Weak Periodic Signal Research Articles

Extremely multi-stable grid-scroll memristive chaotic system with omni-directional extended attractors and application of weak signal detection

The extreme multi-stability and omni-directional expansion of the attractors in chaotic systems play an indispensable role in the chaos-based engineering applications. In this study, a novel extremely multi-stable grid-scroll memristive chaotic system with omni-directional extended attractors is proposed, and applies it to weak signal detection. Firstly, a flux-controlled non-volatile memristor with a typical 8-shaped pinched hysteresis loop, and three piecewise linear functions that can promote the position offset of the attractor are designed. On this basis, we construct a novel grid-scroll memristive chaotic system with infinite equilibrium points, which can generate n × n × n-scroll attractors. The piecewise linear functions lead to the infinite expansion of the chaotic attractor in the x, y, and z directions, which also indirectly causes the position offset in the w direction. This phenomenon has not been discovered in existing researches. The numerical analysis demonstrates that the memristive chaotic system has infinite coexisting attractors, and a built-in parameter that can achieve global amplitude control of the attractor has also been verified. The omni-directional expansion, coexistence and global amplitude control of the attractor illustrates the extreme multi-stability of the designed system. The analog circuit of the memristive chaotic system has been implemented to verify its feasibility and practicability. Finally, a weak signal detection system based on the grid-scroll memristive chaotic system is constructed. This system not only has excellent robustness to various noise, but also is more sensitive to weak periodic signals. The detection signal-to-noise ratio (SNR) threshold reaches -63 dB. The applicability of this method in practical engineering is verified through the detection of ship radiation signals submerged in ocean background noise.

Acoustic enhancement and weak signal detection based on quasibound states in the continuum

Acoustic signal detection is important in several fields of research. However, realizing weak-signal detection remains a challenge. Recently, the bound state in continuum (BIC) has attracted considerable attention because of its ultrahigh quality-factor (Q-factor) and strong field enhancement. In this study, we achieved two Fabry–Perot BICs (bonding and anti-bonding BICs) in a coupled-resonator system and a mirror-induced BIC in a single-resonator system. And the acoustic enhancement from quasi-BICs of the coupled-resonator system and single-resonator system was investigated in the simulation. Compared to the coupled-resonator system, the amplification performance of the single-resonator system was better and verified in the experiment. The experimental results agreed with the numerical results, and the maximum pressure magnification was approximately 28×. Furthermore, the single-resonator system enhanced the weak harmonic signal, weak periodic impulse signal, and weak modulated signal in the presence of strong background noise, making signal detection much easier. We believe that this work provides a new method to realize weak signal detection based on acoustic enhancement.

Multiplicative noise induced bistability and stochastic resonance

Abstract Stochastic resonance is a well established phenomenon, which proves relevant for a wide range of applications, of broad trans-disciplinary breath. Consider a one dimensional bistable stochastic system, characterized by a deterministic double well potential and shaken by an additive noise source. When subject to an external periodic drive, and for a proper choice of the noise strength, the system swings regularly between the two existing deterministic fixed points, with just one switch for each oscillation of the imposed forcing term. This resonant condition can be exploited to unravel weak periodic signals, otherwise inaccessible to conventional detectors. Here, we will set to revisit the stochastic resonance concept by operating in a modified framework where bistability is induced by the nonlinear nature of the multiplicative noise. A candidate model is in particular introduced which fulfils the above requirements while allowing for analytical progress to be made. Working with reference to this case study, we elaborate on the conditions for the onset of the generalized stochastic resonance mechanism. As a byproduct of the analysis, a novel resonant regime is also identified which displays no lower bound for the frequencies that can be resolved, at variance with the traditional setting.

Local damage detection in rolling element bearings based on a single ensemble empirical mode decomposition

A Single Ensemble Empirical Mode Decomposition (SEEMD) is proposed to locate the damage in rolling element bearings. The SEEMD method eliminates the need for adding or subtracting noise repeatedly to process signals, unlike other techniques that rely on multiple ensembles. The SEEMD requires a single sifting process of a modified raw signal to reduce the computation time significantly. The other advantage of the SEEMD method is its success in dealing with non-Gaussian or non-stationary perturbing signals. In SEEMD, a fractional Gaussian noise (FGN) is initially added to the raw signal to emphasize the signal's high frequencies. Then, a convoluted white Gaussian noise is multiplied on the resulting signal, changing its spectral content, which helps in extracting the weak periodic signal. Finally, the obtained signal is decomposed using a single sifting process. The proposed methodology is applied to the raw signals obtained from the mining industry. These signals are difficult to analyze since cyclic impulsive components are obscured by noise and other interference. Based on the results, the proposed method can effectively detect the fault where the signal of interest (SOI) has been extracted with good quality.

Weak signal detection technique based on Durbin-Watson test and one-bit sampling.

Correlation-based detection techniques are widely used in the weak periodic signal detection field. Traditionally, they are based on extracting the correlation of a weak signal from noise. Considering the impact of a weak signal on the randomness of background noise, this article takes the opposite approach and proposes a weak signal detection technique based on the Durbin-Watson (DW) test and one-bit sampling, detecting the weak signal due to the extent to which the randomness of noise is affected. The randomness of noise is analyzed through the DW test, which is a method for detecting the randomness of data sequences through first-order autocorrelation. One-bit sampling is adopted to reduce the complexity of the sampling circuit and data processing algorithm. The effectiveness of the DW test in the situation of one-bit sampling is demonstrated through simulation and analysis. Simulation results show that the proposed technique is capable of detecting weak sinusoidal and square-wave signals with a signal-to-noise ratio (SNR) above -30 dB, and the frequency or SNR of a weak signal can be further estimated based on mutual constraints. The measured results confirm the capability. In addition, the factors of coherent sampling, noise bandwidth, and comparator threshold that influence the performance of the proposed technique are simulated and discussed in detail.

Thermally activated escape rate and dynamics of a particle under a harmonic potential

In this paper, we study the dynamics of particles along a semiconductor layer by imposing a confinement potential assisted by both thermal noise strength D and trap potential ϕ. By applying a nonhomogeneous cold temperature alongside the uniform background temperature, the system is driven towards a phase transition. When a weak signal is pass across a semiconductor layer, the thermally activated particles become easily hop from one lattice site to another lattice site. We perform a numerical simulation of the trajectory of a particle under a harmonic potential represents a bistable and tristable effective potential as a function of thermal noise. As a result, at an optimal level of noise, the particle synchronizes with a weak periodic signal.

Fault diagnosis of needle selector drive parts based on adaptive stochastic resonance with improved generative adversarial networks

Piezoelectric needle selectors, as key weaving components in the jacquard knitting process of knitting machinery, are widely used in textile equipment. Accurate diagnostic procedures for needle selector drive faults are crucial to ensure the normal operation of the equipment. However, traditional vibration diagnosis methods cannot detect weak periodic signals, resulting in low accuracy of monitoring results. To address this issue, this paper proposes an adaptive stochastic resonance (SR) method based on an improved generative adversarial network (IGAN). Firstly, in order to solve the problem of difficulty in obtaining stochastic resonance parameters, SR is combined with IGAN, and IGAN provides the optimal SR parameters. Secondly, a soft threshold residual attention mechanism and residual network were introduced in the GAN network, and multiple generators were utilized to alleviate the problem of model collapse, in order to adapt to the actual working environment. In addition, due to the large amount of data, it is recommended to use feature parameters for training to improve the efficiency of model training. Finally, through a typical vibration data, the influence of different parameter quantities on the training accuracy of the model was studied, and the superiority of the proposed model compared to other models and the stability of the model under different environmental influences were explored. The results show that this method can effectively detect weak periodic signals of the needle selection driver, effectively alleviate the problem of model collapse in different environments, and is superior to existing methods in terms of accuracy and stability.

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.

Detecting a periodic signal by a population of spiking neurons in the weakly nonlinear response regime

Motivated by experimental observations, we investigate a variant of the cocktail party problem: the detection of a weak periodic stimulus in the presence of fluctuations and another periodic stimulus which is stronger than the periodic signal to be detected. Specifically, we study the response of a population of stochastic leaky integrate-and-fire (LIF) neurons to two periodic signals and focus in particular on the question, whether the presence of one of the stimuli can be detected from the population activity. As a detection criterion, we use a simple threshold-crossing of the population activity over a certain time window. We show by means of the receiver operating characteristics (ROC) that the detectability depends only weakly on the time window of observation but rather strongly on the stimulus amplitude. Counterintuitively, the detection of the weak periodic signal can be facilitated by the presence of a strong periodic input current depending on the frequencies of the two signals and on the dynamical regime in which the neurons operate. Beside numerical simulations of the model, we present an analytical approximation for the ROC curve that is based on the weakly nonlinear response theory for a stochastic LIF neuron.Graphic abstract

Stochastic Resonance in a Single-Ion Nonlinear Mechanical Oscillator

Stochastic resonance is a counterintuitive phenomenon amplifying the weak periodic signal by application of external noise. We demonstrate the enhancement of a weak periodic signal by stochastic resonance in a trapped-ion oscillator when the oscillator is excited to the nonlinear regime and subject to an appropriate noise. Under the full control of the radio-frequency drive voltage, this amplification originates from the nonlinearity due to asymmetry of the trapping potential, which can be described by a forced Duffing oscillator model. Our scheme and results provide an interesting possibility to make use of controllable nonlinearity in the trapped ion, and pave the way toward a practical atomic sensor for sensitively detecting weak periodic signals from real noisy environment.

Enhanced signal response in globally coupled networks of bistable oscillators: Effects of mean field density and signal shape.

This paper studies a set of globally coupled bistable oscillators, all subjected to the same weak periodic signal and identical coupling. The effect of mean field density (MFD) on global dynamics is analyzed. The oscillators switch from intra- to interwell motion as MFD increases, clearly demonstrating MFD-enhanced signal amplification. A maximum amplification also occurs at a moderate level of MFD, indicating that the response exhibits a nonmonotonic sensitivity to MFD. The MFD-enhanced response depends mainly on the signal intensity but not on the signal frequency or the network topology. The analytical investigation provides a simplified model to study the mechanism underlying this resonancelike behavior. It is shown that by modifying the bistability nature of the potential energy, the mean field density can promote well-to-well oscillations and larger amplitude motions. Finally, the robustness of this phenomenon to various signal waveforms is examined. It can therefore be used alternatively to efficiently amplify weak signals in practical situations with large network sizes.

Stochastic Resonance with Parameter Estimation for Enhancing Unknown Compound Fault Detection of Bearings.

Although stochastic resonance (SR) has been widely used to enhance weak fault signatures in machinery and has obtained remarkable achievements in engineering application, the parameter optimization of the existing SR-based methods requires the quantification indicators dependent on prior knowledge of the defects to be detected; for example, the widely used signal-to-noise ratio easily results in a false SR and decreases the detection performance of SR further. These indicators dependent on prior knowledge would not be suitable for real-world fault diagnosis of machinery where their structure parameters are unknown or are not able to be obtained. Therefore, it is necessary for us to design a type of SR method with parameter estimation, and such a method can estimate these parameters of SR adaptively by virtue of the signals to be processed or detected in place of the prior knowledge of the machinery. In this method, the triggered SR condition in second-order nonlinear systems and the synergic relationship among weak periodic signals, background noise and nonlinear systems can be considered to decide parameter estimation for enhancing unknown weak fault characteristics of machinery. Bearing fault experiments were performed to demonstrate the feasibility of the proposed method. The experimental results indicate that the proposed method is able to enhance weak fault characteristics and diagnose weak compound faults of bearings at an early stage without prior knowledge and any quantification indicators, and it presents the same detection performance as the SR methods based on prior knowledge. Furthermore, the proposed method is more simple and less time-consuming than other SR methods based on prior knowledge where a large number of parameters need to be optimized. Moreover, the proposed method is superior to the fast kurtogram method for early fault detection of bearings.

Stochastic resonance behavior of FitzHugh–Nagumo neurons induced by electromagnetic field driven by phase noise

Noise widely exists in the nervous system, and plays an extremely important role in the information processing of the nervous system, which can enhance or weaken the ability of the nervous system to process information. Nerve cells exist in complex and changeable electromagnetic fields, and their potential changes are significantly regulated by electromagnetic induction. In response to this, first, a memristor is used to simulate the electromagnetic field environment where the nervous system is located, when using different weak periodic signals as the input of the neuron system, the rich stochastic resonance behavior of the FitzHugh–Nagumo neuron system is analyzed under the drive of phase noise. Second, taking the amplitude, period and intensity of phase noise as the main change parameters, and the changes of the parameters of the memristor and the period of the external signal as auxiliary conditions, the stochastic resonance dynamics analysis is carried out from three perspectives: the amplitude and period of phase noise, the amplitude and intensity of phase noise and the intensity and period of phase noise.

Weak signal detection method based on novel composite multistable stochastic resonance

The weak signal detection method based on stochastic resonance is usually used to extract and identify the weak characteristic signal submerged in strong noise by using the noise energy transfer mechanism. We propose a novel composite multistable stochastic-resonance (NCMSR) model combining the Gaussian potential model and an improved bistable model. Compared with the traditional multistable stochastic resonance method, all the parameters in the novel model have no symmetry, the output signal-to-noise ratio can be optimized and the output amplitude can be improved by adjusting the system parameters. The model retains the advantages of continuity and constraint of the Gaussian potential model and the advantages of the improved bistable model without output saturation, the NCMSR model has a higher utilization of noise. Taking the output signal-to-noise ratio as the index, weak periodic signal is detected based on the NCMSR model in Gaussian noise and α noise environment respectively, and the detection effect is good. The application of NCMSR to the actual detection of bearing fault signals can realize the fault detection of bearing inner race and outer race. The outstanding advantages of this method in weak signal detection are verified, which provides a theoretical basis for industrial practical applications.

Context dependent prediction in DNA sequence using neural networks.

One way to better understand the structure in DNA is by learning to predict the sequence. Here, we trained a model to predict the missing base at any given position, given its left and right flanking contexts. Our best-performing model was a neural network that obtained an accuracy close to 54% on the human genome, which is 2% points better than modelling the data using a Markov model. In likelihood-ratio tests, the neural network performed significantly better than any of the alternative models by a large margin. We report on where the accuracy was obtained, first observing that the performance appeared to be uniform over the chromosomes. The models performed best in repetitive sequences, as expected, although their performance far from random in the more difficult coding sections, the proportions being ~70:40%. We further explored the sources of the accuracy, Fourier transforming the predictions revealed weak but clear periodic signals. In the human genome the characteristic periods hinted at connections to nucleosome positioning. We found similar periodic signals in GC/AT content in the human genome, which to the best of our knowledge have not been reported before. On other large genomes similarly high accuracy was found, while lower predictive accuracy was observed on smaller genomes. Only in the mouse genome did we see periodic signals in the same range as in the human genome, though weaker and of a different type. This indicates that the sources of these signals are other or more than nucleosome arrangement. Interestingly, applying a model trained on the mouse genome to the human genome resulted in a performance far below that of the human model, except in the difficult coding regions. Despite the clear outcomes of the likelihood-ratio tests, there is currently a limited superiority of the neural network methods over the Markov model. We expect, however, that there is great potential for better modelling DNA using different neural network architectures.

Roll Eccentricity Signal Detection and Its Engineering Application Based on SFFT-IAA

The roll eccentricity signal is a weak and complex periodic signal that is difficult to be identified. To improve the detection accuracy of the roll eccentricity signal and to compensate effectively, this study proposed a roll eccentricity signal detection method by combining the sparse fast Fourier transform (SFFT) and the iterative adaptive approach (IAA). The proposed method can rapidly determine the frequency range of the roll eccentricity signal by using the SFFT. Then, it divides the frequency range into several small frequency bands. In each small frequency band, the frequency, amplitude, and phase angle of each harmonic component of the roll eccentricity signal were estimated by using IAA. The simulation results show that the proposed method can find all frequency components, and the frequency estimation accuracy is higher than 99.88%. Finally, the engineering application of this method and the eccentricity compensation control were investigated. In engineering applications, the proposed method can reduce the thickness fluctuation of the finished strip by 89.2%, and the product quality is improved significantly. The simulation results and engineering experiments show that the proposed method has an excellent effect on detecting and compensating roll eccentricity signals.

Parameter-tuning stochastic resonance as a tool to enhance wavelength modulation spectroscopy using a dense overlapped spot pattern multi-pass cell.

The parameter-tuning stochastic resonance (SR) method can convert part of the noise energy into the signal energy to suppress the noise and amplify the signal, comparing with traditional weak periodic signal detection methods (e.g., time average method, filtering method, and correlation analysis method). In this work, the numerical calculation is conducted to find the optimal resonance parameters for applying the SR method to the wavelength modulation spectroscopy (WMS). Under the stochastic resonance state, the peak value of 2f signal (a constant concentration of CH4∼20 ppm) is effectively amplified to ∼0.0863 V, which is 3.8 times as much as the peak value of 4000-time average signal (∼0.0231 V). Although the standard deviation also increases from ∼0.0015 V(1σ) to ∼0.003 V(1σ), the SNR can be improved by 1.83 times (from ∼25.9 to ∼15.8) correspondingly. A linear spectral response of SR 2f signal peak value to raw 2f signal peak value is obtained. It suggests that the SR method is effective for enhancing photoelectric signal under strong noise background.

Tri-stable stochastic resonance coupling system driven by dual-input signals and its application in bearing fault detection

Stochastic resonance is of great significance for extracting fault signals of bearings. A novel tri-stable stochastic resonance coupling system driven by dual-input signals(DTDTSR) is proposed in this paper, which significantly improve Spectral Amplification(SA) and amplitude of traditional two-dimensional tri-stable stochastic resonance system(TDTSR). Firstly, under the condition of adiabatic approximation theory, the Steady-state Probability Density(SPD), Mean First Pass Time(MFPT) and SA are derived, and the system parameters’ influence on them are analyzed. Then, using SA as the measurement index, numerical simulations are carried out and system parameters are optimized by adaptive genetic algorithm to achieve optimal performance. So DTDTSR, TDTSR and classical tri-stable stochastic resonance system(CTSR) are applied to weak periodic signals detection and compared with each other. The experimental results show that DTDTSR has a large SA and amplitude, which proves that the synergistic effect of coupled system and dual input signal drive can better promote the generation of stochastic resonance. Finally, the three systems and wavelet transform method are applied in two kinds of engineering bearing fault detection, and adaptive genetic algorithm is also used to optimize the system parameters. The experiments reveal are similar to the previous one, proving that DTDTSR is indeed optimal among the three systems. This system is therefore very adaptable and advanced in practical engineering applications.

Application of Improved Phase Lock Method in Weak Signal Extraction

The existing method of the weak signal under the background of strong noise (signal amplitude relative to the noise amplitude is much smaller) analysis is not very ideal. This study proposes an improved phase lock method to analyze the weak periodic signal under Gaussian white noise. Experimental results show that this method can better analyze weak signal-related information than the stochastic resonance method in a certain range of signal-to-noise ratio, and the amount of calculation is small, and the correlation theory is simple and adapted to the rapid detection of the signal; in order to further reduce the amount of calculation, the introduction of a high-order accumulation of the signal presence detection, experiments verify that the high-order accumulation can detect whether there is a weak signal in the Gaussian noise. The combination of high-order cumulant and improved phase lock method has a good effect on the analysis of weak periodic signals under strong noise backgrounds.

Role of Weak Periodic Signal in Binocular Rivalry

Role of Weak Periodic Signal in Binocular Rivalry