Auto-power Spectrum Research Articles

MEASUREMENTS OF E-MODE POLARIZATION AND TEMPERATURE-E-MODE CORRELATION IN THE COSMIC MICROWAVE BACKGROUND FROM 100 SQUARE DEGREES OF SPTPOL DATA

We present measurements of $E$-mode polarization and temperature-$E$-mode correlation in the cosmic microwave background (CMB) using data from the first season of observations with SPTpol, the polarization-sensitive receiver currently installed on the South Pole Telescope (SPT). The observations used in this work cover 100~\sqdeg\ of sky with arcminute resolution at $150\,$GHz. We report the $E$-mode angular auto-power spectrum ($EE$) and the temperature-$E$-mode angular cross-power spectrum ($TE$) over the multipole range $500 < \ell \leq5000$. These power spectra improve on previous measurements in the high-$\ell$ (small-scale) regime. We fit the combination of the SPTpol power spectra, data from \planck\, and previous SPT measurements with a six-parameter \LCDM cosmological model. We find that the best-fit parameters are consistent with previous results. The improvement in high-$\ell$ sensitivity over previous measurements leads to a significant improvement in the limit on polarized point-source power: after masking sources brighter than 50\,mJy in unpolarized flux at 150\,GHz, we find a 95\% confidence upper limit on unclustered point-source power in the $EE$ spectrum of $D_\ell = \ell (\ell+1) C_\ell / 2 \pi < 0.40 \ \mu{\mbox{K}}^2$ at $\ell=3000$, indicating that future $EE$ measurements will not be limited by power from unclustered point sources in the multipole range $\ell < 3600$, and possibly much higher in $\ell.$

Probing small-scale non-Gaussianity from anisotropies in acoustic reheating

We give new constraints on small-scale non-Gaussianity of primordial curvature perturbations by the use of anisotropies in acoustic reheating. Mixing of local thermal or local kinetic equilibrium systems with different temperatures yields a locally averaged temperature rise, which is proportional to the square of temperature perturbations damping in the photon diffusion scale. Such secondary temperature perturbations are indistinguishable from the standard temperature perturbations linearly coming from primordial curvature perturbations and hence should be subdominant compared to the standard ones. We show that small-scale higher order correlation functions (connected non-Gaussian and disconnected Gaussian parts) of primordial curvature perturbations can be probed by investigating auto power spectrum of the generated secondary perturbations and the cross power spectrum with the standard perturbations. This is simply because these power spectra come from higher order correlation functions of primordial curvature perturbations with non-linear parameters such as fNL and τNL since secondary temperature perturbations are second order effects. Thus, the observational results l(l+1)CTTl≃ 6× 10−10 at large scales give a robust and universal upper bound on small-scale non-Gaussianities of primordial curvature perturbations.

Wavelet-based detection of abrupt changes in natural frequencies of time-variant systems

Detection of abrupt changes in natural frequencies from vibration responses of time-variant systems is a challenging task due to the complex nature of physics involved. It is clear that the problem needs to be analysed in the combined time–frequency domain. The paper proposes an application of the input–output wavelet-based Frequency Response Function for this analysis. The major focus and challenge relate to ridge extraction of the above time–frequency characteristics. It is well known that classical ridge extraction procedures lead to ridges that are smooth. However, this property is not desired when abrupt changes in the dynamics are considered. The methods presented in the paper are illustrated using simulated and experimental multi-degree-of-freedom systems. The results are compared with the classical Frequency Response Function and with the output only analysis based on the wavelet auto-power response spectrum. The results show that the proposed method captures correctly the dynamics of the analysed time-variant systems.

CROSS-CORRELATION BETWEEN THE CMB LENSING POTENTIAL MEASURED BYPLANCKAND HIGH-zSUBMILLIMETER GALAXIES DETECTED BY THEHERSCHEL-ATLAS SURVEY

We present the first measurement of the correlation between the map of the cosmic microwave background (CMB) lensing potential derived from the \emph{Planck} nominal mission data and $z\gtrsim 1.5$ galaxies detected by the \emph{Herschel}-ATLAS (H-ATLAS) survey covering about $600\,\hbox{deg}^2$, i.e. about 1.4\% of the sky. We reject the hypothesis that there is no correlation between CMB lensing and galaxy detection at a $20\,\sigma$ significance, checking the result by performing a number of null tests. The significance of the detection of the theoretically expected cross-correlation signal is found to be $10\,\sigma$. The galaxy bias parameter, $b$, derived from a joint analysis of the cross-power spectrum and of the auto-power spectrum of the galaxy density contrast is found to be $b=2.80^{+0.12}_{-0.11}$, consistent with earlier estimates for H-ATLAS galaxies at similar redshifts. On the other hand, the amplitude of the cross-correlation is found to be a factor $1.62 \pm 0.16$ higher than expected from the standard model and also found by cross-correlation analyses with other tracers of the large-scale structure. The enhancement due to lensing magnification can account for only a fraction of the excess cross-correlation signal. We suggest that part of it may be due to an incomplete removal of the contamination of the CIB, that includes the H-ATLAS sources we are cross-correlating with. In any case, the highly significant detection reported here using a catalog covering only 1.4\% of the sky demonstrates the potential of CMB lensing correlations with submillimeter surveys.

Subspace-Based Identification of Acoustic Noise Spectra in Induction Motors

In this paper, we study the identification of acoustic noise spectra in induction motors by using a recently developed frequency-domain cross-power spectrum estimation algorithm. This algorithm is a noniterative high-resolution spectral estimator. In a test rig, from multiple experiments sound data are collected by an array of five-microphones placed hemispherically around motors in a reverberant and noisy room. In order to explore the issue of assembly micromisalignments, each motor is removed from the test rig and then replaced, after which the experiment is then repeated. The identification algorithm is used to detect changes in acoustic noise spectra of induction motors due to mechanical and electrical faults most frequently encountered in industry. Not only the autopower spectra of the individual microphones, but also the cross-power spectra of the microphone pairs are estimated. As a byproduct, it is demonstrated that one microphone is sufficient to identify noise spectra. The estimated acoustic spectra, or more compactly statistics extracted from them, can be used in the development of preventive maintenance programs for induction motors in service.

Assessment of Autonomic Function in Children with Autism and Normal Children Using Spectral Analysis and Posture Entrainment: A Pilot Study

Objective: The dysfunction of the autonomic nervous system investigated in Children with Autism compared with healthy one. Cardiovascular autonomic disturbances are possibly associated with the pathogenesis of Autism in children. The purpose of this study is to use the spectral and coherence analysis of heart rate variability signal (HRV), respiration signal and peripheral blood flow signal (PBF) to assess the autonomic activity of normal children and children with Autism for the clinical usefulness of the applied methods of signal processing and timefrequency analysis for screening and treatment of Autism in children. Methods: Twenty four children who had Autism and who were not taking any medications and Twenty three age and sex matched controls (Children) were participated in this study at Department of Neurology at Johns Hopkins Hospital, Baltimore, MD, USA and Regional Medical Center, Cookeville, TN, USA. PBF and respiration signals as well as HRV signal derived from Electrocardiogram (ECG) were measured during supine and standing positions. Autopower, cross power and coherence spectra were produced to investigate the sympathetic and parasympathetic activity in both groups. Results: The results clearly indicate that in children with Autism, the coherence values are less than in control group in both low frequency (LF) and high frequency (HF) bands at coherence spectra between HRV and PBF as well as HRV and respiration in both supine and standing position. Also, the ratio of amplitude at nearly frequency of 0.1 Hz in auto power spectra and coherence spectra is less in Autism group than in matched control (p<0.001). Conclusion: Autopower and coherence spectra analysis for Children with Autism compared to normal Children seems useful in the assessment of autonomic function for Autism patients. The decreased of autonomic function specially parasympathetic activity in patients with Autism revealed by auto power and coherence spectra analysis is significant and may be related to the effective of treatment of Autism children in this disorder compared to controls. Further studies is needed using other tests and methods of signal analysis to introduce clinical indices for early detection of autonomic function in patients with Autism.

The Effect of Viagra on Autonomic Function Using Spectral Analysis and Approximate Entropy Method

Objective: Autonomic nervous system involvement in patients with Erectile Dysfunction (ED) has shown conflicting results. Our main purpose was to assess the effect of treatment with Viagra on autonomic function of group of ED patients in comparison with another group with control subjects with ED treated by herbal substances by measuring the frequency gain response of the two groups. Other aim of this study was to determine wither the duration of Viagra treatment correlated with measures of heart rate variability signal (HRV) using approximate entropy index (ApEn). Methods: Twenty two patients treated for ED by Viagra (100 mg) and twenty one matched control subjects treated ED by herbal were evaluated at Erectile Dysfunction Center, Johns Hopkins Hospital, Maryland, USA during 2012/ 2013 by measuring the breathing at different rates and HRV signal derived from Electrocardiogram (ECG).The autopower and cross power spectra between HRV signal and breathing signal at different breathing rate were calculated and frequency gain response for both groups were obtained. ApEn described as measure of regularity of HRV was calculated for both patients with Viagra treatment and herbal treatment for control subjects. Results: Both frequencies gain response and ApEn measures were increased in patients treated with Viagra in comparison with control group. The power spectra of patients with Viagra men showed both increase High Frequency (HF) value and higher low frequency bands with respect to control subjects. On other hand, ApEn measure was significantly increased in longer Viagra taking duration than in herbal group. Conclusion: These findings suggest that the spectral analysis of HRV signal using breathing at different frequencies may detect balance of autonomic of autonomic system of ED patients treated with Viagra specially with increasing the sympathetic activity (higher low frequency) and as well as the parasympathetic tone(higher frequency gain response) which can lead to reduce sudden deaths in patients with treating with viagra. APEn may be marker related to duration of taking Viagra. Further studies are needed to include more patients to strengthen the quantitive and qualitative indices proposed in this paper.

The Lyman β forest as a cosmic thermometer

We present a comprehensive analysis of high resolution hydrodynamic simulations in terms of Lyman α and Lyman β one dimensional flux power spectra Pαα and Pββ). In particular, we focus on the behaviour that the flux auto-power spectra and cross-power spectra Pαβ) display when the intergalactic medium (IGM) thermal history is changed in a range of values that bracket a reference model, while cosmological parameters are kept fixed to best fit the cosmic microwave background data. We present empirical fits that describe at the sub-percent level the dependence of the power spectra on the thermal parameters. At the largest scales, the power spectra show a constant bias between each other that is set by the parameters describing the IGM thermal state. The cross-power spectrum has an oscillatory pattern and crosses zero at a scale which depends on T0, the IGM temperature at the mean density, for reasonable values of the power-law index γ of the IGM temperature-density relation T=T0(1+δ)γ-1). By performing a Fisher matrix analysis, we find that the power spectrum Pββ is more sensitive to the thermal history than Pαα alone, due to the fact that it probes denser regions than Lyman α. When we combine the power and cross spectra the constraints on γ can be improved by a factor ∼ 4, while the constraints on T0 improve by a factor of ∼ 2. We address the role of signal-to-noise and resolution by mocking realistic observations and we conclude that the framework presented in this work can significantly improve the knowledge of the IGM thermal state, which will in turn guarantee better constraints on IGM-derived cosmological parameters.

Large-scale clustering of cosmic voids

We study the clustering of voids using $N$-body simulations and simple theoretical models. The excursion-set formalism describes fairly well the abundance of voids identified with the watershed algorithm, although the void formation threshold required is quite different from the spherical collapse value. The void cross bias ${b}_{\mathrm{c}}$ is measured and its large-scale value is found to be consistent with the peak background split results. A simple fitting formula for ${b}_{\mathrm{c}}$ is found. We model the void auto-power spectrum taking into account the void biasing and exclusion effect. A good fit to the simulation data is obtained for voids with radii $\ensuremath{\gtrsim}30\text{ }\text{ }\mathrm{Mpc}\text{ }{h}^{\ensuremath{-}1}$, especially when the void biasing model is extended to 1-loop order. However, the best-fit bias parameters do not agree well with the peak-background results. Being able to fit the void auto-power spectrum is particularly important not only because it is the direct observable in galaxy surveys, but also our method enables us to treat the bias parameters as nuisance parameters, which are sensitive to the techniques used to identify voids.

Velocity and mass bias in the distribution of dark matter haloes

The non-linear, scale-dependent bias in the mass distribution of galaxies and the underlying dark matter is a key systematic affecting the extraction of cosmological parameters from galaxy clustering. Using 95 million halos from the Millennium-XXL N-body simulation, we find that the mass bias is scale independent only for $k<0.1 h{\rm Mpc}^{-1}$ today ($z=0$) and for $k<0.2 h{\rm Mpc}^{-1}$ at $z=0.7$. We test analytic halo bias models against our simulation measurements and find that the model of Tinker et al. 2005 is accurate to better then 5% at $z=0$. However, the simulation results are better fit by an ellipsoidal collapse model at $z=0.7$. We highlight, for the first time, another potentially serious systematic due to a sampling bias in the halo velocity divergence power spectra which will affect the comparison between observations and any redshift space distortion model which assumes dark matter velocity statistics with no velocity bias. By measuring the velocity divergence power spectra for different sized halo samples, we find that there is a significant bias which increases with decreasing number density. This bias is approximately 20% at $k=0.1h$Mpc$^{-1}$ for a halo sample of number density $\bar{n} = 10^{-3} (h/$Mpc$)^3$ at both $z=0$ and $z=0.7$ for the velocity divergence auto power spectrum. Given the importance of redshift space distortions as a probe of dark energy and the on-going major effort to advance models for the clustering signal in redshift space, our results show this velocity bias introduces another systematic, alongside scale-dependent halo mass bias, which cannot be neglected.

Halo bias in mixed dark matter cosmologies

The large-scale distribution of cold dark matter halos is generally assumed to trace the large-scale distribution of matter. In a universe with multiple types of matter fluctuations, as is the case with massive neutrinos, the relation between the halo field and the matter fluctuations may be more complicated. We develop a method for calculating the bias factor relating fluctuations in the halo number density to fluctuations in the mass density in the presence of multiple fluctuating components of the energy density. In the presence of massive neutrinos we find a small but pronounced feature in the halo bias near the neutrino free-streaming scale. The neutrino feature is a small step with amplitude that increases with halo mass and neutrino mass density. The scale-dependent halo bias lessens the suppression of the small-scale halo power spectrum and should therefore weaken constraints on neutrino mass from the galaxy auto-power spectrum and correlation function. On the other hand, the feature in the bias is itself a novel signature of massive neutrinos that can be studied independently.

Integrated perturbation theory and one-loop power spectra of biased tracers

General and explicit predictions from the integrated perturbation theory (iPT) for power spectra and correlation functions of biased tracers are derived and presented in the one-loop approximation. The iPT is a general framework of the nonlinear perturbation theory of cosmological density fields in presence of nonlocal bias, redshift-space distortions, and primordial non-Gaussianity. Analytic formulas of auto and cross power spectra of nonlocally biased tracers in both real and redshift spaces are derived and the results are comprehensively summarized. The main difference from previous formulas derived by the present author is to include effects of generally nonlocal Lagrangian bias and primordial non-Gaussianity, and the derivation method of the new formula is fundamentally different from the previous one. Relations to recent work on improved methods of nonlinear perturbation theory in literature are clarified and discussed.

Peculiar velocities in redshift space: formalism, N-body simulations and perturbation theory

Direct measurements of peculiar velocities of galaxies and clusters of galaxies can in principle provide explicit information on the three dimensional mass distribution, but this information is modulated by the fact that velocity field is sampled at galaxy positions, and is thus probing galaxy momentum. We derive expressions for the cross power spectrum between the density and momentum field and the auto spectrum of the momentum field in redshift space, by extending the distribution function method to these statistics. The resulting momentum cross and auto power spectra in redshift space are expressed as infinite sums over velocity moment correlators in real space, as is the case for the density power spectrum in redshift space. We compute each correlator using Eulerian perturbation theory (PT) and halo biasing model and compare the resulting redshift-space velocity statistics to those measured from N-body simulations for both dark matter and halos. We find that in redshift space linear theory predictions for the density-momentum cross power spectrum as well as for the momentum auto spectrum fail to predict the N-body results at very large scales. On the other hand, our nonlinear PT prediction for these velocity statistics, together with real-space power spectrum for dark matter from simulations, improves the accuracy for both dark matter and halos. We also present the same analysis in configuration space, computing the redshift-space pairwise mean infall velocities and velocity correlation function and compare to nonlinear PT.

Forced-Vibration Testing and Experimental Modal Analysis of a Steel Footbridge for Structural Identification

Abstract Dynamic characteristic identification provides an important insight about structural behavior of steel structures. The experimental modal analysis is used to detect dynamic characteristics and consists of several phases. First, forced-vibration tests are carried out, spectral functions are produced, dynamic characteristics are determined by analyzing processed spectral functions, and, finally, analytical models are calibrated or updated depending on experimental analysis results. In this study, forced-vibration testing is conducted on the steel footbridge by using an impact hammer. Low-amplitude broadband excitations are applied using an impact hammer to excite the bridge. The excitation force and measured responses are processed by passing them through a band-pass filter to obtain frequency-response functions, cross-power spectra, auto-power spectra, power spectral densities, and spectrograms. The system-identification procedure is based on input–output measurements. The obtained system-identification results are compared with the analytical results, which were obtained in a different previous study. A very good agreement is observed, thus providing a reliable set of identified modal properties (natural frequencies, damping ratios, and mode shapes) of the structure. The good correlations between analytical and experimental analyses show that no anomalies are detected along the structure. The experimental mode shapes are similar to what is expected from this type of structure. There is not any unexpected mechanism that changes the dynamic characteristics of the system.

Full-scale experimental modal analysis of an arch dam: The first experience in Iran

Forced vibration field tests and finite-element studies were conducted on the Shahid Rajaee concrete arch dam in Northern Iran to determine the dynamic properties of the dam–reservoir–foundation system. The first forced vibration tests on the dam were performed with two different types of exciter units, with a limited maximum force, bolted on the dam crest for alternative in-phase and out-of-phase sequencing. Because of an insufficient number of recording sensors, two arrangements of sensors were used to cover sufficient points on the dam crest and one gallery during tests. Two kinds of vibration tests, on–off and frequency sweeping, were carried out on the dam. The primary natural frequencies of the coupled system for both symmetric and anti-symmetric vibration modes were approximated during on–off tests in two types of sequencing of exciters, in phase and out-of-phase, with a maximum frequency of 14Hz. The principal forced vibration tests were performed at precise resonant frequencies based on the results of the on–off tests in which sweeping around the approximated frequencies at 0.1Hz increments was performed. Baseline correction and suitable bandpass filtering were applied to the test records and then signal processing was carried out to compute the auto power, cross power and coherence spectra. Nine middle modes of vibration of the coupled system and corresponding damping ratios were estimated. The empirical results are compared against the results from calibrated finite-element modeling of the system using former ambient vibration tests, considering the dam–reservoir–foundation interaction effects. Good agreement is obtained between experimental and numerical results for eight middle modes of the dam–reservoir–foundation system.

CMB distortion anisotropies due to the decay of primordial magnetic fields

We investigate the power spectrum of the distortion of the cosmic microwave background (CMB) due to the decay of the primordial magnetic fields. It is known that there are two types of the CMB distortions, so-called $\ensuremath{\mu}$ and $y$ types, and we find that the signal of the $y$-type distortion becomes larger than that of the $\ensuremath{\mu}$-type one. We also discuss cross power spectra between the CMB distortions and the CMB temperature anisotropy, which are naturally generated due to the existence of the primordial magnetic fields. We find that such cross power spectra have small amplitudes compared with the autopower spectra of the CMB distortions because of the Silk damping effect of the temperature anisotropy. We also investigate the possibility of detecting such a signal in the future CMB experiments, including not only absolutely calibrated experiments such as PIXIE but also relatively calibrated experiments such as LiteBIRD and CMBpol.

Cosmology from cross correlation of CMB lensing and galaxy surveys

In recent years cross correlation of lensing of the Cosmic Microwave Background (CMB) with other large scale structure (LSS) tracers has been used as a method to detect CMB lensing. Current experiments are also becoming sensitive enough to measure CMB lensing without the help of auxiliary tracers. As data quality improves rapidly, it has been suggested that the CMB lensing-LSS cross correlation may provide new insights into parameters describing cosmological structure growth. In this work we perform forecasts that combine the lensing potential auto power spectrum from various future CMB experiments, the galaxy power spectrum from galaxy surveys, as well as the cross power spectrum between the two, marginalizing over a number galactic and non-galactic cosmological parameters. We find that the CMB lensing-LSS cross correlation contains significant information on parameters such as the redshift distribution and bias of LSS tracers. We also find that the cross correlation information will lead to independent probes of cosmological parameters such as neutrino mass and the reionization optical depth.

Detection of thermal SZ-CMB lensing cross-correlation in Planck nominal mission data

The nominal mission maps from the Planck satellite contain a wealth of information about secondary anisotropies in the cosmic microwave background (CMB), including those induced by the thermal Sunyaev-Zel'dovich (tSZ) effect and gravitational lensing. As both the tSZ and CMB lensing signals trace the large-scale matter density field, the anisotropies sourced by these processes are expected to be correlated. We report the first detection of this cross-correlation signal, which we measure at 6.2σ significance using the Planck data. We take advantage of Planck's multifrequency coverage to construct a tSZ map using internal linear combination techniques, which we subsequently cross-correlate with the publicly-released Planck CMB lensing potential map. The cross-correlation is subject to contamination from the cosmic infrared background (CIB), which is known to correlate strongly with CMB lensing. We correct for this contamination via cross-correlating our tSZ map with the Planck 857 GHz map and confirm the robustness of our measurement using several null tests. We interpret the signal using halo model calculations, which indicate that the tSZ-CMB lensing cross-correlation is a unique probe of the physics of intracluster gas in high-redshift, low-mass groups and clusters. Our results are consistent with extrapolations of existing gas physics models to this previously unexplored regime and show clear evidence for contributions from both the one- and two-halo terms, but no statistically significant evidence for contributions from diffuse, unbound gas outside of collapsed halos. We also show that the amplitude of the signal depends rather sensitively on the amplitude of fluctuations (σ8) and the matter density (Ωm), scaling as σ86.1Ωm1.5 at ℓ = 1000. We constrain the degenerate combination σ8(Ωm/0.282)0.26 = 0.824±0.029, a result that is in less tension with primordial CMB constraints than some recent tSZ analyses. We also combine our measurement with the Planck measurement of the tSZ auto-power spectrum to demonstrate a technique that can in principle constrain both cosmology and the physics of intracluster gas simultaneously. Our detection is a direct confirmation that hot, ionized gas traces the dark matter distribution over a wide range of scales in the universe ( ∼ 0.1–50 Mpc/h).

Galaxy And Mass Assembly (GAMA): improved cosmic growth measurements using multiple tracers of large-scale structure

We present the first application of a "multiple-tracer" redshift-space distortion (RSD) analysis to an observational galaxy sample, using data from the Galaxy and Mass Assembly survey (GAMA). Our dataset is an r < 19.8 magnitude-limited sample of 178,579 galaxies covering redshift interval z < 0.5 and area 180 deg^2. We obtain improvements of 10-20% in measurements of the gravitational growth rate compared to a single-tracer analysis, deriving from the correlated sample variance imprinted in the distributions of the overlapping galaxy populations. We present new expressions for the covariances between the auto-power and cross-power spectra of galaxy samples that are valid for a general survey selection function and weighting scheme. We find no evidence for a systematic dependence of the measured growth rate on the galaxy tracer used, justifying the RSD modelling assumptions, and validate our results using mock catalogues from N-body simulations. For multiple tracers selected by galaxy colour, we measure normalized growth rates in two independent redshift bins f*sigma_8(z=0.18) = 0.36 +/- 0.09 and f*sigma_8(z=0.38) = 0.44 +/- 0.06, in agreement with standard GR gravity and other galaxy surveys at similar redshifts.

Flutter Prediction for Flight/Wind-Tunnel Flutter Test Under Atmospheric Turbulence Excitation

In this paper, a flutter-boundary prediction technique for an aeroelastic/aeroservoelastic structure is introduced. This approach uses time-series flight/wind-tunnel flutter test data to compute an accurate estimate of the flutter speed. The flutter-boundary prediction tool discussed in this paper can be categorized into three steps.1)Signal preprocessing techniques are introduced to estimate the frequency-response function if the external excitation signal is measurable or compute the autopower spectrum when only responses from sensors can be measured due to a strong turbulence perturbation during flight flutter test.2)A frequency-domain system-identification methodology combined with a stabilization diagram is implemented to extract the elastic modes of a flexible structure. Accuracy of modes estimated in the second step directly affects the robustness of flutter prediction.3)The flutter-prediction analysis can therefore be performed with the implementation of an appropriate flutter-prediction tool such as the Zimmerman–Weissenburger flutter margin and/or damping trends extrapolation methods.Application of the proposed flutter-boundary prediction method to the Aeroelastic Test Wing I and SuperSonic SemiSpan Transport model demonstrates that it is an efficient tool for flutter-boundary prediction of aeroelastic/aeroservoelastic structures.