Superconvergence of Direct Discontinuous Galerkin Methods:Eigen-structure Analysis Based on Fourier Approach

This paper investigates superconvergence properties of the direct discontinuous Galerkin(DDG)method with interface corrections and the symmetric DDG method for diffusion equations.We apply the Fourier analysis technique to symbolically compute eigenvalues and eigenvectors of the amplification matrices for both DDG methods with different coefficient settings in the numerical fluxes.Based on the eigen-structure analysis,we carry out error estimates of the DDG solutions,which can be decomposed into three parts:(i)dissipation errors of the physically relevant eigenvalue,which grow linearly with the time and are of order 2k for P^(k)(k=2,3)approximations;(ii)projection error from a special projection of the exact solution,which is decreasing over the time and is related to the eigenvector corresponding to the physically relevant eigenvalue;(iii)dissipative errors of non-physically relevant eigenvalues,which decay exponentially with respect to the spatial mesh sizeΔx.We observe that the errors are sensitive to the choice of the numerical flux coefficient for even degree P^(2)approximations,but are not for odd degree P^(3)approximations.Numerical experiments are provided to verify the theoretical results.

Improved Responses with Multitaper Spectral Analysis for Magnetotelluric Time Series Data Processing:Examples from Field Data

In order to attain good quality transfer function estimates from magnetotelluric field data(i.e.,smooth behavior and small uncertainties across all frequencies),we compare time series data processing with and without a multitaper approach for spectral estimation.There are several common ways to increase the reliability of the Fourier spectral estimation from experimental(noisy)data;for example to subdivide the experimental time series into segments,taper these segments(using single taper),perform the Fourier transform of the individual segments,and average the resulting spectra.

Stability Analysis of Inverse Lax-Wendroff Procedure for a High order Compact Finite Difference Schemes

This paper considers the finite difference(FD)approximations of diffusion operators and the boundary treatments for different boundary conditions.The proposed schemes have the compact form and could achieve arbitrary even order of accuracy.The main idea is to make use of the lower order compact schemes recursively,so as to obtain the high order compact schemes formally.Moreover,the schemes can be implemented efficiently by solving a series of tridiagonal systems recursively or the fast Fourier transform(FFT).With mathematical induction,the eigenvalues of the proposed differencing operators are shown to be bounded away from zero,which indicates the positive definiteness of the operators.To obtain numerical boundary conditions for the high order schemes,the simplified inverse Lax-Wendroff(SILW)procedure is adopted and the stability analysis is performed by the Godunov-Ryabenkii method and the eigenvalue spectrum visualization method.Various numerical experiments are provided to demonstrate the effectiveness and robustness of our algorithms.

Comparative Analysis of Climate Characteristics of Extremely Short-Time Severe Precipitation in Guizhou Based on Two Types of Rainfall Data

In order to fill the gaps of the research on the data of automatic weather stations(referred to as automatic stations)not used for the climate characteristics of extremely short-time severe precipitation in Guizhou Province,the climate characteristics of extremely short-time severe precipitation in Guizhou Province were compared and analyzed based on the hourly precipitation data of the automatic stations and the national weather stations(referred to as the national stations)from April to September during 2010-2019.The results show that the average state of maximum hourly precipitation of all stations(the automatic stations and the national stations)and national stations both are representative,but the data of all stations are more representative when the maximum hourly precipitation is extreme.The 99.5 th quantile is the most reasonable threshold of extremely short-time severe precipitation in each station.The spatial distribution of extremely short-time severe precipitation intensity in all stations and national stations is generally that the southern region is stronger than the northern region,and the intensity values are concentrated in the range of 40-50 mm/h.All stations data can better reflect the distribution characteristics of<40 and≥50 mm/h.The national stations data underestimates the precipitation intensity in the southern and northeastern marginal areas of Guizhou,and slightly exaggerates the precipitation intensity in the northern part of Guizhou.The monthly and diurnal variations of the frequency of extremely short-time severe precipitation in all stations and national stations are very obvious and the variation trend is the same,but the intensity of extremely short-time severe precipitation has no obvious monthly variation characteristics.There is no significant diurnal variation in the intensity of extremely short-time severe precipitation in all stations,but the diurnal variation in the data of national stations is significant.Since the frequency of extremely short-time severe precipitation in national stations is less,the diurnal variation in the intensity of extremely short-time severe precipitation in all stations is more statistically significant.

Carbonization mechanism of bamboo (phyllostachys) by means of Fourier Transform Infrared and elemental analysis

通过测定在200-600℃炭化竹材得到的固体产物的碳、氢、氧元素的含量及它们的红外光谱,研究了在炭化过程中竹材中半纤维素、纤维素及木素的变化规律。结果表明,结合元素分析,红外光谱分析方法是研究竹材炭化机理的有效手段。在200℃以前,竹材中的半纤维素和纤维素的大量羟基断裂,并结合成水而失去。在200-250℃之间,竹材中的纤维素被降解,其中的吡喃型环也遭到破坏。并且木素中的甲氧基也被脱去。竹材中的木素网状结构在250-400℃之间遭到完全的破坏。竹炭中的碳原子在600℃已基本上完成了芳环化。图3表2参15。

基于Fourier Analysis对造球机开式齿轮异常情况的诊断

利用Fourier Analysis对造球机开式齿轮异常情况进行了诊断,诊断结果表明,Fourier Analysis结果与开式齿轮实际运行状况相吻合。通过Fourier频域分析解释了齿轮啮合频率及边频对造球机振动的影响,得出了开式齿轮的异常情况是由于齿轮磨损造成齿形误差的结论。这对造球机开式齿轮的修复或更换提供了科学的依据。

NYFR output pulse radar signal TOA analysis using extended Fourier transform and its TOA estimation

Nyquist folding receiver (NYFR) is a typical wideband analog-to-information architecture. Focusing on the non-cooperative receiving, the pulse radar signal intercepted by the NYFR in time domain is analyzed. The NYFR outputs under different input conditions are investigated based on the extended Fourier transform (EFT) and the sampling theorem. Combining with the characteristic of the NYFR output in time domain, a new time of arrival (TOA) estimation method based on the energy envelope and the wavelet transform is proposed. The proposed estimation method can be adapted for the non-cooperative situation. It has no requirement for prior information to determine the threshold and is not necessary to transform the signal into baseband. Simulation results prove the correctness of the NYFR output expressions and show the efficacy of the proposed estimation method. © 2017 Beijing Institute of Aerospace Information.

Mathematic Models for Analysis of Quality Components in Sugarcane Juice with Fourier Transform Near Infrared Spectroscopy

With the technique of Fourier transform near infrared (FT-NIR) spectroscopy, the calibration models for quantitative analysis of sucrose and polarization in sugarcane juice were developed by using transmission mode and calibrating with partial least square (PLS) algorithm. The determination coefficients (R2) of the predicted models for sucrose and polarization in juice were 0. 9980 and 0. 9979 respectively; the root mean square errors of cross validation (RMSECV) were 0. 143 and 0. 155% for sucrose and polarization in juice respectively. The predictive errors measured by FT-NIR were close to those by routine laboratory methods. The results demonstrated that the FT-NIR methods had high accuracy and they were able to replace the routine laboratory analysis. It was also demonstrated that as a rapid and accurate measurement, the FT-NIR technique had potential applications in quality control of mill sugarcane, establishment of payment system based on sugarcane quality, and selection of clones in sugarcane breeding.

Wind turbine clutter mitigation using morphological component analysis with group sparsity

To address the problem that dynamic wind turbine clutter(WTC)significantly degrades the performance of weather radar,a WTC mitigation algorithm using morphological component analysis(MCA)with group sparsity is studied in this paper.The ground clutter is suppressed firstly to reduce the morphological compositions of radar echo.After that,the MCA algorithm is applied and the window used in the short-time Fourier transform(STFT)is optimized to lessen the spectrum leakage of WTC.Finally,the group sparsity structure of WTC in the STFT domain can be utilized to decrease the degrees of freedom in the solution,thus contributing to better estimation performance of weather signals.The effectiveness and feasibility of the proposed method are demonstrated by numerical simulations.

A New'Condition and Applications in Fourier Analysis(Ⅱ)

As we already mentioned in [6], in Fourier analysis, since Fourier coefficients are computable and applicable, people have established many nice results by assuming monotonicty of the coefficients. Generally speaking, it became an important topic how to generalize monotonicity. In many studies the generalization follows by this way:

Adaptive Fourier Decomposition Based Time-Frequency Analysis

The attempt to represent a signal simultaneously in time and frequency domains is full of challenges. The recently proposed adaptive Fourier decomposition （AFD） offers a practical approach to solve this problem. This paper presents the principles of the AFD based time-frequency analysis in three aspects： instantaneous frequency analysis, frequency spectrum analysis, and the spectrogram analysis. An experiment is conducted and compared with the Fourier transform in convergence rate and short-time Fourier transform in time-frequency distribution. The proposed approach performs better than both the Fourier transform and short-time Fourier transform.

Imaging Analysis by Means of Fractional Fourier Transform

Starting from the diffraction imaging process,we have discussed the relationship between optical imaging system and fractional Fourier transform, and proposed a specific system which can form an inverse amplified image of input function.

Adaptive Short-Time Fractional Fourier Transform Based on Minimum Information Entropy

Traditional short-time fractional Fourier transform(STFrFT)has a single and fixed window function,which can not be adjusted adaptively according to the characteristics of fre-quency and frequency change rate.In order to overcome the shortcomings,the STFrFT method with adaptive window function is proposed.In this method,the window function of STFrFT is ad-aptively adjusted by establishing a library containing multiple window functions and taking the minimum information entropy as the criterion,so as to obtain a time-frequency distribution that better matches the desired signal.This method takes into account the time-frequency resolution characteristics of STFrFT and the excellent characteristics of adaptive adjustment to window func-tion,improves the time-frequency aggregation on the basis of eliminating cross term interference,and provides a new tool for improving the time-frequency analysis ability of complex modulated sig-nals.

Mode analysis of structures using the Fourier p-element method

The Fourier p-element method is an improvement to the finite element method,and is particularly suitable for vibration analysis due to the well-behaved Fourier series.In this paper,an iteration procedure is presented for solving the resulting nonlinear eigenvalue problem.Three types of Fourier version shape functions are constructed for analyzing the circular shaft torsional vibration,the plate in-plane vibration and annular plate flexural vibration modes,respectively. The numerical results show that this method can achieve higher accuracy and converge much faster than the FEM based on polynomial interpolation,especially for higher mode analysis.

A novel stochastic modeling framework for coal production and logistics through options pricing analysis

We propose a novel stochastic modeling framework for coal production and logistics using option pricing theory.The problem of valuing the inherent real optionality a coal producer has when mining and processing thermal coal is modelled as pricing spread options of three assets under the stochastic volatility model.We derive a three-dimensional Fast Fourier Transform(“FFT”)lower bound approximation to value the inherent real optionality and for robustness check,we compare the semi-analytical pricing accuracy with the Monte Carlo simulation.Model parameters are estimated from the historical monthly data,and stochastic volatility parameters are obtained by matching the Kurtosis of the low-ash diff data to the Kurtosis of the stochastic volatility process which is assumed to follow Cox–Ingersoll–Ross(“CIR”)model.

Spectral Analysis and Validation of Parietal Signals for Different Arm Movements

Brain signal analysis plays a significant role in attaining data related to motor activities.The parietal region of the brain plays a vital role in muscular movements.This approach aims to demonstrate a unique technique to identify an ideal region of the human brain that generates signals responsible for muscular movements;perform statistical analysis to provide an absolute characterization of the signal and validate the obtained results using a prototype arm.This can enhance the practical implementation of these frequency extractions for future neuro-prosthetic applications and the characterization of neurological diseases like Parkinson’s disease(PD).To play out this handling method,electroencepha-logram(EEG)signals are gained while the subject is performing different wrist and elbow movements.Then,the frontal brain signals and just the parietal signals are separated from the obtained EEG signal by utilizing a band pass filter.Then,feature extraction is carried out using Fast Fourier Transform(FFT).Subse-quently,the extraction process is done by Daubechies(db4)and Haar wavelet(db1)in MATLAB and classified using the Levenberg-Marquardt Algorithm.The results of the frequency changes that occurred during various wrist move-ments in the parietal region are compared with the frequency changes that occurred in frontal EEG signals.This proposed algorithm also uses the deep learn-ing pattern analysis network to evaluate the matching sequence for each action that takes place.Maximum accuracy of 97.2%and maximum error range of 0.6684%are achieved during the analysis.Results of this research confirm that the Levenberg-Marquardt algorithm,along with the newly developed deep learn-ing hybrid PatternNet,provides a more accurate range of frequency changes than any other classifier used in previous works of literature.Based on the analysis,the peak-to-peak value is used to define the threshold for the prototype arm,which performs all the intended degrees of freedom(DOF),verifying the results.These results would aid the specialists in their decision-making by facilitating the ana-lysis and interpretation of brain signals in the field of neuroscience,specifically in tremor analysis in PD.

Determination of creatinine level in patient blood samples by Fourier NIR spectroscopy and multivariate analysis in comparison with biochemical assay

In this paper,in vivo spectra from 23 patients'blood samples with various Creatinine(Cr)concentration levels ranging from 0.96 to 12.5 mg/dL were measured using Fourier transform near-infrared spectrometer(FT-NIRS)and spectrum quantitative analysis method.Since Cr undergoes passive filtration,it serves as a key biomarker of kidneys function via the estimation of glomerular filtration rate.Thus,increased blood Cr concentration reflects impaired renal func-tion.After spectra pre processing and outlier exclusion,a spectral model was developed based on partial least squares regression(PLSR)method,wherein Cr concentrations correlated with filtered NIR spectra across several peaks,where Cr is know n to absorb NIR light.Several statistical metrics were applied to estimate the model efficiency during data analysis.Comparison of spectra-derived concentrations to reference Cr measurements by the current gold-standard Jaffe's method held in hospital lab revealed a Cr prediction accuracy of 1.64 mg/dL with good corre-lation of R=0.9.Bland-Altman plots were used to compare between our calculations and ref-erence lab values and reveal minimal bias between the two.The finding presented the potential of FT-NIRS coupled with PLSR technique for Cr determination.

基于Fourier变换红外光谱分析咖啡豆成分

采用Fourier变换红外光谱对不同产区、不同海拔的5组浅中烘焙的咖啡豆样品进行分析,根据官能团的红外光谱特征峰分析样品主要成分;为进一步分析5组样品的成分差异,对原始光谱进行二阶导数处理,结合聚类分析理论建立平均偏离分析方法,计算出5组样品间的平均偏离大小并进行分析.结果表明:5组样品的红外光谱特征峰峰形相似,即主要成分相同;根据红外光谱得到平均偏离大小与产区海拔差值呈正相关.研究结果为分析咖啡豆产区和海拔提供鉴别依据,并对红外光谱研究提供一定参考.

Application of short-time Fourier transform to high-rise frame structural-health monitoring based on change of inherent frequency over time

The high-rise frame structure has become more and more widespread, like its damage from the complication of the environment. The traditional method of damage detection, which is only suitable for the stationary signal, does not apply to a high-rise frame structure because its damage signal is non-stationary. Thus, this paper presents an application of the short-time Fourier transform(STFT) to damage detection of high-rise frame structures. Compared with the fast Fourier transform, STFT is found to be able to express the frequency spectrum property of the time interval using the signal within this interval. Application of STFT to analyzing a Matlab model and the shaking table test with a twelve-story frame-structure model reveals that there is a positive correlation between the slope of the frequency versus time and the damage level. If the slope is equal to or greater than zero, the structure is not damaged. If the slope is smaller than zero, the structure is damaged, and the less the slope is, the more serious the damage is. The damage results from calculation based on the Matlab model are consistent with those from the shaking table test, demonstrating that STFT can be a reliable tool for the damage detection of high-rise frame structures.

Quantum-Classical Algorithm for an Instantaneous Spectral Analysis of Signals:A Complement to Fourier Theory

A quantum time-dependent spectrum analysis, or simply, quantum spectral analysis (QSA) is presented in this work, and it’s based on Schr&#246;dinger’s equation. In the classical world, it is named frequency in time (FIT), which is used here as a complement of the traditional frequency-dependent spectral analysis based on Fourier theory. Besides, FIT is a metric which assesses the impact of the flanks of a signal on its frequency spectrum, not taken into account by Fourier theory and lets alone in real time. Even more, and unlike all derived tools from Fourier Theory (i.e., continuous, discrete, fast, short-time, fractional and quantum Fourier Transform, as well as, Gabor) FIT has the following advantages, among others: 1) compact support with excellent energy output treatment, 2) low computational cost, O(N) for signals and O(N2) for images, 3) it does not have phase uncertainties (i.e., indeterminate phase for a magnitude = 0) as in the case of Discrete and Fast Fourier Transform (DFT, FFT, respectively). Finally, we can apply QSA to a quantum signal, that is, to a qubit stream in order to analyze it spectrally.