MAD system.

Extracting non-stationary signal under strong noise background: Time-varying system analysis

The extraction of non-stationary feature information under strong noise background is a difficult problem. In this paper, a novel general time-varying scale transformation aperiodic stochastic resonance is proposed to extract and enhance the weak non-stationary signal under strong noise background. The theoretical framework of a parameters time-varying Duffing system is built for aperiodic stochastic resonance. By studying the resonance region migration when scale coefficient takes different values, an optimal scale transformation is achieved. Also, the time-varying system is optimized with cross-correlation coefficient as the index. Compared with the existing methods, the proposed method can be applied to stronger noise background and has stronger noise robustness. When under the same noise background, the proposed method can provide output with higher signal-to-noise ratio and higher cross-correlation coefficient. Finally, experimental analysis of faulty bearing vibration signal verifies the high accuracy, which indicates a good signal extraction and enhancement ability of the proposed method.

Rolling Bearing Fault Diagnosis by Aperiodic Stochastic Resonance Under Variable Speed Conditions

The fault characteristic of rolling bearings under variable speed condition is a typical non-stationary stochastic signal. It is difficult to extract due to the interference of strong background noise makes the applicability of traditional noise reduction methods less. In this paper, an aperiodic stochastic resonance (ASR) method is proposed to study the fault diagnosis of rolling bearings under variable speed conditions. Based on numerical simulation, the effect of noise intensity and damping coefficient on the ASR of the second-order underdamped system is discussed, and an appropriate damping coefficient is found to reach the optimal ASR. The proposed method enhances the fault characteristic information of bearing fault simulation signal. Corresponding to rising-stationary and the stationary-declining running conditions, the method is verified by both simulated and experimental signals. It provides reference for fault diagnosis under variable speed condition.

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.

Aperiodic stochastic resonance in neural information processing with Gaussian colored noise.

The aim of this paper is to explore the phenomenon of aperiodic stochastic resonance in neural systems with colored noise. For nonlinear dynamical systems driven by Gaussian colored noise, we prove that the stochastic sample trajectory can converge to the corresponding deterministic trajectory as noise intensity tends to zero in mean square, under global and local Lipschitz conditions, respectively. Then, following forbidden interval theorem we predict the phenomenon of aperiodic stochastic resonance in bistable and excitable neural systems. Two neuron models are further used to verify the theoretical prediction. Moreover, we disclose the phenomenon of aperiodic stochastic resonance induced by correlation time and this finding suggests that adjusting noise correlation might be a biologically more plausible mechanism in neural signal processing.

Algorithm Used to Detect Weak Signals Covered by Noise in PIND

Detection of the loose particles is urgently required in the spacecraft production processes. PIND (particle impact noise detection) is the most commonly used method for the detection of loose particles in the aerospace electronic components. However, when the mass of loose particles is smaller than 0.01 mg, the weak signals are difficult to be detected accurately. In this paper, the aperiodic stochastic resonance (ASR) is firstly used to detect weak signals of loose particles. The loose particle signal is simulated by the oscillation attenuation signal. The influences of structure parameters on the potential height and detection performance of ASR are studied by a numerical iteration method. The cross-correlation coefficient C1 between input and output is chosen as a criterion for whether there is an existing a particle or not. Through normalization, the loose particle signal-labeled high frequency of 135 kHz is converted into the low-frequency band, which can be detected by the ASR method. According to the algorithm, weak signals covered by noise could be detected. The experimental results show that the detection accuracy is 66.7%. This algorithm improves the detection range of weak loose particle signals effectively.

Aperiodic Stochastic Resonance in the Fractional-Order Bistable System

The aperiodic stochastic resonance (ASR) in the bistable fractional-order system is further studied when the fractional-order lies in the interval (0, 2). In previous works, the ASR can only process aperiodic binary signal with large pulse width. However, for the signal with small pulse width, the method cannot work. Actually, the signals with small pulse width are also common in the information transmission field. It greatly limits the application of the fractional stochastic resonance. Hence, we mainly focus on the enhancement of aperiodic binary signal with small pulse width. To solve the aforementioned technical problem, the general scale transformation is introduced, which allows us to achieve the ASR successfully. By this method, the equivalent system with large system parameters is able to match the input character signal with arbitrary small pulse width well, where the scale parameter is a key to achieve resonance. During the process, the fractional-order system presents rich dynamical behaviors in processing the aperiodic binary signals. Especially, as the order increases, the output signal at optimal noise intensity might be better and be more similar to the input one. This indicates the fractional order can optimize the stochastic resonance. The results might provide some reference to the engineering field, such as digital transmission and image processing field.

Self-similarity and adaptive aperiodic stochastic resonance in a fractional-order system

We investigate the aperiodic stochastic resonance (ASR) in a bistable fractional-order system when the fractional order lies in the interval (0, 2]. We find that a weak aperiodic signal can be amplified and optimized by varying the fractional order in the nonlinear system, no matter whether it has the assistance of the noise or not. We focus mainly on the self-similarity of the response to the input aperiodic signal and the adaptive ASR. The self-similarity is a characteristic that the response of a nonlinear system matches the input signal well, in the absence of the noise excitation. The adaptive ASR is a technique for the optimal ASR to occur by modulating the fractional order, the noise intensity, or the bistable system parameters. In order to make the optimal ASR occur, an adaptive particle swarm optimization (APSO) algorithm is used in this work as the method of parameter optimization. In previous works, only the periodic signal is optimized in a noisy bistable fractional-order system and the ASR induced by the fractional-order system has not been achieved. In engineering and scientific fields, not only periodic signals need to be processed, but also weak aperiodic ones. Moreover, the optimal ASR shows better results based on the APSO algorithm. We believe that the results of this paper might have a positive contribution in the dynamics research.

An alternate protocol to achieve stochastic and deterministic resonances.

Periodic and Aperiodic Stochastic Resonance (SR) and Deterministic Resonance (DR) are studied in this paper. To check for the ubiquitousness of the phenomena, two unrelated systems, namely, FitzHugh-Nagumo and a particle in a bistable potential well, are studied. Instead of the conventional scenario of noise amplitude (in the case of SR) or chaotic signal amplitude (in the case of DR) variation, a tunable system parameter ("a" in the case of FitzHugh-Nagumo model and the damping coefficient "j" in the bistable model) is regulated. The operating values of these parameters are defined as the "setpoint" of the system throughout the present work. Our results indicate that there exists an optimal value of the setpoint for which maximum information transfer between the input and the output signals takes place. This information transfer from the input sub-threshold signal to the output dynamics is quantified by the normalised cross-correlation coefficient ( |CCC|). |CCC| as a function of the setpoint exhibits a unimodal variation which is characteristic of SR (or DR). Furthermore, |CCC| is computed for a grid of noise (or chaotic signal) amplitude and setpoint values. The heat map of |CCC| over this grid yields the presence of a resonance region in the noise-setpoint plane for which the maximum enhancement of the input sub-threshold signal is observed. This resonance region could be possibly used to explain how organisms maintain their signal detection efficacy with fluctuating amounts of noise present in their environment. Interestingly, the method of regulating the setpoint without changing the noise amplitude was not able to induce Coherence Resonance (CR). A possible, qualitative reasoning for this is provided.

Intrinsic periodic and aperiodic stochastic resonance in an electrochemical cell.

In this paper we show the interaction of a composite of a periodic or aperiodic signal and intrinsic electrochemical noise with the nonlinear dynamics of an electrochemical cell configured to study the corrosion of iron in an acidic media. The anodic voltage setpoint (V_{0}) in the cell is chosen such that the anodic current (I) exhibits excitable fixed point behavior in the absence of noise. The subthreshold periodic (aperiodic) signal consists of a train of rectangular pulses with a fixed amplitude and width, separated by regular (irregular) time intervals. The irregular time intervals chosen are of deterministic and stochastic origins. The amplitude of the intrinsic internal noise, regulated by the concentration of chloride ions, is then monotonically increased, and the provoked dynamics are analyzed. The signal to noise ratio and the cross-correlation coefficient versus the chloride ions' concentration curves have a unimodal shape indicating the emergence of an intrinsic periodic or aperiodic stochastic resonance. The abscissa for the maxima of these unimodal curves correspond to the optimum value of intrinsic noise where maximum regularity of the invoked dynamics is observed. In the particular case of the intrinsic periodic stochastic resonance, the scanning electron microscope images for the electrode metal surfaces are shown for certain values of chloride ions' concentrations. These images, qualitatively, corroborate the emergence of order as a result of the interaction between the nonlinear dynamics and the composite signal.

Binary image enhancement based on aperiodic stochastic resonance

The enhancement of noisy images has been playing a key role in improving the visual effect and the performance of image processing. Traditional methods for image enhancement are mainly focusing on eliminating noise, which cannot acquire good effect under low peak-signal-to-noise ratio (PSNR) conditions. Stochastic resonance (SR), on the contrary, is a technique using noise to enhance signal. Owing to the unique feature of SR, a novel binary image enhancement scheme based on aperiodic SR (ASR) technique is proposed. In this study, the authors take the improvement in PSNR as a measure of the ASR-based binary image enhancement system, which provides a guideline for the realisation of the ASR system. On this basis, they obtain the PSNR expression of the ASR-based binary image enhancement system. Simulation results show that the proposed method is superior to the traditional binary image enhancement methods both in visual effect and PSNR performance.

Tracking stochastic resonance curves using an assisted reference model

The optimal noise amplitude for Stochastic Resonance (SR) is located employing an Artificial Neural Network (ANN) reference model with a nonlinear predictive capability. A modified Kalman Filter (KF) was coupled to this reference model in order to compensate for semi-quantitative forecast errors. Three manifestations of stochastic resonance, namely, Periodic Stochastic Resonance (PSR), Aperiodic Stochastic Resonance (ASR), and finally Coherence Resonance (CR) were considered. Using noise amplitude as the control parameter, for the case of PSR and ASR, the cross-correlation curve between the sub-threshold input signal and the system response is tracked. However, using the same parameter the Normalized Variance curve is tracked for the case of CR. The goal of the present work is to track these curves and converge to their respective extremal points. The ANN reference model strategy captures and subsequently predicts the nonlinear features of the model system while the KF compensates for the perturbations inherent to the superimposed noise. This technique, implemented in the FitzHugh-Nagumo model, enabled us to track the resonance curves and eventually locate their optimal (extremal) values. This would yield the optimal value of noise for the three manifestations of the SR phenomena.

Variational superposed Gaussian approximation for time-dependent solutions of Langevin equations.

We propose a variational superposed Gaussian approximation (VSGA) for dynamical solutions of Langevin equations subject to applied signals, determining time-dependent parameters of superposed Gaussian distributions by the variational principle. We apply the proposed VSGA to systems driven by a chaotic signal, where the conventional Fourier method cannot be adopted, and calculate the time evolution of probability density functions (PDFs) and moments. Both white and colored Gaussian noises terms are included to describe fluctuations. Our calculations show that time-dependent PDFs obtained by VSGA agree excellently with those obtained by Monte Carlo simulations. The correlation between the chaotic input signal and the mean response are also calculated as a function of the noise intensity, which confirms the occurrence of aperiodic stochastic resonance with both white and colored noises.

Aperiodic signals processing via parameter-tuning stochastic resonance in a photorefractive ring cavity

Based on solving numerically the generalized nonlinear Langevin equation describing the nonlinear dynamics of stochastic resonance by Fourth-order Runge-Kutta method, an aperiodic stochastic resonance based on an optical bistable system is numerically investigated. The numerical results show that a parameter-tuning stochastic resonance system can be realized by choosing the appropriate optical bistable parameters, which performs well in reconstructing aperiodic signals from a very high level of noise background. The influences of optical bistable parameters on the stochastic resonance effect are numerically analyzed via cross-correlation, and a maximum cross-correlation gain of 8 is obtained by optimizing optical bistable parameters. This provides a prospective method for reconstructing noise-hidden weak signals in all-optical signal processing systems.

Noise-enhanced transmission efficacy of aperiodic signals in nonlinear systems

We study the aperiodic signal transmission in a static nonlinearity in the context of aperiodic stochastic resonance. The performance of a nonlinearity over that of the linear system is defined as the transmission efficacy. The theoretical and numerical results demonstrate that the noise-enhanced transmission efficacy effects occur for different signal strengths in various noise scenarios.

Noise-enhanced kinaesthesia: a psychophysical and microneurographic study

We first explored whether the ability of subjects to detect the direction of slow ramp imposed movements may be improved by the application of mechanical noise to muscle tendons. Movements were plantar/dorsal flexion of the ankle at 0.04°/s, and the amplitude was just sub-threshold for each subject. A white noise signal (random vibration), low-pass filtered to 100 Hz and distributed uniformly in amplitude, was applied to both the extensor and the flexor ankle muscle tendons with four different mean amplitudes (20, 30, 100, 280 μm). The population of subjects was observed to exhibit clear stochastic-type behaviour: their ability to determine the direction of sub-threshold movements significantly increased when the two lower levels of noise were added and subsequently decreased when the noise magnitude was enhanced. Second, using microneurography, we explored the response of 9 primary muscle spindle afferents and 8 cutaneous afferents to the same imposed movements with and without noise application. While these conditions of ankle mobilisation were too small to induce a response in most of the recorded afferents, two muscle afferents exhibited responses that were characteristic of aperiodic stochastic resonance behaviour: the unit movement response was either triggered or improved by the application of an optimal level of noise. All cutaneous afferents were unresponsive to the imposed movements with or without noise application. We conclude that ankle movement sense can be significantly improved by adding an optimal level of mechanical noise to ankle muscle tendons and discuss the optimisation of the response of movement-encoding receptors that may account for this improvement. The application of a mechanical noise on ankle muscle tendons may constitute a means of improving postural stability in subjects with sensory deficits.

Intrinsic noise induced resonance in presence of sub-threshold signal in Brusselator

In a system of non-linear chemical reactions called the Brusselator, we show that intrinsic noise can be regulated to drive it to exhibit resonance in the presence of a sub-threshold signal. The phenomena of periodic stochastic resonance and aperiodic stochastic resonance, hitherto studied mostly with extrinsic noise, is demonstrated here to occur with inherent systemic noise using exact stochastic simulation algorithm due to Gillespie. The role of intrinsic noise in a couple of other phenomena is also discussed.

RESIDUAL APERIODIC STOCHASTIC RESONANCE IN LÉVY NOISE

We investigate the effect of Lévy noise on the noise-induced residual aperiodic stochastic resonance (ASR). It is shown that, the residual ASR still exists when the noise is Lévy distributed. However, it is reduced by Lévy noise compared to that in the Gaussian noise with the same intensity. It is also shown that, the minimum bit error rate (BER) of the Lévy-noise-induced ASR is slightly higher than that of the Gaussian-noise-induced ASR, which indicates that tuning system parameters is a better approach to get the optimal performance.