Statistical Signal Research Articles

Spectral Variability in Fixed Windows using Fractional Fourier Transform: Application in Power Spectral Density Estimation

In statistical signal processing, power spectral density estimation is a frequency domain analysis in which power contents of a signal are measured with respect to frequency components of that signal. The power estimation of a signal can be carried out more precisely by using a window with a narrower 3-dB bandwidth and higher side-lobe attenuation. Theoretically, these two spectral parameters show trade-off in variable windows and remain constant in fixed windows. In this work, spectral behavior of fixed windows has been elaborated using Fractional Fourier Transform (FRFT) keeping their inherent time domain behavior intact. The FRFT is an extension of conventional Fourier transform with an additional variable parameter, known as rotation angle, which makes it more flexible and useful in various signal processing applications viz. power estimation and designing of tunable transition band FIR filters. In this article, variability in 3-dB bandwidth and sidelobe attenuation of fixed windows has been achieved by exploiting the available flexibility in FRFT and obtained variability has been applied in the estimation of signal power. Simulation results demonstrate that both of these two spectral parameters are improved and hence, trade-off problem between resolution and spectral leakage in the power spectral density estimation is overcome upto an extent.

Vibration amplitude normalization enhanced fault diagnosis under conditions of variable speed and extremely limited samples

Intelligent fault diagnosis of rotating equipment is increasingly reliant on algorithms that are driven by big data. By contrast, signal processing was once widely utilized for fault diagnosis in machinery as a classical tool for signal analysis due to its capability to investigate the fault-related mechanism and almost no demand on the number of data samples. This investigation was motivated by the notion that signal processing and data-driven algorithms are combined to exploit their respective characteristics and strengths. Furthermore, in engineering practice, numerous complex factors such as time-variable operating conditions of equipment, non-stationary properties of signals, and extremely limited samples available for model training, can make it difficult to learn discriminative features from input data, thereby diminishing the diagnostic accuracy. In this paper, a novel framework of vibration amplitude normalization (VAN) enhanced fault diagnosis is proposed. Firstly, after dissects deeply the effects of the time-varying speed conditions on vibration signal and its characteristics, VAN technique is proposed for non-stationary signal processing to obtain the approximate stationary signal, so as to facilitate the subsequent state characteristics mining from the vibration signal. Then, two VAN enhanced fault diagnosis methods—i.e. signal amplitude normalization integrated with shallow learning by cascade and VAN integrated with deep learning by embedding—are developed to capture discriminative features from approximate stationary signal for fault diagnosis under conditions of variable speed and extremely limited samples. Finally, the feasibility and effectiveness of the proposed methods are verified using actual vibration datasets measured on test rig and in-site wind turbines. The number of samples required to achieve the same diagnostic accuracy is reduced by an average of 60%, demonstrating the superiority.

Numerical solution of stochastic Volterra integral equations based on uniform Haar wavelets by using direct method

Nowadays, wavelets have played a crucial role in approximating the solution of a wide range of problems arising in science and engineering. Wavelets have been used in numerous areas of applied mathematics as diverse as signal analysis, statistics, computer-aided geometric, image processing and numerical analysis. The uniform Haar wavelets are most widely used wavelets for solving stochastic integral equations, outperforming Legendre, Daubechies, etc. The uniform Haar wavelets are generated from pairs of piecewise constant functions and can be simply integrated. Furthermore, the uniform Haar functions are orthogonal and form a good transform basis. In this paper, we have proposed an efficient numerical method to solve a class of stochastic linear Volterra integral equations (SLVIEs) based on the uniform Haar wavelets. The aim of this paper is to apply numerical method to obtain approximate solution of SLVIEs. By using this method, the SLVIEs can be reduced to a linear system of algebraic equations. Also, the error analysis of this method is performed. Finally, some numerical examples are given to demonstrate pertinent features of this method. Furthermore, we compare obtained results from this method with the achieved results from relevant studies.

Chirp cyclic moment for chirp cyclostationary processes: Definitions and estimators

In high-mobility wireless communications and radar systems, a higher carrier frequency and higher moving speed/acceleration of terminals enhance the impact of the time-varying Doppler effect. This effect alters the cyclostationarity of the transmitted signal and characterizes the received signal as a chirp cyclostationary (CCS) signal. The generalized cyclic statistics of CCS signals are defined based on Fourier analysis, which is either zero-value or non-bandlimited, and is thus inefficient. In this study, the linear canonical transform (LCT), a generalized form of the Fourier transform, was used to address these issues. The moment function is a k-dimensional variable comprising a single time variable and k−1 lag variables. The chirp cyclic moment and the time-varying canonical spectrum were designed as the LCT of the moment with respect to the time and lag variables, respectively. Furthermore, an estimator of the chirp cyclic moment was defined, which is demonstrated to be asymptotic unbiased, asymptotic mean-square-consistent and asymptotic complex normal. Applications of the chirp cyclic moment in radar parameter estimation and electrocardiogram signal characterization were verified using simulated and real-life data.

A simple control and high accuracy measurement method of open-cell four-electrode conductivity electrode

The paper presents a simple control and high-accuracy measurement method for a four-electrode conductivity probe based on the principle of the bi-directional voltage pulse. The two-way differential AC (alternating current) pulse voltage signal for the reference resistance and solution resistance is modulated into the single DC stationary voltage response signal to drop the demand for software and hardware and effectively eliminate the influence of excitation voltage pulse amplitude on measurement accuracy, and then the synchronous rectification DC measurement is proposed without any control timing. Meanwhile, the mathematical expression between the single output DC voltage signal and the solution conductivity is given. The test results in the laboratory and in the field indicate that the relative error of the conductivity measurement is within 2.5% in a conductance range of 10 uS/cm to 200 mS/cm, and the proposed measurement method has a good application prospect in application.

Convergence Analysis of the Phase-Scheduled-Command FXLMS Algorithm with Phase Error

In this paper, a phase-scheduled-command filtered-x least mean square (FXLMS) algorithm with a phase error between the disturbance and command signal is analyzed in detail. The influence of the phase error on the control effort, convergence time constant and performance of convergence is explained for both stationary and nonstationary disturbance signal cases. An estimation ratio, in both stationary and nonstationary disturbance cases, of the pseudo-error MSE convergence performance is also developed and discussed. Simulation results were collected to verify the analysis. The results show that, for both stationary and nonstationary disturbance, the phase error may heavily increase the distance of the optimum vector from the initial value, leading to a large control effort, a large convergence time constant and poor convergence performance. The estimation ratio also has a satisfactory performance for estimating the influence of the phase error.

Statistical feature-based EEG signals classification using ANN and SVM classifiers for Parkinson’s disease detection

Parkinson's disease (PD) is a neurological disorder which is progressive in nature. Although there is no cure to this disease, symptomatic treatments are available. These treatments can slow the progressive development of the symptoms. Medications can treat some of the symptoms of the PD up to a great extent that in turn may help the patients to live a normal life. Besides these medications, the patients can also be provided with various therapies based on the types of their symptoms. But for providing any treatment, detection of its symptoms at an early stage is very important. This can reduce its future complexities considerably. Early diagnosis along with proper medications may treat the symptoms of PD significantly. This motivates to propose a new and effective methodology for detection and analysis of PD. In this work, an approach has been proposed for identification of PD patients by using Electroencephalogram (EEG) signals. Here, the EEG signals of normal persons and PD patients are processed in three stages. First, the raw EEG signals are pre-processed for removal of noises and artefacts present. Out of various techniques, Wavelet transform is used for this purpose. In the MATLAB environment, de-noising can be executed by using the in-built functions. Performances of the de-noising techniques are examined with the performance parameters namely Root Mean Square Error (RMSE) as well as Signal to Noise Ratio (SNR). In the second stage, statistical features are extracted from the pre-processed EEG signals. In this work, five statistical features are considered for performing the classification. In the final stage, the extracted features are classified using Artificial Neural Network (ANN) and Support Vector Machine (SVM) techniques. ANN is an efficient classifier that predicts the human brain's working manners. SVM on the other hand has been proven as one of the most prevailing classification algorithms that gives highly accurate and robust results. This is a novel approach of analyzing the performances of the classification techniques by evaluating the best performing feature. In both the classifiers accuracy, precision, sensitivity and specificity are calculated from the confusion matrix evaluated from the values of the statistical features. In ANN, results using six different training algorithms at different hidden layers are calculated and compared. This proves the training algorithm Levenberg-Marquardt back-propagation with hidden layer 20 as the best combination for performing the classification. From the results it is seen that both ANN and SVM classifiers provide significant classification accuracies of 94.7% and 96.5% respectively. Amongst the five considered features, Mean performs the best in terms of classification accuracy.

Enhanced Tidal Sensitivity of Seismicity Before the 2019 Magnitude 7.1 Ridgecrest, California Earthquake

AbstractEarth's crust is continuously subjected to oscillatory stress perturbations due to the solid Earth and ocean tides. The seismic response to such stress modulations carries information on earthquake physics and crustal properties. Experimental and observational studies suggested but could not demonstrate that the strength of tidal modulation of seismicity increases before large earthquakes. We tested this hypothesis by (a) developing a new, comprehensive 10‐year long earthquake catalog preceding the 6 July 2019 magnitude 7.1 Ridgecrest, CA earthquake, and (b) applied our novel method for extracting a statistical signal of tidal modulation. Our results show enhanced tidal sensitivity of seismicity along the fault starting about 1.5 years before the mainshock, corroborating the hypothesis. This observation suggests that small magnitude earthquakes may be used to gain insight into subtle changes in fault conditions, bringing new promise for studying the earthquake preparation process.

High-speed railway wheel polygon detection framework using improved frequency domain integration

Timely monitoring of wheel polygon is of great importance for the formulation of railway wheel maintenance strategies. In this study, a novel data-driven method for onboard and quantitative detection of wheel polygon is presented. First, the axle box acceleration (ABA) signal preprocessing method and stationarity test are introduced to select the relatively stationary signal from the measured data of ABA. Next, an iterative algorithm is developed to accurately extract the quasi-stationary ABA signals, representing each wheel rotation period. Then, an improved frequency domain integration method is developed to quantitatively capture the orders and roughness levels of the wheel polygon. Finally, the effectiveness and superiority of the proposed method is verified using the field-measured data of ABA and the wheel polygon in one cycle of wheel re-profiling. The results show that the proposed method can quantitatively capture the dominant characteristics of single- and multi-orders wheel polygons at different operating mileages with minimum and maximum absolute errors of 0.04 dB re 1 µm and −2.33 dB re 1 µm, respectively. The comparative analysis demonstrates that the proposed method outperforms the traditional time and frequency domain integration algorithms in the detailed characterisation of wheel polygon roughness levels.

Inter-aural separation during hearing by bilateral bone conduction stimulation

Cross-head transmission inherent in bone conduction (BC) hearing is one of the most important factors that limit the performance of BC binaural hearing compared to air conduction (AC) binaural hearing. In AC, cross-head transmission is imperceptible leading to a clear understanding of the nature and position of the sound source(s). In this study, the prominence of cross-head transmission in BC hearing is addressed using the fact that ipsilateral cochlear excitation can be canceled by controlled bilateral BC stimulation.A cancellation experiment was conducted on twenty participants with normal hearing at thirteen third-octave frequencies between 250 and 4000 Hz. Both stationary and transient BC stimulation at the mastoid was used. The technique employed multiple stages of masking enabling adjustments of the stimulation level and phase until the tones got canceled in the ipsilateral ear. In addition, the ear canal sound pressure was obtained for ipsilateral and contralateral BC stimulation in isolation, and with bilateral BC stimulation at perceptual cancellation.The inter-aural level differences of both the types of stimulations were found to be the same. Crosstalk was found to be the lowest around 2 kHz and the highest around 1 kHz. The unwrapped inter-aural phase difference from stationary signal cancellation showed an overall increase with frequency starting at around no difference (35°) at 250 Hz to reach 607° at 4 kHz. Cycle-adjusted inter-aural time difference was very low (61 µs) at 250 Hz and increased to 1.1 ms at 800 Hz before falling to 0.6 ms at 4 kHz. It was also found that the ear canal sound pressure was not cancelled at the same phase as the sound in the cochlea.

Robust estimators of two dimensional sinusoidal model parameters

In this paper we consider the two dimensional (2-D) sinusoidal model. This particular model has several applications in the statistical signal processing and in texture analysis. Extensive work has been done in developing several efficient procedures and establishing their properties. The least squares estimators (LSEs) are known to be the most efficient estimators in presence of additive noise. But it is observed that the LSEs are quite sensitive in presence of outliers. In this paper we propose to use the weighted least squares estimators (WLSEs) of the unknown parameters in presence of additive white noise. It is observed that in presence of outliers, the WLSEs are more robust than the least squares estimators (LSEs) and they behave very similarly to some of the other well known robust estimators, for example the least absolute deviation estimators (LADEs). It is observed that developing the properties of the LADEs is not immediate. We derive the consistency and asymptotic normality properties of the WLSEs. Extensive simulations have been performed to show the effectiveness of the proposed method. One synthetic data set has been analyzed to illustrate how the proposed method can be used in practice.

Automatic Classification of Field Winding Faults in Synchronous Motors Based on Bicoherence Image Segmentation and Higher Order Statistics of Stray Flux Signals

In this work, the application of the bicoherence (a squared normalized version of the bispectrum) of the stray flux signal is proposed as a way of detecting faults in the field winding of synchronous motors. These signals are analyzed both under the starting and at steady state regime. Likewise, two quantitative indicators are proposed, the first one based on the maximum values of the asymmetry and the kurtosis of the bicoherence matrix obtained from the flux signals and the second one relying on an algorithm based on the bicoherence image segmentation of the obtained pattern for each analyzed state. The results are analyzed through a comparative study for the two considered motor regimes, obtaining satisfactory results that sustain the potential application of the proposed methodology for the automatic field winding fault detection in real applications.

Simpsons paradox in the correlations between excess mortality and covid-19 injections: a case study of iatrogenic pandemic for elderly Australians

Background: Conflicting findings in correlation studies between COVID-19 injections and excess deaths have been published. Negative correlations with 2021 data appear to justify the official claim that COVID-19 injections reduce illness and death and therefore should be prioritized for vulnerable elderly (over-75s) Australians. This claim needs to be reviewed including 2022 data. Method: Simpson’s Paradox is illustrated to explain how the negative correlations, supporting injection effectiveness can come from 2021 data, while positive correlations, suggesting injection ineffectiveness, have come from inclusion of 2022 data. Excess deaths of Australian elderly in the COVID pandemic are analysed in detail for their statistical significance. Results: Negative correlations from 2021 data are refuted in this paper as false causality, because the results have insufficient temporal separation between cause and effect. Strong positive correlation (69 to 74 percent) in Australian data is confirmed when the effects of excess mortality are lagged optimally by 21 weeks after COVID-19 injections [1]. A strong statistical signal (2.5 standard deviations) is shown in this paper in the mortality of elderly Australians, who suffered the greatest relative harm from the injections, even when adjusted for agedependent high expected mortality. Conclusion: Earlier epidemiological evidence that COVID injections reduce illness and death is now methodologically invalidated, and the claim that the injections are beneficial for the vulnerable is refuted. The injections explain the mystery of significant numbers of non-COVID excess deaths. The Australian pandemic is shown to be iatrogenic particularly for the elderly, who have suffered disproportionate harm. Deliberately ignoring this clear evidence is tantamount to iatrogenic geronticide.

Adaptive Jamming Attack Detection Under Noise Uncertainty in mmWave Massive MIMO Systems

This paper addresses jamming attack detection issue in a millimeter Wave (mmWave) massive MIMO system under noise uncertainty. Specifically, we apply the generalized likelihood ratio test (GLRT) to develop a one-step GLRT scheme for detecting jamming attack under the homogeneous and partially homogeneous noise environments, and exploit training data to estimate the unknown noise statistical information and replace it with resulting estimation in deriving GLRT procedure to obtain adaptive GLRT detection scheme. We also design a two-step GLRT scheme, where we first assume the unknown noise statistical information is known, and derive GLRT based on test data, and then replace it by the sample covariance matrix based on training data only to achieve a fully adaptive jamming attack detector. With the help of statistical signal subspace analysis and composite hypothesis testing theories, we further examine the statistical distributions of the jamming attack detection schemes and present the closed-form expressions of false alarm and detection probabilities for the proposed schemes under different noise environments. Finally, we implement extensive simulations to validate the theoretical results and evaluate the detection efficiency under various parameters.

The Farey map exploited in the construction of a Farey mother wavelet

The wavelet analysis of a function passes through its so-called wavelet transform. Such a transform is mathematically defined as a convolution product of the analyzed function with another analyzing function known as the mother wavelet by involving the scale and the translation parameters. This means that the mother wavelet construction is the starting and major point in the wavelet analysis. Besides, the choice of the mother wavelet remains a major problem in wavelet applications such as statistical series, time series, signal, and image processing. This needs more candidates of mother wavelets to be constructed. The main aim of the present paper is to construct a new mother wavelet by exploiting the well-known Farey map. We showed indeed that such a map may be a mother wavelet owing properties such as admissibility, moments, 2-scale relation, and reconstruction rule already necessary in the wavelet analysis of functions. By a suitable choice of translation-dilation parameters on the original Farey map, we succeeded to prove the main properties of a Farey wavelet analysis. The constructed mother looks to be suitable for many complicated applications such as hyperbolic PDEs.

A Novel Data-Driven Fault Detection Method Based on Stable Kernel Representation for Dynamic Systems.

With the steady improvement of advanced manufacturing processes and big data technologies, modern industrial systems have become large-scale. To enhance the sensitivity of fault detection (FD) and overcome the drawbacks of the centralized FD framework in dynamic systems, a new data-driven FD method based on Hellinger distance and subspace techniques is proposed for dynamic systems. Specifically, the proposed approach uses only system input/output data collected via sensor networks, and the distributed residual signals can be generated directly through the stable kernel representation of the process. Based on this, each sensor node can obtain the identical residual signal and test statistic through the average consensus algorithms. In addition, this paper integrates the Hellinger distance into the residual signal analysis for improving the FD performance. Finally, the effectiveness and accuracy of the proposed method have been verified in a real multiphase flow facility.

Data-driven denoising of stationary accelerometer signals

Modern navigation solutions are largely dependent on the performances of the standalone inertial sensors, especially at times when no external sources are available. During these outages, the inertial navigation solution is likely to degrade over time due to instrumental noises sources, particularly when using consumer low-cost inertial sensors. Conventionally, model-based estimation algorithms are employed to reduce noise levels and enhance meaningful information, thus improving the navigation solution directly. However, guaranteeing their optimality often proves to be challenging as sensors performance differ in manufacturing quality, process noise modeling, and calibration precision. In the literature, most inertial denoising models are model-based when recently several data-driven approaches were suggested primarily for gyroscope measurements denoising. Data-driven approaches for accelerometer denoising task are more challenging due to the unknown gravity projection on the accelerometer axes. To fill this gap, we propose several learning-based approaches and compare their performances with prominent denoising algorithms, in terms of pure noise removal, followed by stationary coarse alignment procedure. Based on the benchmarking results, obtained in field experiments, we show that the learning-based models outperform traditional signal processing filtering in terms of pure inertial signal reconstruction. Moreover, they are shown to improve angular errors by one order of magnitude, given a navigation-related task.

Statistical Analysis and EEG Signal Filtering Using Design of Window Function Based on Optimization Methods

The window functions, which are widely used in Finite Impulse Response (FIR) digital filter design with the Fourier Series Methods, aim to eliminate the oscillations adversely affecting the filter performance that occur during the filter design. Window functions, which were developed with different methods in the literature, were designed with three different optimization techniques in this study. By using Particle Swarm Optimization (PSO), Grey Wolf Colony Optimization (GWCO), Cuckoo Search Optimization (CSO) algorithms, which are among current metaheuristic optimization methods, new window functions are designed for FIR digital filter design such that the designed new window functions have different window coefficients and design parameters. The difference of the designed window functions was analyzed with the Friedman and Wilcoxon tests, which are statistical data analysis methods, and the originality of the designed window functions was proven. FIR digital filters that can perform the same operation as the designed window functions have been produced and the results obtained by performing the filtering application of the EEG signal with the produced filters are presented in the study.

Genetic diversity and signatures of selection in four indigenous horse breeds of Iran

Indigenous Iranian horse breeds were evolutionarily affected by natural and artificial selection in distinct phylogeographic clades, which shaped their genomes in several unique ways. The aims of this study were to evaluate the genetic diversity and genomewide selection signatures in four indigenous Iranian horse breeds. We evaluated 169 horses from Caspian (n = 21), Turkmen (n = 29), Kurdish (n = 67), and Persian Arabian (n = 52) populations, using genomewide genotyping data. The contemporary effective population sizes were 59, 98, 102, and 113 for Turkmen, Caspian, Persian Arabian, and Kurdish breeds, respectively. By analysis of the population genetic structure, we classified the north breeds (Caspian and Turkmen) and west/southwest breeds (Persian Arabian and Kurdish) into two phylogeographic clades reflecting their geographic origin. Using the de-correlated composite of multiple selection signal statistics based on pairwise comparisons, we detected a different number of significant SNPs under putative selection from 13 to 28 for the six pairwise comparisons (FDR < 0.05). The identified SNPs under putative selection coincided with genes previously associated with known QTLs for morphological, adaptation, and fitness traits. Our results showed HMGA2 and LLPH as strong candidate genes for height variation between Caspian horses with a small size and the other studied breeds with a medium size. Using the results of studies on human height retrieved from the GWAS catalog, we suggested 38 new putative candidate genes under selection. These results provide a genomewide map of selection signatures in the studied breeds, which represent valuable information for formulating genetic conservation and improved breeding strategies for the breeds.

The therapeutic validation of long COVID

The therapeutic validation of long COVID