Power Spectral Density Estimation Research Articles

Direct estimation of evolutionary power spectral density of nonstationary winds: A unified formulation

Estimating the evolutionary power spectral density (EPSD) of non-stationary winds (e.g., tropical storms and downbursts) is necessary to predict the response of structures under such extreme winds. Following the review of the existing direct estimation methods of EPSD, this paper offers a two-step unified formulation, i.e., raw estimation and associated error reduction. The raw estimation is expressed in terms of a time-frequency transform with a general kernel function. It is shown that if the kernel function is described by a time-frequency analysis tool such as the short-time Fourier transform, the wavelet transform, and the S-transform, the generalized raw EPSD estimation becomes a particular case of the existing methods. The unified estimation method presented here can be viewed as a filter bank with adjustable time and frequency resolution. The analysis of error in the raw estimation is carried out on the bias and random errors accounting for the approximation in both the time and frequency domains. Various techniques for reducing such errors are then summarized and recast in the unified formulation, including series expansion, short-time window smoothing, and multi-tapering. Based on the unified perspective, a discussion and some prospects of EPSD estimating are provided.

Performance of Energy Detection Spectrum Sensing for Cognitive Radio Using GNU Radio

The increasing number of wireless communication applications has led to spectrum scarcity problems. On the other hand, the current system in allocating the spectrum frequency is inefficient. To mitigate this issue, a cognitive radio (CR) system is proposed. CR is a smart radio that is able to sense the environment, locate the spectrum holes, and adapt its transmission parameter to exploit the existing spectrum holes. This underlines the importance of the spectrum sensing module to enable the operation of the CR system. The objective of the spectrum sensing module is to achieve the best utility from the available spectrum frequency. CR system is implemented in the unlicensed secondary users allowed to rent the spectrum currently not used by primary users (PU). In this paper, energy-detection-based spectrum sensing is implemented on the GNU Radio platform. We first implement the power spectral density (PSD) estimation method based on the periodogram by exploiting the Embedded Python block facility on the GNU Radio. Next, we implement the spectrum sensing decision module in the GNU Radio, which compares the PSD estimate of the PU signals corrupted by noise with a threshold. The PU signal is simulated as a bandpass random process occupying a particular frequency band. The spectrum sensing decision module is developed to allow the computation of the probability of detection (PD) and the probability of false alarm (PFA), which is performed by exploiting the Embedded Python block. One indicator to evaluate the performance of the spectrum sensing module is the receiver operating characteristic curve based on the computed PD and PFA on the GNU Radio. We evaluate the performance of the spectrum sensing for different SNRs and thresholds. The result shows that the energy-detection-based spectrum sensing is able to locate the existence of the PU when the signal-to-noise ratio (SNR) is sufficiently high.

Feed hardness and acoustic emissions of autogenous/semi-autogenous (AG/SAG) mills

In this study, the relationship between acoustic emissions and hardness of different rock types (model quartz, model calcite, and real iron ore) coupled with binary mix ratios of model quartz and iron ore (1:3, 1:1 and 3:1) was investigated in a laboratory-based AG/SAG mill. The acoustic emission response and sensitivity of the mill were compared, along with its product particle size distribution. Features, such as discrete wavelet transform (DWT), power spectral density estimate (PSDE), and statistical root mean square (RMS) were extracted from the mill acoustic emissions. From the results, it was evident that the mill acoustic emission response can be used to classify different rock hardness and their binary mixtures. Model quartz emitted the highest acoustic response, followed by iron ore and model calcite at the initial stages of grinding (5 min). The results further indicated that as the rock feed sizes reduced, the average mill noise also increased as a function of grinding time. Accordingly, the acoustic emission presented a contrasting effect with model calcite and model quartz emitting the highest and lowest noise emission, respectively. The proportions of different mineral types (model quartz and iron ore) were reflected well in the acoustic emissions. The study has demonstrated that the integration of acoustic sensing techniques in AG/SAG mills can serve as a proxy for online measurement of different rock/ore hardness, for example, as a fast track method to determine the hardness of ores in comparison to the traditional ore grindability procedures, such as Bond work index (BWI) and SAG power index(SPI) tests which can be laborious and time-consuming.

Application of power spectral density and the support vector machine to fault diagnosis for permanent magnet synchronous motor

The present study proposes a new technique for diagnosing the Inter-Turn Stator-Winding fault in Permanent Magnet Synchronous Motors. Under faulty operating conditions, the system’s model is built while considering specific parameters linked to fault location and sharpness. The proposed fault-detection method is principally based on the Power Spectral Density estimator’s association with the Support Vector Machine. This classifier is used to separate different regions of system performance. It has been trained to associate the Power Spectral Density current’s magnitude and the stator’s current negative sequence with the fault severity. This method has shown exceptional performance as long as it achieves a fault detection rate of 98.5% for different fault severities. Two Power Spectral Density estimators were compared in terms of their ability to extract fault characteristics, namely Burg’s method and Welch’s method. It was concluded from this study that Welch’s has a higher frequency resolution than Burg’s method.

Aerodynamic loads correction method based on wavelet packet transform in high-frequency force balance tests

High-frequency force balance (HFFB) technique is a commonly used method for acquiring wind-induced response of tall buildings in wind tunnel tests. However, the resonance buffeting of the balance-model system (BMS) results in the distortion of measured aerodynamic loads. When the signal distortion is complicated due to additional vibration modes and noise interference, the existing methods fail to obtain correction results. Thus, a new correction method based on wavelet packet transform (WPT) is proposed in this paper to address the issue. The distorted signals are decomposed by WPT, and the relationship between wavelet packet coefficients and power spectral density (PSD) estimation is established. Then, the reference line that conforms to the aerodynamic attenuation characteristics is extracted by a single-degree-of-freedom (SDOF) correction method combined with a parameter identification method. Subsequently, the wavelet packet coefficients of SDOF correction results are adjusted according to the reference line. Finally, the time history of the aerodynamic load after correction is reconstructed by inverse WPT (IWPT). The proposed method is validated by a numerical example and applied to a HFFB test. Compared with the existing methods, the proposed method can address more complex distortion scenes and extend the correction frequency range to the Nyquist frequency.

An automated detection of atrial fibrillation from single‑lead ECG using HRV features and machine learning

BackgroundAtrial fibrillation (AF) is a disorder of the heart rhythm where irregular and rapid heartbeats are observed. This supraventricular arrhythmia may increase the risk of blood clots, stroke, heart failure, and other serious heart complications. Automatic analysis of AF that is based on machine learning (ML) plays an important role in detecting this heart disease. MethodsA new approach for automated AF detection is presented using heart rate variability (HRV) features and machine learning. A set of time-domain, frequency-domain and nonlinear features are extracted from the R-R intervals. A new method for frequency-domain analysis of R-R intervals using the Fourier Decomposition Method is presented, which provides promising results as compared to the usual method of power spectral density estimation. We train the algorithm on the Massachusetts Institute of Technology-Beth Israel Hospital (MIT-BIH) atrial fibrillation database and perform a comprehensive analysis using statistical tests to obtain the results without any intra-patient bias. ResultsThe proposed method is able to achieve average result of 95.16% sensitivity, 92.46% specificity and 94.43% accuracy and its performance is better than the existing approaches. Furthermore, the efficacy of the proposed algorithm is tested on eight records from a previously unseen MIT-BIH Arrhythmia Database. ConclusionThis work shows that the proposed HRV features and ML approach can be effectively used for the analysis, detection, and classification of AF.

Online Monitoring of Surface Quality for Diagnostic Features in 3D Printing

Investigation into non-destructive testing and evaluation of 3D printing quality is relevant due to the lack of reliable methods for non-destructive testing of 3D printing defects, including testing of the surface quality of 3D printed parts. The article shows how it is possible to increase the efficiency of online monitoring of the quality of the 3D printing technological process through the use of an optical contactless high-performance measuring instrument. A comparative study of contact (R130 roughness tester) and non-contact (LJ-8020 laser profiler) methods for determining the height of irregularities on the surface of a steel reference specimen was performed. It was found that, in the range of operation of the contact method (Ra 0.03–6.3 µm and Rz 0.2–18.5 µm), the errors of the contactless method in determining the standard surface roughness indicators Ra and Rz were 23.7% and 1.6%, respectively. Similar comparative studies of contact and non-contact methods were performed with three defect-free samples made of plastic polylactic acid (PLA), with surface irregularities within the specified range of operation of the contact method. The corresponding errors increased and amounted to 65.96% and 76.32%. Finally, investigations were carried out using only the non-contact method for samples with different types of 3D printing defects. It was found that the following power spectral density (PSD) estimates can be used as diagnostic features for determining 3D printing defects: Variance and Median. These generalized estimates are the most sensitive to 3D printing defects and can be used as diagnostic features in online monitoring of object surface quality in 3D printing.

A harmonic input method for computing time-varying response PSD of linear time-invariant structures subjected to nonstationary stochastic excitations

A number of stochastic response analysis methods have been successfully developed for computing the time-varying response power spectral density (PSD) of structures subjected to nonstationary stochastic excitations. However, how to compute the time-varying response PSD when transient response components have significant impacts on the stochastic responses remains largely unsolved. To this end, this paper proposes a harmonic input method (HIM) for accurately and efficiently computing time-varying response PSD of linear time-invariant structures subjected to nonstationary stochastic excitations, which can consider the transient response impact. The accuracy of the proposed HIM method is verified via comparison against the Monte Carlo simulations of an SDOF system and an MDOF system, which outperforms the classical methods if the transient response components are of significance. This study offers a high-efficient and high-accurate approach for response PSD estimation, particularly for a low-damping structural system subjected to short-duration nonstationary stochastic excitations.

The influence of shock absorber characteristics’ nonlinearities on suspension Frequency Response Function estimation and possibilities of simplified characteristics modelling

The paper shortly presents shock absorber design evolution and resulting achieved characteristics. The way in which suspension performance is evaluated is described giving information about models used for suspension parameter tuning during simulation testing of suspension transmissibility (FRF - Frequency Response Function) for most important suspension assessment criteria. More detailed information about models of shock absorber (damper) nonlinearities of characteristics allows for description of methods of linear and nonlinear suspension models FRF estimation. Testing linear suspension model is possible with the use of analytical transfer function formulas which were used to verify methods for estimation FRF using estimated power spectral density functions of excitation and response signals. Designing appropriate input signal allowing to get useful response signals was necessary to for the success of this research. Proposed FRF estimation method was used for linear estimation of nonlinear suspension for a given range of working condition. It was demonstrated that there is no single value of a damping coefficient which would make the linear model responses similar to the responses of the nonlinear one. Then the bilinear model was proposed, giving good damper static nonlinear characteristic.

Low Complexity Multiplierless Welch Estimator Based on Memory-Based FFT

This paper proposes a novel hardware efficient low power Welch power spectral density (PSD) estimator. The presented multiplier-less hardware uses a combined coefficient selection and shift-and-add implementation (CCSSI) unit in order to prevent multiplications in FFT computation. Two filtering operations, which are implemented in folded architecture, are utilized. The micro-rotation resources of the CCSSI unit can be shared with estimator’s modules simultaneously. The proposed architecture is a nonparametric estimator that operates based on a modified, memory-based, 128-point scalable radix-22 FFT processor. It uses bidirectional fractional delay filter to estimate half delay sample in merging two FFTs. Using modified safe-scaling, the final output would be valid, without any averaging operation. Another important feature of the proposed method is its capability of operating in short word lengths (WL). Artix-7, as an ideal option for DSP applications, is the utilized FPGA in this research. As results demonstrate, the hardware has a high capability in operating in short WLs which results in high performance in low-power applications.

Automatic detection of the spike-and-wave discharges in absence epilepsy for humans and rats using deep learning

Automatic detection of spike-and-wave discharges (SWDs) of absence seizures, is a highly time-consuming process requiring trained technicians or neurologists to categorize thousands of non-overlapping epochs of electroencephalography (EEG) data by visually inspecting several interconnections among different channels. This paper aims to develop an algorithm for a non-invasive real-time detection of SWDs in the EEG recordings of humans with absence epilepsy and a genetic model of absence epilepsy. We develop a SWD detection framework using Convolutional Neural Networks. Our approach utilizes the nature of EEG signals; as the brain signals are dynamics in discrete time, we found that it is more efficient and useful to represent the signal’s power as a function of frequency and time using Thomson’s multitaper power spectral density estimation analysis. Our experiments show that the developed method classified SWDs in humans and rats with high diagnostic performance similar to that of the trained neurologists while using fewer channels, proving that the proposed algorithm can be applied to different domains where the main focus is the detection of SWDs. Although there are different methods to detect SWDs in humans and animals, we showed the need for efficient and more accurate SWD detection. The proposed method, characterized by low computational and memory requirements using non-invasive EEG techniques with fewer channels, offers an efficient multi-purposed deep learning framework to be implemented in wearable or portable devices for accurate real-time detection of SWD patterns in EEG signals. Eventually, the proposed method is a step towards detecting seizures and closed-loop seizure interventions.

A recommendation prediction method based on the estimation of PSD of sampled signals on graph

In recommendation system, the rating prediction is a very challenging problem. In this paper, we model users (items) and their relationships as a weighted undirected graph, and propose a rating prediction model based on graph signal reconstruction. Different from the existing reconstruction model, the proposed model takes into account the frequency structure of the signal itself, and tends to protect the frequency contents with higher power spectral density (PSD) and impose large penalties on those with lower PSD when reconstructing a signal. Furthermore, based on the assumption of the stationarity of the graph signal, we propose a method to estimate the PSD of a stationarity stochastic graph signal directly from some sampled signals without its any other complete implementation. Related theoretical analysis is also given. Finally, a rating prediction algorithm based on the graph signal reconstruction is derived. Experimental results show that the proposed model leads a significant improvement of the predictive accuracy.

Acoustic rainfall detection with linear discriminant functions of principal components

Ma and Nystuen (2005) pioneered passive acoustic measurement of rainfall rates. This project extends their work with signal processing algorithms exploiting the full frequency band of the acoustic signals. We also extend Schwock and Abadi’s order-statistic power spectral density (PSD) estimation for outlier rejection to reject recreational anthropogenic noise sources and reject diurnal biological sources using two hydrophones spaced by 1 m. Ma and Nystuen reduced the data dimensionality by extracting a few "discriminant frequencies." Our proposed detection algorithm implements principal component analysis (PCA) to reduce the estimated PSD to two principal components. Linear discriminant analysis (LDA) provides a simple detection statistic from the two dimensional principal components. We evaluated our algorithm on four months of acoustic and meteorological data collected from a dock in New Bedford, MA in shallow water (3 m deep). For 1% false alarms, the proposed PCA/LDA algorithm correctly detected 36% (±7%) of rain events exceeding 1 mm/hr, including 64% (±7%) of the rain by volume. Applying Ma and Nystuen’s algorithm to the same data set for the same false alarm rate detected 23% (±11%) of events containing 52% (±26%) of the rainfall volume. [Work supported by ONR.]

The Multitaper Spectrum Analysis Package in Python

Abstract Spectral analysis has been a fundamental tool in analyzing seismic signals for studying the earthquake source, propagation of seismic waveforms through the Earth, and even monitoring changes in Earth’s structure. I present an open-source Python package, multitaper, for spectral analysis using the multitaper algorithm. The package not only includes power spectral density estimation (with confidence intervals) but also includes bivariate problems such as coherence, dual-frequency correlations, and deconvolution estimation. Implementation of the sine and quadratic multitaper algorithms is also available. For the reader to quickly learn how to use the package, I briefly present several examples using earthquake records from the 2019 Mw 6.0 Mesetas, Colombia, earthquake and its aftershocks recorded at regional distances for estimating time–frequency spectrograms, spectral ratio and source time functions, and correlations between neighboring frequencies. Jupyter Notebooks are shared to reproduce the figures.

4D-Var data assimilation using satellite sea surface temperature to improve the tidally-driven interior ocean dynamics estimates in the Indo-Australian Basin

Estimating ocean processes in regions with sparse observations, and where dynamics are dominated by strong barotropic and baroclinic tides, poses a significant modelling challenge. In this study, a Four-Dimensional Variational (4D-Var) data assimilation method, incorporating remotely sensed sea surface temperature (SST) data observations only, was used to improve estimates of the internal tide dynamics in the ocean between Australia and Indonesia. In this region, local internal tide generation, propagation and interference of the internal tides is highly variable and dependent on the 3D density field and mesoscale dynamics. The results of this study show that assimilation of remotely sensed SST data not only reduced the surface temperature root mean squared error (RMSE) from 0.8 °C to 0.3 °C, and removed a 0.4 °C cold bias (compared to a non-assimilative model), but also improved estimates of through-water-column variables — with the latter evaluated against ARGO profiling floats and two independent mooring sites. Overall, the depth-averaged temperature RMSE was reduced by as much as 38%, and ocean currents by ∼20% at the two mooring sites. The improvements were most significant in the top 100 m, where the internal tide signature was significantly corrected despite no depth-varying variables being assimilated. The study also showed that assimilating 2 km resolution SST observations resulted in more realistic SST wavenumber power spectral density estimates than those without assimilating data; in particular, the scheme reduced the energy at mesoscale length scales and improved the spectral slope towards the smaller submesoscale dynamics. It is concluded that 4D-Var assimilation using only SST improves estimates of upper 100 m ocean dynamics in tropical regions where there is sensitivity to the air–sea fluxes.

Classification of ground deformation using sentinel-1 persistent scatterer interferometry time series

ABSTRACT Displacement time series (TS) provides temporal and spatial information related to ground deformation. This study aims to investigate temporal behavior of ground deformation TS, including classification of displacement trends and periodicity evaluation, which ease the interpretation of movements. To this end, we propose several modifications to an existing automatic classification workflow of Persistent Scatterers Interferometry (PSI) TS using new tests to classify ground deformations into seven main trends: Stable, Linear, Quadratic, Bilinear, Phase Unwrapping Errors (PUE), Discontinuous with constant and different velocities. We illustrate our approach over 1500 km2 of the Granada region and the metropolitan area of Barcelona, which were monitored using Sentinel-1 images and a PSI technique. This study provided the spatial distribution of different ground movement types and was useful to detect several TS anomalies due to PUE. The proposed approach also identified stable targets, which were wrongly classified as moving scatterers by the existing classification method. A periodicity analysis was finally performed using the Welch’s power spectral density estimator to investigate seasonal and yearly fluctuations. The method was validated using simulated data, where the classified TSs characterized by probable phase unwrapping errors were verified by PSI experts. The overall classification accuracy was 77.8%, indicating that the proposed method has a considerable TS classification potential.

Determination of the Bessel light beam cone parameter by Fourier analysis of the diametral distribution of the intensity

Power spectral density (PSD) of the intensity distribution of an ideal Bessel light beam (BLB) expressions are obtained. It is shown that the PSD of the intensity distribution of an ideal BLB is limited and the upper boundary of the PSD is equal to the doubled cone parameter (the product of the wave number and the sine of the half angle of the cone of wave vectors), and the number of zeros in the PSD of an ideal BLB located in the interval from zero frequency to the upper boundary of the spectrum, is equal to the order of the beam. A technique is proposed for estimating the cone parameter of BLBs by analysing the PSD estimates of diametral distributions – one-dimensional intensity distributions obtained in the transverse plane of the beam along a line passing through the beam axis from transverse two-dimensional BLB intensity distributions recorded in the form of digital computer images. The influence of clipping (the end of the distribution at the boundary of the sensitive sensor), Gaussian and cosine modulations of the diametral distribution on the shape of the spectrum and, in case of clipping, the error in the cone parameter estimation using the proposed method is investigated. The technique is tested on the example of the analysis of experimental BLBs of different orders (BLBm, m = 0, 1, 2). The proposed technique can be used to assess the quality parameters of the BLB. The results of the analysis of the influence of cosine modulation on the shape of the PSD can be used to assess the magnitude of the rounding of the apex of the axicon forming the BLB for control the quality of the axicon manufacturing.

Multi-sensory sound source enhancement for unmanned aerial vehicle recordings

A method to effectively perform sound source enhancement from an unmanned aerial vehicle (UAV)-mounted audio recording system is proposed. The objective of this study is to utilise audio recordings and non-acoustical UAV rotor characteristics to improve rotor noise power spectral density (PSD) estimation accuracy and robustness. The improved rotor noise PSD estimate in turn improves the effectiveness of the rotor noise postfilter, leading to improvement in source enhancement performance. The performance of the proposed source enhancement algorithm is evaluated via experiments, with recordings made in an outdoor environment with an in-flight UAV. Experiment results show PSD estimation accuracy to within 1.5 dB log spectral distortion regardless of the given input conditions, such as the presence of surrounding sound sources. The method also achieves a consistent ∼20–25 dB improvement in source enhancement performance, where the effects of rotor noise from the noisy microphone recordings are significantly reduced. The proposed method also outperforms existing state-of-the-art such as the beamformer with postfilter and speech distortion weighted multichannel Wiener filter frameworks.

Experimental investigation and comparative study of signal processing techniques dedicated for the diagnosis of rotor failures in the induction motors

PurposeThe purpose of this paper is to propose applications of advanced signal-processing techniques for the diagnosis and detection of rotor fault in an induction machine. Two techniques are used: spectral analysis techniques and time frequency techniques for the diagnosis of an electrical machine. One is based on the power spectral density estimation techniques, such as periodogram and Welch periodogram. The second method is based on Hilbert transform (HT) to extract the envelope for the stator current. Then, this signal is processed via discrete wavelet transform (DWT) for determining the faulty components in the spectrum of the stator current envelope and identifying the eigenvalues of energies (HDWT).Design/methodology/approachFirst, this paper focused on theoretical development and a comparative study of these signal-processing techniques, which are based on the periodogram, Welch periodogram, HT and the DWT to extract the envelope for the stator current; it is used to compute the energy stored in each decomposition level obtained by the stator current envelope (HDWT). Moreover, the Welch periodogram is applied to obtain the envelope spectrum.FindingsThe simulation obtained and the experimental validation results of the proposed methods through MATLAB environment show the effectiveness of the proposed approaches with a good accuracy by power spectral density estimation techniques (periodogram and Welch periodogram). Moreover, the faults are manifested through the appearance of new frequencies components, as well as the envelope for the stator current (HT and DWT). This approach is effective for non-stationary and stationary signal to extract useful information for the detection of broken bar fault.Originality/valueThe current paper proposes a new diagnosis method for the detection and characterization of broken rotor bars defects early; it is founded primarily on theoretical development, and the comparison is based on the power spectral density technique (periodogram and Welch periodogram) and the computation of the energy stored in each decomposition level (precisely the HT and DWT). Moreover, the Welch periodogram is applied to obtain the envelope spectrum. The main advantages of the proposed techniques increase their reliability and availability.

Improved Speech Enhancement Considering Speech PSD Uncertainty

Speech enhancement based on statistical models has been studied for several decades. Recently, the speech enhancement adopting a speech power spectral density (PSD) uncertainty model has been proposed. This approach distinguishes the true speech PSD from its estimate and considers both as random variables. It incorporates a prior distribution of speech spectra and speech PSD estimators to derive the PSD uncertainty-aware counterpart to conventional clean speech estimators, which results in performance improvement. However, the speech PSD uncertainty model has not yet been adopted for parameter estimations such as <inline-formula><tex-math notation="LaTeX"><?TeX $\mathit{a posteriori}$?></tex-math></inline-formula> speech presence probability, noise PSD, and speech power spectra estimations in the speech enhancement framework. In this paper, we incorporate the speech PSD uncertainty model to all the components of the statistical model-based speech enhancement framework by deriving PSD uncertainty-aware counterparts to conventional parameter estimators. Specifically, we derive the <inline-formula><tex-math notation="LaTeX"><?TeX $\mathit{a posteriori}$?></tex-math></inline-formula> speech presence probability (SPP) where the likelihood function for each hypothesis is based on the speech PSD uncertainty. With this <inline-formula><tex-math notation="LaTeX"><?TeX $\mathit{a posteriori}$?></tex-math></inline-formula> SPP, a novel SPP-based noise PSD estimator is derived. Also, we derive the minimum mean-square error (MMSE) estimator for the power spectrum of the clean speech in the current frame under speech PSD uncertainty which is exploited to refine the speech PSD estimator. Finally, the refined speech PSD estimator is incorporated into the spectral gain function based on the speech PSD uncertainty model. The proposed approach showed improved noise PSD estimation performance in terms of the averaged logarithmic error distance, and improved speech enhancement performance in terms of the noise reduction, segmental signal-to-noise ratio, perceptual evaluation of speech quality (PESQ) scores and short-time objective intelligibility in our experiments. It also exhibited comparable performance with a real-time deep learning-based speech enhancement system in terms of the PESQ scores and composite measures for the VoiceBank-DEMAND dataset.