Blind source separation of ship-radiated noise based on generalized Gaussian model

When the distribution of the sources cannot be estimated accurately, the ICA algorithms failed to separate the mixtures blindly. The generalized Gaussian model （GGM） is presented in ICA algorithm since it can model non- Ganssian statistical structure of different source signals easily. By inferring only one parameter, a wide class of statistical distributions can be characterized. By using maximum likelihood （ML） approach and natural gradient descent, the learning rules of blind source separation （BSS） based on GGM are presented. The experiment of the ship-radiated noise demonstrates that the GGM can model the distributions of the ship-radiated noise and sea noise efficiently, and the learning rules based on GGM gives more successful separation results after comparing it with several conventional methods such as high order cumnlants and Gaussian mixture density function.

A Gaussian Model for Anisotropic Strange Quark Stars

For studying the anisotropie strange quark stars, we assume that the radial pressure inside an anisotropic star can be obtained simply by isotropie pressure plus an additional Gaussian term with three free parameters （A, μ and X）. According to recent observations, a pulsar in a mass range of 1.97±0.04M has been measured. Hence, we take this opportunity to set the free parameters of our model. We fix X by applying boundary and stability conditions and then search the A - μ parameter space For a maximum mass range of 1.9M 〈 Mmax 〈 2.1M. Our results indicate that anisotropy increases the maximum mass M and also its corresponding radius R for a typical strange quark star. Furthermore, our model shows magnetic field and electric charge increase the anisotropy factor △. In fact, △ has a maximum on the surface and this maximum goes up in the presence of magnetic field and electric charge. Finally, we show that anisotropy can be more effective than either magnetic field or electric charge in raising maximum mass of strange quark stars.

Case Study of Atmospheric Pollutant Diffusion Data Based on Gaussian Model

Air pollution as one of the major environmental issues in modern society,has already brought severe impact to human life and production,thus it is an urgent task for studying environmental and ecological science to solve this issue that has bothered human society for the last centuries.Scientists have endeavored to figure out the laws of atmospheric pollutant diffusion using various mathematical models and statistical models,and drawn some precious conclusions.This paper explored the basic model of atmospheric diffusion—modeling and solution of Gaussian Diffusion Model,clarify its principles and operation forms,then applied the model into the PM_(2.5) atmospheric diffusion cases,make the program planning base on the results of model calculation,and get the final conclusion.

Blind source separation based on generalized gaussian model

Since in most blind source separation(BSS)algorithms the estimations of probability density function(pdf)of sources are fixed or can only switch between one sup-Gaussian and other sub-Gaussian model,they may not be efficient to separate sources with different distributions.So to solve the problem of pdf mismatch and the separation of hybrid mixture in BSS,the generalized Gaussian model(GGM)is introduced to model the pdf of the sources since it can provide a general structure of univariate distributions.Its great advantage is that only one parameter needs to be determined in modeling the pdf of different sources,so it is less complex than Gaussian mixture model.By using maximum likelihood(ML)approach,the convergence of the proposed algorithm is improved.The computer simulations show that it is more efficient and valid than conventional methods with fixed pdf estimation.

Online Predictive Monitoring and Prediction Model for a Periodic Process Through Multiway Non-Gaussian Modeling

一新为周期的生物过程的联机预兆的监视和预言模型被建议用多方法 non-Gaussian 建模。这条途径的基本想法是多使用方法 non-Gaussian 当模特儿在一个周期的过程从每日的正常操作数据提取某主导的关键组分，并且随后把这些部件与预兆的统计过程监视相结合技术。建议预兆的监视方法被使用了在生物废水处理过程指责察觉和诊断，它基于强壮日报特征。结果显示出力量和优点连续法的建议预兆的监视用多方法预兆监视概念，它因此能为一个每日的监视过程并且也给很有用的概念的结果比另外的传统的监视方法启用过程差错的更快速的察觉。

Critical Behavior of Gaussian Model on X Fractal Lattices in External Magnetic Fields

Using the renormalization group method, the critical behavior of Gaussian model is studied in external magnetic fields on X fractal lattices embedded in two-dimensional and d-dimensional (d ＞ 2) Euclidean spaces, respectively. Critical points and exponents are calculated. It is found that there is long-range order at finite temperature for this model, and that the critical points do not change with the space dimensionality d (or the fractal dimensionality dr). It is also found that the critical exponents are very different from results of Ising model on the same lattices, and that the exponents on X lattices are different from the exact results on translationally symmetric lattices.

Marginalized cubature Kalman filtering algorithm based on linear/nonlinear mixed-Gaussian model

Aiming at improving the estimation accuracy and real-time of nonlinear system with linear Gaussian sub-structure,a novel marginalized cubature Kalman filter is proposed in Bayesian estimation framework. Firstly,the marginalized technique is adopted to model the target system dynamics with nonlinear state and linear state separately,and the two parts are estimated by cubature Kalman filter and standard Kalman filter respectively. Therefore,the linear part avoids the generation and propagation process of cubature points. Accordingly,the computational complexity is reduced.Meanwhile,the accuracy of state estimation is improved by taking the difference of nonlinear state estimation as the measurement of linear state. Furthermore,the computational complexity of marginalized cubature Kalman filter is discussed by calculating the number of floating-point operation. Finally,simulation experiments and analysis show that the proposed algorithm can improve the performance of filtering precision and real-time effectively in target tracking system.

Critical Behavior of the Gaussian Model with Periodic Interactions on Diamond—Type Hierarchical Lattices in External Magnetic Fields

The Gaussian spin model with periodic interactions on the diamond-type hierarchical lattices is constructed by generalizing that with uniform interactions on translationally invariant lattices according to a class of substitution sequences. The Gaussian distribution constants and imposed external magnetic fields are also periodic depending on the periodic characteristic of the interaction bonds. The critical behaviors of this generalized Gaussian model in external magnetic fields are studied by the exact renormalization-group approach and spin rescaling method. The critical points and all the critical exponents are obtained. The critical behaviors are found to be determined by the Gaussian distribution constants and the fractal dimensions of the lattices. When all the Gaussian distribution constants are the same, the dependence of the critical exponents on the dimensions of the lattices is the same as that of the Gaussian model with uniform interactions on translationally invariant lattices.

Generalized Variational Merging of Multi-source Precipitation Data Based on the Non-Gaussian Model

Different from other domestic and foreign research in which the optimum interpolation(OI) merging algorithm is commonly used,this paper constructs the non-Gaussian model for generalized variational precipitation data merging research based on the non-Gaussianity of precipitation data. For CMORPH data correction,the probability density function( PDF) matching method is adopted,during which the GAMMA function fitting is utilized,and the generalized variational merging based on non-Gaussian model is used to merge corrected CMORPH precipitation data and station ground observation precipitation data. Meanwhile,we carry out an experiment on CMORPH precipitation data correction and the merging of multisource precipitation data based on non-Gaussian model. By measuring the structural similarity between the merged field and the reference field,we get a merging method that can better retain useful " outliers" which represent weather phenomena. The experimental results accord with our expectations.

Splitting of Gaussian Models via Adapted BML Method Pertaining to Cry-Based Diagnostic System

In this paper,we make use of the boosting method to introduce a new learning algorithm for Gaussian Mixture Models (GMMs) called adapted Boosted Mixture Learning (BML). The method possesses the ability to rectify the existing problems in other conventional techniques for estimating the GMM parameters, due in part to a new mixing-up strategy to increase the number of Gaussian components. The discriminative splitting idea is employed for Gaussian mixture densities followed by learning via the introduced method. Then, the GMM classifier was applied to distinguish between healthy infants and those that present a selected set of medical conditions. Each group includes both full-term and premature infants. Cry-pattern for each pathological condition is created by using the adapted BML method and 13-dimensional Mel-Frequency Cepstral Coefficients (MFCCs) feature vector. The test results demonstrate that the introduced method for training GMMs has a better performance than the traditional method based upon random splitting and EM-based re-estimation as a reference system in multi-pathological classification task.

Optimal consumption–investment under partial information in conditionally log-Gaussian models

Certain Merton type consumption−investment problems under partial information are reduced to the ones of full information and within the framework of a complete market model.Then,specializing to conditionally log−Gaussian diffusion models,concrete analysis about the optimal values and optimal strategies is performed by using analytical tools like Feynman−Kac formula,or HJB equations.The explicit solutions to the related forward-backward equations are also given.

Persymmetric adaptive polarimetric detection of subspace range-spread targets in compound Gaussian sea clutter

This paper focuses on the adaptive detection of range and Doppler dual-spread targets in non-homogeneous and nonGaussian sea clutter.The sea clutter from two polarimetric channels is modeled as a compound-Gaussian model with different parameters,and the target is modeled as a subspace rangespread target model.The persymmetric structure is used to model the clutter covariance matrix,in order to reduce the reliance on secondary data of the designed detectors.Three adaptive polarimetric persymmetric detectors are designed based on the generalized likelihood ratio test(GLRT),Rao test,and Wald test.All the proposed detectors have constant falsealarm rate property with respect to the clutter texture,the speckle covariance matrix.Experimental results on simulated and measured data show that three adaptive detectors outperform the competitors in different clutter environments,and the proposed GLRT detector has the best detection performance under different parameters.

A Robust Indoor Localization Algorithm Based on Polynomial Fitting and Gaussian Mixed Model

Wireless sensor network(WSN)positioning has a good effect on indoor positioning,so it has received extensive attention in the field of positioning.Non-line-of sight(NLOS)is a primary challenge in indoor complex environment.In this paper,a robust localization algorithm based on Gaussian mixture model and fitting polynomial is proposed to solve the problem of NLOS error.Firstly,fitting polynomials are used to predict the measured values.The residuals of predicted and measured values are clustered by Gaussian mixture model(GMM).The LOS probability and NLOS probability are calculated according to the clustering centers.The measured values are filtered by Kalman filter(KF),variable parameter unscented Kalman filter(VPUKF)and variable parameter particle filter(VPPF)in turn.The distance value processed by KF and VPUKF and the distance value processed by KF,VPUKF and VPPF are combined according to probability.Finally,the maximum likelihood method is used to calculate the position coordinate estimation.Through simulation comparison,the proposed algorithm has better positioning accuracy than several comparison algorithms in this paper.And it shows strong robustness in strong NLOS environment.

A blast furnace fault monitoring algorithm with low false alarm rate:Ensemble of greedy dynamic principal component analysis-Gaussian mixture model

The large blast furnace is essential equipment in the process of iron and steel manufacturing. Due to the complex operation process and frequent fluctuations of variables, conventional monitoring methods often bring false alarms. To address the above problem, an ensemble of greedy dynamic principal component analysis-Gaussian mixture model(EGDPCA-GMM) is proposed in this paper. First, PCA-GMM is introduced to deal with the collinearity and the non-Gaussian distribution of blast furnace data.Second, in order to explain the dynamics of data, the greedy algorithm is used to determine the extended variables and their corresponding time lags, so as to avoid introducing unnecessary noise. Then the bagging ensemble is adopted to cooperate with greedy extension to eliminate the randomness brought by the greedy algorithm and further reduce the false alarm rate(FAR) of monitoring results. Finally, the algorithm is applied to the blast furnace of a large iron and steel group in South China to verify performance.Compared with the basic algorithms, the proposed method achieves lowest FAR, while keeping missed alarm rate(MAR) remain stable.

Propagation of Gaussian Schell-Model Array Beams through a Jet Engine Exhaust

Here a Gaussian Shell Model Array (GSMA) beam is used to investigate the propagation characteristics in the jet engine exhaust region. It has great significance to improve various optical systems for wide application in trapping cold atoms, creating gratings, and atmospheric optical communication. We calculate analytical formulas for the spectral density (SD) and the propagation factors Mx2 and My2 of a GSMA beam. The influence of inner scale of turbulence in the jet engine exhaust region on its power spectrum has been also analyzed. According to these results, the influence of turbulence in a jet engine exhaust on a GSMA beam has been reduced by changing the parameters of light source and turbulence. For example, it is an excellent tool for mitigation of the jet engine exhaust-induced anisotropy of turbulence to increase the source coherence length, the root-mean-squared (rms) beam width, the wavelength or reduce the outer scale of turbulence.

A Probabilistic Trust Model and Control Algorithm to Protect 6G Networks against Malicious Data Injection Attacks in Edge Computing Environments

Future 6G communications are envisioned to enable a large catalogue of pioneering applications.These will range from networked Cyber-Physical Systems to edge computing devices,establishing real-time feedback control loops critical for managing Industry 5.0 deployments,digital agriculture systems,and essential infrastructures.The provision of extensive machine-type communications through 6G will render many of these innovative systems autonomous and unsupervised.While full automation will enhance industrial efficiency significantly,it concurrently introduces new cyber risks and vulnerabilities.In particular,unattended systems are highly susceptible to trust issues:malicious nodes and false information can be easily introduced into control loops.Additionally,Denialof-Service attacks can be executed by inundating the network with valueless noise.Current anomaly detection schemes require the entire transformation of the control software to integrate new steps and can only mitigate anomalies that conform to predefined mathematical models.Solutions based on an exhaustive data collection to detect anomalies are precise but extremely slow.Standard models,with their limited understanding of mobile networks,can achieve precision rates no higher than 75%.Therefore,more general and transversal protection mechanisms are needed to detect malicious behaviors transparently.This paper introduces a probabilistic trust model and control algorithm designed to address this gap.The model determines the probability of any node to be trustworthy.Communication channels are pruned for those nodes whose probability is below a given threshold.The trust control algorithmcomprises three primary phases,which feed themodel with three different probabilities,which are weighted and combined.Initially,anomalous nodes are identified using Gaussian mixture models and clustering technologies.Next,traffic patterns are studied using digital Bessel functions and the functional scalar product.Finally,the information coherence and content are analyzed.The noise content and abnormal information sequences are detected using a Volterra filter and a bank of Finite Impulse Response filters.An experimental validation based on simulation tools and environments was carried out.Results show the proposed solution can successfully detect up to 92%of malicious data injection attacks.

Critical behavior of the Gaussian model on fractal lattices in external magnetic field

For inhomogeneous lattices we generalize the classical Gaussian model, i. e. it is pro-posed that the Gaussian type distribution constant and the external magnetic field of site / in this model depend on the coordination number q, of site i, and that the relation bq1/bq1 = q1/q1 holds among bq1s, where bq1 is the Gaussian type distribution constant of site /. Using the decimation real-spacerenormalization group following the spin-rescaling method, the critical points and critical exponents of the Gaussian model are calculated on some Koch type curves and a family of the diamond-type hierar-chical (or DH) lattices. At the critical points, it is found that the nearest-neighbor interaction and the magnetic field of site i can be expressed in the form K’ = bq1/q1 and hq =0, respectively. it is also found that most critical exponents depend on the fractal dimensionality of a fractal system. For the family of the DH lattices, the results are identical with the exact results on translation symmetric lattices,

RBMDO Using Gaussian Mixture Model-Based Second-Order Mean-Value Saddlepoint Approximation

Actual engineering systems will be inevitably affected by uncertain factors.Thus,the Reliability-Based Multidisciplinary Design Optimization(RBMDO)has become a hotspot for recent research and application in complex engineering system design.The Second-Order/First-Order Mean-Value Saddlepoint Approximate(SOMVSA/-FOMVSA)are two popular reliability analysis strategies that are widely used in RBMDO.However,the SOMVSA method can only be used efficiently when the distribution of input variables is Gaussian distribution,which significantly limits its application.In this study,the Gaussian Mixture Model-based Second-Order Mean-Value Saddlepoint Approximation(GMM-SOMVSA)is introduced to tackle above problem.It is integrated with the Collaborative Optimization(CO)method to solve RBMDO problems.Furthermore,the formula and procedure of RBMDO using GMM-SOMVSA-Based CO(GMM-SOMVSA-CO)are proposed.Finally,an engineering example is given to show the application of the GMM-SOMVSA-CO method.

Color-texture segmentation using JSEG based on Gaussian mixture modeling

An improved approach for J-value segmentation （JSEG） is presented for unsupervised color image segmentation. Instead of color quantization algorithm, an automatic classification method based on adaptive mean shift （AMS） based clustering is used for nonparametric clustering of image data set. The clustering results are used to construct Gaussian mixture modelling （GMM） of image data for the calculation of soft J value. The region growing algorithm used in JSEG is then applied in segmenting the image based on the multiscale soft J-images. Experiments show that the synergism of JSEG and the soft classification based on AMS based clustering and GMM overcomes the limitations of JSEG successfully and is more robust.

Application of a Novel Method for Machine Performance Degradation Assessment Based on Gaussian Mixture Model and Logistic Regression

The currently prevalent machine performance degradation assessment techniques involve estimating a machine＇s current condition based upon the recognition of indications of failure features,which entail complete data collected in different conditions.However,failure data are always hard to acquire,thus making those techniques hard to be applied.In this paper,a novel method which does not need failure history data is introduced.Wavelet packet decomposition（WPD） is used to extract features from raw signals,principal component analysis（PCA） is utilized to reduce feature dimensions,and Gaussian mixture model（GMM） is then applied to approximate the feature space distributions.Single-channel confidence value（SCV） is calculated by the overlap between GMM of the monitoring condition and that of the normal condition,which can indicate the performance of single-channel.Furthermore,multi-channel confidence value（MCV）,which can be deemed as the overall performance index of multi-channel,is calculated via logistic regression（LR） and that the task of decision-level sensor fusion is also completed.Both SCV and MCV can serve as the basis on which proactive maintenance measures can be taken,thus preventing machine breakdown.The method has been adopted to assess the performance of the turbine of a centrifugal compressor in a factory of Petro-China,and the result shows that it can effectively complete this task.The proposed method has engineering significance for machine performance degradation assessment.