Presence Of non-Gaussian Noise Research Articles

Identification, Decomposition and Segmentation of Impulsive Vibration Signals with Deterministic Components-A Sieving Screen Case Study.

Condition monitoring is a well-established field of research; however, for industrial applications, one may find some challenges. They are mostly related to complex design, a specific process performed by the machine, time-varying load/speed conditions, and the presence of non-Gaussian noise. A procedure for vibration analysis from the sieving screen used in the raw material industry is proposed in the paper. It is more for pre-processing than the damage detection procedure. The idea presented here is related to identification and extraction of two main types of components: (i) deterministic (D)—related to the unbalanced shaft(s) and (ii) high amplitude, impulsive component randomly (R) appeared in the vibration due to pieces of ore falling down of moving along the deck. If we could identify these components, then we will be able to perform classical diagnostic procedures for local damage detection in rolling element bearing. As deterministic component may be AM/FM modulated and each impulse may appear with different amplitude and damping, there is a need for an automatic procedure. We propose a method for signal processing that covers two main steps: (a) related to R/D decomposition and including signal segmentation to neglect AM/FM modulations, iterative sine wave fitting using the least square method (for each segment), signal filtering technique by subtraction fitted sine from the raw signal, the definition of the criterion to stop iteration by residuals analysis, (b) impulse segmentation and description (beginning, end, max amplitude) that contains: detection of the number of impulses in a decomposed random part of the raw signal, detection of the max value of each impulse, statistical analysis (probability density function) of max value to find regime-switching), modeling of the envelope of each impulse for samples that protrude from the signal, extrapolation (forecasting) envelope shape for samples hidden in the signal. The procedure is explained using simulated and real data. Each step is very easy to implement and interpret thus the method may be used in practice in a commercial system.

Power System Mode Metering in the Presence of Non-Gaussian Noise

This letter presents a robust generalized correlation approach for monitoring of power system oscillatory modes. Due to the non-Gaussian nature of measurement noise, and presence of impulsive outliers, the wide-sense stationarity assumption of power system measurement data is violated even under ambient conditions thus limiting the effectiveness of conventional autocorrelation based approaches in mode metering. The fundamental definition of correlation function for power system measurements is extended to a generalized correlation function in order to incorporate higher order statistics into existing modal estimation technique. Simulations on synthetic and real-life test signals have been conducted to demonstrate the robustness of the proposed method.

Informative frequency band selection in the presence of non-Gaussian noise – a novel approach based on the conditional variance statistic with application to bearing fault diagnosis

In this paper a novel approach to local damage detection in the presence of non-Gaussian impulsive noise is introduced. The proposed approach is applied to bearing damage detection in technological processes of ore defragmentation. From the signal processing perspective, this corresponds to the identification of cyclic and non-cyclic impulses in the vibrations. A new informative frequency band selector based on the conditional variance statistic is proposed and studied in details. In particular, it is shown that the proposed method is superior to many common alternatives based e.g. on Kurtosis or Alpha selectors, especially when non-cyclic impulses dominate over the cyclic ones. Moreover, it is shown that the approach based on conditional variance is simple to implement and much more robust concerning various problem specifications like cyclic to non-cyclic impulse number ratio or amplitude ratio. The Monte Carlo method is used to validate the robustness of the method in the statistical sense.

A Novel Approach to 3D-DOA Estimation of Stationary EM Signals Using Convolutional Neural Networks.

This paper proposes a novel three-dimensional direction-of-arrival (3D-DOA) estimation method for electromagnetic (EM) signals using convolutional neural networks (CNN) in a Gaussian or non-Gaussian noise environment. First of all, in the presence of Gaussian noise, four output covariance matrices of the uniform triangular array (UTA) are normalized and then fed into four neural networks for 1D-DOA estimation with identical parameters in parallel; then four 1D-DOA estimations of the UTA can be obtained, and finally, the 3D-DOA estimation could be obtained through post-processing. Secondly, in the presence of non-Gaussian noise, the array output covariance matrices are normalized by the infinity-norm and then processed in Gaussian noise environment; the infinity-norm normalization could effectively suppress impulsive outliers and then provide appropriate input features for the neural network. In addition, the outputs of the neural network are controlled by a signal monitoring network to avoid misjudgments. Comprehensive simulations demonstrate that in Gaussian or non-Gaussian noise environment, the proposed method is superior and effective in computation speed and accuracy in 1D-DOA and 3D-DOA estimations, and the signal monitoring network could also effectively control the neural network outputs. Consequently, we can conclude that CNN has better generalization ability in DOA estimation.

Robust identification for fault detection in the presence of non-Gaussian noises: application to hydraulic servo drives

Intensive research in the field of mathematical modeling of hydraulic servo systems has shown that their mathematical models have many important details which cannot be included in the model. Due to impossibility of direct measurement or calculation of dimensions of certain components, leakage coefficients or friction coefficients, it was supposed that parameters of the hydraulic servo system are random. On the other side, it has been well known that the hydraulic servo system can be approximated by a linear model with time-varying parameters. An estimation of states and time-varying parameters of linear state-space models is of practical importance for fault diagnosis and fault-tolerant control. Previous works on this topic consider estimation in Gaussian noise environment, but not in the presence of outliers. The known fact is that the measurements have inconsistent observations with the largest part of the observation population (outliers). They can significantly make worse the properties of linearly recursive algorithms which are designed to work in the presence of Gaussian noises. This paper proposes the strategy of parameter–state robust estimation of linear state-space models in the presence of all possible faults and non-Gaussian noises. Because of its good features in robust filtering, Masreliez–Martin filter represents a cornerstone for realization of the robust algorithm. The good features of the proposed robust algorithm to identification of the hydraulic servo system are illustrated by intensive simulations.

Enhanced Frequency Band Entropy Method for Fault Feature Extraction of Rolling Element Bearings

Frequency band entropy (FBE) has been proved usable in the fault diagnosis of rolling bearings, but its performance is poor in the presence of non-Gaussian noise and a low signal-to-noise ratio. In order to extract the transient impulsive signals more effectively, wavelet packet transform (WPT) is considered as an alternative method for signal decomposition. Therefore, by introducing WPT into FBE, this article introduces an enhanced FBE (EFBE) adopting WPT as the filter of FBE to overcome the shortcomings of the original FBE. Then, the depth of EFBE is optimized using adaptive resonance bandwidth and power amplitude spectrum entropy (PASE). Third, a novel method based on the indicator PASE is introduced to select the optimal node of EFBE. Finally, the filtered signal is combined with the envelope power spectrum to extract the fault feature frequency. In addition, an evaluation indicator is proposed to evaluate the performance of the EFBE. The simulation and cases are used to demonstrate the effectiveness and improved performance of the EFBE compared with the original FBE and other typical methods. The results show that the EFBE can detect various rolling bearing failures and implement its fault diagnosis effectively.

Denoising Hyperspectral Images Using an Improved SSTV Correntropy based Method in the Presence of Non-Gaussian Noise

Denoising hyperspectral images (HSIs) has attracted a lot of attention in remote sensing due to its high significance in the enhancement of the quality of these images. The present methods for denoising HSIs are generally focused on Gaussian noisy environments while in practical cases, non-Gaussian noise usually exists in HSIs. In order to consider this fact, first a general model for noise is introduced. This model constitutes a non-Gaussian noise accompanied with sparse noise. Later, we use information theoretic learning criteria to introduce a cost function based on Correntropy which is formulated as an optimization problem in order to solve the denoising problem. Finally, this problem is solved using the Half-Quadratic algorithm. The results of the experiment with real data show that the proposed method can significantly reduce the noise in these images which is actually a more general form of noise.

Робастна ідентифікація об'єктів на основі мінімізації комбінованого функціоналу

Розглянуто задачу ідентифікації параметрів лінійного об'єкта за наявністю негаусівських завад на основі мінімізації комбінованого функціоналу, який поєднує властивості МНК та МНМ та забезпечує робастність одержуваних оцінок. Досліджено статистичні властивості градієнтного алгоритму ідентифікації, в результаті чого визначено умови його збіжності в середньому і середньоквадратичному. Для дослідження властивостей в алгоритму використано функції Ляпунова. Отримано аналітичні оцінки неасимпотичних та асимптотичних значень помилки оцінювання параметрів і точності ідентифікації. Показано, що ці значення помилки оцінювання і точності ідентифікації залежать від вибору параметра змішування. Отримані оцінки є досить загальними і залежать від статистичних характеристик корисних сигналів і завад. Тому для їх практичного застосування слід скористатися оцінками цих параметрів. Результати експериментального дослідження властивостей алгоритму при ідентифікації об’єкту, вихід якого вимірюється з незалежним шумом з розподілом Релея, некорельованим з сигналами, свідчать про ефективність підходу, що розвивається. Отримані в роботі оцінки дозволяють досліднику при вирішенні практичних завдань попередньо оцінити можливості досліджуваного алгоритму і ефективність його застосування.

Robust DOA Estimator Under Non-Gaussian Noise and Insufficient Sample Support

In this paper, we develop a robust algorithm for improving the accuracy of direction-of-arrival estimation under non-Gaussian noise and insufficient sample support. (The number of sensors is large, while the number of samples is relatively small.) Unlike the traditional peak-search techniques, our approach is based on an enhanced covariance matrix estimation, where we exploit the thoughts of the M-estimator and the shrinkage estimator, but devise a new target matrix equation and iterative solution procedure. Numerical results indicate that the proposed algorithm significantly performs better than the existing methods in the presence of non-Gaussian noise and finite samples.

JOINT ESTIMATION OF STATES AND PARAMETERS OF LINEAR SYSTEMS WITH PARAMETER FAULTS UNDER NON-GAUSSIAN NOISES

Joint estimation of states and time-varying parameters of linear state space models is of practical importance for the fault diagnosis and fault tolerant control. Previous works on this topic consider the joint estimation in the Gaussian noise environment, but not in the presence of outliers. The known fact is that the measurements have inconsistent observations with the largest part of the observation population (outliers). They can significantly make worse the properties of linearly recursive algorithms which are designed to work in the presence of Gaussian noises. This paper proposes the strategy of the joint parameter-state robust estimation of linear state space models in the presence of non-Gaussian noises. The case of parameter-dependent matrices is considered. Because of its good features in robust filtering, the extended Masreliez-Martin filter represents a cornerstone for realization of the robust algorithms for joint state-parameter estimation of linear time-varying stochastic systems in the presence of non-Gaussian noises. The good features of the proposed robust algorithm for joint estimation of linear time-varying stochastic systems are illustrated by intensive simulations.

Optimal learning with Gaussians and correntropy loss

Correntropy-based learning has achieved great success in practice during the last decades. It is originated from information-theoretic learning and provides an alternative to classical least squares method in the presence of non-Gaussian noise. In this paper, we investigate the theoretical properties of learning algorithms generated by Tikhonov regularization schemes associated with Gaussian kernels and correntropy loss. By choosing an appropriate scale parameter of Gaussian kernel, we show the polynomial decay of approximation error under a Sobolev smoothness condition. In addition, we employ a tight upper bound for the uniform covering number of Gaussian RKHS in order to improve the estimate of sample error. Based on these two results, we show that the proposed algorithm using varying Gaussian kernel achieves the minimax rate of convergence (up to a logarithmic factor) without knowing the smoothness level of the regression function.

The Cauchy Conjugate Gradient Algorithm with Random Fourier Features

Random Fourier mapping (RFM) in kernel adaptive filters (KAFs) provides an efficient method to curb the linear growth of the dictionary by projecting the original input data into a finite-dimensional space. The commonly used measure in RFM-based KAFs is the minimum mean square error (MMSE), which causes performance deterioration in the presence of non-Gaussian noises. To address this issue, the minimum Cauchy loss (MCL) criterion has been successfully applied for combating non-Gaussian noises in KAFs. However, these KAFs using the well-known stochastic gradient descent (SGD) optimization method may suffer from slow convergence rate and low filtering accuracy. To this end, we propose a novel robust random Fourier features Cauchy conjugate gradient (RFFCCG) algorithm using the conjugate gradient (CG) optimization method in this paper. The proposed RFFCCG algorithm with low complexity can achieve better filtering performance than the KAFs with sparsification, such as the kernel recursive maximum correntropy algorithm with novelty criterion (KRMC-NC), in stationary and non-stationary environments. Monte Carlo simulations conducted in the time-series prediction and nonlinear system identification confirm the superiorities of the proposed algorithm.

Learning with correntropy-induced losses for regression with mixture of symmetric stable noise

In recent years, correntropy and its applications in machine learning have been drawing continuous attention owing to its merits in dealing with non-Gaussian noise and outliers. However, theoretical understanding of correntropy, especially in the statistical learning context, is still limited. In this study, within the statistical learning framework, we investigate correntropy based regression in the presence of non-Gaussian noise or outliers. Motivated by the practical way of generating non-Gaussian noise or outliers, we introduce mixture of symmetric stable noise, which include Gaussian noise, Cauchy noise, and their mixture as special cases, to model non-Gaussian noise or outliers. We demonstrate that under the mixture of symmetric stable noise assumption, correntropy based regression can learn the conditional mean function or the conditional median function well without resorting to the finite-variance or even the finite first-order moment condition on the noise. In particular, for the above two cases, we establish asymptotic optimal learning rates for correntropy based regression estimators that are asymptotically of type $\mathcal{O}(n^{-1})$. These results justify the effectiveness of the correntropy based regression estimators in dealing with outliers as well as non-Gaussian noise. We believe that the present study completes our understanding towards correntropy based regression from a statistical learning viewpoint, and may also shed some light on robust statistical learning for regression.

NARX Model Identification Using Correntropy Criterion in the Presence of Non-Gaussian Noise

In past years, the system identification area has emphasized the identification of nonlinear dynamic systems. In this field, polynomial nonlinear autoregressive with exogenous (NARX) models are widely used due to flexibility and prominent representation capabilities. However, the traditional identification algorithms used for model selection and parameter estimation with NARX models have some limitation in the presence of non-Gaussian noise, since they are based on second-order statistics that tightly depend on the assumption of Gaussianity. In order to solve this dependence, a novel identification method called simulation correntropy maximization with pruning (SCMP) based on information theoretic learning is introduced by this paper. Results obtained in non-Gaussian noise environment in three experiments (numerical, benchmark data set and measured data from a real plant) are presented to validate the performance of the proposed approach when compared to other similar algorithms previously reported in the literature, e.g., forward regression with orthogonal least squares and simulation error minimization with pruning. The proposed SCMP method has shown increased accuracy and robustness for three different experiments.

Joint correntropy metric weighting and block diagonal regularizer for robust multiple kernel subspace clustering

Nonlinear kernel-based subspace clustering methods that can reveal the multi-cluster nonlinear structure of samples are an emerging research topic. However, the existing kernel subspace clustering methods have the following three flaws: 1) their clustering performance is largely determined by the chosen kernel function; 2) they may lack robustness in the presence of non-Gaussian noise and impulsive noise; and 3) their learned affinity matrix can not hold the desired block diagonal property for clustering purpose, which possibly leads to incorrect clustering when using spectral clustering. In this paper, we propose a Joint Robust Multiple Kernel Subspace Clustering (JMKSC) method for data clustering, which has two primary innovations. First, our multiple kernel weighting strategy introduces the correntropy metric weighting instead of a fixed, or inappropriately assigned weighting, which is more robust to the non-Gaussian noise and contributes to learning the optimal consensus kernel. Second, our method encourages acquiring an affinity matrix with the optimal block diagonal property based on the block diagonal regularizer (BDR) and the self-expressiveness property. Experiments on several different types of datasets confirm that the proposed JMKSC significantly outperforms several state-of-the-art single kernel and multiple kernel subspace clustering methods in terms of accuracy, NMI and purity.

Robust Kalman-Type Filter for Non-Gaussian Noise: Performance Analysis With Unknown Noise Covariances

The Kalman filter (KF) is optimal with respect to minimum mean square error (MMSE) if the process noise and measurement noise are Gaussian. However, the KF is suboptimal in the presence of non-Gaussian noise. The maximum correntropy criterion Kalman filter (MCC-KF) is a Kalman-type filter that uses the correntropy measure as its optimality criterion instead of MMSE. In this paper, we modify the correntropy gain in the MCC-KF to obtain a new filter that we call the measurement-specific correntropy filter (MSCF). The MSCF uses a matrix gain rather than a scalar gain to provide better selectivity in the way that it handles the innovation vector. We analytically compare the performance of the KF with that of the MSCF when either the measurement or process noise covariance is unknown. For each of these situations, we analyze two mean square errors (MSEs): the filter-calculated MSE (FMSE) and the true MSE (TMSE). We show that the FMSE of the KF is less than that of the MSCF. However, the TMSE of the KF is greater than that of the MSCF under certain conditions. Illustrative examples are provided to verify the analytical results.

Convergence Analysis of Zero Attracting Natural Gradient Non-Parametric Maximum Likelihood Algorithm

Recently, a zero-attractor natural gradient non-parametric maximum likelihood (ZA-NG-NPML) algorithm has been proposed for sparse channel estimation in the presence of non-Gaussian noise. The ZA-NG-NPML outperforms existing sparse channel estimation algorithms in the presence of non-Gaussian noise in terms of mean square error (MSE) and convergence. In this brief, a rigorous second order convergence analysis of ZA-NG-NPML algorithm is presented and upper bound on the steady state mean square deviation of active and inactive taps is derived. Further, we also derive the upper bound on the steady state excess MSE for ZA-NG-NPML. Simulation results validate the derived upper bound.

Adaptive Extended Kalman Filter with Correntropy Loss for Robust Power System State Estimation.

Monitoring the current operation status of the power system plays an essential role in the enhancement of the power grid for future requirements. Therefore, the real-time state estimation (SE) of the power system has been of widely-held concern. The Kalman filter is an outstanding method for the SE, and the noise in the system is generally assumed to be Gaussian noise. In the actual power system however, these measurements are usually disturbed by non-Gaussian noises in practice. Furthermore, it is hard to get the statistics of the state noise and measurement noise. As a result, a novel adaptive extended Kalman filter with correntropy loss is proposed and applied for power system SE in this paper. Firstly, correntropy is used to improve the robustness of the EKF algorithm in the presence of non-Gaussian noises and outliers. In addition, an adaptive update mechanism of the covariance matrixes of the measurement and process noises is introduced into the EKF with correntropy loss to enhance the accuracy of the algorithm. Extensive simulations are carried out on IEEE 14-bus and IEEE 30-bus test systems to verify the feasibility and robustness of the proposed algorithm.

Factored-form Kalman-like implementations under maximum correntropy criterion

Abstract The maximum correntropy criterion (MCC) methodology is recognized to be a robust filtering strategy with respect to outliers and shown to outperform the classical Kalman filter (KF) for estimation accuracy in the presence of non-Gaussian noise. However, the numerical stability of the newly proposed MCC-KF estimators in finite precision arithmetic is seldom addressed. In this paper, a family of factored-form (square-root) algorithms is derived for the MCC-KF and its improved variant, respectively. The family traditionally consists of three factored-form implementations: (i) Cholesky factorization-based algorithms, (ii) modified Cholesky, i.e. UD-based methods, and (iii) the recently established SVD-based filtering. All these strategies are commonly recognized to enhance the numerical robustness of conventional filtering with respect to roundoff errors and, hence, they are the preferred implementations when solving applications with high reliability requirements. Previously, only Cholesky-based IMCC-KF algorithms have been designed. This paper enriches a factored-form family by introducing the UD- and SVD-based methods as well. A special attention is paid to array algorithms that are proved to be the most numerically stable and, additionally, suitable for parallel implementations. The theoretical properties are discussed and numerical comparison is presented for determining the most reliable implementations.

Robusna identifikacija za detekciju otkaza i dijagnostiku hidrauličkog servo cilindra

Intensive research in the field of mathematical modeling of hydraulic servo systems has shown that their mathematical models have many important details which cannot be included in the model. Due to impossibility of direct measurement or calculation of dimensions of certain components, leakage coefficients or friction coefficients, it was supposed that parameters of the hydraulic servo system are random (stochastic nature). On the other side, it has been well known that the hydraulic servo cylinder can be approximated by a linear model with time-varying parameters. An estimation of states and time-varying parameters of linear state space models is of practical importance for fault diagnosis and fault tolerant control. Previous works on this topic consider estimation in Gaussian noise environment, but not in the presence of outliers. The known fact is that the measurements have inconsistent observations with the largest part of the observation population (outliers). They can significantly make worse the properties of linearly recursive algorithms which are designed to work in the presence of Gaussian noises. This paper proposes the strategy of parameter-state robust estimation of linear state space models in presence of non-Gaussian noises. The case of robust estimation of states and parameters of linear systems with parameter faults is considered. Because of its good features in robust filtering, the extended Masreliez-Martin filter represents a cornerstone for realization of the robust algorithm. The good features of the proposed robust algorithm to identification of the hydraulic servo cylinder are illustrated by intensive simulations.