Statistical Signal Research Articles

Evaluating the performances of PI controller (2DOF) under linear and nonlinear operations of DFIG-based WECS: A simulation study

Owing to different stochastic characteristics of wind energy systems, there would commonly be uncertainties in the processes of wind energy conversion that may ultimately cause to severely degrade the quality of electric power production. These uncertainties include time-varying fluctuations of mechanical & electrical parameters that can be generated during both linear, and nonlinear operating behaviors of doubly fed induction generator-based wind energy conversion system (DFIG WECS). In order to handle a wind power quality problem, the previous studies largely focused on adjustment of mechanical parameters particularly based on blade pitch angle control by proposing different control strategies, and controller models. This work proposes a rarely studied electrical parameter control method that is particularly used to implement the regulation of rotor current components & electromagnetic torque in a DFIG WECS, based on Indirect Field Oriented Control (IFOC) strategy. Accordingly, a novel Proportional Integral controller model that employs a 2-Degree-of-Freedom [PI (2DOF)] is illustrated for an enhanced control of the rotor current components (quadrature & direct currents), electromagnetic torque under a 2MW DFIG WECS, which is operationally assumed to behave both linearly & nonlinearly. Herein, nonlinear operating behavior signifies a voltage dip that was assumed to be resulting when the system's normal (linear) voltage would suddenly drop by 90%. Furthermore, the overall model of the DFIG system was simulated in MATLAB-SIMULINK environment to evaluate the performances of PI controller (2DOF) under the system's stated operating behaviors. Based on the simulation signal statistics, the quadrature current distortion levels & DC mean values were mainly considered as the criteria for evaluating the controller performances. Finally, the proposed PI controller (2DOF) model has been tested to achieve an enhanced power quality in comparison with the traditional PI controller model.

RKHS Representations for Augmented Quaternion Random Signals: Application to Detection Problems

The reproducing kernel Hilbert space (RKHS) methodology has shown to be a suitable tool for the resolution of a wide range of problems in statistical signal processing both in the real and complex domains. It relies on the idea of transforming the original functional data into an infinite series representation by projection onto an specific RKHS, which usually simplifies the statistical treatment without any loss of efficiency. Moreover, the advantages of quaternion algebra over real-valued three and four-dimensional vector algebra in the modelling of multidimensional data have been proven useful in much relatively recent research. This paper accordingly proposes a generic RKHS framework for the statistical analysis of augmented quaternion random vectors, which provide a complete description of their second order characteristics. It will allow us to exploit the full advantages of the RKHS theory in widely linear processing applications, such as signal detection. In particular, we address the detection of a quaternion signal disturbed by additive Gaussian noise and the discrimination between two quaternion Gaussian signals in continuous time.

Time series modeling and forecasting by mathematical programming

We present an innovative approach to time-series analysis motivated by a desire to automate autoregressive integrated moving average (ARIMA) modeling and by extension, the process of building a reliable forecast. Our approach relies on optimization modeling and the decomposition of a time series into fixed seasonal effects, autoregressive (AR) terms, moving average (MA) terms, white noise, and any free variation outside of the selected model’s framework. The simultaneous selection of appropriately-lagged terms and estimation of their coefficients is achieved via mathematical programming to minimize normed errors subject to constraints that include a limit on the number of combined AR and MA terms to achieve desired parsimony. An estimator for white noise serves as a stationary reference signal for determining the MA coefficients and is modeled using wavelets, which facilitate the formulation of integer linear constraints. We report the results of numerical testing of this methodology on several real-world datasets and discuss the main implications for research and practice. We find that our models (i) achieve one step-ahead forecasting accuracy that outperforms other, widely-used interpretable methodologies, including random forests and gradient boosting models, (ii) offer interpretable results, and (iii) are computationally tractable.

A class of doubly stochastic shift operators for random graph signals and their boundedness

A class of doubly stochastic graph shift operators (GSO) is proposed, which is shown to exhibit: (i) lower and upper L2-boundedness for locally stationary random graph signals, (ii) L2-isometry for i.i.d. random graph signals with the asymptotic increase in the incoming neighbourhood size of vertices, and (iii) preservation of the mean of any graph signal – all prerequisites for reliable graph neural networks. These properties are obtained through a statistical consistency analysis of the proposed graph shift operator, and by exploiting the dual role of the doubly stochastic GSO as a Markov (diffusion) matrix and as an unbiased expectation operator. For generality, we consider directed graphs which exhibit asymmetric connectivity matrices. The proposed approach is validated through an example on the estimation of a vector field.

Revisiting the [C ii] 158 μm line-intensity mapping power spectrum from the EoR using non-uniform line-luminosity scatter

Abstract Detecting the line-intensity mapping (LIM) signal from the galaxies of the epoch of reionization is an emerging tool to constrain their role in reionization. Ongoing and upcoming experiments target the signal fluctuations across the sky to reveal statistical and astrophysical properties of these galaxies via signal statistics, e.g. the power spectrum. Here, we revisit the [C ii]$_{158 \, \mu \text{m}}$ LIM power spectrum under non-uniform line–luminosity scatter, which has a halo-mass variation of statistical properties. Line–luminosity scatter from a cosmological hydrodynamic and radiative transfer simulation of galaxies at $z$ = 6 is considered in this study. We test the robustness of different model frameworks that interpret the impact of the line-luminosity scatter on the signal statistics. We use a simple power-law model to fit the scatter and demonstrate that the mean luminosity–halo mass correlation fit cannot preserve the mean intensity of the LIM signal (hence the clustering power spectrum) under non-uniform scatter. In our case, the mean intensity changes by ∼48 per cent compared to the mean correlation fit in contrast to the general case with semi-analytical scatter. However, we find that the prediction for the mean intensity from the most-probable fit can be modelled robustly, considering the generalized and more realistic non-uniform scatter. We also explore the possibility of diminishing luminosity bias under non-uniform scatter, affecting the clustering power spectrum, although this phenomenon might not be statistically significant. Therefore, we should adopt appropriate approaches that can consistently interpret the LIM power spectrum from observations.

Multi-Channel LSTM-Capsule Autoencoder Network for Anomaly Detection on Multivariate Data

Deep learning techniques have recently shown promise in the field of anomaly detection, providing a flexible and effective method of modelling systems in comparison to traditional statistical modelling and signal processing-based methods. However, there are a few issues that Neural Networks (NN)s face, such as generalisation ability, requiring large volumes of labelled data to train effectively, and understanding spatial context in data. This paper introduces a novel NN architecture to tackle these problems, which utilises a Long-Short-Term-Memory (LSTM) encoder and Capsule decoder in a multi-channel input Autoencoder architecture for use on multivariate time series data. Experimental results show that using Capsule decoders increases the resilience of the model to overfitting and improves training efficiency, which is shown by the improvement of Mean Squared Error (MSE) on unseen data from an average of 10.61 to 2.08 for single channel architectures, and 10.08 to 2.05 for multi-channel architectures. Additionally, results also show that the proposed model can learn multivariate data more consistently, and was not affected by outliers in the training data. The proposed architecture was also tested on an open-source benchmark, where it achieved state-of-the-art performance in outlier detection, and performs best overall with a total accuracy of 0.494 over the metrics tested.

Introducing block-Toeplitz covariance matrices to remaster linear discriminant analysis for event-related potential brain–computer interfaces

Objective. Covariance matrices of noisy multichannel electroencephalogram (EEG) time series data provide essential information for the decoding of brain signals using machine learning methods. However, small datasets and high dimensionality make it hard to estimate these matrices. In brain–computer interfaces (BCI) based on event-related potentials (ERP) and a linear discriminant analysis (LDA) classifier, the state of the art covariance estimation uses shrinkage regularization. As this is a general covariance regularization approach, we aim at improving LDA further by better exploiting the domain-specific characteristics of the EEG to regularize the covariance estimates. Approach. We propose to enforce a block-Toeplitz structure for the covariance matrix of the LDA, which implements an assumption of signal stationarity in short time windows for each channel. Main results. An offline re-analysis of data collected from 213 subjects under 13 different event-related potential BCI protocols showed a significantly increased binary classification performance of this ‘ToeplitzLDA’ compared to shrinkage regularized LDA (up to 6 AUC points, p < 0.001) and Riemannian classification approaches (up to 2 AUC points, p < 0.001). In an unsupervised visual speller application, this improvement would translate to a relative reduction of spelling errors by 81% on average for 25 subjects. Additionally, aside from lower memory and reduced time complexity for LDA training, ToeplitzLDA proves to be robust against drastic increases of the number of temporal features. Significance. The proposed covariance estimation allows BCI researchers to improve classification rates and reduce calibration times of BCI protocols using event-related potentials and thus support the usability of corresponding applications. Its lower computational and memory needs could make it a valuable algorithm especially for mobile BCIs.

Identifying Epileptic Seizure by Optimized Feature Extraction Process Using the Method of Feature Fusion Technique

Epilepsy is a brain disorder that results in seizures; in general seizure is a suddenly occurring uncontrollable electrical disturbance in the brain. These disturbances in the brain can lead to changes in behaviour, feelings, movements, etc. It is highly essential for the patients suffering with epilepsy to be diagnosed and treated. The normal detection of epilepsy is done using EEG signals which are time consuming. This paper aims at proposing a methodology to diagnose epilepsy by the use of EEG signals by establishing a correlation between statistical calculations and EEG signals. A various set of features are applied to the epilepsy and non-epilepsy dataset. Features such as time domain frequency which include mean, skewness, variance, kurtosis, standard deviation, approximate entropy, zero crossings, power spectrum and frequency domain features that include signal energy and total signal area, average DWT coefficient, signal relation features and human brain graph features. Further, considering these features, feature fusion and optimization aka FFO is carried out which helps in analysing the features in an optimal way for further classification. Moreover, feature fusion and its optimization helps in exploring the new features that helps in enhancing the distinguish between classes. These features help diagnosis of the brain disorder in a very time efficient manner with higher accuracy. In this paper, we propose a feature fusion methodology for the most efficient working of the system.

Toeplitz Cyclic-MUSIC Algorithms for DOA Estimation of the SOCS Correlated Signals

This letter addresses the problem of direction-of-arrival (DOA) estimation for cyclostationary signal when the second-order cyclic statistics (SOCS) of signals are correlated. We first present a Toeplitz Cyclic-MUSIC algorithm for multichannels receiver by exploiting signal cyclostationarity. Based on cyclic autocorrelation of the received signal, a new pesudocyclic covriance matrix, which is Toeplitz, is constructed. The rank of Toeplitz matrix is equal to the number of signals even if the SOCS of signals are correlated. So the MUSIC algorithm can be used to estimate the DOAs of sources. Moreover, a single channel Toeplitz Cyclic-MUSIC algorithm for the the single-channel receiver is proposed to avoid the affect of channel inconsistency. The effectiveness of the proposed algorithms is verified by computer simulation, and the performance of the proposed algorithms is compared with the existing algorithms correspondingly.

Fast and Accurate Linear Fitting for an Incompletely Sampled Gaussian Function With a Long Tail [Tips &amp; Tricks

Fitting experiment data onto a curve is a common signal processing technique to extract data features and establish the relationship between variables. Often, we expect the curve to comply with some analytical function and then turn data fitting into estimating the unknown parameters of a function. Among analytical functions for data fitting, Gaussian function is the most widely used one due to its extensive applications in numerous science and engineering fields. To name just a few, Gaussian function is highly popular in statistical signal processing and analysis, thanks to the central limit theorem [1]; Gaussian function frequently appears in the quantum harmonic oscillator, quantum field theory, optics, lasers, and many other theories and models in Physics [2]; moreover, Gaussian function is widely applied in chemistry for depicting molecular orbitals, in computer science for imaging processing and in artificial intelligence for defining neural networks.

Blind Source Separation with Multi-Objective Optimization for Denoising

Blind Source Separation is an optimization method frequently used in statistical signal processing applications. There are many application areas such as ambient listening, denoising, signal detection, and so on. In this study, a new Strength Pareto Evolutionary Algorithm 2-based signal separation method is proposed, which combines Multi-Objective Optimization and Blind Source Separation algorithms. The proposed method has been tested for denoising, which is widely used in biomedical signal processing. That is, the Electrocardiogram (ECG) and White Gaussian Noise are mixed together with normally distributed random numbers and the original signals of the mixed signals are obtained again. To evaluate the performance of the proposed method and others (Multi-Objective Blind Source Separation and Independent Component Analysis), the Signal-to-Noise Ratio (SNR) of the ECG signal obtained from mixed signals has been measured. As a result of the simulation studies, it is seen that the performance of the proposed method is satisfactory.

A Concise Tutorial on Functional Analysis for Applications to Signal Processing

Functional analysis is a well-developed field in the discipline of Mathematics, which provides unifying frameworks for solving many problems in applied sciences and engineering. In particular, several important topics (e.g., spectrum estimation, linear prediction, and wavelet analysis) in signal processing had been initiated and developed through collaborative efforts of engineers and mathematicians who used results from Hilbert spaces, Hardy spaces, weak topology, and other topics of functional analysis to establish essential analytical structures for many subfields in signal processing. This paper presents a concise tutorial for understanding the theoretical concepts of the essential elements in functional analysis, which form a mathematical framework and backbone for central topics in signal processing, specifically statistical and adaptive signal processing. The applications of these concepts for formulating and analyzing signal processing problems may often be difficult for researchers in applied sciences and engineering, who are not adequately familiar with the terminology and concepts of functional analysis. Moreover, these concepts are not often explained in sufficient details in the signal processing literature; on the other hand, they are well-studied in textbooks on functional analysis, yet without emphasizing the perspectives of signal processing applications. Therefore, the process of assimilating the ensemble of pertinent information on functional analysis and explaining their relevance to signal processing applications should have significant importance and utility to the professional communities of applied sciences and engineering. The information, presented in this paper, is intended to provide an adequate mathematical background with a unifying concept for apparently diverse topics in signal processing. The main objectives of this paper from the above perspectives are summarized below: (1) Assimilation of the essential information from different sources of functional analysis literature, which are relevant to developing the theory and applications of signal processing. (2) Description of the underlying concepts in a way that is accessible to non-specialists in functional analysis (e.g., those with bachelor-level or first-year graduate-level training in signal processing and mathematics). (3) Signal-processing-based interpretation of functional-analytic concepts and their concise presentation in a tutorial format.

Estimation of Parameters on Probability Density Function Using Enhanced GLUE Approach.

The most essential process in statistical image and signal processing is the parameter estimation of probability density functions (PDFs). The estimation of the probability density functions is a contentious issue in the domains of artificial intelligence and machine learning. The study examines challenges related to estimating density functions from random variables. Based on minimal predictions regarding densities, the study discusses a framework for evaluating probability density functions. During the Bayesian approach, which is to generate correct samplings that reflect the probability aspect of the variables, sampling is widely used to estimate as well as define the probabilistic model of unknown variables. Because of its effectiveness and extensive application, the generalized likelihood uncertainty estimation (GLUE) method has earned the most popularity among the various methodologies. The Bayesian technique allows parameters of the model to be estimated using prior expertise in the parameter results and experimental observations. The study uses a number of engineering issues that were lately looked into to illustrate the effectiveness of the upgraded GLUE. As the focus is on the examination of sampling effectiveness in view of engineering components, only a brief summary is provided to describe every challenge. The suggested GLUE method's outcomes are contrasted with those obtained using MCMC. Nevertheless, using the GLUE approach, the model's mean squared error of prediction is substantially higher than that of the previous algorithms. The methods' results are affected by the assumptions being made on parameter values in advance. The concepts of prediction accuracy, as well as the utility of geometric testing, are presented. Such notions are valuable in demonstrating that the GLUE approach defines an inconsistent and incoherent statistical inference process.

Performance of subspace-based algorithms associated with the sample sign covariance matrix

Complex-valued data in statistical signal processing applications have many advantages over their real-valued counterparts. It allows us to use the complete statistical information of the signal thanks to its statistical property of non-circularity. This paper presents a general framework for developing asymptotic theoretical results on the distribution-free sample sign covariance matrix (SSCM) under circular complex-valued elliptically symmetric (C-CES) and non-circular CES (NC-CES) multidimensional distributed data. It extends some partial asymptotic results on SSCM derived for real elliptically symmetric (RES) distributed data. In particular closed-form expressions of the first and second-order of the SSCM are derived for arbitrary spectra of eigenvalues for C-CES and NC-CES distributed data which facilitates the derivation of numerous statistical properties. Then, the asymptotic distributions of associated projectors are deduced, which are applied in the study of asymptotic performance analysis of SSCM-based subspace algorithms, followed by a comparison to the asymptotic results derived using Tyler's M estimate. However, a more in-depth analytical analysis of the efficiency of the SSCM relative to Tyler's M estimate is performed, yielding that the performances of the SSCM and Tyler's M estimate are close for a high-dimensional data and not too small dimension of the principal component space. We conclude therefore that, although the SSCM is inefficient relative to Tyler's M estimate, it is of great interest from the point of view of its lower computational complexity for high-dimensional data. Finally, numerical results illustrating the theoretical analysis are presented through the direction-of-arrival (DOA) estimation CES data models.

Deep learning categorization of infrasound array data.

We develop a deep learning-based infrasonic detection and categorization methodology that uses convolutional neural networks with self-attention layers to identify stationary and non-stationary signals in infrasound array processing results. Using features extracted from the coherence and direction-of-arrival information from beamforming at different infrasound arrays, our model more reliably detects signals compared with raw waveform data. Using three infrasound stations maintained as part of the International Monitoring System, we construct an analyst-reviewed data set for model training and evaluation. We construct models using a 4-category framework, a generalized noise vs non-noise detection scheme, and a signal-of-interest (SOI) categorization framework that merges short duration stationary and non-stationary categories into a single SOI category. We evaluate these models using a combination of k-fold cross-validation, comparison with an existing "state-of-the-art" detector, and a transportability analysis. Although results are mixed in distinguishing stationary and non-stationary short duration signals, f-scores for the noise vs non-noise and SOI analyses are consistently above 0.96, implying that deep learning-based infrasonic categorization is a highly accurate means of identifying signals-of-interest in infrasonic data records.

Adaptive beamformer with echo statistics

Delay-and-sum (DAS) beamforming is commonly used in commercial scanners and computationally efficient for real-time imaging. However, the ability to suppress off-axis signals is limited. A minimum variance (MV) beamformer realizes a superior performance in suppression of off-axis signals and improves lateral resolution significantly. On the other hand, MV degrades the contrast-to-noise ratio (CNR) compared to DAS because it alters speckle statistics. In this study, we developed a method for improvement of CNR in MV beamforming by evaluating envelope statistics of echo signals. It is well known that the envelope statistic of speckle echoes from a random medium obeys the Rayleigh distribution. The echo envelope statistics were evaluated using the shape parameter of the Nakagami distribution. The proposed beamformer is worked as DAS for speckle echoes and MV for non-speckle echoes by referring to the Nakagami shape parameter. In the phantom experiment, the lateral resolution of MV was 0.18 mm, which was significantly better than 0.53 mm obtained by DAS. However, CNR was degraded from 6.73 dB to 4.05 dB by MV. The proposed beamformer realized a lateral resolution of 0.25 mm, which was significantly better than DAS, with a CNR value of 6.03 dB, which was comparable to DAS.

Tracy-Widom Distribution for Heterogeneous Gram Matrices With Applications in Signal Detection

Detection of the number of signals corrupted by high-dimensional noise is a fundamental problem in signal processing and statistics. This paper focuses on a general setting where the high-dimensional noise has an unknown complicated heterogeneous variance structure. We propose a sequential test which utilizes the edge singular values (i.e., the largest few singular values) of the data matrix. It also naturally leads to a consistent sequential testing estimate of the number of signals. We describe the asymptotic distribution of the test statistic in terms of the Tracy-Widom distribution. The test is shown to be accurate and have full power against the alternative, both theoretically and numerically. The theoretical analysis relies on establishing the Tracy-Widom law for a large class of Gram type random matrices with non-zero means and completely arbitrary variance profiles, which can be of independent interest.

An Intelligent Detection Logic for Fan-Blade Damage to Wind Turbines Based on Mounted-Accelerometer Data

Many wind turbines operate in harsh marine or shore environments. This study assists industry by establishing a real-time condition-monitoring and fault-detection system, with rules for recognizing a wind turbine’s abnormal operation mainly caused by different types of fan-blade damage. This system can ensure ideal wind turbine operation by monitoring the health status of the blades, detecting sudden anomalies, and performing maintenance almost in real time. This is especially significant for wind farms in areas subject to frequent natural disasters (e.g., earthquakes and typhoons). Turbines might fail to endure these because the manufacturers have built them according to the standards developed for areas less prone to natural disasters. The system’s rules are established by utilising concepts and methods from data analytics, digital signal processing (DSP) and statistics to analyse data from the accelerometer, which measures the vibration signals in three dimensions on the platform of the wind turbine’s base. The patterns for those cases involving fan-blade damage are found to establish the rules. With the anomalies detected and reported effectively, repairs and maintenance can be carried out on the faulty wind turbines. This enables ‘maintenance by prediction’ actions for unplanned maintenance as a supplement to the ‘predictive maintenance’ tasks for regular planned maintenance.

Deep Sparse Representation Based Image Restoration With Denoising Prior

As a powerful statistical signal modeling technique, sparse representation has been widely used in various image restoration (IR) applications. The sparsity-based methods have achieved leading performance in the past few decades. However, in recent years it has been surpassed by other methods, especially the recent deep learning based methods. In this paper, we address the question that whether sparse representation can be competitive again. The way we answer this question is to redesign it with a deep architecture. To be specific, we propose an end-to-end deep architecture that follows the process of the sparse representation based IR. In particular, we learn a sparse convolutional dictionary to replace the traditional dictionary, and a convolutional neural network (CNN) denoising prior to replace the image prior. Through end-to-end training, the parameters in convolutional dictionary and CNN denoiser can be jointly optimized. Experimental results on several representative IR tasks, including image denoising, deblurring and super-resolution, demonstrate that the proposed deep network can achieve superior performance against state-of-the-art model-based and learning-based methods.

Deep Learning-Based 2-D Frequency Estimation of Multiple Sinusoidals.

Frequency estimation of 2-D multicomponent sinusoidal signals is a fundamental issue in the statistical signal processing community that arises in various disciplines. In this article, we extend the DeepFreq model by modifying its network architecture and apply it to 2-D signals. We name the proposed framework 2-D ResFreq. Compared with the original DeepFreq framework, the 2-D convolutional implementation of the matched filtering module facilitates the transformation from time-domain signals to frequency-domain signals and reduces the number of network parameters. The additional upsampling layer and stacked residual blocks are designed to perform superresolution. Moreover, we introduce frequency amplitude information into the optimization function to improve the amplitude accuracy. After training, the signals in the test set are forward-mapped to 2-D accurate and high-resolution frequency representations. Frequency and amplitude estimation are achieved by measuring the locations and strengths of the spectral peaks. We conduct numerical experiments to demonstrate the superior performance of the proposed architecture in terms of its superresolution capability and estimation accuracy.