Power Spectral Density Estimation Research Articles

Acoustic emissions in vertebral cortical shell failure

Understanding the initiation of bony failure is critical in assessing the progression of bone fracture and in developing injury criteria. Detection of acoustic emissions in bone can be used to identify fractures more sensitively and at an earlier inception time compared to traditional methods. However, high rate loading conditions, complex specimen-device interaction or geometry may cause other acoustic signals. Therefore, characterization of the isolated local acoustic emission response from cortical bone fracture is essential to distinguish its characteristics from other potential acoustic sources. This work develops a technique to use acoustic emission signals to determine when cortical bone failure occurs by characterization using both a Welch power spectral density estimate and a continuous wavelet transform. Isolated cortical shell specimens from thoracic vertebral bodies with attached acoustic sensors were subjected to quasistatic loading until failure. The resulting acoustic emissions had a wideband frequency response with peaks from 20 to 900 kHz, with the spectral peaks clustered in three bands of frequencies (166 ± 52.6 kHz, 379 ± 37.2 kHz, and 668 ± 63.4 kHz). Using these frequency bands, acoustic emissions can be used as a monitoring tool in biomechanical spine testing, distinguishing bone failure from structural response. This work presents a necessary set of techniques for effectively utilizing acoustic emissions to determine the onset of cortical bone fracture in biological material testing. Acoustic signatures can be developed for other cortical bone regions of interest using the presented methods.

A Multi-Taper S-Transform Method for Spectral Estimation of Stationary Processes

The S-transform (ST) is a method of time-frequency analysis of time series. We develop here the Multi-taper S-transform (MTST) for spectral estimation of multi-variate stationary processes through replacing the scalable Gaussian window of the ST with scalable, adjustable orthogonal time-frequency Hermite functions. The MTST is shown to reduce bias and variance of power spectral density (PSD) estimates and coherence over the entire frequency domain and compares favourably with the estimates obtained with the Welch and Multi-taper methods. The MTST method has been successfully applied to data from two anemometers in Hong Kong, during Typhoon Mangkhut, for the estimation of PSD and coherence.

An Investigation on the Current Collection Quality of Railway Pantograph-Catenary Systems With Contact Wire Wear Degradations

In railway pantograph-catenary systems, the contact surfaces undergo wear in long-term operations, directly affecting interaction performance and potentially deteriorating the current collection quality. The effect of contact wire wear (CWW) on the current collection quality should be evaluated to understand the system’s health status in operations. This article presents a stochastic analysis of the pantograph–catenary interaction performance with different levels of CWW based on four years of measurement data. The power spectral density (PSD) estimation is carried out on the measured CWW to obtain their frequency representations. The random time histories of CWW are generated based on the PSDs. A nonlinear finite element model of catenary with a lumped-mass pantograph is built. Using the Monte Carlo method, the stochastic analysis of pantograph-catenary contact force is carried out to investigate the distribution and dispersion of assessment indices with different levels of CWW. The results indicate that the CWW mainly affects the maximum and minimum contact forces instead of the contact force standard deviation. The optimal pantograph–catenary interaction performance is observed certain years after CWW is formed, depending on the traffic density of the railway line, which is at the second year in the presented case study. Then, the performance declines with an increase in service time. Also, higher operating speed causes a more significant dispersion in assessment indices representing a lower current collection quality, particularly at the maximum operating speed (70% of the catenary wave propagation speed).

Damage Detection in CFST Column by Simulation of Ultrasonic Waves Using STFT-Based Spectrogram and Welch Power Spectral Density Estimate

Damage Detection in CFST Column by Simulation of Ultrasonic Waves Using STFT-Based Spectrogram and Welch Power Spectral Density Estimate

Confidence interval of the ‘single-moment’ fatigue damage calculated from an estimated power spectral density

This article develops a theoretical approach to account for the uncertainty of the fatigue damage caused by the sampling variability of a power spectral density estimated from a finite length stationary record. The moment generating function of the estimated spectral moments is obtained and used to approximate their probability distribution with that of a chi-square random variable with a newly chosen number of degrees of freedom. This approximate distribution allows the confidence interval of both the ‘true’ spectral moments and ‘single-moment’ damage to be derived. A numerical example is finally presented to demonstrate the correctness of the proposed solutions.

Evaluation of speech enhancement algorithms applied to electrolaryngeal speech degraded by noise

Electrolaryngeal speech, for persons who have lost their larynx, suffers from the drawback of susceptibility to acoustic noise, which includes inherent electrolarynx motor noise as well as environmental noise. Interactions with electrolarynx users motivated the authors to investigate a crucial drawback of electrolaryngeal speech: degradation of electrolaryngeal speech under noisy environments. The effect of contemporary methods of speech enhancement, viz. noise power spectral density estimation based d-dimensional amplitude trimmed estimation (DATE), and non-negative matrix factorization (NMF) based algorithms, were studied and evaluated for electrolaryngeal speech degraded by noise. Electrolaryngeal speech was corrupted using three types of noisy scenarios at low signal to noise ratios (0, −5 and −10 dB SNR). Objective testing based on the perceptual evaluation of speech quality (PESQ) standard, as well as subjective testing by 14 participants based on the ITU-T P.835 standard were performed. Word-centric intelligibility testing was also performed. The results indicated an improvement in the speech quality. The subjective testing results were further analyzed using one-way analysis of variance (ANOVA) and multiple paired comparison using Tukey’s honest significant difference (HSD) criterion. The overall speech quality of NMF algorithms was found to be significantly higher than that of DATE-based algorithms for the test conditions. The results show that speech enhancement algorithms can aid in improving the electrolaryngeal user experience by reducing the effect of acoustic noise.

Application of the Lomb-Scargle Periodogram to InvestigateHeart Rate Variability during Haemodialysis.

Short-term cardiovascular compensatory responses to perturbations in the circulatory system caused by haemodialysis can be investigated by the spectral analysis of heart rate variability, thus providing an important variable for categorising individual patients' response, leading to a more personalised treatment. This is typically accomplished by resampling the irregular heart rate to generate an equidistant time series prior to spectral analysis, but resampling can further distort the data series whose interpretation can already be compromised by the presence of artefacts. The Lomb–Scargle periodogram provides a more direct method of spectral analysis as this method is specifically designed for large, irregularly sampled, and noisy datasets such as those obtained in clinical settings. However, guidelines for preprocessing patient data have been established in combination with equidistant time-series methods and their validity when used in combination with the Lomb–Scargle approach is missing from literature. This paper examines the effect of common preprocessing methods on the Lomb–Scargle power spectral density estimate using both real and synthetic heart rate data and will show that many common techniques for identifying and editing suspect data points, particularly interpolation and replacement, will distort the resulting power spectrum potentially misleading clinical interpretations of the results. Other methods are proposed and evaluated for use with the Lomb–Scargle approach leading to the main finding that suspicious data points should be excluded rather than edited, and where required, denoising of the heart rate signal can be reliably accomplished by empirical mode decomposition. Some additional methods were found to be particularly helpful when used in conjunction with the Lomb–Scargle periodogram, such as the use of a false alarm probability metric to establish whether spectral estimates are valid and help automate the assessment of valid heart rate records, potentially leading to greater use of this powerful technique in a clinical setting.

Machine learning, waveform preprocessing and feature extraction methods for classification of acoustic startle waveforms

The acoustic startle response (ASR) is an involuntary muscle reflex that occurs in response to a transient loud sound and is a highly-utilized method of assessing hearing status in animal models. Currently, a high level of variability exists in the recording and interpretation of ASRs due to the lack of standardization for collecting and analyzing these measures. An ensembled machine learning model was trained to predict whether an ASR waveform is a startle or non-startle using highly-predictive features extracted from normalized ASR waveforms collected from young adult CBA/CaJ mice. Features were extracted from the normalized waveform as well as the power spectral density estimates and continuous wavelet transforms of the normalized waveform. Machine learning models utilizing methods from different families of algorithms were individually trained and then ensembled together, resulting in an extremely robust model.•ASR waveforms were normalized using the mean and standard deviation computed before the startle elicitor was presented•9 machine learning algorithms from 4 different families of algorithms were individually trained using features extracted from the normalized ASR waveforms•Trained machine learning models were ensembled to produce an extremely robust classifier

Automated system for weak periodic signal detection based on Duffing oscillator

The periodic signals that have predictable and deterministic characteristics are used in the analysis and modelling of dynamical systems in diverse fields. These signals can be detected as the weak signals within the time series obtained from the measurable processes of dynamical systems. The Duffing oscillator is effective in detecting weak periodic signals with a very low signal-to-noise ratio. In this study, the authors present a method to automate the weak periodic signal detection of the Duffing oscillator using a quantitative index for the classification of the periodic and non-periodic signals. In this method, the authors use the wavelet scale index as the quantitative index in the classification of signals. Thus, they are able to plot the wavelet scale index spectrum of the Duffing oscillator where the frequency values of the weak periodic signals correspond to near-zero wavelet scale index parameters. First, the authors perform simulations using the method and detect weak periodic signals embedded in noise. Then, they employ two electroencephalogram signals to demonstrate the feasibility of the proposed method in the empirical data. Lastly, they compare the method to the periodogram power spectral density estimate based on fast Fourier transform.

Gravitational-wave astronomy with an uncertain noise power spectral density

In order to extract information about the properties of compact binaries, we must estimate the noise power spectral density of gravitational-wave data, which depends on the properties of the gravitational-wave detector. In practice, it is not possible to know this perfectly, only to estimate it from the data. Multiple estimation methods are commonly used and each has a corresponding statistical uncertainty. However, this uncertainty is widely ignored when measuring the physical parameters describing compact binary coalescences, and the appropriate likelihoods which account for the uncertainty are not well known. In order to perform increasingly precise astrophysical inference and model selection, it will be essential to account for this uncertainty. In this work, we derive the correct likelihood for one of the most widely used estimation methods in gravitational-wave transient analysis, the median average. We demonstrate that simulated Gaussian noise follows the predicted distributions. We then examine real gravitational-wave data at and around the time of GW151012, a relatively low-significance binary black hole merger event. We show that the data are well described by stationary-Gaussian noise and explore the impact of different noise power spectral density estimation methods on the astrophysical inferences we draw about GW151012.

A rapid coarse-grained blind wideband spectrum sensing method for cognitive radio networks

Spectrum sensing aims to sense the potential spectrum resources available in the cognitive radio environment. It is also the premise of spectrum management and spectrum sharing in cognitive radio systems. To perceive the primary user’s activity and make full use of spectrum holes, rapid detection of a broad frequency span is an essential part of cognitive radio technology. Reducing the observation time for the data collection, the data storage requirements, and hardware/software computational complexity are urgent and challenging issues in wideband spectrum sensing. High accuracy power spectral density estimation is not the primary requirement; of course, the accuracy must be controlled within the appropriate range and can support the primary user activity’s determination. This paper proposes a sub-Nyquist wideband spectrum sensing method based on compressive covariance sensing for the rapid wideband spectrum sensing. Compared with the traditional Nyquist-rate method, this method can use low-speed ADC to detect wideband signals and effectively control the observation time and computational complexity. This paper’s main contributions include: (1) developing a sub-Nyquist sampling structure based on the multi-coset sampling banks, (2) proposing a coarse-grained power spectral density estimation method for wideband spectrum sensing with short observation time and low complexity. Simulations show that the proposed method exhibits this method is suitable for fast spectral detection. At the same time, the error of spectrum analysis is basically within the acceptable range.

Estimating higher-order spectra via filtering-averaging

This work proposes a new estimator for higher-order spectra. Higher-order spectra determine periodical properties of data by cross-frequency correlation. They are defined as the decomposition of central moments and cumulants over frequency and form a powerful tool to assess nonlinear, non-Gaussian or non-stationary systems and processes. The estimation theory of higher-order spectra has emerged from the research on power spectral density estimation. The estimator proposed here complements the existing estimators with a generalized theory of frequency-domain smoothing. It represents the domain-reversed counterpart of the popular method of averaging raw spectra from short-time Fourier transforms. The main selling points are the consistent approach to smoothing with a better bias-variance trade-off, its computational efficiency by averaging in the time domain and its flexibility and simplicity. These properties, the mathematical derivation and the analogy to averaging of raw spectra are presented. Numerical studies outline basic properties of the estimator.

Differences in Power Spectral Densities and Phase Quantities Due to Processing of EEG Signals.

There has been a growing interest in computational electroencephalogram (EEG) signal processing in a diverse set of domains, such as cortical excitability analysis, event-related synchronization, or desynchronization analysis. In recent years, several inconsistencies were found across different EEG studies, which authors often attributed to methodological differences. However, the assessment of such discrepancies is deeply underexplored. It is currently unknown if methodological differences can fully explain emerging differences and the nature of these differences. This study aims to contrast widely used methodological approaches in EEG processing and compare their effects on the outcome variables. To this end, two publicly available datasets were collected, each having unique traits so as to validate the results in two different EEG territories. The first dataset included signals with event-related potentials (visual stimulation) from 45 subjects. The second dataset included resting state EEG signals from 16 subjects. Five EEG processing steps, involved in the computation of power and phase quantities of EEG frequency bands, were explored in this study: artifact removal choices (with and without artifact removal), EEG signal transformation choices (raw EEG channels, Hjorth transformed channels, and averaged channels across primary motor cortex), filtering algorithms (Butterworth filter and Blackman–Harris window), EEG time window choices (−750 ms to 0 ms and −250 ms to 0 ms), and power spectral density (PSD) estimation algorithms (Welch’s method, Fast Fourier Transform, and Burg’s method). Powers and phases estimated by carrying out variations of these five methods were analyzed statistically for all subjects. The results indicated that the choices in EEG transformation and time-window can strongly affect the PSD quantities in a variety of ways. Additionally, EEG transformation and filter choices can influence phase quantities significantly. These results raise the need for a consistent and standard EEG processing pipeline for computational EEG studies. Consistency of signal processing methods cannot only help produce comparable results and reproducible research, but also pave the way for federated machine learning methods, e.g., where model parameters rather than data are shared.

Improvement of Intake Structures in a Two-Way Pumping Station with Experimental Analysis

Pumping stations are important regulation facilities in a water distribution system. Intake structures can generally have a great influence on the operational state of the pumping station. To analyze the effects of the bell mouth height of the two-way intake on the performance characteristics and the pressure pulsations of a two-way pumping station, the laboratory-sized model pump units with three different intakes were experimentally investigated. To facilitate parameterized control, ellipse and straight lines were used to construct the profile of the bell mouth. The frequency domain and time-frequency domain of the pressure pulsations on the wall of intakes were analyzed by the Welch’s power spectral density estimate and the continuous wavelet transform (CWT) methods, respectively. The results showed that the bell mouth height (H) has significant influences on the uniformity of the impeller inflow and the operation stability of the pump unit. When H = 204 mm, the data fluctuated greatly throughout the test process and the performance curves are slightly lower than the other two schemes. As the bell mouth height gradually decreases, the average pressure difference of each measuring point began to decrease, more homogeneous velocity distribution of impeller inflow can be ensured. The amplitude of blade passing frequency is obvious in the spectrum. While when (H) is more than 164 mm, the main frequency of pressure pulsations at three points fluctuates with the rotation of the impeller. When H decreases to 142 mm, pressure pulsations will be independent of the operating conditions and positions which contributes to the long-term stable operation of the pump unit.

On the Estimation of Power Spectral Density and Lagged Coherence of Time Transformed Nonstationary Seismic Ground Motions and Their Use to Simulate Synthetic Records

ABSTRACT Ground motions could be modelled as amplitude and frequency modulated process. The frequency modulation through a time transformation results in the modelled motions in the new timescale being a stationary process except for the amplitude modulation. The assessment of power spectral density (PSD) and the lagged coherence in the transformed timescale is presented in this study. It is shown theoretically and numerically that the PSD functions obtained through time transformation in the original timescale should not be used as an amplitude modulation function, and that the lagged coherence in the new or auxiliary timescale differs from that in the original timescale.

Optimum step-size control for a variable step-size stereo acoustic echo canceller in the frequency domain

The frequency-domain adaptive filter (FDAF) is a competitive candidate for stereo acoustic echo cancellation (SAEC) because of its good convergence and computational efficiency. However, there is a conflict between the convergence rate and the steady-state misalignment when using a constant step size. In this paper, a variable step-size approach is proposed for the stereo echo canceller in the frequency domain. The proposed method uses a first-order Markov model to describe the time-varying echo paths between the loudspeakers and the microphone. Following a statistical convergence analysis of the two-channel FDAF algorithm, the state recursion of the system distance in each frequency bin is given. The optimal step size is then derived by minimizing the system distance. Several practical problems, including noise power spectral density estimation and echo paths change detection, are discussed in details. Moreover, a close link between the proposed optimum step-size control method and the multichannel state–space frequency-domain adaptive filter is established. We show that the proposed variable step-size approach can also be incorporated into the block extended least-mean-square algorithm to fully exploit their benefits. Finally, computer simulations demonstrate that the proposed algorithm exhibits an excellent convergence performance and is very robust to the double talk.

Horizontal-to-Vertical Spectral Ratio (HVSR) IRIS Station Toolbox

AbstractThe horizontal-to-vertical spectral ratio (HVSR) for seismic ambient noise is a popular method that can be used to estimate the predominant frequency at a given site. In this article, we introduce the Incorporated Research Institutions for Seismology (IRIS) Data Management Center’s (DMC’s) openly available HVSR station toolbox. These tools offer a variety of ways to compute the spectral ratio by providing different averaging routines. The options range from the simple average of spectral ratios to the ratio of spectral averages. Computations take advantage of the available power spectral density estimates of ambient noise for the seismic stations, and they can be used to estimate the predominant frequency of the many three-component seismic stations available from the IRIS DMC. Furthermore, to facilitate the identification of the peaks in HVSR profiles for the assessment of the predominant frequency of station sites, the toolbox can also process the results of HVSR analysis to detect and rank HVSR peaks. To highlight the toolbox capabilities, three different examples of possible use of this toolbox for routine site-effect analysis are discussed: (1) site effects related to thawing in Arctic regions, (2) ground-motion amplification in urban area, and (3) estimation of station VS30.

Hardware-Efficient Bartlett Spectral Density Estimator Based on Optimized R22FFT Processor Using CCSSI Method

This paper offers a novel, low-power, hardware-efficient, yet high-frequency architecture for a power spectral density (PSD) estimator, based on the Bartlett method, for low-power biomedical applications. The Bartlett method is a nonparametric method for PSD estimation. The proposed architecture operates based on a modified multiplierless 64-point optimized radix-22single-path delay feedback (R22SDF) FFT processor. To obtain the final result, it also uses modified safe-scaling in a way that removes the need to use several extra hardware units. It takes advantage of combined coefficient selection and shift-and-add implementation (CCSSI) for computing twiddle factors which is a new algorithm based on digital computer coordinate rotation (CORDIC) for generating trigonometric values. The proposed method has the capability of operating on short word lengths (WLs). Artix-7 is the FPGA used in this research and Verilog is the language used for hardware design. For 8-bit WL and 244-mW power, a frequency of 286 MHz has been achieved. Several vital signals are used for performance comparison of the proposed technique with state-of-the-art designs.

Separation of movement direction concepts based on independent component analysis algorithm, linear discriminant analysis, deep belief network, artificial and fuzzy neural networks

Brain signals have various scientific and practical applications, such as Medical Science, Cognitive Science, Neuroscience, and Brain Computer Interfaces. Brain signal analysis is faced with complex challenges including small sample size, high dimensionality and noisy signals. Because of the non-stationarity of brain signals and the impacts of mental states on brain function, brain signals are associated with an inherent uncertainty. In this study, it is tried to present a plausible method for detecting and distinguishing the directions from EEG signals. Recording single-polarized signals was carried out utilizing a 19-channel cap Micromed device with the use of Cz as reference electrode. The statistical population used involved ten 25–35 year old male volunteers. The designed task consisted of 24 slides of up, down, left and right directions. After preprocessing level, ICA algorithm was employed to extract artifacts, to decrease signal dimension and to determine the target signal. In feature extraction section, AR coefficients extracted to feed the ANN, FNN and LDA. Data for Deep Belief Network provided from Autoregressive power spectral density estimate with order of 20 employed on the data set.Classifiers’ results reveal that 2.5 s time window leads to the best separation accuracy.DBN surprisingly leads to the highest level of accuracy in comparison to the other proposed methods.Based on the 10-fold Cross Validation, the performance of the classifiers measured in terms of accuracy, sensitivity and specificity. The obtained average accuracies for LDA, ANN, FNN and DBN respectively are 61.86 ± 1.69 %, 57.18 ± 1.88 %, 66.79 ± 2.14 % and 91.06 ± 0.68.

Automated classification of acoustic startle reflex waveforms in young CBA/CaJ mice using machine learning

BackgroundThe acoustic startle response (ASR) is a simple reflex that results in a whole body motor response after animals hear a brief loud sound and is used as a multisensory tool across many disciplines. Unfortunately, a method of how to record, process, and analyze ASRs has yet to be standardized, leading to high variability in the collection, analysis, and interpretation of ASRs within and between laboratories. New methodASR waveforms collected from young adult CBA/CaJ mice were normalized with features extracted from the waveform, the resulting power spectral density estimates, and the continuous wavelet transforms. The features were then partitioned into training and test/validation sets. Machine learning methods from different families of algorithms were used to combine startle-related features into robust predictive models to predict whether an ASR waveform is a startle or non-startle. ResultsAn ensemble of several machine learning models resulted in an extremely robust model to predict whether an ASR waveform is a startle or non-startle with a mean ROC of 0.9779, training accuracy of 0.9993, and testing accuracy of 0.9301. Comparison with existing methodsASR waveforms analyzed using the threshold and RMS techniques resulted in over 80% of accepted startles actually being non-startles when manually classified versus 2.2% for the machine learning method, resulting in statistically significant differences in ASR metrics (such as startle amplitude and pre-pulse inhibition) between classification methods. ConclusionsThe machine learning approach presented in this paper can be adapted to nearly any ASR paradigm to accurately process, sort, and classify startle responses.