Additive White Noise Research Articles

Emergent behaviors of the Justh-Krishnaprasad model with uncertain communications

We study stochastic alignment of the Justh-Krishnaprasad(J-K) model under a multiplicative noise. Justh and Krishnaprasad proposed a planar Newtonian particle model for an ensemble of flocking agents moving with a unit speed, where the dynamics of the heading angles (of velocities) is governed by a generalized Kuramoto-type model with a communication weight. In this paper, we are interested in the random perturbation of the communication weight, which is represented by a multiplicative noise. Unlike the additive white noise perturbation, the multiplicative one is known not to violate collective behaviors. We present sufficient conditions leading to the nematic alignment of velocities in terms of the system parameters and initial data. Our analysis begins with the two-body system, where it turns out to be stable under the effect of noise, showing that the nematic alignment occurs when the communication is sufficiently strong with respect to the noise strength. For the general many-body system with a corresponding condition, we showed the accumulation of heading angles modulo π/2 and the stochastic stability of nematic alignment under the assumption of the constant communication weight, which suggests a strong evidence for the nematic alignment. This analysis is done by transporting the system into a similar form to the stochastic Kuramoto model, where we refined the order parameter analysis in order to extend local stochastic stability results to the whole circle of heading angles. We present several numerical simulations and compare them with analytical results.

White-noise-induced double coherence resonances in reduced Hodgkin-Huxley neuron model near subcritical Hopf bifurcation.

Coherence resonance (CR) describes a counterintuitive phenomenon in which the optimal oscillatory responses in nonlinear systems are shaped by a suitable noise amplitude. This phenomenon has been observed in neural systems. In this research, the generation of double coherence resonances (DCRs) due to white noise is investigated in a three-dimensional reduced Hodgkin-Huxley neuron model with multiple-timescale feature. We show that additive white noise can induce DCRs from the resting state near a subcritical Hopf bifurcation. The appearance of DCRs is related to the changes of the firing pattern aroused by the increases of the noise amplitude. The underlying dynamical mechanisms for the appearance of the DCRs and the changes of the firing pattern are interpreted using the phase space analysis and the dynamics of the stable focus-node near the subcritical Hopf bifurcation. We find that the multiple-timescale dynamics is essential for generating the DCRs and different firing patterns. The results not only present a case in which noise can induce DCRs near a Hopf bifurcation but also provide its dynamical mechanism, which enriches the phenomena in nonlinear dynamics and provides further understanding on the roles of noise in neural systems with multiple-timescale feature.

Signal-to-Noise Ratio Based Fault Detection and Identification

In this work, we introduce signal-to-noise ratio (SNR) based fault detection and identification mechanisms for a networked control system feedback loop, where the network component is represented by an additive white noise (AWN) channel. The SNR approach is known to be a steady-state analysis and design tool, thus we first introduce a finite time approximation for the estimated AWN channel SNR. We then consider the case of a general linear time-invariant plant model with one unstable pole. The potential faults that we discuss here cover simultaneously the plant model gain and/or the unstable pole. The fault detection is performed relative to the estimated AWN channel SNR. The fault identification is performed using recursive least squares ideas and then further validated with the observed SNR value, when a fault has been previously detected. We show that the proposed SNR-based fault mechanism (fault detection plus fault identification) is capable of processing the proposed faults. We conclude discussing future research based on the contributions exposed in the present work.

Invariant sample measures and random Liouville type theorem for the two-dimensional stochastic Navier-Stokes equations

In this article, we first prove some sufficient conditions guaranteeing the existence of invariant sample measures for random dynamical systems via the approach of global random attractors. Then we consider the two-dimensional incompressible Navier-Stokes equations with additive white noise as an example to show how to check the sufficient conditions for concrete stochastic partial differential equations. Our results generalize the Liouville type theorem to the random case and reveal that the invariance of the sample measures is a particular situation of the random Liouville type theorem.

Weak fault feature extraction of rolling bearings based on improved ensemble noise-reconstructed EMD and adaptive threshold denoising

Extracting weak fault features under noise interference is crucial for the fault diagnosis of rolling bearings at an early stage. In this paper, a new method based on improved ensemble noise-reconstructed empirical mode decomposition (IENEMD) and adaptive threshold denoising (ATD) is proposed for the weak fault feature extraction of rolling bearings. Firstly, to tackle the drawbacks of EEMD which utilizes the additional Gaussian white noise resulting in submersion of the weak fault features, the inherent noise hidden in the raw signals is automatically extracted and leveraged in the IENEMD to decompose the raw signals into intrinsic mode functions (IMFs). The IENEMD not only avoids the mode mixing issues of the original EMD but also reduces the interference of inherent noise. Then, the ATD consisting of informative IMF selection and threshold denoising is executed on the decomposed IMFs. Taking the health signals of rolling bearings as the benchmarks, the meaningful IMFs rich in fault information are efficiently selected, which are further denoised by a newly constructed self-adaptive threshold. Finally, weak fault features are extracted from the reconstructed denoised signals employing the envelope analysis approach. A simulation case and two actual cases of rolling bearings in the early fault stage are utilized to verify the robustness and feasibility of the proposed IENEMD-ATD. The results indicate that the proposed approach exceeds other state-of-the-art techniques in extracting weak fault features of rolling bearings.

Analysis of families of divergences to compare Gaussian processes modeled by sums of complex exponentials disturbed by additive white noises

The purpose of this paper is first to derive the expressions of various divergences that can be expressed from the Chernoff coefficient in order to compare two probability density functions of vectors storing k consecutive samples of a sum of complex exponentials disturbed by an additive white noise. This includes the Chernoff divergence and the α-divergence for instance. Tsallis, reversed Tsallis and Sharma-Mittal divergences are also addressed as well as the β-, γ- and αγ-divergences. The behaviors of the divergences are studied when k increases and tends to infinity. Depending on the divergence used, the divergence rate or the asymptotic normalized increment is considered. Expressions that encompass the divergence rate or the asymptotic normalized increment of the divergences are also given. Comments and illustrations to compare random processes are then given. This study makes it possible to show the advantages of the Kullback-Leibler divergence when studying this type of process.

The voltage and spiking responses of subthreshold resonant neurons to structured and fluctuating inputs: persistence and loss of resonance and variability.

We systematically investigate the response of neurons to oscillatory currents and synaptic-like inputs and we extend our investigation to non-structured synaptic-like spiking inputs with more realistic distributions of presynaptic spike times. We use two types of chirp-like inputs consisting of (i) a sequence of cycles with discretely increasing frequencies over time, and (ii) a sequence having the same cycles arranged in an arbitrary order. We develop and use a number of frequency-dependent voltage response metrics to capture the different aspects of the voltage response, including the standard impedance (Z) and the peak-to-trough amplitude envelope ([Formula: see text]) profiles. We show that Z-resonant cells (cells that exhibit subthreshold resonance in response to sinusoidal inputs) also show [Formula: see text]-resonance in response to sinusoidal inputs, but generally do not (or do it very mildly) in response to square-wave and synaptic-like inputs. In the latter cases the resonant response using Z is not predictive of the preferred frequencies at which the neurons spike when the input amplitude is increased above subthreshold levels. We also show that responses to conductance-based synaptic-like inputs are attenuated as compared to the response to current-based synaptic-like inputs, thus providing an explanation to previous experimental results. These response patterns were strongly dependent on the intrinsic properties of the participating neurons, in particular whether the unperturbed Z-resonant cells had a stable node or a focus. In addition, we show that variability emerges in response to chirp-like inputs with arbitrarily ordered patterns where all signals (trials) in a given protocol have the same frequency content and the only source of uncertainty is the subset of all possible permutations of cycles chosen for a given protocol. This variability is the result of the multiple different ways in which the autonomous transient dynamics is activated across cycles in each signal (different cycle orderings) and across trials. We extend our results to include high-rate Poisson distributed current- and conductance-based synaptic inputs and compare them with similar results using additive Gaussian white noise. We show that the responses to both Poisson-distributed synaptic inputs are attenuated with respect to the responses to Gaussian white noise. For cells that exhibit oscillatory responses to Gaussian white noise (band-pass filters), the response to conductance-based synaptic inputs are low-pass filters, while the response to current-based synaptic inputs may remain band-pass filters, consistent with experimental findings. Our results shed light on the mechanisms of communication of oscillatory activity among neurons in a network via subthreshold oscillations and resonance and the generation of network resonance.

Blind estimation of noise level based on pixels values prediction

Noise parameters estimation is needed for many tasks of digital image processing. Many efficient algorithms of noise variance estimation were proposed during last two decades. However, most of those estimators are efficient only for a specific kind of noise for which they were designed. For example, methods of estimation of variance of white additive Gaussian noise (AWGN) fail in the case of additive colored Gaussian noise (ACGN) or for noises with other distributions. In this paper a new fully blind method of noise level estimation is proposed. For a given image, a distorted image with a removed part of pixels (around 10%) is generated. Then an inpainting (or impulse noise removal) method is used to recover missed pixels values. The difference between true and recovered values is used for a robust estimation of noise level. The algorithm is applied for different image scales to estimate noise spectrum. In the paper we propose a convolutional neural network PIXPNet for effective prediction of values of missing pixels. A comparative analysis shows that the proposed PIXPNet provides smallest error of recovered pixels values among all existing methods. A good efficiency of usage of the proposed approach in both AWGN and spatially correlated noise suppression is demonstrated.

Random exponential attractor for stochastic non-autonomous suspension bridge equation with additive white noise

<p style='text-indent:20px;'>In this paper, we mainly consider the existence of random attractor and random exponential attractor for stochastic non-autonomous suspension bridge equation with additive white noise. First step, the well-posedness and the existence of a random attractor for the cocycle associated with the considered system is established. Second step, the upper semicontinuity of random attractors is also provided when the coefficient of random term approaches zero. Third step, we prove the regularity of random attractor in a higher regular space by the "iteration" method. Finally, we give the existence of a random exponential attractor for the considered system, which implies the finiteness of fractal dimension of random attractor.</p>

Wong-Zakai approximations and long term behavior of second order non-autonomous stochastic lattice dynamical systems with additive noise

<abstract><p>In this article, we investigate the Wong-Zakai approximations of a class of second order non-autonomous stochastic lattice systems with additive white noise. We first prove the existence and uniqueness of tempered pullback random attractors for the original stochastic system and its Wong-Zakai approximation. Then, we establish the upper semicontinuity of these attractors for Wong-Zakai approximations as the step-length of the Wiener shift approaches zero.</p></abstract>

Multi-valued random dynamics of stochastic wave equations with infinite delays

<p style='text-indent:20px;'>This paper is devoted to the asymptotic behavior of solutions to a non-autonomous stochastic wave equation with infinite delays and additive white noise. The nonlinear terms of the equation are not expected to be Lipschitz continuous, but only satisfy continuity assumptions along with growth conditions, under which the uniqueness of the solutions may not hold. Using the theory of multi-valued non-autonomous random dynamical systems, we prove the existence and measurability of a compact global pullback attractor.</p>

Interpolated DFT Algorithm for Frequency Estimation by Using Maximum Sidelobe Decay Windows

A sinusoidal frequency estimator based on interpolated Discrete Fourier Transform (DFT) algorithm by using Maximum Sidelobe Decay (MSD) windows is proposed in this paper. Firstly, the received sinusoid is weighted by an appropriate MSD window. Then DFT is carried out on the weighted sinusoid and the coarse estimation is acquired by finding the position of the maximum DFT sample. Different from all the existing algorithms, the presented estimator adopts the maximum DFT sample and two Discrete Time Fourier Transform (DTFT) spectral lines which are on the same side of the maximum DFT sample in the fine estimation step. MSE formulas of the presented estimator in additive white noise are derived. Simulation results indicate that the presented estimator outperforms the competing estimators.

Existence of unstable stationary solutions for nonlinear stochastic differential equations with additive white noise

<p style='text-indent:20px;'>This paper is concerned with the existence of unstable stationary solutions for nonlinear stochastic differential equations (SDEs) with additive white noise. Assume that the nonlinear term <inline-formula><tex-math id="M1">\begin{document}$ f $\end{document}</tex-math></inline-formula> is monotone (or anti-monotone) and the global Lipschitz constant of <inline-formula><tex-math id="M2">\begin{document}$ f $\end{document}</tex-math></inline-formula> is smaller than the positive real part of the principal eigenvalue of the competitive matrix <inline-formula><tex-math id="M3">\begin{document}$ A $\end{document}</tex-math></inline-formula>, the random dynamical system (RDS) generated by SDEs has an unstable <inline-formula><tex-math id="M4">\begin{document}$ \mathscr{F}_+ $\end{document}</tex-math></inline-formula>-measurable random equilibrium, which produces a stationary solution for nonlinear SDEs. Here, <inline-formula><tex-math id="M5">\begin{document}$ \mathscr{F}_+ = \sigma\{\omega\mapsto W_t(\omega):t\geq0\} $\end{document}</tex-math></inline-formula> is the future <inline-formula><tex-math id="M6">\begin{document}$ \sigma $\end{document}</tex-math></inline-formula>-algebra. In addition, we get that the <inline-formula><tex-math id="M7">\begin{document}$ \alpha $\end{document}</tex-math></inline-formula>-limit set of all pull-back trajectories starting at the initial value <inline-formula><tex-math id="M8">\begin{document}$ x(0) = x\in\mathbb{R}^n $\end{document}</tex-math></inline-formula> is a single point for all <inline-formula><tex-math id="M9">\begin{document}$ \omega\in\Omega $\end{document}</tex-math></inline-formula>, i.e., the unstable <inline-formula><tex-math id="M10">\begin{document}$ \mathscr{F}_+ $\end{document}</tex-math></inline-formula>-measurable random equilibrium. Applications to stochastic neural network models are given.</p>

Wong-Zakai approximations and pathwise dynamics of stochastic fractional lattice systems

<p style='text-indent:20px;'>This paper is concerned with the pathwise dynamics of stochastic fractional lattice systems driven by Wong-Zakai type approximation noises. The existence and uniqueness of pullback random attractor are established for the approximate system with a wide class of nonlinear diffusion term. For system with linear multiplicative noise and additive white noise, the upper semicontinuity of random attractors for the corresponding approximate system are also proved when the step size of the approximation approaches zero.</p>

Improving Bit Error Rate of MIMO-OFDM System Using Discrete Wavelet Transformation

This paper has developed a discrete wavelet transform (DWT) for multicarrier modulation in MIMO-OFDM system. The proposed system used additive Gaussian white noise (AGWN) and Rayleigh flat fading channel with respect to SNR using binary phase shift keying (BPSK). The algorithms for various scenarios of MIMO-OFDM system have been developed and simulated in MATLAB environment. The performance metric of the system was based on bit error ratio (BER) variation over values of signal to noise ratio (SNR) for different transmit and receive antennas including single input multiple output (SIMO) arrangement. The simulation results showed that the performance of DWT based MIMO-OFDM outperformed DFT based MIMO-OFDM. For the 2×1, 2×2, 2×3 MISO and MIMO systems, the DWT scheme offered reduced BER of 1.803e-05, 1.502e-05, and 1.413e-05 against 0.005847, 0.005361, and 0.005325 for the DFT scheme with respect to signal to noise ratio (SNR) at 10 dB. Generally, the results showed that using DWT scheme in OFDM for wireless communication system does not require an extra subcarrier to provide cyclic prefix function that serves as additional cost burden and reduces bandwidth.

A Novel Scheme for the Construction of the SCMA Codebook

As a code-domain non-orthogonal multiple access technique, sparse code multiple access (SCMA) is considered as a promising technique for future wireless Internet of Things (IoT) networks. The minimum Euclidean distance (MED) and minimum product distance (MPD) have been highlighted as the key performance indicators of the codebook in additive gaussian white noise (AWGN) and downlink Rayleigh channels respectively. In this paper, based on the mother codebook, a novel codebook design scheme is proposed to achieve better error performance in both AWGN and downlink Rayleigh channels. The problem of constructing the mother codebook is considered as the quadratic assignment problem (QAP), where the Tabu searching algorithm is employed to reduce the complexity of searching for the best permutation result. Then, the rotation matrix is adopted to find the best degrees for the generation of the constellation group, and two algorithms are proposed to assign the obtained constellation in factor graph matrix. Taking the degree optimization and the constellation assignments into joint consideration, an improved unified optimization is further explored to maximize the MED of each user. Besides, a novel polarized modulation scheme is proposed, which places the symbols in the three dimensional (3D) stokes parameters to improve the performance of the system. Finally, simulation results are provided to show the performance of the proposed codebooks, and the comparisons of symbol error performance (SER) in different codebooks are also discussed in detail.

A Novel Technique of Noise Cancellation based on Stationary Bionic Wavelet Transform and WATV: Application for ECG Denoising

In this paper, is proposed a novel technique of Electrocardiogram (ECG) denoising. It is based on the application of Wavelet/Total-Variation (WATV) denoising approach in the domain of the Stationary Bionic Wavelet Transform (SBWT). It consists firstly in applying the SBWT to the noisy ECG signal for obtaining two noisy coefficients namedwtb1 and wtb2 which are respectively details and approximation coefficients. For estimating the level of noise altering the signal, namedσ, we use wtb1. This noise is an additive Gaussian white noise. The thresholding ofwtb1 is secondly performed employing the soft thresholding and a denoised coefficient wtd1 is obtained. This thresholding requires the use of a certain threshold, thr which is computed using σ. Thedenoising ofwtb2 is performed using WATV denoising method and we obtain a denoised coefficient, wtd2. This WATV denoising method also uses σ. The denoised ECG signal is finally obtained by applying the inverse of SBWT (SBWT-1) to wtd1 and wtd2. The proposed technique performance is justified by the results obtained from the computations of Signal to Noise Ratio (SNR), Minimum Square Error (MSE), Mean Absolute Error (MAE), Peak-SNR (PSNR) and Cross-Correlation (CC).

Pulmonary Nodule Clinical Trial Data Collection and Intelligent Differential Diagnosis for Medical Internet of Things.

In this paper, the medical Internet of things (IoT) is used to pool data from clinical trials of pulmonary nodules, and on this basis, intelligent differential diagnosis techniques are investigated. A filtered orthogonal frequency division multiplexing model based on polarisation coding is proposed, where the input data are fed to a modulator after polarisation cascade coding, and the system performance is analysed under a medical Internet of things modulated additive Gaussian white noise channel. The above polarisation-coded filtered orthogonal frequency division multiplexing system components are applied to electroencephalogram (EEG) signal transmission, to which a threshold compression module and a vector reconstruction module are added to address the system power burden associated with the acquisition and transmission of large amounts of real-time EEG data in the medical IoT. In the threshold compression module, the inherent characteristics of EEG signals are analysed, and the generated EEG data are decomposed into multiple symbolic streams and compressed by applying different thresholds to improve the compression ratio while ensuring the quality of service of the application. A deep neural network-based approach is proposed for the detection and diagnosis of lung nodules. Automatic identification and measurement of simulated lung nodules and the corresponding volumes of nodules in images under different conditions are applied. The sensitivity of each AIADS in identifying lung nodules under different convolution kernel conditions, false positives (FP), false negatives (FN), relative volume errors (RVE), the miss detection rate (MDR) for different types of lung nodules, and the performance of each system in predicting the four types of nodules are calculated. In this paper, an interpretable multibranch feature convolutional neural network model is proposed for the diagnosis of benign and malignant lung nodules. It is demonstrated that the proposed model not only yields interpretable lung nodule classification results but also achieves better lung nodule classification performance with an accuracy rate of 97.8%.

Alleviating Class Imbalance Problem in Automatic Sleep Stage Classification

For real-world automatic sleep stage classification tasks, various existing deep learning based models are biased towards the majority with high proportion. Because of the unique sleep structure, most of the current polysomnography datasets suffer an inherent class imbalance problem (CIP), in which the number of each sleep stage is severely unequal. In this study, we first define the class imbalance factor (CIF) to describe the level of CIP quantitatively. Afterwards, we propose two balancing methods to alleviate this problem from the dataset quantity and the relationship between the class distribution and the applied model respectively. The first one is to employ the data augmentation (DA) with the generative adversarial network (GAN) model and different intensities Gaussian white noise to balance samples, thereinto, Gaussian white noise addition is specifically tailored to deep learning based models, which can work on raw electroencephalogram (EEG) data while preserving their properties. In addition, we try to balance the relationship between the imbalanced class and biased network model to achieve a balanced state with the help of class distribution and neuroscience principles. We further propose an effective deep convolutional neural network (CNN) model utilizing bidirectional Long Short-Term Memory (Bi-LSTM) with single-channel EEG as the Baseline. It is used for evaluating the efficiency of two balancing approaches on three imbalanced polysomnography datasets (CCSHS, Sleep-EDF and Sleep-EDF-V1). The qualitative and quantitative evaluation of experimental results demonstrates that the proposed methods could not only show the superiority of class balancing through the confusion matrix and class-wise metrics, but also get better N1 stage and whole stages classification accuracies compared to other state-of-the-art approaches.

Stochastic filter-based fatigue crack growth prediction for pipelines considering unknown model parameters and measurement uncertainty

In this study a methodology is developed and implemented in Python for fatigue crack growth prediction in pipelines, by leveraging measurement data and fatigue growth model predictions. Specifically, Particle Filter (PF) algorithm, Paris law, and the stress intensity factor (SIF) model in API 579 are integrated into a tool to use noisy crack size measurements for estimating the current crack size and fatigue model parameters, also known as joint state-parameter estimation. For illustration purpose, pseudo-data set for crack size measurements is generated considering additive Gaussian white noise of two different noise levels, aiming to mimic crack size data obtained from In-line Inspection (ILI) tools. It is found that the crack state can be reliably estimated compared to noisy measurements and initial model predictions, and the true model parameters can be updated with good accuracy. As such, the current crack size estimated and model parameters updated can be used in the fatigue growth model (i.e., Paris law) to predict the future trajectory of the fatigue crack growth. As more measurement data becomes available, the developed tool more reliably estimates the future crack growth trajectory.