Harmonic Decomposition Research Articles

Handling-Qualities Perspective on Rotorcraft Load Alleviation Control

The objective of this research effort is to assess the impact of load alleviation control on the quantitative handling-qualities specifications (also known as predicted handling qualities) of both conventional helicopters and compound rotorcraft in forward flight. First, an overview on how the harmonic decomposition methodology is used toward load alleviation control is presented. Next, flight control laws are developed based on an explicit model-following architecture. Parametric studies are performed to provide insights on how both the feedforward and feedback paths of the model-following control laws can be used to alleviate the rotor loads. The impact of load alleviation on predicted handling qualities is studied. It is shown that, for the standard helicopter configuration considered, load alleviation comes at the cost of a degradation in handling qualities. However, for the compound rotorcraft considered, allocation of the control signal to the redundant control surfaces provides load alleviation without degradation in predicted handling qualities. The flight control laws are subsequently optimized using the Control Designer’s Unified Interface to meet a comprehensive set of stability, handling-qualities, and performance specifications for specific mission task elements while minimizing the unsteady rotor loads.

Data-adaptive harmonic analysis of oceanic waves and turbulent flows.

We introduce new features of data-adaptive harmonic decomposition (DAHD) that are showcased to characterize spatiotemporal variability in high-dimensional datasets of complex and mutsicale oceanic flows, offering new perspectives and novel insights. First, we present a didactic example with synthetic data for identification of coherent oceanic waves embedded in high amplitude noise. Then, DAHD is applied to analyze turbulent oceanic flows simulated by the Regional Oceanic Modeling System and an eddy-resolving three-layer quasigeostrophic ocean model, where resulting spectra exhibit a thin line capturing nearly all the energy at a given temporal frequency and showing well-defined scaling behavior across frequencies. DAHD thus permits sparse representation of complex, multiscale, and chaotic dynamics by a relatively few data-inferred spatial patterns evolving with simple temporal dynamics, namely, oscillating harmonically in time at a given single frequency. The detection of this low-rank behavior is facilitated by an eigendecomposition of the Hermitian cross-spectral matrix and resulting eigenvectors that represent an orthonormal set of global spatiotemporal modes associated with a specific temporal frequency, which in turn allows to rank these modes by their captured energy and across frequencies, and allow accurate space-time reconstruction. Furthermore, by using a correlogram estimator of the Hermitian cross-spectral density matrix, DAHD is both closely related and distinctly different from the spectral proper orthogonal decomposition that relies on Welch's periodogram as its estimator method.

Mixed higher-order anisotropic flow and nonlinear response coefficients of charged particles in mathrm {PbPb} collisions at sqrt{smash [b]{s_{_{mathrm {NN}}}}} = 2.76 and 5.02,text {TeV}

Anisotropies in the initial energy density distribution of the quark-gluon plasma created in high energy heavy ion collisions lead to anisotropies in the azimuthal distributions of the final-state particles known as collective anisotropic flow. Fourier harmonic decomposition is used to quantify these anisotropies. The higher-order harmonics can be induced by the same order anisotropies (linear response) or by the combined influence of several lower order anisotropies (nonlinear response) in the initial state. The mixed higher-order anisotropic flow and nonlinear response coefficients of charged particles are measured as functions of transverse momentum and centrality in mathrm {PbPb} collisions at nucleon-nucleon center-of-mass energies sqrt{smash [b]{s_{_{mathrm {NN}}}}} = 2.76 and 5.02,text {TeV} with the CMS detector. The results are compared with viscous hydrodynamic calculations using several different initial conditions, as well as microscopic transport model calculations. None of the models provides a simultaneous description of the mixed higher-order flow harmonics and nonlinear response coefficients.

Interlocked attosecond pulse trains in slightly bi-elliptical high harmonic generation

The ellipticity of high harmonics driven by bi-chromatic (e.g. ) co-propagating fields can be fully tuned by varying the polarization of the pump components. In order to start revealing the underlying mechanism of this control, we explore a relatively simple regime of this scheme that still gives rise to full control over the harmonics ellipticities. In this regime, the pumps are only slightly elliptical and the high harmonic radiation consists of two (different) interlocked attosecond pulse trains (APTs). We formulate a semi-analytic model that maps the high harmonic ellipticity to properties of the APTs harmonic decompositions. Utilizing this model, we reconstruct these APTs variables from measurements of the high harmonics ellipticities. This ellipticity-resolved spectroscopy of interlocked APTs may be useful for ultrafast probing of chiral degrees of freedom.

Layered crustal anisotropy and deformation in the SE Tibetan plateau revealed by Markov-Chain-Monte-Carlo inversion of receiver functions

The southeastern (SE) Tibetan plateau is uplifting accompanying strong seismicity, but the relationship between the crustal structure and tectonic process in this region is still unclear. Seismic anisotropy provides important clues for the deformation mechanism. Here we applied the harmonic decomposition approach and further conducted a Markov-Chain-Monte-Carlo (MCMC) inversion to analyze the crustal anisotropy from receiver functions using waveforms recorded by dense stations in the SE Tibetan plateau. More spatial details on the crustal anisotropy and interface are determined consequently. While the anisotropies in the upper crust are relatively weak (~2%), the anisotropies in the mid-lower crust are mostly stronger than 4%. The fast polarization directions (FPDs) in the mid-lower crust show a dominant circular pattern, in good coherence with the topographic contours, indicating that the crustal deformations in the SE Tibetan plateau may be mainly controlled by the gravity potential. Because of the significant Moho steps along the plateau margin, the extruded deep crustal materials are blocked by the strong crust around so that the minerals are aligned to be sub-parallel to the plateau margins.

Determination of the corrosion resistance of low alloyed steels by magnetic method

An innovative method of measuring and control of the steel corrosion rate by changing magnetic characteristics is developed. The impact of heat treatment on the corrosion rate of the samples of high-carbon steels (maximum corrosion loss is observed at a tempering temperature of 400°C) is attributed to the appearance of micro-galvanic pairs (MGP) between the phase components of the material. MGP undergo redistribution under heat treatment thus changing conditions of the galvanic current flow. The structural phase composition, in turn, determines the magnetic properties of steel and correlation between the magnetic properties and corrosiveness. The goal of the study is demonstration of the possibility and expediency of using the magnetic parameters of steel for determination of the steel corrosion rate. A close correlation dependence is observed between the coercive force and the electrochemical potential (relative to the silver chloride electrode) which are direct indicators of the corrosiveness. Case study of a pipeline made of 09G2S steel along which change in the coercive force attained 25% revealed rather high risk of developing micro-galvanic pairs. A rapid method of scanning magnetic parameters is proposed to detect potentially corrosive zones. A multi-parameter approach can be used to solve the problem of the ambiguity of the relationship between the corrosiveness and magnetic parameters. Harmonic decomposition of magnetic hysteresis loops of 45Kh steel samples is used to obtain a number of odd harmonics. Some of them weakly correlate with the corrosion loss, whereas complexes of several harmonics correlate to a greater extent. The results can be used in technical diagnostics and prediction of the corrosion activity of steel structures before their operation. The results can be used in technical diagnostics and forecasting of the corrosiveness of steel structures prior to their operation.

A novel method for leaf chlorophyll retrieval based on harmonic analysis: a case study on Spartina alterniflora

Spartina alterniflora is the main invasive vegetation in wetland ecosystems, and information on its chlorophyll content is important data for quantitative research on the key ecological functions of wetland ecosystems. The Dongtan wetland of the Yangtze River estuary was used as the experimental research area, and the artificial cultivation field of Eupatorium was taken as the research object. To prevent uncertainty in the calculation of the chlorophyll content inversion factor for Spartina alterniflora leaves, harmonic analysis theory was adopted in this study. First, the original measured spectral data in the range of 400 nm ~ 1000 nm were decomposed and reconstructed by empirical mode decomposition (EMD), and the harmonic characteristic parameters of the EMD reconstruction spectral data were obtained by harmonic analysis (HA). Meanwhile, using the PROSPECT-D radiation transfer model, the simulated data was used to validate the inversion model. Based on these harmonic characteristic parameters, harmonic analysis-back propagation (HA-BP) and stepwise multiple linear regression (SMLR) models were established. Finally, the model was validated with data simulated by the PROSPECT-D model and compared the measured chlorophyll contents using the inversion values of the two models. The results show that the inversion accuracy of the HA-BP model was highest for the measured data. The determination coefficient (R2) and root mean square error (RMSE) of the model were 0.8528 and 6.8968 (μg/cm2), respectively, and the inversion accuracy of the simulated data was slightly lower than that of the measured data. The results show that the original spectral noise could be effectively suppressed by EMD and reconstruction, while harmonic analysis could compress the signal and prevent uncertainty in the spectral parameter calculation. Thus, the harmonic decomposition method could be applied to the inversion of Spartina alterniflora chlorophyll contents. The methods in this research provide a theoretical basis and technical support for the use of frequency domain parameters for the inversion of vegetation pigment contents.

Scalar perturbations in f(T) gravity using the 1 + 3 covariant approach

The cosmological scalar perturbations of standard matter are investigated in the context of extended teleparallel f(T) gravity theories using the 1+3 covariant formalism. After a review of the background gravitational field equations of f(T) gravity and the introduction of the covariant perturbation variables, the usual scalar and harmonic decomposition have been performed, and the analysis of the growth of the density contrasts in the quasi-static approximation for two non-interacting fluids scenarios, namely torsion-dust and torsion-radiation mixtures is presented for the generic f(T) gravity theory. Special applications to two classes of f(T) gravity toy models, namely f(T) = mu T_0 Big (frac{T}{T_0}Big )^n and f(T) = T+ mu T_0 Big (-frac{T}{T_0}Big )^n, have then been made within the observationally viable regions of their respective parameter spaces, and the growth of the matter density contrast for both torsion-dust and torsion-radiation epochs of the Universe has been examined. The exact solutions of the dust perturbations, with growing amplitudes in cosmic time, are obtained for some limiting cases of n. Similarly, the long- and short-wavelength modes in the torsion-radiation case are treated, with the amplitudes either oscillating or monotonically growing with time. Overall, it is noted that f(T) models contain a richer set of observationally viable structure growth scenarios that can be tested against up-and-coming observational data and can accommodate currently known features of the large-scale structure power spectrum in the general relativistic and varLambda CDM limits.

Symmetry Classes and Matrix Representations of the 2D Flexoelectric Law

We determine the different symmetry classes of bi-dimensional flexoelectric tensors. Using the harmonic decomposition method, we show that there are six symmetry classes. We also provide the matrix representations of the flexoelectric tensor and of the complete flexoelectric law, for each symmetry class.

A Novel Method to Remove Interference Fringes for Hyperspectral SWIR Imagers

A hyperspectral short-wave infrared (SWIR) imager with a HgCdTe focal plane detector usually suffers from interference fringes in spectral and spatial dimension due to the etalon effect. It can cause a modulation of sensitivity higher than 15% when the spectral resolution is higher than 10 nm. In this article, a two-step method is proposed and evaluated to remove interference fringes for hyperspectral SWIR imagers. First, we extract the spectral data, conduct harmonic decomposition to suppress the fringes in spectral dimension, and calculate the correction coefficients. Second, we optimize the correction coefficients according to the distribution of the interference fringes in spatial dimension. Sample SWIR images acquired from the Advanced Hyperspectral Imager (AHSI) on China’s GaoFen-5 satellite are used to evaluate the performance of the algorithm. It shows that the proposed method can well preserve the original spectral pattern and reduce the peak-to-peak amplitude of spatial fringing from ±15% to ±4%. The method is compared with three other previously proposed methods. It turns out that the newly proposed method has strong adaptability, high accuracy, and high efficiency.

The solar wind from a stellar perspective

Context.Due to the effects that they can have on the atmospheres of exoplanets, stellar winds have recently received significant attention in the literature. Alfvén-wave-driven 3D magnetohydrodynamic models, which are increasingly used to predict stellar wind properties, contain unconstrained parameters and rely on low-resolution stellar magnetograms.Aims.In this paper, we explore the effects of the input Alfvén wave energy flux and the surface magnetogram on the wind properties predicted by the Alfvén Wave Solar Model (AWSoM) model for both the solar and stellar winds.Methods.We lowered the resolution of two solar magnetograms during solar cycle maximum and minimum using spherical harmonic decomposition. The Alfvén wave energy was altered based on non-thermal velocities determined from a far ultraviolet spectrum of the solar twin 18 Sco. Additionally, low-resolution magnetograms of three solar analogues, 18 Sco, HD 76151, and HN Peg, were obtained using Zeeman Doppler imaging and used as a proxy for the solar magnetogram. Finally, the simulated wind properties were compared to Advanced Composition Explorer (ACE) observations.Results.AWSoM simulations using well constrained input parameters taken from solar observations can reproduce the observed solar wind mass loss and angular momentum loss rates. The simulated wind velocity, proton density, and ram pressure differ from ACE observations by a factor of approximately two. The resolution of the magnetogram has a small impact on the wind properties and only during cycle maximum. However, variation in Alfvén wave energy influences the wind properties irrespective of the solar cycle activity level. Furthermore, solar wind simulations carried out using the low-resolution magnetogram of the three stars instead of the solar magnetogram could lead to an order of a magnitude difference in the simulated solar wind properties.Conclusions.The choice in Alfvén energy has a stronger influence on the wind output compared to the magnetogram resolution. The influence could be even stronger for stars whose input boundary conditions are not as well constrained as those of the Sun. Unsurprisingly, replacing the solar magnetogram with a stellar magnetogram could lead to completely inaccurate solar wind properties, and should be avoided in solar and stellar wind simulations. Further observational and theoretical work is needed to fully understand the complexity of solar and stellar winds.

Probing the azimuthal environment of galaxies around clusters

Galaxy clusters are connected at their peripheries to the large-scale structures by cosmic filaments that funnel accreting material. These filamentary structures are studied to investigate both environment-driven galaxy evolution and structure formation and evolution. In the present work, we probe in a statistical manner the azimuthal distribution of galaxies around clusters as a function of the cluster-centric distance, cluster richness, and star-forming or passive galaxy activity. We performed a harmonic decomposition in large photometric galaxy catalogue around 6400 SDSS clusters with masses M > 1014 solar masses in the redshift range of 0.1 < z < 0.3. The same analysis was performed on the mock galaxy catalogue from the light cone of a Magneticum hydrodynamical simulation. We used the multipole analysis to quantify asymmetries in the 2D galaxy distribution. In the inner cluster regions at R < 2R500, we confirm that the galaxy distribution traces an ellipsoidal shape, which is more pronounced for richest clusters. In the outskirts of the clusters (R = [2 − 8]R500), filamentary patterns are detected in harmonic space with a mean angular scale mmean = 4.2 ± 0.1. Massive clusters seem to have a larger number of connected filaments than lower-mass clusters. We also find that passive galaxies appear to trace the filamentary structures around clusters better. This is the case even if the contribution of star-forming galaxies tends to increase with the cluster-centric distance, suggesting a gradient of galaxy activity in filaments around clusters.

Acoustic Sensing of Forces Driving Fast Capillary Flows.

The popping sound of a bursting soap bubble is acquired using microphone arrays and analyzed using spherical harmonics decomposition. Using the theoretical framework of aeroacoustics, we demonstrate that this acoustic emission originates mainly from the capillary stresses exerted by the liquid soap film on the air and that it quantitatively reflects the out-of-equilibrium evolution of the flowing liquid film. This constitutes the proof of concept that the acoustic signature of violent events of physical or biological origin could be used to measure the forces at play during these events.

A Causality-Based View of the Interaction between Synoptic- and Planetary-Scale Atmospheric Disturbances

AbstractThis paper reports preliminary yet encouraging findings on the use of causal discovery methods to understand the interaction between atmospheric planetary- and synoptic-scale disturbances in the Northern Hemisphere. Specifically, constraint-based structure learning of probabilistic graphical models is applied to the spherical harmonics decomposition of the daily 500-hPa geopotential height field in boreal winter for the period 1948–2015. Active causal pathways among different spherical harmonics components are identified and documented in the form of a temporal probabilistic graphical model. Since, by definition, the structure learning algorithm used here only robustly identifies linear causal effects, we report only causal pathways between two groups of disturbances with sufficiently large differences in temporal and/or spatial scales, that is, planetary-scale (mainly zonal wavenumbers 1–3) and synoptic-scale disturbances (mainly zonal wavenumbers 6–8). Daily reconstruction of geopotential heights using only interacting scales suggest that the modulation of synoptic-scale disturbances by planetary-scale disturbances is best characterized by the flow of information from a zonal wavenumber-1 disturbance to a synoptic-scale circumglobal wave train whose amplitude peaks at the North Pacific and North Atlantic storm-track region. The feedback of synoptic-scale to planetary-scale disturbances manifests itself as a zonal wavenumber-2 structure driven by synoptic-eddy momentum fluxes. This wavenumber-2 structure locally enhances the East Asian trough and western Europe ridge of the wavenumber-1 planetary-scale disturbance that actively modulates the activity of synoptic-scale disturbances. The winter-mean amplitude of the actively interacting disturbances are characterized by pronounced fluctuations across interannual to decadal time scales.

Model-based estimation of vortex shedding in unsteady cylinder wakes

This paper considers single-sensor estimation of vortex shedding in cylinder wakes at $Re=100$ in simulations and at $Re=1036$ in experiments. A model based on harmonic decomposition is developed to capture the periodic dynamics of vortex shedding. Two model-based methods are proposed to estimate time-resolved flow fields. First, Linear Estimation (LE) which implements a Kalman Filter to estimate the flow. Second, Linear-Trigonometric Estimation (LTE), which utilizes the same Kalman Filter together with a nonlinear relationship between harmonics of the vortex shedding frequency. LTE shows good performance and outperforms LE regarding the reconstruction of vortex shedding. Physically this suggests that, at the Reynolds numbers considered, the higher harmonic motions in the cylinder wake are slave to the fundamental frequency.

Spherical Fraction Beamforming

This paper describes a beamforming method for one-eighth, quarter, and half-spaces, bounded by rigid planes. The proposed approach is based on the spherical fraction harmonic decomposition, similar to that of spherical harmonics decomposition for the whole sphere. The definition of these functions is given in detail. It is also proved that they form a sub-basis of the spherical harmonics, with a fraction-dependent normalization gain, which makes it easy to adapt from existing spherical harmonics implementation. Taking advantage of the rigid boundary condition, it is shown that the number of spherical fraction harmonics used to construct a beamformer is less than the number of spherical harmonics used in the case of an unbounded domain. However, image beams are generated and can degrade the performance of the beamformer. For the response to a plane wave, it is shown that the angular error on the maximum, as well as the directivity factor are a function of the spherical fraction under consideration, the plane wave direction of arrival and the degree of decomposition $L$. As the latter increases and the spherical fraction is large, these two parameters are converging towards the unbounded case values with fewer functions to evaluate. An application case is presented.

Measuring Low-Order Photometric Parameters of Light Fields: Methods Exploration and Simulations

Low-order photometric parameters of light fields are important aspects determining lighting qualities but difficult to be measured. In this article, we did a systematical investigation into the performance of a cubic meter and a tetrahedron meter as well as an HDR panoramic map-based method in simultaneously recovering light density, direction, and diffuseness. Five metrics were introduced with two based on the measurement using a cubic illumination meter, two based on a tetrahedron shaped illumination meter and one based on SH decomposition of HDR panoramic maps. Furthermore, the measurement of five metrics was simulated under six HDR Panoramic maps of natural scenes in various postures which mimic the complexity of real environments. The results indicate that the measurement of low-order photometric parameters of light fields using Spherical Harmonics (i.e. latter referred to as SH) decomposition of HDR panoramic map gave the most reliable results. The tetrahedron meter based metrics gave more robust results in the measurement of light density while the cubic meter based metrics performed better when measuring light direction. This study also provides a solution for a more robust measurement of light diffuseness based on the ratio between the vector strength measured with a cubic meter and light density measured with a tetrahedron meter. With the quick development of high-speed built-in camera and mobile computing techniques, this research provides confidence in developing applications in mobile phone by capturing HDR panoramic maps or built in light meters to measure the low-order photometric parameters of light fields in 3D spaces.

A Deep Learning Framework for Robust DOA Estimation Using Spherical Harmonic Decomposition

Spherical harmonic decomposition facilitates decomposing the sound pressure at different microphones into independent functions of frequency, azimuth and elevation of the source and microphone locations. This decomposition facilitates the extraction of two sets of features containing different information about elevation and azimuth of the source for the direction of arrival (DOA) estimation. These features can be given as input to a learning approach for the estimation of azimuth and elevation separately. This approach aims at breaking down the problem of DOA estimation into azimuth and elevation estimation separately. An advantage of this is the reduction in computational complexity when compared with the joint DOA estimation. This facilitates a straightforward extension of this approach to denser DOA search grids. The contribution of this paper is threefold. First, we propose spherical harmonic magnitude and phase features and discuss the information present in these features regarding the azimuth and elevation of the source. Second, we propose the convolutional neural network architectures for DOA estimation. Third, we analyse the training, run-time computational complexities and propose to extend the DOA estimation approach to dense DOA search grid rather than restricting to a sparse DOA search grid. The performance of conventional DOA estimation approaches degrades in case of a noisy and reverberant environment. Several advancements to the existing DOA estimation approaches have been recently proposed. However, to the best of the authors’ knowledge, learning approaches to DOA estimation with dense DOA search grids with few frames in the context of spherical arrays have not been proposed. Performance evaluation is carried out using simulated as well as real datasets. The proposed approach is also evaluated on LOCATA dataset in the context of a moving source. The results are motivating enough to consider the application of the proposed method in practical scenarios.

Focusing and Frequency Smoothing for Arbitrary Arrays With Application to Speaker Localization

The coherent signal subspace method (CSSM) enables the direction-of-arrival (DoA) estimation of coherent sources with subspace localization methods. The focusing process that aligns the signal subspaces within a frequency band to its central frequency is central to the CSSM. Within current focusing approaches, a direction-independent focusing approach may be more suitable for reverberant environments since no initial estimation of the sources' DoAs is required. However, these methods use integrals over the steering function, and cannot be directly applied to arrays around complex scattering structures, such as robot heads. In this article, current direction-independent focusing methods are extended to arrays for which the steering function is available only for selected directions, typically in a numerical form. Spherical harmonics decomposition of the steering function is then employed to formulate several aspects of the focusing error. A case of two coherent sources is studied and guidelines for the selection of the frequency smoothing bandwidth are suggested. The performance of the proposed methods is then investigated for an array that is mounted on a robot head. The focusing process is integrated within the direct-path dominance (DPD) test method for speaker localization, originally designed for spherical arrays, extending its application to arrays with arbitrary configurations. Finally, experiments with real data verify the feasibility of the proposed method to successfully estimate the DoAs of multiple speakers under real-world conditions.

A comparison between two modal domain methods for personal audio reproduction.

Personal audio provides private and personalized listening experiences by generating sound zones in a shared space with minimal interference between zones. One challenge of the design is to achieve the best performance with a limited number of microphones and loudspeakers. In this paper, two modal domain methods for personal audio reproduction are compared. One is the spatial harmonic decomposition (SHD) based method and the other is the singular value decomposition (SVD) based method. It is demonstrated that the SVD based method provides a more efficient modal domain decomposition than the SHD method for 2.5 dimensional personal audio design. Simulation results show that the SVD based method outperforms the SHD one by up to 10 dB in terms of acoustic contrast and up to 17 dB in terms of reproduction error for a compact arc array with five loudspeakers, while requiring fewer microphones around the zone boundaries. The SVD based method retains the inherent efficiency of optimizing in a modal domain while avoiding the inherent geometric limitations of using SHD basis functions. Thus, this approach is advantageous for applications with flexible system geometries and a small number of loudspeakers and microphones.