Input Power Spectrum Research Articles

The riding comfort improvement by the paralleled semi-active magnetorheological damper and passive inertance suspension from the power perspective

Extensive research demonstrates that a semi-active damper in combination with inerter-based suspension could improve the ride comfort and road-holding performance of vehicles. However, the inherent dynamics of a semi-active damper is always neglected. The underlying mechanism of the controller with inerter in different frequency ranges is not well understood. Accordingly, this paper investigated the quarter-car suspension consisting of the paralleled nonlinear hysteretic semi-active magnetorheological (MR) damper and a passive inerter. To study the influence of different strategies, the clipped optimum controlled- (COC) and the mixed skyhook power-driven damper (SKYPDD) controlled- MR damper with the inerter are both adopted and denoted as COCI and SKYPDI, respectively. The optimal inertance is selected to minimize the sprung acceleration. Since there lacks quantitative method to analyze the working mechanism of semi-active controllers, an innovative power-based criterion was proposed in this paper. The trajectory of the control force and the sprung mass velocity determines the equivalent damping ratio added to the sprung mass and the input power it receives from the unsprung mass. The sprung mass vibration is reduced by decreasing the input power or increasing the damping ratio. Under harmonic excitation, the additional inertance decreases the power input to the sprung mass in the low-frequency range and isolates the sprung mass from the forced vibration at the unsprung resonance. Under the broadband stochastic excitation, SKYPDI and COCI can effectively decrease the input power spectrum and increase the damping ratio spectrum in the dominant sprung mass resonance. A parametric study on varying stiffness ratio demonstrates the semi-active strategy takes effects mainly in the high-stiffness-ratio range where the additional inertance more evidently enhances the damping ratio, especially for COCI. In summary, this paper proposes the power-based criterion for analyzing the working mechanism of semi-active strategies in ride comfort improvement.

Analysis method for 3D power spectrum of projected tensor fields with fast estimator and window convolution modeling: An application to intrinsic alignments

Rank-2 tensor fields of large-scale structure, e.g. a tensor field inferred from shapes of galaxies, open up a window to directly access 2-scalar, 2-vector and 2-tensor modes, where the scalar fields can be measured independently from the standard density field that is traced by distribution of galaxies. Here we develop an estimator of the multipole moments of power spectra for the three-dimensional tensor field, taking into account the projection onto plane perpendicular to the line-of-sight direction. To do this, we find that a convenient representation of the power spectrum multipoles can be obtained by the use of the associated Legendre polynomials in the form which allows for the fast Fourier transform estimations under the local plane-parallel (LPP) approximation. The formulation also allows us to obtain the Hankel transforms to connect the two-point statistics in Fourier and configuration space, which are needed to derive theoretical templates of the power spectrum including convolution of a survey window. To validate our estimators, we use the simulation data of the projected tidal field assuming a survey window that mimics the BOSS-like survey footprint. We show that the LPP estimators fairly well recover the multipole moments that are inferred from the global plane-parallel approximation. We find that the survey window causes a more significant change in the multipole moments of projected tensor power spectrum at $k\lesssim 0.1\,h{\rm Mpc}^{-1}$ from the input power spectrum, than in the density power spectrum. Nevertheless, our method to compute the theory template including the survey window effects successfully reproduces the window-convolved multipole moments measured from the simulations. The analysis method presented here paves the way for a cosmological analysis using three-dimensional tensor-type tracers of large-scale structure for current and future surveys.

Inpainting CMB maps using partial convolutional neural networks

We present a novel application of partial convolutional neural networks (PCNN) that can inpaint masked images of the cosmic microwave background. The network can reconstruct both the maps and the power spectra to a few percent for circular and irregularly shaped masks covering up to 10% of the image area. By performing a Kolmogorov-Smirnov test we show that the reconstructed maps and power spectra are indistinguishable from the input maps and power spectra at the 99.9% level. Moreover, we show that PCNNs can inpaint maps with regular and irregular masks to the same accuracy. This should be particularly beneficial to inpaint irregular masks for the CMB that come from astrophysical sources such as Galactic foregrounds. The proof of concept application shown in this paper shows that PCNNs can be an important tool in data analysis pipelines in cosmology.

Redshift-space distortions in Lagrangian perturbation theory

We present the one-loop 2-point function of biased tracers in redshift space computed with Lagrangian perturbation theory, including a full resummation of both long-wavelength (infrared) displacements and associated velocities. The resulting model accurately predicts the power spectrum and correlation function of halos and mock galaxies from two different sets of N-body simulations at the percent level for quasi-linear scales, including the damping of the baryon acoustic oscillation signal due to the bulk motions of galaxies. We compare this full resummation with other, approximate, techniques including the moment expansion and Gaussian streaming model. We discuss infrared resummation in detail and compare our Lagrangian formulation with the Eulerian theory augmented by an infrared resummation based on splitting the input power spectrum into “wiggle” and “no-wiggle” components. We show that our model is able to recover unbiased cosmological parameters in mock data encompassing a volume much larger than what will be available to future galaxy surveys. We demonstrate how to efficiently compute the resulting expressions numerically, making available a fast Python code capable of rapidly computing these statistics in both configuration and Fourier space.

Machine-learning-based EDFA gain estimation [Invited

Optical transmission systems with high spectral efficiency require accurate quality of transmission estimation for optical channel provisioning. However, the wavelength-dependent gain effects of erbium-doped fiber amplifiers (EDFAs) complicate precise optical channel power prediction and low-margin operation. In this work, we examine supervised machine learning methods using multiple artificial neural networks (ANNs) to build models for gain spectra prediction of optical transmission line EDFAs under different operating conditions. Channel-loading configurations and channel input power spectra are used as an a posteriori knowledge data feature for model training. In a hybrid learning approach, estimated gain spectra calculated by an analytical model are added as an a priori input data feature to further improve the EDFA ANN model performance in terms of prediction accuracy, training time, and quantity of training data. Using these methods, the root mean square error and maximum absolute error of the predicted channel output power can be as low as 0.144 dB and 1.6 dB, respectively.

Multi-Degrees-of-Freedom Energy Analysis for Identification of Failure Risk in Structural Components Subjected to Random Vibration and Shock Loading

AbstractWhen designing or analyzing a mechanical system, energy quantities provide insight into the severity of shock and vibration environments; however, the energy methods in the literature do not address localized behavior because energy quantities are usually computed for an entire structure. The main objective of this paper is to show how to compute the energy in the components of a mechanical system. The motivation for this work is that most systems fail functionally due to component failure, not because the primary structure was overloaded, and the ability to easily compute the spatial distribution of energy helps identify failure-sensitive components. The quantity of interest is input energy. That input energy can be decoupled modally is well known. What is less appreciated is that input energy can be computed at the component level exactly, using the component effective modal mass. We show that the steady-state input energy can be decomposed both spatially and modally and computed using input power spectra. A numerical example illustrates the spatial and modal decomposition of input energy and its utility in identifying components at risk of damage in random vibration and shock environments. We show that the modal properties of the structure and the spectral content of the input must be considered together to assess damage risk. Because input energy includes absorbed energy as well as relative kinetic energy and dissipated energy, it is the recommended energy quantity for assessing the severity of both random vibration and shock environments on a structure.

Contrasting open-loop dynamic characteristics of sympathetic and vagal systems during baroreflex-mediated heart rate control in rats.

Although heart rate (HR) is governed by the sympathetic and parasympathetic nervous systems, a head-to-head comparison of the open-loop dynamic characteristics of the total arc from a baroreceptor pressure input to the HR response has yet to be performed. We estimated the transfer function from carotid sinus pressure input to the HR response (HCSP→HR) before and after bilateral vagotomy (n = 7) as well as before and after the administration of a β-blocker propranolol (n = 8) in anesthetized male Wistar-Kyoto rats. The carotid sinus pressure was perturbed according to a Gaussian white noise signal so that the input power spectra were relatively flat between 0.01 and 1 Hz. The gain plot of HCSP→HR was V-shaped. Vagotomy reduced the dynamic gain at 1 Hz (0.0598 ± 0.0065 to 0.0025 ± 0.0004 beats·min-1·mmHg-1, P < 0.001) but not at 0.01 or 0.1 Hz. β-Blockade reduced the dynamic gain at 0.01 Hz (0.247 ± 0.069 to 0.077 ± 0.017 beats·min-1·mmHg-1, P = 0.020) but not at 0.1 or 1 Hz. We also estimated the efferent limb transfer function from electrical vagal efferent stimulation to the HR response (HVN→HR) under β-blockade conditions. We associated the model parameters of HVN→HR with the mean HR and the standard deviation of HR so that HVN→HR could be estimated based only on the HR data. We finally estimated the neural arc transfer function from a pressure input to efferent vagal nerve activity by dividing HCSP→HR by HVN→HR. The mathematically determined vagal neural arc showed derivative characteristics with its phase near zero radians at the lowest frequency.

Three-harmonic optimal multisine input power spectrum for bioimpedance identification

Objective: The attention towards optimal signals for measuring electrical bioimpedance (EBI) has increased recently due to the many advantages they offer such as, for example, reduced measuring time. Here, the design of a three-harmonic optimized multisine input power spectrum for measuring bioimpedance is considered. Approach: The approach is based on designing the input power spectrum multisine excitation by optimizing a scalar function of the information matrix using the Fricke–Morse model. Main results: Simple analytical equations are provided that can be adopted by the reader to optimize the multisine input power spectrum to satisfy any specific application-related EBI measurement. Significance: The presented signal may be a good choice of excitation signal in EBI applications where optimal excitation power spectrum is desired.

Quadrotor aircraft intelligent system identification experiment design

Aircraft prototyping and modeling is usually associated with resource expensive techniques and significant post flight analysis. The NASA Learn-To-Fly concept targets the replacement of the conventional ground-based aircraft model development and prototyping approaches with an efficient real time paradigm. The work presented herein describes the development of an intelligent excitation input design technique that determines excitation frequencies based on predefined rotational motion dynamic model. The input design is then evaluated on quadcopter unmanned aircraft that utilizes the new multisine input design. In order to minimize flight excursions without compromising the modeling capabilities, multisine input power spectrum is optimized based on the vehicle’s frequency response. The proposed methodology emphasizes excitation of modal frequencies which yields flight data rich information content. The generated optimized multisine input design is utilized for a quadcopter aircraft system identification and the performance is compared to conventional uniform amplitudes design. Simulation results show highly accurate model estimation in all identification results in addition to reduction of induced perturbations and power consumption. Additionally, the generated model prediction capabilities are not compromised after power spectrum optimization. Overall, the proposed technique introduces an efficient and intelligent system identification experiment design that can minimize the time and effort spent during excitation input design.

A unified pseudo-Cℓ framework

The pseudo-$C_\ell$ is an algorithm for estimating the angular power and cross-power spectra that is very fast and, in realistic cases, also nearly optimal. The algorithm can be extended to deal with contaminant deprojection and $E/B$ purification, and can therefore be applied in a wide variety of scenarios of interest for current and future cosmological observations. This paper presents NaMaster, a public, validated, accurate and easy-to-use software package that, for the first time, provides a unified framework to compute angular cross-power spectra of any pair of spin-0 or spin-2 fields, contaminated by an arbitrary number of linear systematics and requiring $B$- or $E$-mode purification, both on the sphere or in the flat-sky approximation. We describe the mathematical background of the estimator, including all the features above, and its software implementation in NaMaster. We construct a validation suite that aims to resemble the types of observations that next-generation large-scale structure and ground-based CMB experiments will face, and use it to show that the code is able to recover the input power spectra in the most complex scenarios with no detectable bias. NaMaster can be found at https://github.com/LSSTDESC/NaMaster, and is provided with comprehensive documentation and a number of code examples.

Robustness of the covariance matrix for galaxy clustering measurements

We present a study on the robustness of the covariance matrix estimation for galaxy clustering measurements depending on the cosmological parameters and galaxy bias. To this end, we have produced 9000 galaxy mock catalogues relying on the effective Zel'dovich approximation implemented in the EZmocks computer code, using different input cosmological models and bias parameters. The reference catalogue has also been produced with this code making our study insensitive to the approximation at least on a relative-qualitative level. Our findings indicate that the covariance matrix is insensitive to the input power spectrum (including $\sigma_8$), as long as the 2- and 3-point galaxy clustering measurements agree with the given data. In fact, the covariance matrix shows a bias at small scales ($r\lesssim40 h^{-1}$Mpc) when the chosen galaxy bias parameters yield a 3-point statistics, which is not compatible with the reference one within the error bars, even though the 2-point statistics agree within 1%. Nevertheless, the error becomes negligible at large scales making the covariance matrix still reliable for data analysis using only measurements in that regime (e.g., measuring baryon acoustic oscillations). High precision in cosmological parameter estimation is expected for covariance matrices extracted from mock galaxy catalogues which take accurately into account both the 2- and the 3- point statistics. This is independent of whether this is achieved by using the right cosmology and galaxy bias (which are not a priori known) or just any combination of both fitting the net observed galaxy clustering.

Experimental estimation of transmissibility matrices for industrial multi-axis vibration isolation systems

Abstract Vibration isolation is essential for industrial high-precision systems to suppress external disturbances. The aim of this paper is to develop a general identification approach to estimate the frequency response function (FRF) of the transmissibility matrix, which is a key performance indicator for vibration isolation systems. The major challenge lies in obtaining a good signal-to-noise ratio in view of a large system weight. A non-parametric system identification method is proposed that combines floor and shaker excitations. Furthermore, a method is presented to analyze the input power spectrum of the floor excitations, both in terms of magnitude and direction. In turn, the input design of the shaker excitation signals is investigated to obtain sufficient excitation power in all directions with minimum experiment cost. The proposed methods are shown to provide an accurate FRF of the transmissibility matrix in three relevant directions on an industrial active vibration isolation system over a large frequency range. This demonstrates that, despite their heavy weight, industrial vibration isolation systems can be accurately identified using this approach.

Validating a novel angular power spectrum estimator using simulated low frequency radio-interferometric data

The “Tapered Gridded Estimator” (TGE) is a novel way to directly estimate the angular power spectrum from radio-interferometric visibility data that reduces the computation by efficiently gridding the data, consistently removes the noise bias, and suppresses the foreground contamination to a large extent by tapering the primary beam response through an appropriate convolution in the visibility domain. Here we demonstrate the effectiveness of TGE in recovering the diffuse emission power spectrum through numerical simulations. We present details of the simulation used to generate low frequency visibility data for sky model with extragalactic compact radio sources and diffuse Galactic synchrotron emission. We then use different imaging strategies to identify the most effective option of point source subtraction and to study the underlying diffuse emission. Finally, we apply TGE to the residual data to measure the angular power spectrum, and assess the impact of incomplete point source subtraction in recovering the input power spectrum Cℓ of the synchrotron emission. This estimator is found to successfully recovers the Cℓ of input model from the residual visibility data. These results are relevant for measuring the diffuse emission like the Galactic synchrotron emission. It is also an important step towards characterizing and removing both diffuse and compact foreground emission in order to detect the redshifted 21 cm signal from the Epoch of Reionization.

FAST-PT II: an algorithm to calculate convolution integrals of general tensor quantities in cosmological perturbation theory

Cosmological perturbation theory is a powerful tool to predict the statistics of large-scale structure in the weakly non-linear regime, but even at 1-loop order it results in computationally expensive mode-coupling integrals. Here we present a fast algorithm for computing 1-loop power spectra of quantities that depend on the observer's orientation, thereby generalizing the FAST-PT framework (McEwen et al., 2016) that was originally developed for scalars such as the matter density. This algorithm works for an arbitrary input power spectrum and substantially reduces the time required for numerical evaluation. We apply the algorithm to four examples: intrinsic alignments of galaxies in the tidal torque model; the Ostriker-Vishniac effect; the secondary CMB polarization due to baryon flows; and the 1-loop matter power spectrum in redshift space. Code implementing this algorithm and these applications is publicly available at https://github.com/JoeMcEwen/FAST-PT.

FAST-PT: a novel algorithm to calculate convolution integrals in cosmological perturbation theory

We present a novel algorithm, FAST-PT, for performing convolution or mode-coupling integrals that appear in nonlinear cosmological perturbation theory. The algorithm uses several properties of gravitational structure formation—the locality of the dark matter equations and the scale invariance of the problem—as well as Fast Fourier Transforms to describe the input power spectrum as a superposition of power laws. This yields extremely fast performance, enabling mode-coupling integral computations fast enough to embed in Monte Carlo Markov Chain parameter estimation. We describe the algorithm and demonstrate its application to calculating nonlinear corrections to the matter power spectrum, including one-loop standard perturbation theory and the renormalization group approach. We also describe our public code (in Python) to implement this algorithm. The code, along with a user manual and example implementations, is available at https://github.com/JoeMcEwen/FAST-PT.

Optimal weights for measuring redshift space distortions in multitracer galaxy catalogues

Since the volume accessible to galaxy surveys is fundamentally limited, it is extremely important to analyse available data in the most optimal fashion. One way of enhancing the cosmological information extracted from the clustering of galaxies is by weighting the galaxy field. The most widely used weighting schemes assign weights to galaxies based on the average local density in the region (FKP weights) and their bias with respect to the dark matter field (PVP weights). They are designed to minimize the fractional variance of the galaxy power-spectrum. We demonstrate that the currently used bias dependent weighting scheme can be further optimized for specific cosmological parameters. We develop a procedure for computing the optimal weights and test them against mock catalogues for which the values of all fitting parameters, as well as the input power-spectrum are known. We show that by applying these weights to the joint power-spectrum of Emission Line Galaxies and Luminous Red Galaxies from the Dark Energy Spectroscopic Instrument survey, the variance in the measured growth rate parameter can be reduced by as much as 36 per cent.

Gaussian covariance matrices for anisotropic galaxy clustering measurements

Measurements of the redshift-space galaxy clustering have been a prolific source of cosmological information in recent years. Accurate covariance estimates are an essential step for the validation of galaxy clustering models of the redshift-space two-point statistics. Usually, only a limited set of accurate N-body simulations is available. Thus, assessing the data covariance is not possible or only leads to a noisy estimate. Further, relying on simulated realisations of the survey data means that tests of the cosmology dependence of the covariance are expensive. With these points in mind, this work presents a simple theoretical model for the linear covariance of anisotropic galaxy clustering observations with synthetic catalogues. Considering the Legendre moments (`multipoles') of the two-point statistics and projections into wide bins of the line-of-sight parameter (`clustering wedges'), we describe the modelling of the covariance for these anisotropic clustering measurements for galaxy samples with a trivial geometry in the case of a Gaussian approximation of the clustering likelihood. As main result of this paper, we give the explicit formulae for Fourier and configuration space covariance matrices. To validate our model, we create synthetic HOD galaxy catalogues by populating the haloes of an ensemble of large-volume N-body simulations. Using linear and non-linear input power spectra, we find very good agreement between the model predictions and the measurements on the synthetic catalogues in the quasi-linear regime.

Finite model order asymptotic analysis in Wiener system identification

In this paper, we derive the linear part's asymptotic covariance matrices under white noise and coloured noise respectively in the Wiener system. The model orders do not exist in these two asymptotic covariance forms. And we use some reproducing kernel function constructed by a group of orthogonal basis functions to replace the model order. So when some priori information about Wiener system are known, these two asymptotic covariance matrices approximate their true sample values accurately. When some assumption conditions are relaxed, the cross spectrum can be decomposed as a constant matrix multiply its spectrum. Based on this conclusion, the asymptotic covariance matrices are generalised to other simplified cases. Additionally, based on these asymptotic covariance matrices, we construct an optimisation problem with respect to the input power spectrum. By solving this optimisation problem with some constraint conditions, the optimal input power spectrum used to excite the Wiener system is obtained.

Errors-in-variables identification of dynamic systems excited by arbitrary non-white input

This work deals with the identification of dynamic systems from noisy input–output observations, where the noise-free input is not parameterized. The basic assumptions made are (1) the dynamic system can be modeled by a (discrete- or continuous-time) rational transfer function model, (2) the temporal input–output disturbances are mutually independent, identically distributed noises, and (3) the input power spectrum is non-white (not necessarily rational) and is modeled nonparametrically. The system identifiability is guaranteed by exploiting the non-white spectrum property of the noise-free input. A frequency domain identification strategy is developed to estimate consistently the plant model parameters and the input–output noise variances. The uncertainty bound of the estimates is calculated and compared to the Cramér–Rao lower bound. The efficiency of the proposed algorithm is illustrated on numerical examples.

Equivalent linear stochastic seismic analysis of cylindrical base-isolated liquid storage tanks

Seismic performance of cylindrical liquid storage tanks base-isolated by bilinear bearings is investigated. The paper displays a stochastic parametrical study in which three design parameters, namely isolation period, yield strength and viscous damping ratio, characterizing the isolation system are taken into consideration. The earthquake excitation, modeled as a stationary random process, is characterized by a power spectral density function calculated via a compatible seismic design spectrum. The stochastic response of the base-isolated cylindrical tanks is obtained by the convolution between the frequency response function of the system and the input power spectrum. To determine effective damping and stiffness coefficients corresponding to the equivalent linear system a statistical linearization scheme was used. For the purpose of evaluating the seismic behavior under different conditions, two liquid levels (aspect ratios) and soil types (soft and stiff soil) were considered.Thus, the study demonstrates the influence of each characteristic parameter of the isolation system and soil conditions on the response of cylindrical base-isolated tanks and principally allows visualizing the seismic performance that can be achieved through the selection of those parameters under certain soil conditions. Further, it is confirmed that soft soil conditions amplify the overall response of the system specially the base and sloshing displacements, as well as the normalized base shear to a lesser extent.