Frequency-domain Formulation Research Articles

Simplified permeable surface correction for frequency-domain Ffowcs Williams and Hawkings integrals

A simplified surface correction formulation is proposed to diminish the far-field spurious sound generated by the quadrupole source term in Ffowcs Williams and Hawkings (FW-H) integrals. The proposed formulation utilizes the far-field asymptotics of the Green's function to simplify the computation of its high-order derivatives, which circumvents the difficulties reported in the original frequency-domain surface correction formulation. The proposed formulation has been validated by investigating the benchmark case of sound generated by a convecting vortex. The results show that the proposed formulation successfully eliminates the spurious sound. The applications of the proposed formulation to flows with some special parameters are also discussed.

A revisit of the tonal noise of small rotors.

In this study, asymptotic analysis of the frequency-domain formulation to compute the tonal noise of the small rotors in the now ubiquitously multi-rotor powered drones is conducted. Simple scaling laws are proposed to evaluate the impacts of the influential parameters such as blade number, flow speed, rotation speed, unsteady motion, thrust and observer angle on the tonal noise. The rate of noise increment with thrust (or rotational speed) is determined by orders of blade passing frequency harmonics and the unsteady motion. The axial mean flow influence can be approximated by quadratic functions. At given thrust, the sound decreases rapidly with the radius and blade number as the surface pressure becomes less intensive. The higher tonal harmonics are significantly increased if unsteady motions, although of small-amplitude, are existed, as indicated by the defined sensitivity function, emphasizing that the unsteady motions should be avoided for quiet rotor designs. The scaling laws are examined by comparing with the full computations of the rotor noise using the frequency-domain method, the implementation of which has been validated by comparing with experiments. Good data collapse is obtained when the proposed scaling laws, which highlights the dominant influence of the design parameters, are incorporated.

Modeling Vibration-Induced Tire-Pavement Interaction Noise in the Mid-frequency Range

ABSTRACT Tire-pavement interaction noise (TPIN) is one of the main sources of exterior noise produced by vehicles traveling at greater than 50 kph. The dominant frequency content is typically within 500–1500 Hz. Structural tire vibrations are among the principal TPIN mechanisms. In this work, the structure of the tire is modeled and a new wave propagation solution to find its response is proposed. Multiple physical effects are accounted for in the formulation. In an effort to analyze the effects of curvature, a flat plate and a cylindrical shell model are presented. Orthotropic and nonuniform structural properties along the tire's transversal direction are included to account for differences between its sidewalls and belt. Finally, the effects of rotation and inflation pressure are also included in the formulation. Modeled frequency response functions are analyzed and validated. In addition, a new frequency-domain formulation is presented for the computation of input tread pattern contact forces. Finally, the rolling tire's normal surface velocity response is coupled with a boundary element model to demonstrate the radiated noise at the leading and trailing edge locations. These results are then compared with experimental data measured with an on-board sound intensity system.

Porting Wire-Grid MoM Framework to Reconfigurable Computing Technology

In this letter, a CPU/field-programmable gate array (FPGA) coprocessing implementation of the matrix assembly phase of the method of moments (MoM) is presented. The approach combines the frequency-domain integral equation-based formulation with piecewise-linear (triangular) basis function and method of images to evaluate the radiation pattern of the localizer antenna system. To benefit from the given hardware architecture, the code executed on the device runs only one single work-item OpenCL kernel. Using the Nallatech 385 A device featuring one Intel Arria 10 FPGA, a speedup ratio of about 2.08× is reported when compared to the reference single-core CPU approach, and about 1.11× when compared to the two-core CPU implementation.

Floquet higher-order topological insulators and superconductors with space-time symmetries

Floquet higher-order topological insulators and superconductors (HOTI/SCs) with an order-two space-time symmetry or antisymmetry are classified. This is achieved by considering unitary loops, whose nontrivial topology leads to the anomalous Floquet topological phases, subject to a space-time symmetry/antisymmetry. By mapping these unitary loops to static Hamiltonians with an order-two crystalline symmetry/antisymmetry, one is able to obtain the $K$ groups for the unitary loops and thus complete the classification of Floquet HOTI/SCs. Interestingly, we found that for every order-two nontrivial space-time symmetry/antisymmetry involving a half-period time translation, there exists a unique order-two static crystalline symmetry/antisymmetry, such that the two symmetries/antisymmetries give rise to the same topological classification. Moreover, by exploiting the frequency-domain formulation of the Floquet problem, a general recipe that constructs model Hamiltonians for Floquet HOTI/SCs is provided, which can be used to understand the classification of Floquet HOTI/SCs from an intuitive and complimentary perspective.

The Frisch scheme for EIV system identification: time and frequency domain formulations

Several estimation methods have been proposed for identifying errors-in-variables systems, where both input and output measurements are corrupted by noise. One of the more interesting approaches is the Frisch scheme. The method can be applied using either time or frequency domain representations. This paper investigates the general mathematical and geometrical aspects of the Frisch scheme, illustrating the analogies and the differences between the time and frequency domain formulations.

Angular Distribution and Polarization of Superradiant Emission from Atomic Ensembles

A density-matrix approach is developed to provide a theoretical description of the intensity, angular distribution, and polarization of superradiative emission from an ensemble of many-electron atomic systems. The many-electron atomic systems are described as cooperatively interacting by means of forces that can be long range. Particular emphasis is given to the coherent excitation of the collective atomic-ensemble states, which may be produced by incident laser radiation. The initial excitation and spontaneous emission processes may be described as independent. Both frequency-domain and time-domain formulations of the density-matrix approach are developed. The collective atomic-ensemble states are specified in a detailed hyperfine representation, corresponding to successively coupling the individual hyperfine angular momenta F pertaining to the many-electron atoms. A less detailed fine-structure angular-momentum representation may also be used. In the density-operator approach, account can be taken of the coherent excitation of a particular subspace of the initial atomic-ensemble states. For a comprehensive and unified development of time-domain (equation-of-motion) and frequency-domain (resolvent-operator) formulations, a reduced-density-matrix (quantum-open-systems) approach is introduced. The non-equilibrium atomic-ensemble-state kinetics and the homogeneous spectral-line shapes can thereby be systematically and self-consistently determined. The collective atomic-ensemble states may be obtained using a variety of different methods. These states can be determined using a dressed-state approach, in which the required states are calculated in the presence of an electromagnetic field.

Personal Sound Zones by Subband Filtering and Time Domain Optimization

Personal Sound Zones (PSZ) systems aim to render independent sound signals to multiple listeners within a room by using arrays of loudspeakers. One of the algorithms used to provide PSZ is Weighted Pressure Matching (wPM), which computes the filters required to render a desired response in the listening zones while reducing the acoustic energy arriving to the quiet zones. This algorithm can be formulated in time and frequency domains. In general, the time-domain formulation (wPM-TD) can obtain good performance with shorter filters and delays than the frequency-domain formulation (wPM-FD). However, wPM-TD requires higher computation for obtaining the optimal filters. In this article, we propose a novel approach to the wPM algorithm named Weighted Pressure Matching with Subband Decomposition (wPM-SD), which formulates an independent time-domain optimization problem for each of the subbands of a Generalized Discrete Fourier Transform (GDFT) filter bank. Solving the optimization independently for each subband has two main advantages: 1) lower computational complexity than wPM-TD to compute the optimal filters; 2) higher versatility than the classic wPM algorithms, as it allows different configurations (sets of loudspeakers, filter lengths, etc.) in each subband. Moreover, filtering the input signals with a GDFT filter bank (as in wPM-SD) requires lower computational effort than broadband filtering (as in wPM-TD and wPM-FD), which is beneficial for practical PSZ systems. We present experimental evaluations showing that wPM-SD offers very similar performance to wPM-TD. In addition, two cases where the versatility of wPM-SD is beneficial for a PSZ system are presented and experimentally validated.

A general time-domain formulation of equation-of-motion coupled-cluster theory for linear spectroscopy.

A time-dependent (TD) formulation of equation-of-motion (EOM) coupled-cluster (CC) theory is developed, which, unlike other similar TD-EOM-CC approaches [D. R. Nascimento and A. E. DePrince III, J. Chem. Theory Comput. 12, 5834-5840 (2016)], can be applied to any type of linear electronic spectroscopy. The TD-EOM-CC method is formally equivalent to the standard frequency-domain formulation of EOM-CC theory, with a potential computational advantage of a comparatively low memory footprint. This general TD-EOM-CC framework is applied to the linear absorption and electric circular dichroism spectra of several small oxirane derivatives.

The generalized standard-linear-solid model and the corresponding viscoacoustic wave equations revisited

Summary The generalized standard-linear-solid model, also called the Zener model, is widely used in viscoacoustic/viscoelastic wavefield forward and inverse modeling, because the wave equations in this model can be written in differential equation form, which can be solved efficiently by time-domain numerical methods such as finite difference method, spectral element method, etc. For this model, however, two different expressions for the relaxation function (or complex modulus) appear in the literature somewhat confusingly. In addition to this confusion, the time- and frequency-domain versions of the wave equations for the generalized standard-linear-solid model are scattered throughout the literature. Here, we revisit the generalized standard-linear-solid model and seek to overcome the confusion concerning the expression for the relaxation function (or modulus). We present a unified approach to derive the viscoacoustic wave equations. We start with the time- and frequency-domain formulations separately to derive two sets of viscoacoustic wave equations. All these viscoacoustic wave equations are expressed in a simple and compact form. The two sets of viscoacoustic wave equations are equivalent to each other. The proposed method to derive the appropriate viscoacoustic wave equations can be extended to derive wave equations for other dissipative media.

Validation of Jet Noise Simulations and Resulting Insights of Acoustic Near Field

A hybrid lattice Boltzmann method–very-large-eddy simulation (LBM-VLES) solver for high-speed nonisothermal subsonic flows is used to simulate the unsteady jet flow exhausting from a single axi-symmetric nozzle, as well as the associated noise spectra and directivity. The jet exit Mach number and temperature ratio are set according to three representative operating conditions from the NASA SMC000 experimental campaign. The far-field noise is computed through a Ffowcs Williams and Hawkings analogy applied to a fluid surface encompassing the jet plume. Both time- and frequency-domain formulations are used, the latter in combination with an azimuthal Fourier transform of the linear source terms to analyze the contribution of the different azimuthal components. A resolution study is carried out for both aerodynamic and acoustic results. The near- and far-field results confirm that the underlying flow features and noise mechanisms are fully represented by the numerical solution. A wavelet decomposition technique is applied to analyze the source mechanisms for a heated core case. This is achieved by separating the coherent flow motion from the chaotic perturbations in the turbulent flows. Finally, a frequency-domain integral formulation is used to analyze the acoustic far-field of the two segregated components.

Fast 2D full-waveform modeling and inversion using the Schur complement approach

In most full-waveform inversion (FWI) problems, sufficient prior information is available to constrain the velocity of certain parts of the model, e.g., the water column or, in some cases, near-surface velocities. We take advantage of this situation and develop a fast Schur-complement-based forward modeling and inversion approach by partitioning the velocity model into two parts. The first part consists of the constrained zone that does not change during the inversion, whereas the second part is the anomalous zone to be updated during the inversion. For this decomposition, we partially factorize the governing system of linear equations by computing a Schur complement for the anomalous zone. The Schur complement system is then solved to compute the fields in the anomalous zone, which are then back substituted to compute the fields in the constrained region. For each successive modeling steps with new anomalous zone velocities, the corresponding Schur complement is easily computed using simple algebra. Because the anomalous part of the model is comparatively smaller than the whole model, considerable computational savings can be achieved using our Schur approach. Additionally, we showed that the Schur complement method maintains the accuracy of standard frequency-domain finite difference formulations, but this comes at a slightly higher peak memory requirement. Our FWI workflow shows reduced runtime by 15%–57% depending upon the depth of the water column without losing any accuracy compared to the standard method.

A parallel computing framework for performing structural-acoustic optimization with stochastic forcing

Structural-acoustic optimization procedures can be used to find the optimal design for reduced noise or vibration in many real-world scenarios. However, the time required to compute the structural-acoustic quantity of interest often limits the size of the model. Additionally, structural-acoustic optimization using state-of-the-art evolutionary algorithms may require tens of thousands of system solutions, which add to the limitations for large full-scale systems. To reduce the time required for each function evaluation, parallel processing techniques are used to solve the system in a highly scalable fashion. The approach reduces the analysis time by solving the system using a frequency-domain formulation and distributing solution frequencies amongst processors to solve in parallel. To demonstrate, the sound radiated from a curved panel under the influence of a turbulent boundary layer is minimized in the presence of added point masses, which are varied during the optimization procedure. The total mass is also minimized and the Pareto front relating the trade-off between added mass and reduced noise is determined. Solver scaling information is provided that demonstrates the utility of the parallel processing approach.

A Finite-Difference Approach for Plasma Microwave Imaging Profilometry

Plasma diagnostics is a topic of great interest in the physics and engineering community because the monitoring of plasma parameters plays a fundamental role in the development and optimization of plasma reactors. Towards this aim, microwave diagnostics, such as reflectometric, interferometric, and polarimetric techniques, can represent effective means. Besides the above, microwave imaging profilometry (MIP) may allow the obtaining of tomographic, i.e., volumetric, information of plasma that could overcome some intrinsic limitations of the standard non-invasive diagnostic approaches. However, pursuing MIP is not an easy task due to plasma’s electromagnetic features, which strongly depend on the working frequency, angle of incidence, polarization, etc., as well as on the need for making diagnostics in both large (meter-sized) and small (centimeter-sized) reactors. Furthermore, these latter represent extremely harsh environments, wherein different systems and equipment need to coexist to guarantee their functionality. Specifically, MIP entails solution of an inverse scattering problem, which is non-linear and ill-posed, and, in addition, in the one-dimensional case, is also severely limited in terms of achievable reconstruction accuracy and resolution. In this contribution, we address microwave inverse profiling of plasma assuming a high-frequency probing regime when magnetically confined plasma can be approximated as both an isotropic and weak penetrable medium. To this aim, we adopt a finite-difference frequency-domain (FDFD) formulation which allows dealing with non-homogeneous backgrounds introduced by unavoidable presence of plasma reactors.

A Novel Gauged Potential Formulation for 3-D Electromagnetic Field Analysis Including Both Inductive and Capacitive Effects

In this paper, a novel potential formulation for low-frequency (LF) applications taking into account both inductive and capacitive effects but without considering wave propagation is proposed. Both time-domain and frequency-domain formulations are presented. The resultant fully discrete finite-element matrix is made symmetric by incorporating a gauge condition and also rewriting the current continuity equation. To improve numerical accuracy and computational efficiency, high-order mixed edge elements and nodal elements are adopted to approximate the vector and scalar unknown variables together with high-order time-stepping schemes. Several numerical examples are solved to validate and showcase the accuracy of the proposed methods. The proposed formulations are stable in use for LF electromagnetic field computations by considering inductive and capacitive effects simultaneously, such as finding the resonant frequencies of wireless power transfer devices.

Heterogeneous string stability of unidirectionally interconnected MIMO LTI systems

One-dimensional formations of unidirectionally interconnected heterogeneous, multiple-input multiple-output (MIMO) linear time-invariant (LTI) systems are studied in terms of the spatial propagation of initial conditions, disturbances and reference inputs. The proposed mixed frequency-domain and complex state-space formulation of the string leads to the stability theory of switching and uncertain polytopic systems, and so the tools available there can be adopted for the analysis of interconnected systems. It is shown based on this analogy that in certain important cases string stability conditions for homogeneous and heterogeneous interconnected systems coincide. In addition to presenting general string (in)stability conditions, the necessity of introducing the notion of string performance is demonstrated. Special attention is devoted to interconnected rank one systems, i.e., systems whose transfer matrices are of rank one. The topic is motivated by car following problems for which the available analysis tools fail to provide appropriate heterogeneous string stability conditions. A cooperative adaptive cruise control (CACC) example is presented to illustrate the usefulness of the approach.

Beam Frame Representation for Ultrawideband Radiation From Volume Source Distributions: Frequency-Domain and Time-Domain Formulations

We present two novel beam-summation schemes for radiation from time-harmonic or time-dependent volume source distributions, where the field is expanded using a discrete phase-space set of beam-wave propagators. The generic term “beams” is used here for both the frequency-domain and the time-domain formulations where the propagators are isodiffracting Gaussian beam or isodiffracting pulsed beams, respectively. The formulations are structured upon the recently formulated “beam-frame” theorem that establishes these phase-space beam sets as frame sets everywhere in the propagation domain and not only over the aperture plane as in previous formulations. The expansion coefficients are obtained by projecting the source distributions over the dual beam-frame sets that have essentially the same structure as the basic sets. As such, these formulations constitute local generalization to the conventional plane waves or Green's function formulations, and also reduce the overall degrees of freedom needed to describe the radiated field. As demonstrated by the numerical examples, they resolve the local features of the source distributions in space time, and hence provide a basis for a new local inverse scattering theory to be presented subsequently.

A Data-Cleaning Approach to Robust Multisensor Detection of Improper Signals

We consider the problem of detecting the presence of an improper complex-valued signal, common among two or more sensors (channels), in the presence of spatially independent, colored improper noise and additive outliers. A source of improper noise is in-phase/quadrature-phase imbalance during down-conversion of bandpass noise to baseband at the receiver. For clean data (i.e., known to be outlier free), a nonparametric binary hypothesis testing formulation in frequency-domain, utilizing the discrete Fourier transform of an augmented measurement sequence, has been proposed in the literature, and it results in a generalized likelihood ratio test (GLRT). In this paper we robustify this approach against additive outliers in the data, using a data-cleaning approach. Using some existing robust estimators of multivariate scatter, we first detect the outliers, and subsequently remove and replace them using vector median filtering to yield cleaned data. The existing GLRT is then applied to the cleaned data. The approach is illustrated via simulations. The considered problem has applications in diverse areas including spectrum sensing for cognitive radio.

Robust Spectrum-Based Comparison of Multivariate Complex Random Signals

We consider the problem of comparing two complex multivariate random signal realizations, possibly contaminated with additive outliers, to ascertain whether they have identical power spectral densities. For clean data (i.e., known to be outlier free), a binary hypothesis testing formulation in frequency-domain, utilizing the estimated power spectral density matrices, has been proposed in the literature, and it results in a generalized likelihood ratio test (GLRT). In this paper, we first present an alternative, principled derivation of the existing GLRT using the asymptotic distribution of a frequency-domain sufficient statistic, based on the discrete Fourier transform of the two signal realizations. In order to robustify this GLRT in the presence of additive outliers, we first exploit an existing robust estimator of multivariate scatter to detect the outliers, and subsequently, to clean the data. The existing GLRT is then applied to the cleaned signal realizations. The approach is illustrated through simulations. The considered problem has applications in diverse areas, including user authentication in wireless networks with multi-antenna receivers.

Application of the method of fundamental solutions to predict the acoustic performance of T-shaped thin barriers

A frequency-domain formulation based on Method of Fundamental Solutions (MFS) is used to simulate the sound field generated by a point source in the presence of a T-shaped thin noise barrier. The MFS formulation is here developed by making use of adequate Green's functions, defined by using the image-source technique, that satisfy specific boundary conditions, allowing decreasing the number of discretized surfaces and consequently reducing the computational cost of the numerical model. Both the ground and the building are modeled as infinite rigid plane surfaces, and the barrier is assumed to be absorptive. The surface treatment of the barrier is characterized by a porous material. The Zwikker and Kosten model is here used for predicting the acoustic properties of the porous material. To validate the numerical implementation of the proposed method, the results are compared with solutions of the Dual-BEM formulation. Numerical simulations are carried out in order to demonstrate the efficiency of the proposed method and the performance of the T-shaped thin noise barriers in typical cases of traffic noise.