Traditional Spectral Methods Research Articles

Separating the Spectral Counterparts in NGC 1275/Perseus Cluster in X-Rays

We present a model-independent method for separating the spectral counterparts of the active galactic nucleus (AGN) NGC 1275 from the surrounding emission of the Perseus cluster, as observed by Suzaku/XIS cameras. The Perseus cluster emission extends to higher energies than typically observed in AGN environments, reaching up to 9–10 keV. This necessitates precise separation of AGN and cluster spectra. To circumvent the degeneracy arising from numerous spectral fitting parameters, including elemental abundances, thermal and Compton emissions from the nucleus, and spectral parameters of the jet synchrotron self-Compton/inverse Compton emissions, we avoid traditional spectral fitting methods. Instead, we leverage spatial resolution and employ a double background subtraction approach. We apply this procedure to the complete set of Suzaku/XIS observational data for NGC 1275, resulting in cleaned spectra and a light curve of the AGN emission in this system. To demonstrate the applicability of our method, we also utilize the available XMM-Newton/EPIC data.

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.

The application of matching pursuit spectral blueing in post-stack seismic frequency enhancement

The calculation of the spectral blueing operator in the traditional spectral blueing method has singularity, which leads to poor performance in post-stack seimic frequency expansion. To this end, a frequency spreading technique based on matching pursuit (MP) and spectral blueing is proposed. Through time–frequency analysis processing, it is shown that the seismic signal extracted by matching tracking method has good stability and higher resolution. The specific process of the method in this paper firstly uses the matching tracking method to accurately divide the post-stack seismic data into multiple frequency-division seismic bodies; then, in the process of calculating the spectral blueing ization operators for each frequency band, the weighting idea is used to calculate the weights of the optimized spectral blueing ization operators for each frequency band based on the differences in energy in different frequency bands; finally, the optimized spectral blueing operator is convolved with seismic reflection coefficients to obtain high-resolution seismic data. The actual test results of poststack seismic data have proven that the frequency raising method proposed in this paper is superior to the traditional spectral blueing ization algorithm, greatly improving the high-frequency component information of poststack seismic data. After frequency extension, there are more seismic events and higher resolution. Finally, the practicability and rationality of the seismic data after frequency extraction are verified by a series of operations such as attribute extraction, well seismic calibration and inversion.

Enhancing the variability of simulated random processes using the spectral representation method

In this paper, the traditional spectral representation method for simulating stochastic processes is revisited. The main goal is to introduce various approaches to enhance the variability of the generated sample functions to better reflect variabilities observed in field measurements and experimental data, while keeping the ensemble-averaged power spectra unchanged. The general idea, gradually developed over the last decade, is to randomize the power spectral density function of the uncertain physical quantities by modeling certain parameters as random variables calibrated from experimental data. The potential of such approaches has not been fully explored yet. This work explores the pros and cons of using power spectral density functions with random parameters in the simulation of highly variable, stationary and nonstationary, Gaussian stochastic processes. The main characteristics of a stochastic process, such as distribution of maxima and variability in time and frequency, are examined. The use of a pass-band Butterworth filter to control the variability of the Fourier spectrum of the simulated samples is studied. The Butterworth filter is selected so that the ensemble-averaged power spectral density matches the target power spectrum, but each individual generated sample function possesses different amplitude and frequency distributions. Comparisons between samples generated using the traditional spectral representation method and those generated with enhanced variability are made through a series of illustrative examples. Results show that with the proposed enhanced-variability spectral representation method, certain characteristics of the stochastic process, such as the distribution of maxima, will be significantly different (while the ensemble-averaged power spectra will remain the same). The implications in reliability studies are obvious.

Simulation of multivariate ergodic stochastic processes using adaptive spectral sampling and non-uniform fast Fourier transform

The simulation of multivariate ergodic stochastic processes is critical for structural dynamic analysis and reliability evaluation. Although the traditional spectral representation method (SRM) has a wide application in many areas, it is highly inefficient in simulating stochastic processes with many simulation points or long durations due to the significant computational cost associated with matrix factorizations concerning frequency. To address the encountered challenge, this paper presents an efficient approach for simulating ergodic stochastic processes with limited frequencies. Central to this approach is a fusion of the adaptive spectral sampling and the non-uniform fast Fourier transform (NUFFT) techniques. The adaptive spectral sampling of the envelope spectrum enables the determination of limited non-equispaced frequencies, which are randomly sampled according to a uniform distribution. Thus, the Cholesky decomposition is only required at limited specific frequencies, which dramatically reduces the computational cost of matrix factorizations. Since the randomly sampled frequencies are not equispaced, utilizing FFT to accelerate the summation of trigonometric functions becomes impractical. Then, the NUFFT that adapts the non-equispaced sampling points is employed instead to expedite this process with the non-uniform increment approximated through reduced interpolation. By taking the wind field simulation of a long-span suspension bridge as an example, a parametric analysis is conducted to investigate the effect of random frequencies on the simulation error of the developed approach and the convergence of spectra. Finally, the developed approach is further validated by focusing on the spectra and probabilistic density functions of the simulated wind samples, and the simulation performance is compared with that of the traditional approach. The analytical results demonstrate the efficiency and accuracy of the developed approach in simulating ergodic stochastic processes.

Intelligent Substation Noise Monitoring System: Design, Implementation and Evaluation

In recent years, the State Grid of China has placed significant emphasis on the monitoring of noise in substations, driven by growing environmental concerns. This paper presents a substation noise monitoring system designed based on an end-network-cloud architecture, aiming to acquire and analyze substation noise, and report anomalous noise levels that exceed national standards for substation operation and maintenance. To collect real-time noise data at substations, a self-developed noise acquisition device is developed, enabling precise analysis of acoustic characteristics. Moreover, to subtract the interfering environmental background noise (bird/insect chirping, human voice, etc.) and determine if noise exceedances are originating from substation equipment, an intelligent noise separation algorithm is proposed by leveraging the convolutional time-domain audio separation network (Conv-TasNet), dual-path recurrent neural network (DPRNN), and dual-path transformer network (DPTNet), respectively, and evaluated under various scenarios. Experimental results show that (1) deep-learning-based separation algorithms outperform the traditional spectral subtraction method, where the signal-to-distortion ratio improvement (SDRi) and the scale-invariant signal-to-noise ratio improvement (SI-SNRi) of Conv-TasNet, DPRNN, DPTNet and the traditional spectral subtraction are 12.6 and 11.8, 13.6 and 12.4, 14.2 and 12.9, and 4.6 and 4.1, respectively; (2) DPTNet and DPRNN exhibit superior performance in environment noise separation and substation equipment noise separation, respectively; and (3) 91% of post-separation data maintains sound pressure level deviations within 1 dB, showcasing the effectiveness of the proposed algorithm in separating interfering noises while preserving the accuracy of substation noise sound pressure levels.

Relativistic Quantum Chemical Investigation of Actinide Covalency Measured by Electron Paramagnetic Resonance Spectroscopy.

We investigate actinide covalency effects in two [AnCptt3] (An = Th, U) complexes recently studied with pulsed electron paramagnetic resonance spectroscopy, using the Hyperion package to obtain relativistic hyperfine coupling constants from relativistic multiconfigurational wave functions. 1H and 13C HYSCORE simulations using the computed parameters show excellent agreement with the experimental data, highlighting the accuracy of modern relativistic ab initio methods. The extent of covalency indicated from the calculations on [ThCptt3] is in agreement with the original report based on traditional spectral fitting methods, while the covalency in [UCptt3] is found to be previously overestimated. The latter is due to the paramagnetic spin-orbit effect that arises naturally in a relativistic theory of hyperfine coupling and yet was not accounted for in the original study, thus highlighting the necessity of relativistic approaches for the interpretation of magnetic resonance data pertaining to actinides.

A hybrid ICEEMDAN and OMEDA-based vibrodiagnosis method for the bearing of rolling stock

Purpose. To develop a hybrid method based on ICEEMDAN and OMEDA for high-fidelity detection of the diagnostic features of the technical condition of roller bearing. Methodology. Due to digital signal processing the search was made of the informative components on the broadband spectra, envelope spectra, squared envelope spectra. The usage of the methods of mathematical statistics for the selection of informative IMFs as a result of iterative calculate procedures. The introduction of blind deconvolution method with a proper objective function for the enhancement of impulse fault features. Findings. The use of traditional spectral methods provided an incomplete list of diagnostic features of bearing roller damage. The empirical mode decomposition (EMD) method and its minor versions provide the series of intrinsic mode functions (IMFs). On the broadband vibration spectra of the selected low-frequency IMFs, diagnostic features were not detected in a sufficient number. Further research focused on the development of a hybrid method that takes into account the demodulation procedure of the high-frequency components of those IMFs that were selected according to the complex evaluation index. The Fast Kurtogram technique determined an informative frequency band of 7.2–7.5 kHz for demodulation and construction of the squared envelope spectra, where harmonics of the roller spin frequency and some side bands with a width equal to the separator rotation frequency appeared. The use of OMEDA caused the reduction of residual noise on the squared envelope spectra and bilateral sidebands to appear around all harmonics of the roller spin frequency. Originality. For the first time, the whole list of the diagnostic features of roller faults of the axle-box bearing was identified using the developed hybrid method, which involves steps of noise reduction for enhancing a physical meaning of a proper frequency components, associated with faults. The usage of the optimal minimum entropy deconvolution adjusted method helped to eliminate noise and provide all diagnostic features of the technical condition on the squared envelope spectrum. Practical value. The results of the study help to control the quality of repair of the axle-box rolling bearings on the test rig at the workshop of the freight railway car depot.

Generalized log orthogonal functions spectral collocation method for two dimensional weakly singular Volterra integral equations of the second kind

AbstractIn this article, a generalized log orthogonal functions (GLOFs)‐spectral collocation method to two dimensional weakly singular Volterra integral equations of the second kind is proposed. The mild singularities of the solution at the interval endpoint can be captured by Gauss‐GLOFs quadrature and the shortcoming of the traditional spectral method which cannot well deal with weakly singular Volterra integral equations with limited regular solutions is avoided. A detailed convergence analysis of the numerical solution is carried out. The efficiency of the proposed method is demonstrated by numerical examples.

Rapid spectral parameter prediction for black hole X-ray binaries using physicalized autoencoders

ABSTRACT Black hole X-ray binaries (BHBs) offer insights into extreme gravitational environments and the testing of general relativity. The X-ray spectrum collected by NICER offers valuable information on the properties and behaviour of BHBs through spectral fitting. However, traditional spectral fitting methods are slow and scale poorly with model complexity. This paper presents a new semisupervised autoencoder neural network for parameter prediction and spectral reconstruction of BHBs, showing an improvement of up to a factor of 2700 in speed while maintaining comparable accuracy. The approach maps the spectral features from the numerous outbursts catalogued by NICER and generalizes them to new systems for efficient and accurate spectral fitting. The effectiveness of this approach is demonstrated in the spectral fitting of BHBs and holds promise for use in other areas of astronomy and physics for categorizing large data sets. The code is available via https://github.com/EthanTreg/Spectrum-Machine-Learning.

Efficiently solving fractional delay differential equations of variable order via an adjusted spectral element approach

This paper presents a new approach for solving fractional delay differential equations of variable order using the spectral element method. The proposed method overcomes the limitations of traditional spectral methods, such as poor approximation in long intervals and inefficiency in high degrees. By introducing a variable order differentiation matrix and using basic Lagrangian functions to approximate the solution in each element, the method achieves high accuracy and efficiency. A penalty method is also applied to minimize the jump of fluxes at interface points, and the effectiveness of this approach is analyzed. Finally, three benchmark problems are solved, and the convergence analysis demonstrates the effectiveness and efficiency of the proposed method. In essence, this paper offers a significant contribution to the literature on fractional differential equations and their numerical solution methodologies.

An iterative spectral algorithm for digraph clustering

Abstract Graph clustering is a fundamental technique in data analysis with applications in many different fields. While there is a large body of work on clustering undirected graphs, the problem of clustering directed graphs is much less understood. The analysis is more complex in the directed graph case for two reasons: the clustering must preserve directional information in the relationships between clusters, and directed graphs have non-Hermitian adjacency matrices whose properties are less conducive to traditional spectral methods. Here, we consider the problem of partitioning the vertex set of a directed graph into k≥2 clusters so that edges between different clusters tend to follow the same direction. We present an iterative algorithm based on spectral methods applied to new Hermitian representations of directed graphs. Our algorithm performs favourably against the state-of-the-art, both on synthetic and real-world data sets. Additionally, it can identify a ‘meta-graph’ of k vertices that represents the higher-order relations between clusters in a directed graph. We showcase this capability on data sets about food webs, biological neural networks, and the online card game Hearthstone.

A Discontinuous Galerkin–Finite Element Method for the Nonlinear Unsteady Burning Rate Responses of Solid Propellants

The unsteady combustion of solid propellants under oscillating environments is the key to understanding the combustion instability inside solid rocket motors. The discontinuous Galerkin–finite element method (DG-FEM) is introduced to provide an efficient yet flexible numerical platform to investigate the combustion dynamics of solid propellants. The algorithm is developed for the classical unsteady model, the Zel’dovich–Novozhilov model. It is then validated based on a special analytical solution. The DG-FEM algorithm is then compared with the classical spectral method based on Laguerre polynomials. It is shown that the DG-FEM works more efficiently than the traditional spectral method, providing a more accurate solution with a lower computational cost.

Rapid X-ray fluorescence analysis as a modern alternative to traditional spectral methods in geochemical prospecting

The purpose of the study is to present the research results of the capabilities of modern portable rapid X-ray fluorescence analyzers when solving problems of geological and geochemical prospecting. On example of the applied SciAps X200 analyzer, the metrological indicators for the analysis results by portable instruments have been studied. The accuracy assessment results of analytical studies according to state standard reference samples are shown. Reproducibility of the analysis results is calculated on the basis of samples from promising gold sites of the Bodaibo synclinorium. The method is proved to be of high precision, and measurement errors in many cases are many times lower than the permissible certified values. The reproducibility is shown as 0,5–20 % depending on the element, which in most cases is significantly lower than the methodology permits. The results of interlaboratory comparative tests confirming the comparability of the analytical results of stationary and portable X-ray fluorescence analyzers are presented. For a number of significant elements, the authors have substantiated the lack of need to refine the results of the field rapid X-ray fluorescence analysis using labor-intensive and expensive methods with acid decomposition - atomic emission and atomic absorption spectroscopy. It has been proved that introduction of portable express equipment into geological prospecting works will make it possible to conduct real-time “on site” analytical studies.

Principles, developments, and applications of spatially resolved spectroscopy in agriculture: a review.

Agriculture is the primary source of human survival, which provides the most basic living and survival conditions for human beings. As living standards continue to improve, people are also paying more attention to the quality and safety of agricultural products. Therefore, the detection of agricultural product quality is very necessary. In the past decades, the spectroscopy technique has been widely used because of its excellent results in agricultural quality detection. However, traditional spectral inspection methods cannot accurately describe the internal information of agricultural products. With the continuous research and development of optical properties, it has been found that the internal quality of an object can be better reflected by separating the properties of light, such as its absorption and scattering properties. In recent years, spatially resolved spectroscopy has been increasingly used in the field of agricultural product inspection due to its simple compositional structure, low-value cost, ease of operation, efficient detection speed, and outstanding ability to obtain information about agricultural products at different depths. It can also separate optical properties based on the transmission equation of optics, which allows for more accurate detection of the internal quality of agricultural products. This review focuses on the principles of spatially resolved spectroscopy, detection equipment, analytical methods, and specific applications in agricultural quality detection. Additionally, the optical properties methods and direct analysis methods of spatially resolved spectroscopy analysis methods are also reported in this paper.

An improved estimation of stress drop and its application on induced earthquakes in the Weiyuan Shale Gas Field in China

SUMMARY Stress drop is a proxy of understanding earthquake source process, and it is controversial whether the stress drops of induced earthquakes associated with hydraulic fracturing and injection activities are similar to those of tectonic earthquakes. The measurement of stress drops is usually biased due to the limitations of observation means, or hidden issues in the estimation approaches. Utilizing a local short-period seismic network, we investigate the stress drops of induced earthquakes in Weiyuan Shale Gas Field in Sichuan Province, China from 2019 to 2020. Totally 11 844 earthquakes are involved in the analysis, and their stress drops are obtained using an improved approach on the basis of the traditional spectral decomposition method combined with a global optimization algorithm to avoid stacking of spectra that is found leading to source parameter underestimation. We divide the studied area into three subareas, and the results show strong stress drop heterogeneity across the entire region. We obtain an average stress drop of 2.29 MPa, piecewise stress drop dependence to earthquake magnitude, and complex depth dependence pattern. Our results indicate that stress drops of induced earthquakes are overall consistent with the induced earthquakes in other areas as well as tectonic earthquakes in different environments. Meanwhile, the complexity in the stress drop dependence to depth possibly reflects the variability of stress drops for different earthquake triggering mechanisms.

Generation of Anisotropic Cloud Cover

This paper introduces an advanced mathematical model for generating and analyzing cloud cover images, specifically designed to enhance photovoltaic (PV) partial shading studies. The model development involved a detailed analysis of real cloud cover images, with a particular emphasis on capturing their anisotropic spectral characteristics. This was achieved through a combination of spectral analysis and advanced image processing techniques. The research methodologically focused on developing a four-parameter model to accurately represent cloud formations' spectral properties. Key parameters were identified and fine-tuned to match the real cloud formations' characteristics. This involved analyzing the magnitude and phase spectra of the cloud covers and fitting them to a model capable of replicating these properties accurately. A significant part of the research was dedicated to formulating a novel phase spectrum generation technique. This technique was specifically designed to control the degree of similarity between the synthesized and original images, thereby ensuring the model's effectiveness in various simulation scenarios. The process involved manipulating the phase information of cloud cover images while maintaining their high-frequency components to enhance the detail and realism of the synthesized images. The model's accuracy in replicating cloud cover features was tested against traditional spectral synthesis methods. This comparative analysis involved generating cloud cover images using the developed model and established methods, then comparing these images to the original cloud covers in terms of visual similarity and approximation error. Additionally, the model was utilized to generate pseudo-random cloud cover images by varying the phase spectrum parameters. This process ensured that the generated images, while being random, adhered to the spectral characteristics of the original cloud covers. The research methodology also involved a detailed examination of the images' key characteristics, such as direction, length, and density, to ensure fidelity to the original samples. In summary, this paper details an approach to cloud cover image synthesis, with a focus on the accuracy of spectral properties and the development of an algorithm of model parameters estimation. The research highlights the use of advanced spectral analysis and image processing techniques in deriving key model parameters, leading to a significant advancement in cloud imaging for solar energy applications.

Stability Improvement of the TDLAS-Based CO Monitoring Module in a Coal Mine by Using a Spectral Denoising Algorithm Based on SVR

CO gas is not only lethal but also a significant forecasting indicator for the spontaneous combustion of coal mines. It is imperative that monitoring modules for CO gas that work well in the coal mine environment are available. A feasible solution is the detection of CO by using monitoring modules based on tunable diode laser absorption spectroscopy (TDLAS) over a mid-infrared waveband near 4.6 μm. However, in most cases, the mid-infrared TDLAS-based CO monitoring module tends to introduce severe interference fringe noise into the TDLAS spectral backgrounds which is difficult to filter out using traditional spectral filtering methods, reducing the detection performance of the module. In order to filter out the noise and improve the stability of the module in complex coal mine environments, this work proposed an algorithm based on support vector regression (SVR) to extract the TDLAS spectral backgrounds. Spectral analysis indicates that the TDLAS spectral background can be predicted over the entire scanning spectrum range by using this algorithm, and the noise in the spectral background can be effectively filtered out when calculating the absorbance spectrum based on the Lambert–Beer law. Compared to extracting spectral backgrounds using the traditional least square polynomial fit, the obtained correlation coefficients between regression models of spectral backgrounds and corresponding training point datasets were increased from below 0.998 to above 0.999. The peak-to-peak value of the obtained N2 absorbance spectrum was suppressed below 0.022 from nearly 0.045. The signal-to-noise ratio of the obtained 25 ppm CO absorbance spectrum was increased to 13.35 from 6.95. A CO monitoring module polluted by dust was used to conduct experiments to further test the SVR-based algorithm. The experiment results showed that after programming the SVR-based algorithm to the module, the estimated limit of detection of the module was reduced to 5.46 ppm from 29.08 ppm, and all the absolute measuring errors of the standard CO gases with different low concentrations were reduced to less than 4 ppm from a majority of the errors of more than 10 ppm, compared to least square polynomial fit. The CO monitoring module could still maintain the performance of high-precision quantitative detection when using the SVR-based algorithm even if it had been polluted severely. So, the CO monitoring module has good adaptability to harsh field environments, and its operation stability can be effectively improved by using the algorithm proposed in this work.

Denoising coherent Doppler lidar data based on a U-Net convolutional neural network.

The coherent Doppler wind lidar (CDWL) has long been thought to be the most suitable technique for wind remote sensing in the atmospheric boundary layer (ABL) due to its compact size, robust performance, and low-cost properties. However, as the coherent lidar exploits the Mie scattering from aerosol particles, the signal intensity received by the lidar is highly affected by the concentration of aerosols. Unlike air molecules, the concentration of aerosol varies greatly with time and weather, and decreases dramatically with altitude. As a result, the performance of the coherent lidar fluctuates greatly with time, and the detection range is mostly confined within the planetary boundary layer. The original data collected by the lidar are first transformed into a spectrogram and then processed into radial wind velocities utilizing algorithms such as a spectral centroid. When the signal-to-noise ratio (SNR) is low, these classic algorithms fail to retrieve the wind speed stably. In this work, a radial wind velocity retrieving algorithm based on a trained convolutional neural network (CNN) U-Net is proposed for denoising and an accurate estimate of the Doppler shift in a low-SNR regime. The advantage of the CNN is first discussed qualitatively and then proved by means of a numerical simulation. Simulated spectrum data are used for U-Net training and testing, which show that the U-Net is not only more accurate than the spectral centroid but also achieves a further detection range. Finally, joint observation data from the lidar and radiosonde show excellent agreement, demonstrating that the U-Net-based retrieving algorithm has superior performance over the traditional spectral centroid method both in accuracy and detection range.

Extracting Plastic Greenhouses from Remote Sensing Images with a Novel U-FDS Net

The fast and accurate extraction of plastic greenhouses over large areas is important for environmental and agricultural management. Traditional spectral index methods and object-based methods can suffer from poor transferability or high computational costs. Current deep learning-based algorithms are seldom specifically aimed at extracting plastic greenhouses at large scales. To extract plastic greenhouses at large scales with high accuracy, this study proposed a new deep learning-based network, U-FDS Net, specifically for plastic greenhouse extraction over large areas. U-FDS Net combines full-scale dense connections and adaptive deep supervision and has strong future fusion capabilities, allowing more accurate extraction results. To test the extraction accuracy, this study compiled new greenhouse datasets covering Beijing and Shandong with a total number of more than 12,000 image samples. The results showed that the proposed U-FDS net is particularly suitable for complex backgrounds and reducing false positive conditions for nongreenhouse ground objects, with the highest mIoU (mean intersection over union) an increase of ~2%. This study provides a high-performance method for plastic greenhouse extraction to enable environmental management, pollution control and agricultural plans.