Spectral Decomposition Method Research Articles

Exploration on flutter mechanism of a damaged transonic rotor blade using high-fidelity fluid–solid coupling method

Structural damage in turbomachinery is a primary origin of aeronautic accidents, which is receiving increased attention. This study is thus focused on the aeroelastic analysis of damaged blades, including the onset of flutter and underlying mechanisms. First, a high-fidelity fluid–solid coupling system is established with computational fluid dynamics (CFD) and computational structural dynamics (CSD) technologies, via which the dynamic aeroelastic analysis is conducted based on static aeroelastic deformation. Second, a damaged rotor blade is parametrically modelled with variable damage levels, extents, and positions. Finally, the modal identification method of spectral proper orthogonal decomposition (SPOD) is applied to observe flow details and provide physical insight into the flutter mechanism for damaged blades. Numerical analysis finds that there is a critical damage level below which the aeroelastic stability is positively improved with increasing damage level; otherwise, a significant loss of stability is induced. The damage location and extent further affect this critical damage level and the change rate crossing the threshold. The simulation with CFD/CSD finds that the high pressure near the trailing edge induced from boundary layer separation suppresses vibrations in stable conditions, but motivates vibrations during flutter, which is because of the high-pressure spread to nearing blades. SPOD modes reveal that high-frequency disturbances with large scale are primary factors inducing flutter, which is further stimulated by the high-order disturbances with small scale. This study provides a crucial foundation for the fatigue prediction for rotor blades in service and the optimisation design for high-performance turbomachinery in the near future.

Seismic fault detection with sliding windowed differential cepstrum–based coherence analysis

AbstractCepstral decomposition is beneficial for highlighting certain geological features within the particular quefrency bands which may be deeply buried within the wide quefrency range of the seismic data. Converting seismic traces into the corresponding cepstrum components can better analyse some characteristics of underground strata than the traditional spectral decomposition methods. We propose the sliding windowed differential cepstrum–based coherence analysis approach to delineate the fault features. First, the data are decomposed using a sliding windowed differential cepstrum, which results in multi‐cepstrum data of corresponding quefrency of certain bandwidth. These different multi‐cepstrum data may highlight the different stratigraphic features in a certain quefrency band. We select the first‐order common quefrency volume as the featured attribute. Then, eigenstructure‐based coherence is applied on the first‐order common quefrency data volume to statistically obtain the fault detection result with a finer and sharper image. Synthetic data and field data examples show that the proposed method has the ability to better visualize all the possible subtle and minor faults present in the data more accurately and discernibly than the traditional coherence method. Compared with the ant‐tracking method, the proposed method is more effective in revealing the major faults. It is hoped that this work will complement current fault detection methods with the addition of the cepstral‐based method.

Thermal transport in C6N7 monolayer: a machine learning based molecular dynamics study

The successful synthesis of a novel C6N7carbon nitride monolayer offers expansive prospects for applications in the fields of semiconductors, sensors, and gas separation technologies, in which the thermal transport properties of C6N7are crucial for optimizing the functionality and reliability of these applications. In this work, based on our developed machine learning potential (MLP), molecular dynamics (MD) simulations including homogeneous non-equilibrium, non-equilibrium, and their respective spectral decomposition methods are performed to investigate the effects of phonon transport, temperature, and length on the thermal conductivity of C6N7monolayer. Our results reveal that low-frequency and in-plane phonon modes dominate the thermal conductivity. Notably, thermal conductivity decreases with an increase in temperature due to temperature-induced increase in phonon-phonon scattering of in-plane phonon modes, while it increases with an extension in sample length. Our findings based on MD simulations with MLP contribute new insights into the lattice thermal conductivity of holey carbon nitride compounds, which is helpful for the development of next-generation electronic and photonic devices.

Numerical investigation of serration angle on trailing edge noise reduction

The influence of serration angle on the three-dimensional flow characteristics and noise attenuation mechanisms of a NACA6512-63 airfoil is explored in this research using large eddy simulation (LES) and spectral proper orthogonal decomposition (SPOD) methods. Analysis of the mean flow field reveals the formation of counter-rotating vortex pairs, resulting from the outward flow towards the serration edges and the downwash flow in the valleys. This flow modification alters the effective angle of the serration, which in turn impacts its noise reduction performance. Furthermore, the noise reduction mechanism is investigated by comparing the general solution of Lyu's semi-analytical equation with the SPOD mode results, and the frequency range associated with noise attenuation is analyzed. The findings indicate that the case with λ/h=0.15 demonstrates the most significant noise reduction effect. This research offers valuable insights into the interplay between serration geometry and the resulting flow characteristics and noise reduction mechanisms.

A second-generation URANS model (STRUCT-$$\epsilon $$) applied to a generic side mirror and its impact on sound generation

AbstractA generic side mirror can be approximated to the combination of a half cylinder topped with a quarter of sphere. The flow structure in the wake of the side mirror is highly transient and the turbulence plays an important role affecting aeroacoustics through pressure fluctuation. Thus, this geometry is one of the test cases object of several numerical studies in recent years to assess the aerodynamic and aeroacoustic capabilities of the turbulence models. In this context, this study presents how the second-generation URANS closure STRUCT-$$\epsilon $$ ϵ is able to properly predict the expected stagnation, flow separation and vortex shedding phenomena. Besides, the predictive accuracy for the noise generation mechanism is evaluated by comparing the spectra of the sound pressure level measured at several static pressure sensors with the numerical results obtained with the STRUCT-$$\epsilon $$ ϵ . The response of this turbulence model has exceeded that from other hybrid methods and is in good agreement with the results from Large-Eddy Simulations or the experiments. To conclude the paper, the applicability of STRUCT-$$\epsilon $$ ϵ to construct a Spectral Proper Orthogonal Decomposition method that helps identifying the most energetic modes to appropriately capture the dominant flow structures is also introduced.

Spectral decomposition for collective Thomson scattering based on an improved genetic algorithm.

Collective Thomson scattering (CTS) is a diagnostic technique that obtains ion temperature and ion composition of plasma by spectral decomposition from scattering spectra. Bayesian estimation and least squares fitting are usually applied in this spectral decomposition process. Nevertheless, these spectral decomposition methods strongly rely on measurements of other diagnostic systems, and the measurement errors of other systems would influence the spectral decomposition results. In this article, an improved genetic algorithm is applied to decompose the scattering spectra of CTS. By analyzing the sensitivity of plasma parameters, the width and slope of the scattering spectrum are found to be strongly associated with ion temperature. Based on this correlation relation, a new fitness function is designed to provide a more precise estimation of ion temperature. Meanwhile, adaptive crossover and mutation operators are introduced to solve the premature convergence problem. This improved genetic algorithm with the new fitness function can obtain a more precise ion temperature from scattering spectra of CTS and does not rely on the measurement of other diagnostic systems, which has an extensive application prospect in data processing of CTS.

Statistical data analysis of x-ray spectroscopy data enabled by neural network accelerated Bayesian inference.

Bayesian inference applied to x-ray spectroscopy data analysis enables uncertainty quantification necessary to rigorously test theoretical models. However, when comparing to data, detailed atomic physics and radiation transfer calculations of x-ray emission from non-uniform plasma conditions are typically too slow to be performed in line with statistical sampling methods, such as Markov Chain Monte Carlo sampling. Furthermore, differences in transition energies and x-ray opacities often make direct comparisons between simulated and measured spectra unreliable. We present a spectral decomposition method that allows for corrections to line positions and bound-bound opacities to best fit experimental data, with the goal of providing quantitative feedback to improve the underlying theoretical models and guide future experiments. In this work, we use a neural network (NN) surrogate model to replace spectral calculations of isobaric hot-spots created in Kr-doped implosions at the National Ignition Facility. The NN was trained on calculations of x-ray spectra using an isobaric hot-spot model post-processed with Cretin, a multi-species atomic kinetics and radiation code. The speedup provided by the NN model to generate x-ray emission spectra enables statistical analysis of parameterized models with sufficient detail to accurately represent the physical system and extract the plasma parameters of interest.

HTG transformation: an amplitude modulation method and its application in bearing fault diagnosis

Abstract Rolling bearings are critical components in modern mechanical equipment, and the health monitoring and predictive maintenance of bearings are crucial for the normal operation of machinery. Hence, there is a compelling need to delve into advanced methodologies for enhancing the detection of fault characteristics in bearings. Faulty bearings produce periodic impulses during constant-speed rotation, which can typically be detected through envelope analysis. However, in some complex conditions, the relevant fault frequencies may be hidden within interfering components. This paper presents an amplitude modulation technique called the hyperbolic tangent Gaussian (HTG) transformation, designed to extract weak fault components from signals. Firstly, a family of amplitude modulation functions, known as the HTG functions, is constructed. These functions modulate signals with normalized amplitudes to obtain a series of modulated signals. Simultaneously, a frequency domain amplitude ratio metric is used for the automatic selection of the optimal components. Finally, the HTGgram is introduced, a spectral decomposition method based on trend components, aiming to identify the best combination of filtering and modulation components. Simulations with multi-component bearing fault signals and experimental signals with composite bearing faults demonstrate that this method not only highlights fault features and suppresses noise interference but also adaptively selects frequency bands related to faults, enhancing fault information. This approach exhibits excellent adaptability and effectiveness in complex operating conditions with multiple interference components.

Spectral Decomposition and Transformation for Cross-domain Few-shot Learning

Cross-domain few-shot Learning (CDFSL) is proposed to first pre-train deep models on a source domain dataset where sufficient data is available, and then generalize models to target domains to learn from only limited data. However, the gap between the source and target domains greatly hampers the generalization and target-domain few-shot finetuning. To address this problem, we analyze the domain gap from the aspect of frequency-domain analysis. We find the domain gap could be reflected by the compositions of source-domain spectra, and the lack of compositions in the source datasets limits the generalization. Therefore, we aim to expand the coverage of spectra composition in the source datasets to help the source domain cover a larger range of possible target-domain information, to mitigate the domain gap. To achieve this goal, we propose the Spectral Decomposition and Transformation (SDT) method, which first randomly decomposes the spectrogram of the source datasets into orthogonal bases, and then randomly samples different coordinates in the space formed by these bases. We integrate the above process into a data augmentation module, and further design a two-stream network to handle augmented images and original images respectively. Experimental results show that our method achieves state-of-the-art performance in the CDFSL benchmark dataset.

Integrating multimodal Raman and photoluminescence microscopy with enhanced insights through multivariate analysis

This paper introduces a novel multimodal optical microscope, integrating Raman and laser-induced photoluminescence (PL) spectroscopy for the analysis of micro-samples relevant in Heritage Science. Micro-samples extracted from artworks, such as paintings, exhibit intricate material compositions characterized by high complexity and spatial heterogeneity, featuring multiple layers of paint that may be also affected by degradation phenomena. Employing a multimodal strategy becomes imperative for a comprehensive understanding of their material composition and condition. The effectiveness of the proposed setup derives from synergistically harnessing the distinct strengths of Raman and laser-induced PL spectroscopy. The capacity to identify various chemical species through the latter technique is enhanced by using multiple excitation wavelengths and two distinct excitation fluence regimes. The combination of the two complementary techniques allows the setup to effectively achieve comprehensive chemical mapping of sample through a raster scanning approach. To attain a competitive overall measurement time, we employ a short integration time for each measurement point. We further propose an analysis protocol rooted in a multivariate approach. Specifically, we employ non-negative matrix factorization as the spectral decomposition method. This enables the identification of spectral endmembers, effectively correlated with specific chemical compounds present in samples. To demonstrate its efficacy in Heritage Science, we present examples involving pigment powder dispersions and stratigraphic micro-samples from paintings. Through these examples, we show how the multimodal approach reinforces material identification and, more importantly, facilitates the extraction of complementary information. This is pivotal as the two optical techniques exhibit sensitivity to different materials. Looking ahead, our method holds potential applications in diverse research fields, including material science and biology.

Direct numerical simulation of shock wave/boundary layer interaction controlled by steady microjet in a compression ramp

Shock wave/boundary layer interaction in a 24° turning angle of the compression ramp at Mach number 2.9 controlled by steady microjet is investigated using direct numerical simulation. Three different jet spacings which are termed as sparse, moderate and dense are considered, and the induced vortex system and shock structures are compared. A moderate jet spacing configuration is found to generate counter-rotating vortex pairs that transport high-momentum fluid towards the vicinity of wall and strengthen the boundary layer to resist separation, reducing the separation region. The dense jet spacing configuration creates a larger momentum deficit region, reducing the friction downstream of the corner. Analysis of pressure and pressure gradient reveals that dense jet spacing configuration reduces the intensity of separation shock. The impact of varying jet spacings on the turbulent kinetic energy transport mechanism is also investigated by decomposing the budget terms in the transport equation. Furthermore, the spectral characteristics of the separation region are studied using power spectral density and dynamic mode decomposition methods, revealing that moderate jet spacing configuration suppresses low-frequency fluctuations in the separation region.

Application of Multi-Temporal and Multisource Satellite Imagery in the Study of Irrigated Landscapes in Arid Climates

The study of ancient irrigation is crucial in the archaeological research of arid regions. It covers a wide range of topics, with the Near East being the focus for decades. However, political instability and limited data have posed challenges to these studies. The primary objective is to establish a standardised method applicable to different arid environments using the Google Earth Engine platform, considering local relief of terrain and seasonal differences in vegetation. This study integrates multispectral data from LANDSAT 5, Sentinel-2, SAR imagery from Sentinel 1, and TanDEM-X (12 m and 30 m) DSMs. Using these datasets, calculations of selected vegetation indices such as the SMTVI and NDVSI, spectral decomposition methods such as TCT and PCA, and topography-based methods such as the MSRM contribute to a comprehensive understanding of landscape irrigation. This paper investigates the influence of modern environmental conditions on the visibility of features like levees and palaeo-channels by testing different methods and parameters. This study aims to identify the most effective approach for each case study and explore the possibility of applying a consistent method across all areas. Optimal results are achieved by combining several methods, adjusting seasonal parameters, and conducting a comparative analysis of visible features.

Numerical simulation of Rashba spin–orbit coupling effect on quantum Hall resistivity within tight-binding approximation

A numerical simulation of the effect of Rashba spin–orbit coupling (RSO) on quantum transport properties of electrons confined to a two-dimensional electron gas (2DEG) in the integer quantum Hall regime is presented. The mechanism of quantization and the dependence of the Hall resistivity (HR) on the system built-in and external parameters are studied using the non-equilibrium Green’s function (NEGF) technique. Relevant Green’s functions are computed numerically using spectral decomposition method in combination with recursive techniques. The tight-binding-like representation of the system Hamiltonian including magnetic field is obtained within the finite difference method, using Dirichlet boundary conditions. Corresponding formula linking the Hall resistivity with the transmission function of the system has been derived analytically within the NEGF formalism in a general form, in the sense that the formula can also be used beyond the linear response limit and for nonzero temperatures. In particular, it was shown explicitly that in the presence of the RSO coupling the even- and odd plateaus emerging in the magnetic-field dependence of the quantum Hall resistivity are related to different physical mechanisms.

Elastic and inelastic phonon scattering effects on thermal conductance across Au/graphene/Au interface

Heat dissipation from graphene devices is predominantly limited by heat conduction across the metal contacts with complex phonon scattering. In this work, the effects of elastic and inelastic phonon scattering on the interfacial thermal conductance (ITC) across the Au/graphene/Au interface are studied using both atomistic Green's function (AGF) and reverse non-equilibrium molecular dynamics methods. The results show that the contribution of inelastic phonon scattering to the ITC increases with the enhancement of interfacial bonding strength. Moreover, the overlap of the vibrational density of states across the interface shows that the coupling between the Au layer (adjacent to the Au/graphene interface) and graphene's out-of-plane modes plays the dominant role in ITC across the Au/graphene interface. By comparing the transmission functions calculated with AGF and spectral heat current decomposition methods, the inelastic phonon scattering process facilitates phonon transmission in the lower and higher frequency range but hinders phonon transmission in the intermediate frequency range. It is expected that this study can contribute to a better understanding of the thermal conduction mechanism across the metal/graphene interface, providing guidance for thermal management and heat conduction optimization of graphene in microelectronic devices.

A depth-variant seismic wavelet extraction method for basis pursuit inversion with an impedance trend constraint

The seismic images produced by prestack depth migration indicate more accurate subsurface structures than time images, resulting in a growing need for depth-domain inversion. However, due to the strong nonstationarity exhibited by depth-domain seismic data, time-domain inversion methods based on the convolutional model cannot be directly applied in the depth domain. To address this issue, we develop a method for extracting a depth-variant seismic wavelet, which is then combined with a nonstationary convolutional model to enable direct inversion of the depth-domain acoustic impedance (AI). First, we extend the Morlet wavelet to the depth domain and develop an orthogonal matching pursuit spectral decomposition method using the depth-domain Morlet wavelet. We then investigate the waveforms and wavenumber spectra similarities between the depth-domain Morlet wavelet and depth-domain Ricker wavelet and extract depth-variant Ricker wavelets from the depth-wavenumber spectrum. We add a depth-domain impedance trend constraint to the conventional basis pursuit inversion to enhance the lateral continuity of the inversion results. Then, we attain direct inversion of the depth-domain AI. Tests of synthetic and field data demonstrate that our method achieves high-accuracy inversion results while maintaining high computational efficiency, highlighting our approach’s effectiveness and strong reservoir characterization potential.

A method to assess linear self-predictability of physiologic processes in the frequency domain: application to beat-to-beat variability of arterial compliance.

The concept of self-predictability plays a key role for the analysis of the self-driven dynamics of physiological processes displaying richness of oscillatory rhythms. While time domain measures of self-predictability, as well as time-varying and local extensions, have already been proposed and largely applied in different contexts, they still lack a clear spectral description, which would be significantly useful for the interpretation of the frequency-specific content of the investigated processes. Herein, we propose a novel approach to characterize the linear self-predictability (LSP) of Gaussian processes in the frequency domain. The LSP spectral functions are related to the peaks of the power spectral density (PSD) of the investigated process, which is represented as the sum of different oscillatory components with specific frequency through the method of spectral decomposition. Remarkably, each of the LSP profiles is linked to a specific oscillation of the process, and it returns frequency-specific measures when integrated along spectral bands of physiological interest, as well as a time domain self-predictability measure with a clear meaning in the field of information theory, corresponding to the well-known information storage, when integrated along the whole frequency axis. The proposed measure is first illustrated in a theoretical simulation, showing that it clearly reflects the degree and frequency-specific location of predictability patterns of the analyzed process in both time and frequency domains. Then, it is applied to beat-to-beat time series of arterial compliance obtained in young healthy subjects. The results evidence that the spectral decomposition strategy applied to both the PSD and the spectral LSP of compliance identifies physiological responses to postural stress of low and high frequency oscillations of the process which cannot be traced in the time domain only, highlighting the importance of computing frequency-specific measures of self-predictability in any oscillatory physiologic process.

Spectral feature extraction of rocket exhaust plume using spectral proper orthogonal decomposition

The spectral characterization of flow-field parameters provides a new perspective for understanding the spatiotemporal evolution of unsteady supersonic exhaust plumes and for extracting typical structures. In this study, a large-eddy simulation is performed to calculate the three-dimensional unsteady supersonic plume flow field of rocket engines, and a spectral proper orthogonal decomposition (SPOD) method with a spatiotemporal separation is established. This approach is used to extract the coherent structural features of the unsteady exhaust plume flow field and analyze the mode space structure at different frequencies. The three-dimensional reconstruction and denoising of the exhaust plume flow-field parameters can be achieved via the frequency- and time-domain reconstructions of the SPOD algorithm and oblique projection method, respectively. The ground rocket exhaust plume of ballistic evaluation motor-II is analyzed. The results indicate that the SPOD method can effectively extract the single-frequency mode structure of the reactive supersonic flow field, and that low-order behavior appears in the m = 0 and m = 1 azimuth modes. The potential core exhibits a high-frequency wave-packet structure that is affected by shock waves and shear layers. Time-domain reconstruction based on the oblique projection method facilitates the capture of the dynamic characteristics of the flow field. For the first-order SPOD mode, the frequency- and time-domain reconstruction errors are 3.3% and 1.5%, respectively. The frequency-domain reconstruction method exhibits a 4% improvement in denoising ability compared to low-pass filters. This study provides a novel method for the spectral characterization and spatiotemporal feature extraction of supersonic exhaust plume flow fields.

Multi-User System for Earth Sensing Spacecraft Attitude Calibration and Analysis

The Teledyne Multiple User System for Earth Sensing (“MUSES”) was developed for commercial Earth imaging and instrument technology development on the International Space Station (ISS). MUSES simultaneously hosts up to four Earth ensing instruments and provides inertial pointing and tracking to orient instruments toward planned targets on the ground. Up to four instruments are robotically installed on MUSES and periodically interchanged as warranted. MUSES was delivered to the ISS in June 2017, with initial testing successfully completed and subsequently documented in an initial requirements verification report. Assessing the performance of the MUSES attitude estimation system is challenging due to the lack of an independent attitude estimate of the platform attitude. A novel approach is introduced herein where the ISS attitude estimate, derived from ISS Global Positioning System sensors, is employed as an independent measure of MUSES platform attitude. Spectral decomposition methods are used to account for the contributions of ISS deformations to the variance in disparities between the ISS and MUSES attitudes and thus enable a less conservative estimate of the variance in MUSES attitude error. Implementing the spectral decomposition results in a best estimate upper bound on MUSES attitude errors of 34.5 and 27.7 arcsec, respectively, in the along-track and cross-track axes. Both the simulated and real results obtained from the spacecraft are presented.

Scattering Field Intensity and Orbital Angular Momentum Spectral Distribution of Vortex Electromagnetic Beams Scattered by Electrically Large Targets Comprising Different Materials

In this study, we obtained the intensity and orbital angular momentum (OAM) spectral distribution of the scattering fields of vortex electromagnetic beams illuminating electrically large targets composed of different materials. We used the angular spectral decomposition method to decompose a vortex beam into plane waves in the spectral domain at different elevations and azimuths. We combined this method with the physical optics algorithm to calculate the scattering field distribution. The OAM spectra of the scattering field along different observation radii were analyzed using the spiral spectrum expansion method. The numerical results indicate that for beams with different parameters (such as polarization, topological charge, half-cone angle, and frequency) and targets with different characteristics (such as composition), the scattering field intensity distribution and OAM spectral characteristics varied considerably. When the beam parameters change, the results of scattering from different materials show similar changing trends. Compared with beams scattered by uncoated metal and dielectric targets, the scattering field of the coating target can better maintain the shape and OAM mode of beams from the incident field. The scattering characteristics of metal targets were the most sensitive to beam-parameter changes. The relationship between the beam parameters, target parameters, the scattering field intensity, and the OAM spectra of the scattering field was constructed, confirming that the spiral spectrum of the scattering field carries the target information. These findings can be used in remote sensing engineering to supplement existing radar imaging, laying the foundation for further identification of beam or target parameters.

Solving the time-dependent protein distributions for autoregulated bursty gene expression using spectral decomposition.

In this study, we obtain an exact time-dependent solution of the chemical master equation (CME) of an extension of the two-state telegraph model describing bursty or non-bursty protein expression in the presence of positive or negative autoregulation. Using the method of spectral decomposition, we show that the eigenfunctions of the generating function solution of the CME are Heun functions, while the eigenvalues can be determined by solving a continued fraction equation. Our solution generalizes and corrects a previous time-dependent solution for the CME of a gene circuit describing non-bursty protein expression in the presence of negative autoregulation [Ramos et al., Phys. Rev. E 83, 062902 (2011)]. In particular, we clarify that the eigenvalues are generally not real as previously claimed. We also investigate the relationship between different types of dynamic behavior and the type of feedback, the protein burst size, and the gene switching rate.