Components Of Different Frequencies Research Articles

Stochastic analysis of the non-Gaussian airgap response of a semi-submersible using frequency domain analysis

Airgap is a crucial design parameter for semi-submersibles. The analysis of the extreme airgap statistics is challenging due to nonlinearities in the wave elevation and platform motions, as well as their interactions and phase relationships. In this paper, an efficient frequency domain approach is developed for airgap analysis, using second-order diffraction analysis to model the wave loads. The wave amplification effect is predicted using second-order random wave theory together with linear diffraction/radiation analysis, and the drag forces are linearized. The linear and quadratic transfer functions (sum- and difference frequencies) of the airgap response are derived, preserving all the phase relationships. The crossing rate is a key quantity for characterizing the extreme of a stochastic process. Using the transfer functions, the crossing rate of the non-Gaussian airgap process is derived via a statistical method that preserves the statistical dependency between the linear, sum- and difference-frequency components. In the case studies, the spectral density of the airgap obtained from frequency domain analysis are compared to time domain simulations (which are performed as a benchmark), and the results are found to be in excellent agreement. Moreover, the proposed approach generally provides good estimation of the crossing rate. The results also reveal insights into the airgap behavior; for example, the airgap at the platform center is nearly Gaussian, whereas the off-center locations are significantly non-Gaussian. Finally, the influence of various nonlinearities on the airgap statistics are systematically investigated.

Strong-Field Ionization of Linear Molecules by a Bichromatic Elliptically Polarized Laser Field with Coplanar Counterrotating or Corotating Components of Different Frequencies

We investigate strong-field ionization of linear molecules by a two-color laser field of frequencies rω and sω having coplanar counterrotating or corotating elliptically polarized components (ω is the fundamental laser field frequency and r and s are integers). Using the improved molecular strong-field approximation we analyze direct above-threshold ionization (ATI) and high-order ATI (HATI) spectra. More precisely, reflection and rotational symmetries of these spectra for linear molecules aligned in the laser-field polarization plane are considered. The reflection symmetries for particular molecular orientations, known to be valid for a bicircular field (this is the field with circularly polarized counterrotating components), are valid also for arbitrary component ellipticities. However, specific rotational symmetries that are satisfied for HATI by a bicircular field, are violated for an arbitrary elliptically polarized field with counterrotating components. For the corotating case and the N2 molecule we analyze molecular-orientation-dependent interferences and plateau structures for various ellipticities.

Analysis of the extreme wave elevation due to second-order diffraction around a vertical cylinder

Statistical analysis of nonlinear random waves is important in coastal and ocean engineering. One approach for modeling nonlinear waves is second-order random wave theory, which involves sum- and difference-frequency interactions between wave components. The probability distribution of the non-Gaussian surface elevation can be solved using a technique developed by Kac and Siegert [21]. The wave field can be significantly modified by wave diffraction due to a structure, and the nonlinear diffracted wave elevation can be of interest in certain applications, such as the airgap prediction for an offshore structure. This paper investigates the wave statistics due to second-order diffraction, motivated by the scarcity of prior research. The crossing rate approach is used to evaluate the extreme wave elevation over a specified duration. The application is a bottom-supported cylindrical structure, for which semi-analytical solutions for the second-order transfer functions are available. A new efficient statistical method is developed to allow the distribution of the diffracted wave elevation to be obtained exactly, accounting for the statistical dependency between the linear, sum-frequency and difference-frequency components. Moreover, refinements are proposed to improve the efficiency for computing the free surface integral. The case study yields insights into the problem. In particular, the second-order nonlinearity is found to significantly amplify the extreme wave elevation, especially in the upstream region; conversely, the extreme elevation at an oblique location downstream is attenuated due to sheltering effects. The statistical dependency between the linear and sum-frequency components is also shown to be important for the extreme wave statistics.

Fault feature extraction of rotor broken bar and stator winding inter-turn short circuit of asynchronous motors

In order to accurately identify the stator and rotor faults of three-phase squirrel cage induction motor, it is necessary to extract the fault characteristics of the motor accurately and quickly. A normal induction motor, the stator phase current only have the fundamental component in theory, but it will produce harmonic components of different frequencies or change the energy of the original harmonic components when a fault occurs. Convert the fault current to frequency domain and get its spectrum, will be found that the amplitude of fundamental current is very large and the amplitude of harmonic current is very small, and their frequency is very close when the rotor bar is broken. Because of the influence of fundamental current, it is difficult to identify the fault feature components in the spectrum. In this paper use a hybrid genetic algorithm based on Nelder-Mead simplex method to estimate the fundamental current, obtain the expression of fundamental wave current and remove it from the fault current. In this way, the fault characteristics of motor stator or rotor can be obtained.

NUMERICAL INVESTIGATION OF BREAKING IRREGULAR WAVES OVER A SUBMERGED BAR WITH CFD

The study of breaking irregular waves is of great practical interest, because of the waves found in the nature. Regular waves are seldom found in the field. Irregular waves can be viewed as the superposition of a number of regular waves (wave components) with the different frequencies and the amplitudes. The breaking process for irregular waves is more complex as compared to breaking regular waves. The energy transfer between the individual wave components of different frequencies also takes place during the breaking process. Due to this, the spectral characteristics of the incident wave spectrum change during the breaking process. The main purpose of the study is to investigate the hydrodynamics during the interaction of breaking irregular waves with a submerged bar.

Vibration signal de-noising based on empirical wavelet transform autocorrelation analysis

In diesel engine fault diagnosis, non-stationary vibration signal is easily disturbed by strong noise. In view of the shortcomings of empirical mode decomposition (EMD) and wavelet transform in de-noising, a de-noising method is proposed, which is Empirical Wavelet Transform (EWT) autocorrelation analysis. Taking advantages of EMD and wavelet transform, the Fourier spectrum is adaptively divided by EWT, and the intrinsic mode components of different frequency are extracted through constructed wavelet filter, and the method can effectively eliminate modal aliasing and solve adaptive problems in wavelet de-noising. At the same time, autocorrelation analysis can make the random noise decay to zero, and the modal components with high frequency random noise are dealt by autocorrelation analysis. The method is used to de-noising and compared the de-noising effect of EWT and EMD. Results show that the method can effectively decompose the intrinsic mode component with less number, and there is no false mode, and the de-noising effect is better than EMD de-noising. The method is feasible and effective in de-noising by vibration signals of diesel engine.

Sum-frequency ionic Raman scattering

In a recent report sum-frequency excitation of a Raman-active phonon was experimentally demonstrated for the first time. This mechanism is the sibling of impulsive stimulated Raman scattering, in which difference-frequency components of a light field excite a Raman-active mode. Here we propose that ionic Raman scattering analogously has a sum-frequency counterpart. We compare the four Raman mechanisms, photonic and ionic difference- and sum-frequency excitation, for three different example materials using a generalized oscillator model for which we calculate the parameters with density functional theory. Sum-frequency ionic Raman scattering completes the toolkit for controlling materials properties by means of selective excitation of lattice vibrations.

An Image Transform Based on Temporal Decomposition

Today, very dense synthetic aperture radar (SAR) time series are available through the framework of the European Copernicus Programme. These time series require innovative processing and preprocessing approaches including novel speckle suppression algorithms. Here we propose an image transform for hypertemporal SAR image time stacks. This proposed image transform relies on the temporal patterns only, and therefore fully preserves the spatial resolution. Specifically, we explore the potential of empirical mode decomposition (EMD), a data-driven approach to decompose the temporal signal into components of different frequencies. Based on the assumption that the high-frequency components are corresponding to speckle, these effects can be isolated and removed. We assessed the speckle filtering performance of the transform using hypertemporal Sentinel-1 data acquired over central Germany comprising 53 scenes. We investigated speckle suppression, ratio images, and edge preservation. For the latter, a novel approach was developed. Our findings suggest that EMD features speckle suppression capabilities similar to that of the Quegan filter while preserving the original image resolution.

Methodology for wave force monitoring of bottom-mounted cylinder using the measurement of the wave surface elevation around the body surface

This paper presents a methodology to estimate the wave force on a bottom-mounted cylinder using the measured signals of wave surface elevation around the body surface of the cylinder. Based on the potential theory, the formulae are derived in a general manner for bottom-mounted cylinders of arbitrary cross section. Considering the difficulty of decomposing the signal of wave surface elevation measured by wave gauges, a linear estimation method is developed to achieve an approximate estimation of the wave loads on cylinders. A hydrodynamic experiment was conducted on a circular cylinder in a random wave field to validate the effectiveness of the proposed method. The horizontal wave forces and bending moments directly measured by force balance are employed for the validation of the proposed estimated results using the measurement of the wave surface elevation by wave gauges. Error analysis is also conducted in the frequency domain to investigate the effects of the linear approximation. The analysis results indicate that the proposed method can effectively estimate the wave loads acting on the cylinder. The linear approximation method slightly underestimates the wave loads of the difference-frequency component, while overestimating that in the sum-frequency region.

Nonlinear Resonance of Cavities Filled with Bubbly Liquids: A Numerical Study with Application to the Enhancement of the Frequency Mixing Effect

This paper studies the nonlinear resonance of a cavity filled with a nonlinear biphasic medium made of a liquid and gas bubbles at a frequency generated by nonlinear frequency mixing. The analysis is performed through numerical simulations by mixing two source signals of frequencies well below the bubble resonance. The finite‐volume and finite‐difference based model developed in the time domain simulates the nonlinear interaction of ultrasound and bubble dynamics via the resolution of a differential system formed by the wave and Rayleigh–Plesset equations. Some numerical results, consistent with the literature, validate our procedure. Other results reveal the existence of a frequency shift of the cavity resonance at the difference‐frequency component, which rises with pressure amplitude and evidences the global changes undergone by the bubbly medium under finite amplitudes. Finally, this work shows the enhancement of the amplitude of the difference‐frequency component generated by parametric excitation using the nonlinear resonance shift, which is more pronounced when the second primary frequency is constant, the first one is varied to match the nonlinear resonance, and both have the same amplitude.

Probing the properties of the pulsar wind via studying the dispersive effects in the pulses from the pulsar companion in a double neutron-star binary system

The velocity and density distribution of $e^\pm$ in the pulsar wind are crucial distinction among magnetosphere models, and contains key parameters determining the high energy emission of pulsar binaries. In this work, a direct method is proposed, which might probe the properties of the wind from one pulsar in a double-pulsar binary. When the radio signals from the first-formed pulsar travel through the relativistic $e^\pm$ flow in the pulsar wind from the younger companion, the components of different radio frequencies will be dispersed. It will introduce an additional frequency-dependent time-of-arrival delay of pulses, which is function of the orbital phase. In this paper, we formulate the above-mentioned dispersive delay with the properties of the pulsar wind. As examples, we apply the formula to the double pulsar system PSR J0737-3039A/B and the pulsar-neutron star binary PSR B1913+16. For PSR J0737-3039A/B, the time delay in 300\,MHz is $\lesssim10\mu$s near the superior-conjunction, under the optimal pulsar wind parameters, which is $\sim$ half of the current timing accuracy. For PSR B1913+16, with the assumption that the neutron star companion has a typical spin down luminosity of $10^{33}$\,ergs/s, the time delay is as large as $10\sim20\mu$s in 300\,MHz. The best timing precision of this pulsar is $\sim5\mu$s in 1400\,MHz. Therefore, it is possible that we can find this signal in archival data. Otherwise, we can set an upper-limit on the spin down luminosity. Similar analysis can be apply to other eleven known pulsar-neutron star binaries

A Decoupled Control Strategy of Modular Multilevel Matrix Converter for Fractional Frequency Transmission System

Fractional frequency transmission system (FFTS), also known as low-frequency ac transmission system, is a promising solution to offshore wind power integration. The ac/ac converter is the most important equipment in FFTS. The modular multilevel matrix converter (M3C) is widely regarded as the next-generation ac/ac converter, but its complex control remains a problem. A novel control strategy is proposed featuring its decoupling algorithm in this paper. Different from previous research, the proposed current control regulates current components of different frequencies separately in star-figure subconverters under their synchronous rotating frames (SRFs), where the current is transformed to dq -axis dc signals for a better performance. A novel algorithm named “cross-SRF decoupling algorithm” is proposed to overcome the tight coupling between the circulating currents of two different frequencies. The effectiveness of the proposed control strategy has been verified by the simulation results obtained from a 110 kV, 400 MW M3C system implemented in MATLAB /Simulink.

Numerical models for the study of the nonlinear frequency mixing in two and three-dimensional resonant cavities filled with a bubbly liquid

The objective of this work is to develop versatile numerical models to study the nonlinear distortion of ultrasounds and the generation of low-ultrasonic frequency signals by nonlinear frequency mixing in two and three-dimensional resonators filled with bubbly liquids. The interaction of the acoustic field and the bubble vibrations is modeled through a coupled differential system formed by the multi-dimensional wave equation and a Rayleigh-Plesset equation. The numerical models we develop are based on multi-dimensional finite-volume techniques and a time discretization carried out by finite differences. Numerical experiments are performed for complex modes in many different cavities considering different kinds of boundary conditions and taking advantage of the dispersive character of the bubbly fluid to match specific resonances of the cavities. Results show the distribution of fundamental and harmonics for single frequency excitation and difference-frequency component for two-frequency excitation that are promoted by the strong nonlinearity of the bubbly medium. The numerous simulations analyzed suggest that the new numerical models developed and proposed in this paper are useful to understand the behavior of ultrasounds in bubbly liquids for sonochemical processes and applications of nonlinear frequency mixing.

Simulation of Nonlinear Acoustic Fields Generated by Wave Mixing

Applications of nonlinear acoustics are getting popular in the field of nondestructive characterization of material microstructure and damage. Before the nonlinear acoustic technique is fully utilized, it is important to understand the behavior of nonlinear acoustic fields generated by finite amplitude excitation. A two wave mixing technique can be considered and the difference frequency component can be used to determine the nonlinear material properties. One important advantage of using the difference frequency component is known to minimize the source nonlinearity and to acquire low attenuating nonlinear signals. In this paper, the expression for the difference frequency sound beam is derived from the quasilinear theory of the Westervelt equation which includes the material nonlinearity, beam diffraction and material attenuation. Simulation results are presented and the beam properies are discussed in comparison with the behavior of the second harmonic beam fields.

Multiscale Representation of Deformation via Beltrami Coefficients

Analyzing the deformation pattern of an object is crucial in various fields, such as in computer vision and medical imaging. A deformation can be considered as a combination of local and global deformations at different locations. To fully understand and analyze the deformation pattern, extracting deformation components of various scales and locations is necessary. We propose an algorithm for the multiscale decomposition of a bijective deformation using quasi-conformal theories. A deformation of an object can be described as a orientation-preserving homeomorphism of a two-dimensional domain. The mapping is then represented by its associated Beltrami coefficient (BC), which measures the local geometric (conformality) distortion of the deformation. The BC is a complex-valued function defined on the source domain. By applying the wavelet transform on the BC, the BC can be decomposed into different components of different frequencies compactly supported in different subdomains. Quasi-conformal mappings associated to different components of the BC can be reconstructed by solving Beltrami's equation. A multiscale decomposition of the deformation can then be constructed. To validate our proposed algorithm, we test it on synthetic examples as well as real medical data. Experimental results show the efficacy of our proposed model to decompose deformations at multiple scales and locations.

Influence of Secondary Impact on Printed Wiring Assemblies—Part I: High-Frequency “Breathing Mode” Deformations in the Printed Wiring Board

Design rules for portable electronic device are continuously striving for thinner printed wiring assemblies (PWAs) and smaller clearances because of ever-increasing demand for functionality and miniaturization. As a result, during accidental drop and impact events, there is an increased probability of internal secondary impact between a PWA and adjacent internal structures. In particular, compared to the initial impact, acceleration pulses caused by contact during secondary impacts are typically characterized by significant increase of amplitudes and frequency bandwidth. The resonant response in the thickness direction of printed wiring boards (PWBs) (termed the dynamic “breathing mode” of response, in this study) acts as a mechanical bandpass filter and places miniature internal structures in some components (such as microelectromechanical systems (MEMS)) at risk of failure, if any of them have resonant frequencies within the transmitted frequency bandwidth. This study is the first part of a two-part series, presenting qualitative parametric insights into the effect of secondary impacts in a PWA. This first part focuses on analyzing the frequency spectrum of: (i) the impulse caused by secondary impact, (ii) the energy transmitted by the dynamic “breathing” response of multilayer PWBs, and (iii) the consequential dynamic response of typical structures with high resonant frequencies that are mounted on the PWB. Examples include internal deformable structures in typical surface mount technology (SMT) components and in MEMS components. The second part of this series will further explore the effects of the breathing mode of vibration on failures of various SMT components of different frequencies.

Reconstructing rice phenology curves with frequency-based analysis and multi-temporal NDVI in double-cropping area in Jiangsu, China

Crop phenology retrieval in the double-cropping area of China is of great significance in crop yield estimation and water management under the influences of global change. In this study, rice phenology in Jiangsu Province, China was extracted from multi-temporal MODIS NDVI using frequency-based analysis. Pure MODIS pixels of rice were selected with the help of TM images. Discrete Fourier Transformation (DFT), Discrete Wavelet Transformation (DWT), and Empirical Mode Decomposition (EMD) were performed to decompose time series into components of different frequencies. Rice phenology in the double-cropping area is mainly located on the last 2 IMFs of EMD and the first 2‒3 frequencies of DFT and DWT. Compared with DFT and DWT, EMD is limited to fewer frequencies. Multi-temporal MODIS NDVI data combined with frequency-based analysis can retrieve rice phenology dates with on average 79% valid estimates. The sorting result for effective estimations from different methods is DWT (85%)>EMD (80%)>DFT (74%). Planting date (88%) is easier to estimate than harvesting date (70%). Rice planting date is easily affected by the former cropping mode within the same year in a double-cropping region. This study sheds light on understanding crop phenology dynamics in the frequency domain of multi-temporal MODIS data.

Testing the Q Theory of Investment in the Frequency Domain

We revisit the empirical performance of the Q theory of investment, explicitly taking into account the frequency dependence of investment, Tobin’s Q, and cash flow. The time series are decomposed into orthogonal components of different frequencies using wavelet multiresolution analysis. We find that the Q theory fits the data much better than might be expected (both in-sample and out-of-sample) when the frequency relationship between the variables is taken into account. Merging the wavelet approach and proxies for Q recently suggested in the investment literature also significantly improves the quality of short-term forecasts.

Modeling of Acoustic Field for a Parametric Focusing Source Using the Spheroidal Beam Equation

Abstract A theoretical model of acoustic field for a parametric focusing source on concave spherical surface is proposed. In this model, the source boundary conditions of the Spheroidal Beam Equation (SBE) for difference frequency wave excitation were studied. Propagation curves and beam patterns for difference frequency component of the acoustic field are compared with those obtained for Khokhlov-Zabolotskaya-Kuznetsov (KZK) model. The results demonstrate that the focused parametric model of SBE is good valid for a large aperture angle in the strongly focused acoustic field. It is also investigated that high directivity and good focal ability with the decreasing of downshift ratio and the increasing of half-aperture angle for the focused parametric model of SBE.

Revealing carrier-envelope phase through frequency mixing and interference in frequency resolved optical gating.

We demonstrate that full temporal characterisation of few-cycle electromagnetic pulses, including retrieval of the carrier envelope phase (CEP), can be directly obtained from Frequency Resolved Optical Gating (FROG) techniques in which the interference between non-linear frequency mixing processes is resolved. We derive a framework for this scheme, defined Real Domain FROG (ReD-FROG), for the cases of interference between sum and difference frequency components and between fundamental and sum / difference frequency components. A successful numerical demonstration of ReD-FROG as applied to the case of a self-referenced measurement is provided. A proof-of-principle experiment is performed in which the CEP of a single-cycle THz pulse is accurately obtained and demonstrates the possibility for THz detection beyond optical probe duration limitations inherent to electro-optic sampling.