Power Spectrum Estimation Research Articles

Harmonic-wavelet approach for response spectrum estimation of vehicle and bridge systems with uncertain parameters subjected to stochastic excitation

Vehicle and bridge systems (VBSs) are subjected to stochastic excitations. Significant research effort has been devoted to the stochastic response analysis of VBSs. In most previous studies, VBSs have been treated as deterministic systems with certain parameters. However, the real VBSs always have uncertain parameters, such as the mass and spring stiffness of the vehicles and elastic modulus of the bridge material, which significantly affect the response power spectrum (RPS) estimation. Moreover, the equations of motion of the VBSs are essentially second-order differential equations with time-dependent and random coefficient matrices, and the excitation-response spectral relation cannot be directly described using the frequency response functions. These properties render the available methods unsuitable for the RPS estimation of the VBSs when both structural uncertainty and stochastic excitations are considered. In the present study, a harmonic-wavelet approach is proposed to estimate the time-varying RPSs of the VBSs with random parameters. The second-order differential equations of motion of VBSs with random parameters are first transformed into linear algebraic equations with random coefficient matrices using a harmonic-wavelet analysis technique; then, the excitation-response spectral relation of VBSs is derived based on these linear algebraic equations. Finally, the RPSs of VBSs with uncertain parameters are solved using the perturbation technique. The accuracy of the proposed method was verified by comparing it with the Monte Carlo method using a numerical example of railway VBS. The numerical simulation results show that the parameter uncertainties significantly affect the RPSs of the VBSs and increase the amplitude of the time-varying RPSs. The uncertainty of vehicle stiffness was the most sensitive factor for vehicle RPSs, and the bridge elastic modulus was the most sensitive factor for the bridge RPSs.

Optimal Frequency-domain Analysis for Spacecraft Time Series: Introducing the Missing-data Multitaper Power Spectrum Estimator

While the Lomb–Scargle periodogram is foundational to astronomy, it has a significant shortcoming: the variance in the estimated power spectrum does not decrease as more data are acquired. Statisticians have a 60 yr history of developing variance-suppressing power spectrum estimators, but most are not used in astronomy because they are formulated for time series with uniform observing cadence and without seasonal or daily gaps. Here we demonstrate how to apply the missing-data multitaper power spectrum estimator to spacecraft data with uniform time intervals between observations but missing data during thruster fires or momentum dumps. The F-test for harmonic components may be applied to multitaper power spectrum estimates to identify statistically significant oscillations that would not rise above a white noise–based false alarm probability. Multitapering improves the dynamic range of the power spectrum estimate and suppresses spectral window artifacts. We show that the multitaper–F-test combination applied to Kepler observations of KIC 6102338 detects differential rotation without requiring iterative sinusoid fitting and subtraction. Significant signals reside at harmonics of both fundamental rotation frequencies and suggest an antisolar rotation profile. Next we use the missing-data multitaper power spectrum estimator to identify the oscillation modes responsible for the complex “scallop-shell” shape of the K2 light curve of EPIC 203354381. We argue that multitaper power spectrum estimators should be used for all time series with regular observing cadence.

Study of the Reasonable Acquisition Frequency Evaluation Method of Midspan Deflection of Medium- and Small-Span Beam Bridges

The objective of this study is to further promote and apply the structural monitoring system to medium and small bridges, given the relative delays in scientific research, technical specifications, and engineering practice for the safety monitoring of small and medium-span girder bridges, as well as the relative simplicity of the structural system of these bridges, their well-defined forces, and the relatively large proportion of live load responses during operation. These concepts are proposed based on the evaluation method of live loading (As therefore, this paper suggests the notion of sensor acquisition frequency and appropriate acquisition frequency based on the live load assessment method and the fundamental reliability theory). Based on the time-history curve depicting the midspan deflection response of the vehicle-bridge coupling system, the frequency domain analysis reveals that the power spectrum at −3 dB corresponds to the response cutoff frequency. Significantly, the cutoff frequency mentioned is double the acquisition frequency considered suitable for the study. Based on the definition of a quasi-static response, it can be deduced that the velocity of a load does not exert any influence on the quasi-static response of a bridge structure. As a result, the derivation of the components related to the midspan deflection of a bridge’s quasi-static response is presented, together with a recommended set of methodological guidelines for the extraction of finite elements. This study introduces a novel approach for determining the cutoff frequency of the structural response by utilizing the characteristics of amplitude spectrum estimation and power spectrum estimation in frequency domain analysis. The cutoff frequency of the signal is determined by analyzing the amplitude-frequency curve of the power spectrum. Subsequently, the probability density function of the original time-history curve data is estimated based on the amplitude spectrum. Finally, reliability analysis is conducted by calculating the ratio of the amplitude spectrum area of the signal obtained through a reasonable acquisition frequency to the area of the amplitude spectrum function of the original signal. This analysis verifies the reliability of the proposed method for determining the midspan deflection acquisition frequency.

Non-stationary astrophysical stochastic gravitational-wave background: a new probe to the high-redshift population of binary black holes

ABSTRACT The astrophysical stochastic gravitational-wave background (SGWB) originates from the mergers of compact binary objects that are otherwise undetected as individual events, along with other sources such as supernovae, magnetars, etc. The individual gravitational-wave (GW) signal is time-varying over a time-scale that depends on the chirp mass of the coalescing binaries. Another time-scale that plays a role is the time-scale at which the sources repeat, which depends on the merger rate. The combined effect of these two leads to a breakdown of the time translation symmetry of the observed SGWB and a correlation between different frequency modes in the signal covariance matrix of the SGWB. Using an ensemble of SGWB due to binary black hole coalescence, calculated using simulations of different black hole mass distributions and merger rates, we show how the structure of the signal covariance matrix varies. This structure in the signal covariance matrix brings additional information about the sources on top of the power spectrum. We show that there is a significant improvement in the figure of merit by using this additional information in comparison to only power spectrum estimation for the LIGO–Virgo–KAGRA (LVK) network of detectors with the design sensitivity noise with 2 yr of observation. The inclusion of the off-diagonal correlation in the covariance of the SGWB in the data analysis pipelines will be beneficial in the quest for the SGWB signal in LVK frequency bands as well as in lower frequencies and in getting an insight into its origin.

Lifting Wavelets with OGS for Doppler Profile Estimation

This article discusses the second-generation wavelet transform concept and technique and its application to the noise removal problem of MST radar data. Located near Gadanki in Andhra Pradesh, India, the MST radar is collecting data on climate change. To obtain weather data, the signal collected by the radar needs to be analyzed, which usually requires power spectrum estimation. Most parametric and non-parametric methods cannot predict Doppler at an altitude above 14 KM, which makes to search for introduction of new denoising methods. More research is predominantly done on many denoising algorithms and tested with the simulated signal with various thresholds. It is observed that Lifting wavelets (LWT) with OGS is more effective in denoising the signals. Split, predict, and update are the three phases of lifting transform which on application of these steps reduces noise effectively. The LWT with OGS is applied to MST radar data and the research results shows that the noise level is reduced at higher altitudes and the signal-to-noise ratio is improved.

Large-scale turbulence cascade in the spiral galaxy NGC 6946

ABSTRACT The generation mechanism of compressible fluid turbulence at kiloparsec scales in the interstellar medium is a long-lasting puzzle. In this work, we explore the nature of large-scale turbulence in the external spiral galaxy NGC 6946. We use the visibility moment estimator to measure the H i column density and line-of-sight turbulent velocity power spectra combining the new observations of A array configuration of Karl G. Jansky Very Large Array (VLA) with the VLA B, C, D array observations from The H i Nearby Galaxy Survey. The estimated power spectra are obeying a power law with a slope of −0.96 ± 0.05 in column density and −1.81 ± 0.07 in line-of-sight velocity in length-scales ranging from 6 kpc to 170 pc. This points towards a forward energy cascade in the plane of the disc with a driving scale at least as large as 6 kpc. The values of the power-law indices indicate a combination of solenoidal and compressive force responsible for driving the measured turbulence. The presence of strong regular magnetic fields from the magnetic spiral arms in the galaxy is possibly contributing to the solenoidal part, while self-gravity or gravitational instability can mostly be the input for the compressive part of the forcing in the driving mechanism.

Sub-Nyquist sampling-based wideband spectrum sensing: a compressed power spectrum estimation approach

Sub-Nyquist sampling-based wideband spectrum sensing: a compressed power spectrum estimation approach

Robust Space-Time Adaptive Processing Method for GNSS Receivers in Coherent Signal Environments

In the coherent signal environments caused by multipath propagation, the interference suppression performance of the global navigation satellite systems (GNSS) receivers decreases sharply. In this paper, a robust space-time adaptive processing (STAP) method for GNSS receivers is proposed to suppress interferences in coherent signal environments, by using the modified space-time two-dimensional iterative adaptive approach (ST2D-IAA) spectrum estimation. This method applies the IAA algorithm to the ST2D signal model of GNSS receivers, and further modifies the ST2D-IAA algorithm to accurately estimate the power spectrum and noise power simultaneously. The space-time interference-plus-noise covariance matrix (STINCM) is reconstructed by using the estimated power spectrum and noise power in the interference angle region. Based on the reconstructed STINCM, we construct the STAP beamforming optimization problem for the space-time steering vector (STSV) error vector, and further correct the STSV of GNSS signal. Finally, the weight vector of STAP beamforming is calculated by using the reconstructed STINCM and the corrected STSV of GNSS signal. Simulation results show that the proposed method can suppress interferences in coherent signal environments and outperforms the current methods.

The Impact of Beam Variations on Power Spectrum Estimation for 21 cm Cosmology. II. Mitigation of Foreground Systematics for HERA

One key challenge in detecting a 21 cm cosmological signal at z > 6 is to separate the cosmological signal from foreground emission. This can be studied in a power spectrum space where the foreground is confined to low delay (or, equivalently, k ∥) modes, whereas the cosmological signal can spread out to high delay modes. When there is a calibration error, however, the chromaticity of the gain errors propagates to the power spectrum estimate and contaminates the modes for cosmological detection. The Hydrogen Epoch of Reionization Array (HERA) employs a high-precision calibration scheme using redundancy in measurements. In this study, we focus on the gain errors induced by nonredundancies arising from a feed offset relative to HERA’s 14 m parabolic dish element and investigate how to mitigate the chromatic gain errors using three different methods: restricting baseline lengths for calibration, smoothing the antenna gains, and applying a temporal filter prior to calibration. With 2 cm/2° perturbations for translation/tilting motions, a level achievable under normal HERA operating conditions, the combination of the baseline cut and temporal filtering indicates that the spurious gain feature due to nonredundancies is significantly reduced, and the power spectrum recovers the clean foreground-free region. We found that the mitigation technique works even for large feed motions, but in order to keep a stable calibration process, the feed positions need to be constrained to 2 cm for translation motions and 2° for tilting offset relative to the dish’s vertex.

Method for comparison testing of parametric power spectrum estimates: spectral analysis via time series synthesis

Method for comparison testing of parametric power spectrum estimates: spectral analysis via time series synthesis

Discovering the neuronal dynamics in major depressive disorder using Hidden Markov Model.

Major Depressive Disorder (MDD) is a leading cause of worldwide disability, and standard clinical treatments have limitations due to the absence of neurological evidence. Electroencephalography (EEG) monitoring is an effective method for recording neural activities and can provide electroneurophysiological evidence of MDD. In this work, we proposed a probabilistic graphical model for neural dynamics decoding on MDD patients and healthy controls (HC), utilizing the Hidden Markov Model with Multivariate Autoregressive observation (HMM-MAR). We testified the model on the MODMA dataset, which contains resting-state and task-state EEG data from 53 participants, including 24 individuals with MDD and 29 HC. The experimental results suggest that the state time courses generated by the proposed model could regress the Patient Health Questionnaire-9 (PHQ-9) score of the participants and reveal differences between the MDD and HC groups. Meanwhile, the Markov property was observed in the neuronal dynamics of participants presented with sad face stimuli. Coherence analysis and power spectrum estimation demonstrate consistent results with the previous studies on MDD. In conclusion, the proposed HMM-MAR model has revealed its potential capability to capture the neuronal dynamics from EEG signals and interpret brain disease pathogenesis from the perspective of state transition. Compared with the previous machine-learning or deep-learning-based studies, which regarded the decoding model as a black box, this work has its superiority in the spatiotemporal pattern interpretability by utilizing the Hidden Markov Model.

Accurate estimation of angular power spectra for maps with correlated masks

The widely used MASTER approach for angular power spectrum estimation was developed as a fast ${C}_{\ensuremath{\ell}}$ estimator on limited regions of the sky. This method expresses the power spectrum of a masked map (``pseudo-${C}_{\ensuremath{\ell}}$'') in terms of the power spectrum of the unmasked map (the true ${C}_{\ensuremath{\ell}}$) and that of the mask or weight map. However, it is often the case that the map and mask are correlated in some way, such as point source masks used in cosmic microwave background (CMB) analyses, which have nonzero correlation with CMB secondary anisotropy fields and other mm-wave sky signals. In such situations, the MASTER approach gives biased results, as it assumes that the unmasked map and mask have zero correlation. While such effects have been discussed before with regard to specific physical models, here we derive a completely general formalism for any case where the map and mask are correlated. We show that our result (``reMASTERed'') reconstructs ensemble-averaged pseudo-${C}_{\ensuremath{\ell}}$ to effectively exact precision, with significant improvements over traditional estimators for cases where the map and mask are correlated. In particular, we obtain an improvement in the mean absolute percent error from 30% with the MASTER result to essentially no error with the reMASTERed result for an integrated Sachs-Wolfe (ISW) field map with a mask built from the thresholded ISW field, and 10% to effectively zero for a Compton-$y$ map combined with an infrared source mask (the latter being directly relevant to actual data analysis). An important consequence of our result is that for maps with correlated masks, it is no longer possible to invert a simple equation to obtain the true ${C}_{\ensuremath{\ell}}$ from the pseudo-${C}_{\ensuremath{\ell}}$. Instead, our result necessitates the use of forward modeling from theory space into the observable domain of the pseudo-${C}_{\ensuremath{\ell}}$. Our code is publicly available in reMASTERed.https://github.com/kmsurrao/reMASTERed.

New EoR power spectrum limits from MWA Phase II using the delay spectrum method and novel systematic rejection

ABSTRACT We present an analysis of Epoch of Reionization (EoR) data from Phase II of the Murchison Widefield Array using the simpleds delay spectrum pipeline. Prior work analysed the same observations using the fhd/εppsilon imaging pipeline, and so the present analysis represents the first time that both principal types of 21 cm cosmology power spectrum estimation approaches have been applied to the same data set. Our limits on the 21 cm power spectrum amplitude span a range in k space of $|k| \lt 1 \, h_{100}\, {\rm Mpc}^{-1}$ with a lowest measurement of Δ2(k) ≤ 4.58 × 103 mK2 at $k = 0.190\, h_{100}\, \rm {Mpc}^{-1}$ and z = 7.14. In order to achieve these limits, we need to mitigate a previously unidentified common mode systematic in the data set. If not accounted for, this systematic introduces an overall negative bias that can make foreground contaminated measurements appear as stringent, noise-limited constraints on the 21 cm signal amplitude. The identification of this systematic highlights the risk in modelling systematics as positive-definite contributions to the power spectrum and in ‘conservatively’ interpreting all measurements as upper limits.

Why and when to expect Gaussian error distributions in epoch of reionization 21-cm power spectrum measurements

ABSTRACTWe explore error distributions in Epoch of Reionization 21-cm power spectrum estimators using a combination of mathematical analysis and numerical simulations. We provide closed-form solutions for the error distributions of individual bins in 3d-power spectra for two estimators currently in use in the field, which we designate as ‘straight-square’ and ‘cross-multiply’ estimators. We then demonstrate when the corresponding spherically binned power spectra should (and should not) have Gaussian error distributions, which requires appealing to non-standard statements of the central limit theorem. This has important implications for how upper limits are reported, as well as how cosmological inferences are performed based on power spectrum measurements. Specifically, assuming a Gaussian error distribution can over- or underestimate the upper limit depending on the type of estimator and produces overly compact likelihood functions for the power spectrum.

Design of an intelligent hybrid diagnosis scheme for cyber-physical PV systems at the microgrid level

With focusing on solar photovoltaic (PV) systems operating at microgrid (MG) level, this study investigates the impacts of different physical faults and cyberattacks as well as designing an intelligent faults/attacks detection and diagnosis system. The ability to quickly identify and diagnose faults/attacks enables local controllers and energy management system to accommodate or mitigate the negative effects of physical faults or cyberattacks in a MG. This allows the MG to carry on operating without experiencing any significant interruptions. In this regard, the current paper investigates a hybrid AC/DC MG made up of different distributed energy resources (DER), including solar PV arrays, wind turbines, and battery energy storage systems. An intelligent hybrid diagnosis (IHD) scheme is introduced for online monitoring and diagnosing the data to reflect the real-time status of the PV system operating at the MG level. This hybrid system uses three parallel units, including a “fuzzy inference system (i.e., a rule-based unit)”, a “power spectrum estimator (i.e., a signal-based unit)”, and an “adaptive neuro-fuzzy inference system (i.e., a model-based unit)”. A realistic MG benchmark model with a wide range of operating conditions and dynamic electrical loads in the presence of potential MG disturbances is used to demonstrate the high performance and resilience of the proposed IHD scheme under various types of faults/attacks scenarios.

Estimation of the Full-sky Power Spectrum between Intermediate and Large Angular Scales from Partial-sky CMB Anisotropies Using an Artificial Neural Network

Reliable extraction of cosmological information from observed cosmic microwave background (CMB) maps may require removal of strongly foreground-contaminated regions from the analysis. In this paper, we employ an artificial neural network (ANN) to predict the full-sky CMB angular power spectrum between intermediate and large angular scales from the partial-sky spectrum obtained from a masked CMB temperature anisotropy map. We use a simple ANN architecture with one hidden layer containing 895 neurons. Using 1.2 × 105 training samples of full-sky and corresponding partial-sky CMB angular power spectra at HEALPix pixel resolution parameter N side = 256, we show that the spectrum predicted by our ANN agrees well with the target spectrum at each realization for the multipole range 2 ≤ l ≤ 512. The predicted spectra are statistically unbiased, and they preserve the cosmic variance accurately. Statistically, the differences between the mean predicted and underlying theoretical spectra are within approximately 3σ. Moreover, the probability densities obtained from predicted angular power spectra agree very well with those obtained from “actual” full-sky CMB angular power spectra for each multipole. Interestingly, our work shows that the significant correlations in input cut-sky spectra due to mode–mode coupling introduced on the partial sky are effectively removed, since the ANN learns the hidden pattern between the partial- and full-sky spectra preserving all of the statistical properties. The excellent agreement of statistical properties between the predicted and the ground truth demonstrates the importance of using artificial intelligence systems in cosmological analysis more widely.

All-sky modelling requirements for Bayesian 21 cm power spectrum estimation with bayeseor

ABSTRACT We present a comprehensive simulation-based study of the bayeseor code for 21 cm power spectrum recovery when analytically marginalizing over foreground parameters. To account for covariance between the 21 cm signal and contaminating foreground emission, bayeseor jointly constructs models for both signals within a Bayesian framework. Due to computational constraints, the forward model is constructed using a restricted field of view (FoV) in the image domain. When the only Epoch of Reionization contaminants are noise and foregrounds, we demonstrate that bayeseor can accurately recover the 21 cm power spectrum when the component of sky emission outside this forward-modelled region is downweighted by the beam at the level of the dynamic range between the foreground and 21 cm signals. However, when all-sky foreground emission is included along with a realistic instrument primary beam with sidelobes above this threshold extending to the horizon, the recovered power spectrum is contaminated by unmodelled sky emission outside the restricted FoV model. Expanding the combined cosmological and foreground model to cover the whole sky is computationally prohibitive. To address this, we present a modified version of bayeseor that allows for an all-sky foreground model, while the modelled 21 cm signal remains only within the primary FoV of the telescope. With this modification, it will be feasible to run an all-sky bayeseor analysis on a sizeable compute cluster. We also discuss several future directions for further reducing the need to model all-sky foregrounds, including wide-field foreground subtraction, an image-domain likelihood utilizing a tapering function, and instrument primary beam design.

Impact of instrument and data characteristics in the interferometric reconstruction of the 21 cm power spectrum

ABSTRACT Combining the visibilities measured by an interferometer to form a cosmological power spectrum is a complicated process. In a delay-based analysis, the mapping between instrumental and cosmological space is not a one-to-one relation. Instead, neighbouring modes contribute to the power measured at one point, with their respective contributions encoded in the window functions. To better understand the power measured by an interferometer, we assess the impact of instrument characteristics and analysis choices on these window functions. Focusing on the Hydrogen Epoch of Reionization Array (HERA) as a case study, we find that long-baseline observations correspond to enhanced low-k tails of the window functions, which facilitate foreground leakage, whilst an informed choice of bandwidth and frequency taper can reduce said tails. With simple test cases and realistic simulations, we show that, apart from tracing mode mixing, the window functions help accurately reconstruct the power spectrum estimator of simulated visibilities. The window functions depend strongly on the beam chromaticity and less on its spatial structure – a Gaussian approximation, ignoring side lobes, is sufficient. Finally, we investigate the potential of asymmetric window functions, down-weighting the contribution of low-k power to avoid foreground leakage. The window functions presented here correspond to the latest HERA upper limits for the full Phase I data. They allow an accurate reconstruction of the power spectrum measured by the instrument and will be used in future analyses to confront theoretical models and data directly in cylindrical space.

Problem of power spectra estimation in application to the analysis of heart rate variability

Problem of power spectra estimation in application to the analysis of heart rate variability

Analysis and Estimation of Power Spectrum by EEG During the Kraepelin Test with or Without Rhythm

In this paper, by measuring EEG during the Kraepelin test, it was clarified that the optimal rhythm which maximized the number of answers was found to be 1.2-times, when the rhythm answering without rhythm was set at 1.0-times. It was clarified that when the optimum rhythm was listened to, the ratio of power spectrum for relaxation/concentration was higher, the standard deviation of that ratio was smaller, and the activation of the left and right brains was not unbalanced. The power spectrum of the EEG while listening to the rhythm and answering the Kraepelin test was estimated from the EEG when answering without rhythm, and the error was less than 10%.