Colored Gaussian Noise Research Articles

Impact of multiplexing noise on multilayer networks of bistable maps

We explore numerically the complex dynamics of multilayer networks (consisting of three and one hundred layers) of cubic maps in the presence of noise-modulated interlayer coupling (multiplexing noise). The coupling strength is defined by independent discrete-time sources of color Gaussian noise. Uncoupled layers can demonstrate different complex structures, such as double-well chimeras, coherent and spatially incoherent regimes. Regions of partial synchronization of these structures are identified in the presence of multiplexing noise. We elucidate how synchronization of a three-layer network depends on the initially observed structures in the layers and construct synchronization regions in the plane of multiplexing noise parameters “noise spectrum width – noise intensity”. It is shown that in a hundred-layer network, clusters of synchronized layers can be formed at certain optimal values of multiplexing noise parameters. The performed numerical studies confidently indicate that the spatial dynamics of multilayer networks can be controlled by varying multiplexing noise parameters.

Characterization of the Complexity of Computing the Capacity of Colored Gaussian Noise Channels

Characterization of the Complexity of Computing the Capacity of Colored Gaussian Noise Channels

Response of Gaussian color noise excited oscillators with inertia nonlinearity based on the radial basis function neural network method

Given the widespread utilization of oscillators featuring inertial nonlinear terms across engineering disciplines and the omnipresence of noise excitations, comprehending their response to noise excitation holds paramount importance. In contrast to Gaussian white noise, colored noise stands out as a more adept mathematical model for simulating ambient noise scenarios. The widely used stochastic averaging method is somewhat ineffective in dealing with the response of oscillators with inertial nonlinearity under Gaussian colored noise excitation, as it cannot display the saddle shaped characteristics of the steady-state probability density function (PDF) caused by inertial nonlinearity. To overcome the shortcomings, this paper adopts a semi-analytical method called a radial basis function neural network method (RBFNN) to address this problem. This method represents the solution of the Fokker-Plank-Kolmogorov (FPK) equation of the system as the sum of a series of weighted radial basis functions, and obtains the optimal weight coefficients through the Lagrange multiplier method. This article investigates two examples, one of which has inertial nonlinearity and the other has multiple potential wells. The effects of inertial nonlinearity coefficients and the delay coefficients of colored noise on response are explored. The mean square errors between Monte Carlo (MC) and RBF are presented, which indicates the RBF results perfectly agree with the MC predictions.

Two combination methods of piecewise unsaturated tri-stable stochastic resonance system and bearing fault detection under different noise

In this paper, a piecewise unsaturated tri-stable stochastic resonance (PUTSR) system is proposed to address the issue of output saturation. Firstly, the unsaturated characteristics of the PUTSR system are verified, followed by a discussion on the system performance of PUTSR under two different combinations of coupled and cascaded systems. The two-dimensional coupled piecewise unsaturated tri-stable stochastic resonance (TCPUTSR) system and cascaded piecewise unsaturated tri-stable stochastic resonance (CPUTSR) system are proposed. By implementing the adiabatic approximation theory, the steady-state probability density (SPD) of TCPUTSR system and spectral amplification (SA) coefficient of TCPUTSR and CPUTSR systems are derived respectively. The impact of different system parameters on the SPD and SA are also investigated. Finally, PUTSR, TCPUTSR and CPUTSR systems are applied to detection on the fault signal of bearing. Gaussian white noise and color noise are used to simulate actual noise environments in the experiments, while the adaptive genetic algorithm (AGA) is used to optimize the parameters and measure the system performance via signal-to-noise ratio improvement (SNRI). Results indicate that both coupled and cascaded systems demonstrate better detection capabilities than individual systems, with the CPUTSR system offering better enhancement and detection of bearing fault signals. Under Gaussian white noise, the SNRI of the CPUTSR system is 1.449 dB ~ 3.198 dB higher than that of the PUTSR and TCPUTSR systems, while under color noise it is 1.566 dB ~ 2.849 dB higher. This paper mainly compares the spectral amplification capability and fault signal detection capability of the same system under two different combinations of coupled and cascaded. The theoretical and numerical simulations further verify that the designed cascaded system outperforms the coupled system and proves the great superiority of CPUTSR system. These findings provide crucial theoretical support and practical application prospects for engineering purposes.

Rapid detection of Penaeus vannamei diseases via an improved LeNet

Shrimp disease is a greatly important factor in the culture of Penaeus vannamei, the shrimp species with the highest yield in the world aquaculture industry. Hepatopancreatic necrosis disease (HPND, 37 %), red body disease (RBD, 26 %), and whitish muscle disease (WMD, 18 %) were the most common Penaeus vannamei diseases, all of which are usually classified and identified by two kinds of detection (manual detection and germs purifying method). Most of these detections suffer from the class low accuracy, too complex, or too costly. In this study, we tackle this situation with an improved LeNet, which includes modifying model parameters and computational methods. More particularly, this study proposes a convolutional neural networks (CNN) model that is based on LeNet network framework and can reduce parameters and accelerate calculation. To offer improvements in classification and identification, we increase the number of feature maps. Meanwhile, to firstly take denoise and then strengthen characteristic in pretreatment, HSV color space conversion and Gaussian noise with a level of 20 are led into. We conclude that the model generates the precision at about 96.1 % when the weight parameter learning rate is 0.002 and the number of iterations is 120 after being trained and validated. The study has made tremendous progress in the rapid detection of Penaeus vannamei diseases by providing an effective technological path and suggesting the possibility of realizing early disease warnings in future works.

Optimal Tracking Control of Networked Systems Subject to Model Uncertainty and Additive Colored Gaussian Noise

For control systems with communication links, the various communication parameters can bring negative effects on system’s performance. Taking tracking problem for example, it is extremely difficult to achieve accurate tracking, that is, the tracking error can not be zero because of these communication constraints, such as model uncertainties originate from plant and channel, and additive colored Gaussian noise (ACGN). In this brief, by employing unit feedback controller (UFC) and two-parameters controller (TPC), the output tracking control (OTC) performance of networked systems subject to model uncertainties and ACGN is investigated. Consequently, two exact expressions of OTC performance limitations are derived with UFC and TPC. These results clearly show that OTC performance tightly depends on non-minimum phase zeros (NMPZs) and unstable poles (UPs) of the given plant. Moreover, the existence of uncertainties and ACGN can result in the poor OTC performance.

Quantum Analog Annealing of Gain‐Dissipative Ising Machine Driven by Colored Gaussian Noise

AbstractGain‐dissipative Ising machines (GIMs) are a type of quantum analog equipment that can rapidly determine the optimal solution for combinatorial optimization problems. When the noise intensity is significantly lower than the fixed point of the system, the performance of a GIM is not influenced by the fluctuation of the noise intensity. However, the noise in this study is limited to Gaussian white noise. The influence of prevalent colored noise on GIMs has not been researched. In this study, the influence of common‐colored noise on the performance of GIMs is numerically investigated. The results of a domain clustering dynamics analysis reveal that red noise can better suppress the generation of the noise‐induced irregular temporary domain. Furthermore, several prevalent MAXCUT problem topologies, including the Moebius ladder, random Moebius ladder, and 2D random lattice, are adopted as test benchmarks. The results reveal that GIMs influenced by white, blue, and violet noise perform better at low‐intensity noise condition. In contrast, pink and red noise‐injected GIMs demonstrate higher performances when applied to MAXCUT topologies with both ferromagnetic and antiferromagnetic connections under larger noise intensity conditions. This indicates that the noise dispersion can be used as an additional hyperparameter to optimize the performance of GIMs.

Stochastic resonance in asymmetric bistable coupled network systems driven by Gaussian colored noise

In this work studied is the synergistic effect of asymmetric bistable coupled network systems under the action of Gaussian colored noise and periodic signal. The system is a network model consisting of a large number of oscillators. The interaction and change between individuals produce complex nonlinear behavior patterns. For further research, firstly, the original N-dimensional system is reduced and approximated by using the mean field theory, the unified colored noise approximation theory and the equivalent nonlinearization method. Secondly, the Langevin equation of simplified model is obtained through the slaving principle by using the two-state model theory to derive the theoretical expression of signal-to-noise ratio. It is found that the system produces the phenomenon of scale stochastic resonance. Finally, the effects of Gaussian color noise parameters, system parameters and periodic signal parameters on the stochastic resonance behavior of asymmetric coupled network systems are discussed. The results show that the increase of Gaussian colored noise correlation time and noise intensity can promote the scale stochastic resonance phenomenon; selecting appropriate coupling coefficient can achieve the optimal stochastic resonance effect. And the stochastic resonance phenomenon of the system driven by the Gaussian colored noise and the Gaussian white noise, respectively, are analyzed and compared with each other. Research result shows that Gaussian colored noise is more conducive to enhancing stochastic resonance phenomenon.

A New Technique for ARMA-System Identification Based on QR-Decomposition of Third Order Cumulants Matrix

In this paper a new technique to estimate the coefficients of a general Autoregressive Moving Average (ARMA) (p, q) model is proposed. The ARMA system is excited by an un-observable independently identically distributed (i.i.d) non-Gaussian process. The proposed ARMA coefficients estimation method uses the QR-Decomposition (QRD) of a special matrix built with entries of third order cumulants (TOC) of the available output data only. The observed output may be corrupted with additive colored or white Gaussian noise of unknown power spectral density. The proposed technique was compared with several good methods such as the residual time series (RTS) and the Q-slice algorithm (QSA) methods. Simulations for several examples were tested. The results for these examples confirm the good performance of the proposed technique with respect to existing well-known methods.

Passive MIMO Radar Detection with Unknown Colored Gaussian Noise

The target detection of the passive multiple-input multiple-output (MIMO) radar that is comprised of multiple illuminators of opportunity and multiple receivers is investigated in this paper. In the passive MIMO radar, the transmitted signals of illuminators of opportunity are totally unknown, and the received signals are contaminated by the colored Gaussian noise with an unknown covariance matrix. The generalized likelihood ratio test (GLRT) is explored for the passive MIMO radar when the channel coefficients are also unknown, and the closed-form GLRT is derived. Compared with the GLRT with unknown transmitted signals and channel coefficients but a known covariance matrix, the proposed method is applicable for a more practical case whenthe covariance matrix of colored noise is unknown, although it has higher computational complexity. Moreover, the proposed GLRT can achieve similar performance as the GLRT with the known covariance matrix when the number of training samples is large enough. Finally, the effectiveness of the proposed GLRT is verified by several numerical examples.

The Arbitrarily Varying Channel With Colored Gaussian Noise

We address the arbitrarily varying channel (AVC) with colored Gaussian noise. The work consists of three parts. First, we study the general discrete AVC with fixed parameters, a model that combines the AVC and the time-varying channel. We determine both the deterministic code capacity and the random code capacity. Super-additivity is demonstrated, showing that the deterministic code capacity can be strictly larger than the weighted sum of the parametric capacities. In the second part, we consider the arbitrarily varying Gaussian product channel (AVGPC). Hughes and Narayan characterized the random code capacity through min-max optimization leading to a “double” water filling solution. As in the case of the standard Gaussian AVC, the deterministic code capacity is discontinuous in the input constraint, and depends on which of the input or state constraint is higher. As opposed to Shannon's classic water filling solution, it is observed that deterministic coding using independent scalar codes is suboptimal for the AVGPC. Finally, we establish the capacity of the AVC with colored Gaussian noise, where double water filling is performed in the frequency domain. The analysis relies on our preceding results, on the AVC with fixed parameters and the AVGPC.

A New Detecting Method for Underwater Acoustic Weak Signal Based on Differential Double Coupling Oscillator

For weak signal detection with known frequency, based on the double coupling Duffing oscillator method, a differential double coupling Duffing oscillator and Van der Pol-Duffing oscillator detection method is proposed. Its feasibility is verified by sinusoidal analog signal. It has intuitive detection effect and high sensitivity, and can detect weak signal with lower signal-to-noise ratio (SNR). For underwater acoustic weak signal detection with unknown frequency, based on the above proposed method, a differential double coupling Duffing oscillator and Van der Pol-Duffing oscillator variable step-size detection method is proposed. Compared with the existing double coupling Duffing oscillator variable step-size method and differential double Duffing oscillator variable step-size method, its SNR threshold is respectively reduced by 6.02dB and 2.28dB. The lowest average error rate of frequency estimation in multiple sinusoidal analog signal detection under Gaussian white noise, Gaussian color noise and Rayleigh distribution noise is 0.423%. Its detection effect is verified in the detection of measured underwater acoustic signals from the website http://atlanttic.uvigo.es/underwaternoise/. The results show that it has good detection performance. It provides a new detecting method for underwater acoustic weak signal. In the future, it can be applied to detect weak periodic signal such as square wave and general periodic signal with unknown frequency.

Supervised Machine Learning Classifiers for Diversity Combined Signals in 6G Massive MIMO Receivers

Support Vector Machine (SVM) is a statistical learning tool that was initially developed by Vapnik in 1979 and later developed to a more complex concept of structural risk minimization (SRM). SVM, as a supervised machine learning tool, is playing an increasing role in applications to detection problems in various engineering problems, notably in statistical signal processing, pattern recognition, image analysis, and 6G wireless communication networks. In this paper, SVM is applied to signal detection in 6G communication systems in the presence of channel noise in the form of fully developed Rayleigh multipath fading and receiver noise generalized as additive color Gaussian noise (ACGN). The structure and performance of SVM in terms of the bit error rate (BER) metric is derived and simulated for these advanced stochastic noise models and the computational complexity of the implementation, in terms of average computational time per bit, is also presented. The performance of SVM is then compared to conventional M-ary signaling optimal model-based detector driven by M-ary phase shift keying (MPSK) modulation. We show that the SVM performance is superior to that of conventional detectors which require as much as 7 bits-coding (M≥128) to produce comparable results to those of SVM. Finally, the SVM-based detector is implemented in an uplink SIMO system using both Equal Gain Combiner (EGC) technique and Root Mean Square Gain Combiner (RMSGC) technique in which the later technique will be proven to be superior to the earlier.

Strong-chaos-caused negative mobility in a periodic substrate potential.

We numerically investigate negative mobility of an inertial Brownian particle moving in a periodic double-well substrate potential in the presence of a time-periodic force and a constant bias. For the deterministic case, we find from the average velocity that the varying shape parameter and driving forces can cause negative mobility, differential negative mobility, and giant positive mobility. We analyze these findings via the bifurcation diagram and maximal Lyapunov exponent and find that certain chaos can give rise to negative mobility. For the presence of a Gaussian color noise, the results suggest that the noise intensity can enhance or result in negative and positive mobilities, whereas correlation time can enhance, weaken, or even eliminate them. On the basis of the time series, phase-space map, and power spectrum of various attractors, we unveil how these mobilities connect to strong chaotic attractors (SCAs), including both stable attractor and unstable attractors, and propose an underlying mechanism that SCAs can result in the negative mobility, whereas other attractors do not. Our findings may be potentially useful for research on anomalous transports of the particles and on designs of various devices, such as atomic chains, crystals with dislocations, and superconducting nanowires, etc.

Optimized Basis Functions Under Gaussian Color Noise for Magnetic Target Signal Detection

The orthogonal basis functions (OBFs) method is a viable approach for magnetic target signal detection under the Gaussian white noise. However, its performance would degrade overtly under the Gaussian color noise with the power spectral density of 1/f <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">α</sup> , which is the common environmental magnetic noise. In this letter, based on the linear constrained minimum variance criterion and the generalized likelihood ratio test, respectively, an alternative detection scheme is proposed through the optimization of the basis functions by considering both the signal and noise information. Experiment results using both the simulated data and the measured data show that the present approach can significantly improve the detection performance when compared to the original OBFs method.

Near-Field Noncircular Sources Localization Based on Fourth-Order Cumulant

This paper presents a cumulant-based algorithm for near-field noncircular sources localization with a symmetric uniform linear array. It first constructs three extended matrices. Then, based on the rotational invariance property in extended cumulant-domain signal subspace, coarse direction-of-arrival (DOA) estimates are obtained. With the course results used as reference, the algorithm is able to disambiguate the cyclic phase ambiguities when the equivalent sub-array spacing exceeds a half wavelength. Thus, higher precision DOA estimates can be obtained. Finally, with the estimated DOAs, only one-dimensional searching is needed to obtain the range estimates via rank-reduction algorithm. The proposed algorithm avoids two-dimensional searching and parameters pairing. In addition, compared with the existing near-field noncircular sources localization algorithm, the significant characteristic of the proposed algorithm is that it exploits cumulant and the noncircularity of signal to achieve extended steering vector. Cumulant is insensitive to Gaussian (white or color) noise. Consequently, the proposed one provides DOA estimates with improved precision especially at low signal-to-noise ratios. Furthermore, it doubles the number of detectable sources. Total least square ESPRIT algorithm is exploited to yield search free estimates of near-field bearing parameters. Computer simulations are carried out to demonstrate the superiority of the proposed algorithm.

Non-invasive Decoding of the Motoneurons: A Guided Source Separation Method Based on Convolution Kernel Compensation With Clustered Initial Points.

Despite the progress in understanding of neural codes, the studies of the cortico-muscular coupling still largely rely on interferential electromyographic (EMG) signal or its rectification for the assessment of motor neuron pool behavior. This assessment is non-trivial and should be used with precaution. Direct analysis of neural codes by decomposing the EMG, also known as neural decoding, is an alternative to EMG amplitude estimation. In this study, we propose a fully-deterministic hybrid surface EMG (sEMG) decomposition approach that combines the advantages of both template-based and Blind Source Separation (BSS) decomposition approaches, a.k.a. guided source separation (GSS), to identify motor unit (MU) firing patterns. We use the single-pass density-based clustering algorithm to identify possible cluster representatives in different sEMG channels. These cluster representatives are then used as initial points of modified gradient Convolution Kernel Compensation (gCKC) algorithm. Afterwards, we use the Kalman filter to reduce the noise impact and increase convergence rate of MU filter identification by gCKC. Moreover, we designed an adaptive soft-thresholding method to identify MU firing times out of estimated MU spike trains. We tested the proposed algorithm on a set of synthetic sEMG signals with known MU firing patterns. A grid of 9 × 10 monopolar surface electrodes with 5-mm inter-electrode distances in both directions was simulated. Muscle excitation was set to 10, 30, and 50%. Colored Gaussian zero-mean noise with the signal-to-noise ratio (SNR) of 10, 20, and 30 dB, respectively, was added to 16 s long sEMG signals that were sampled at 4,096 Hz. Overall, 45 simulated signals were analyzed. Our decomposition approach was compared with gCKC algorithm. Overall, in our algorithm, the average numbers of identified MUs and Rate-of-Agreement (RoA) were 16.41 ± 4.18 MUs and 84.00 ± 0.06%, respectively, whereas the gCKC identified 12.10 ± 2.32 MUs with the average RoA of 90.78 ± 0.08%. Therefore, the proposed GSS method identified more MUs than the gCKC, with comparable performance. Its performance was dependent on the signal quality but not the signal complexity at different force levels. The proposed algorithm is a promising new offline tool in clinical neurophysiology.

Directed Transport in Symmetrically Periodic Potentials Induced by Cross-Correlation among Colored Gaussian Noises

Abstract We study the noise induced directed transport of an inertial Brownian particle moving in a symmetric spatially periodic potential and is subjected to correlated colored noises. Under the assumption of small correlation times of colored fluctuations we obtain an analytical expression for resulting current in overdamped systems. Our analytical and numerical calculations indicate the directed current is controlled by the correlation parameters. It has been pointed out that the nonzero correlation time makes an important contribution to current only at large enough values of noise intensities. The role of other system parameters is investigated from the viewpoint of optimization the current amplitude.

Blind Noisy Image Quality Assessment Using Sub-Band Kurtosis.

Noise that afflicts natural images, regardless of the source, generally disturbs the perception of image quality by introducing a high-frequency random element that, when severe, can mask image content. Except at very low levels, where it may play a purpose, it is annoying. There exist significant statistical differences between distortion-free natural images and noisy images that become evident upon comparing the empirical probability distribution histograms of their discrete wavelet transform (DWT) coefficients. The DWT coefficients of low- or no-noise natural images have leptokurtic, peaky distributions with heavy tails; while noisy images tend to be platykurtic with less peaky distributions and shallower tails. The sample kurtosis is a natural measure of the peakedness and tail weight of the distributions of random variables. Here, we study the efficacy of the sample kurtosis of image wavelet coefficients as a feature driving, an extreme learning machine which learns to map kurtosis values into perceptual quality scores. The model is trained and tested on five types of noisy images, including additive white Gaussian noise, additive Gaussian color noise, impulse noise, masked noise, and high-frequency noise from the LIVE, CSIQ, TID2008, and TID2013 image quality databases. The experimental results show that the trained model has better quality evaluation performance on noisy images than existing blind noise assessment models, while also outperforming general-purpose blind and full-reference image quality assessment methods.

Stochastic Dynamic Model of Sulfate Corrosion Reactions in Concrete Materials considering the Effects of Colored Gaussian Noises

The corrosion reactions in concrete materials subjected to external environment attack can lead to the deterioration of concrete. However, the effects of internal fluctuations on the corrosion reaction process have not been reported in current studies on damage of concrete materials. To comprehensively describe the effects of internal fluctuations, the stochastic dynamic model of corrosion reactions in concrete materials subjected to sulfate attack is established based on the law of mass conservation and random process theory, in which internal fluctuations and the parameters of the chemical system are, respectively, regarded as colored Gaussian noises and a series of random variables. An experiment of sulfate corrosion reactions in concrete material is carried out to verify the effectiveness of the proposed method. Furthermore, the effects of variations of the initial reactant concentrations on the concentration evolution processes of the corrosion products are investigated. Results show that the stochastic dynamical responses of the corrosion reactions in concrete can be comprehensively investigated by the proposed stochastic mathematical model; the probabilistic information of the corrosion products can also be obtained conveniently. The concentration evolution process of sulfate corrosion products is a random process. The experimental data are only some samples of the random process. Concentrations of the corrosion products in concrete materials significantly fluctuate with the variations of the initial reactant concentrations.