Motor Fault Diagnosis Based on Short-time Fourier Transform and Convolutional Neural Network

With the rapid development of mechanical equipment, the mechanical health monitoring field has entered the era of big data. However, the method of manual feature extraction has the disadvantages of low efficiency and poor accuracy, when handling big data. In this study, the research object was the asynchronous motor in the drivetrain diagnostics simulator system. The vibration signals of different fault motors were collected. The raw signal was pretreated using short time Fourier transform （STFT） to obtain the corresponding time-frequency map. Then, the feature of the time-frequency map was adap- tively extracted by using a convolutional neural network （CNN）. The effects of the pretreatment method, and the hyper parameters of network diagnostic accuracy, were investigated experimentally. The experimental results showed that the influence of the preprocessing method is small, and that the batch-size is the main factor affecting accuracy and training efficiency. By investigating feature visualization, it was shown that, in the case of big data, the extracted CNN features can represent complex mapping relationships between signal and health status, and can also overcome the prior knowledge and engineering experience requirement for feature extraction, which is used by tra- ditional diagnosis methods. This paper proposes a new method, based on STFT and CNN, which can complete motor fault diagnosis tasks more intelligently and accurately.

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.

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.

考虑衬砌截面协调变形约束的既有隧道受盾构下穿施工影响的Fourier能量变分解

目前关于新建盾构开挖诱发既有地铁隧道变形的理论研究,大多将既有隧道简化为不含接头的Euler-Bernoulli梁,而忽视了衬砌截面的剪切变形与管片接头的局部刚度削弱。此外,既有地基模型理论较少考虑衬砌管片与接触土体的协调变形约束。首先,采用Loganathan-Polous公式计算盾构开挖诱发的土体自由位移场,并将既有隧道视为考虑剪切变形的Timoshenko梁,基于沿轴线变化的抗弯与剪切刚度函数来描述管片接头的局部削弱作用;然后,结合能量变分原理与连续弹性体Mindlin解,建立考虑衬砌截面协同变形约束的隧道位移控制方程,将盾构开挖诱发的附加荷载施加于既有隧道,并使用Fourier级数方法求解既有隧道纵向变形;最后,将Fourier能量变分解与3组工程实测数据进行对比验证,取得了较好的一致性。此外,考虑隧道抗弯刚度、剪切刚度、接头刚度削弱作用、土体参数与隧道空间位置等因素的共同影响,使用抗弯系数、剪切系数及接头系数进行敏感性分析。结果表明,考虑截面变形协调约束的理论解更为符合实际,不考虑变形协调约束所得隧道位移结果偏大;衬砌接头局部刚度的削弱作用将造成隧道弯矩沿轴线在接头处发生明显锯齿状突变;抗弯系数与剪切系数的增长均导致隧道结构所受弯矩降低;剪切系数由低到高的增长将导致隧道变形模式发生“弯曲控制-弯剪混合-剪切控制”三阶段变化;隧道变形模式进入“剪切控制”阶段的过程中,抗弯刚度的变化对隧道内力影响逐渐降低;接头系数的增长将造成隧道所受弯矩降低,但隧道抗弯刚度较大时其影响逐渐减弱。

Microstructural evolution in Al–Zn–Mg–Cu–Sc–Zr alloys during short-time homogenization

Abstract： Microstructural evolution in a new kind of aluminum （A1） alloy with the chemical composition of AI-8.82Zn-2.08Mg- 0.80Cu-3.31Sc-0.3Zr was investigated. It is found that the secondary phase MgZn2 is completely dissolved into the matrix during a short homogenization treatment （470℃, 1 h）, while the primary phase A13（Sc,Zr） remains stable. This is due to Sc and Zr additions into the A1 al- loy, high Zn/Mg mass ratio, and low Cu content. The experimental findings fit well with the results calculated by the homogenization diffusion kinetics equation. The alloy shows an excellent mechanical performance after the short homogenization process followed by hot-extrusion and T6 treatment. Consequently, a good combination of low energy consumotion and favorable mechanical properties is obtained.

Differentially Expressed Proteome of Microcystis under Short-time Ultrasonic Stress

This study was conducted to explore the regulation mechanism for key protein expression. The Microcystis treated by short-time ultrasonic wave was select-ed to analyze the total protein based on 2-DE. The results showed that there were 71 up-regulated protein spots, 56 down-regulated protein spots, 54 new protein spots and 21 protein spots disappeared under short-time ultrasonic stress. Eight dif-ferential proteins were chosen for further MALDI-TOFTOF/MS analysis, and the re-sults showed that 2 unknown proteins and 6 functional proteins were detected. These proteins were relevant to some physiological processes, such as antioxidation and anti-inflammatory process, phosphate synthesis and electron transfer, which is beneficial to the metabolic balance and self-protection under short-time ultrasonic stress.

An HHT-based method to eliminate short-time strong disturbance from measured signals of bridge

According to the characteristic that Hilbert-Huang transform （HHT） can detect abnormity in signals, an HHT-based method to eliminate short-time strong disturbance was proposed. The signal with short-time strong disturbance was decomposed into a series of intrinsic mode functions （IMFs） and a residue by the empirical mode decomposition （EMD）. The instantaneous amplitudes and frequencies of each IMF were calculated. And at abnormal section, instantaneous amplitudes and frequencies were fired according to the data at normal section, replacing the fitted data for the original ones. A new set of IMFs was reconstructed by using the processed instantaneous amplitudes and frequencies. For the residue, abnormal fluctuations could be directly eliminated. And a new signal with the short-time strong disturbance eliminated was reconstructed by superposing all the new IMFs and the residue, The numerical simulation shows that there is a good correlation between the reconstructed signal and the undisturbed signal, The correlation coefficient is equal to 0.999 1. The processing results of the measured strain signal of a bridge with short-time strong disturbance verify the practicability of the method.

Characteristics of Radar Echo Parameters and Microphysical Structure Simulation of a Short-Time Heavy Precipitation Supercell

By using the conventional observations, radar data, NCEP/NCAR FNL 1°×1° reanalysis data and numerical simulation data and with the construction and calculation of radar echo parameters, this paper presents the structural characteristics and physical processes of a short-time heavy precipitation supercell that occurred in the squall line process in Shanxi Province on 24 June 2020. The results show that this squall line event occurred in front of a surface cold front,combined with infiltration of low-level cold air and continuous increase of near-surface humidity in the afternoon. The surface mesoscale convergence line and mesoscale dew point front contributed to the development and systemization of the squall line by a large degree. The short-time extremely heavy precipitation in Pingshun County was caused by the development of a supercell from thunderstorm cells on the front side of the squall line. The characteristics of sharp increase in vertical integral liquid water content, persistent increase in reflectivity factor and continuous rise in the echo top height appeared about 23 min earlier than the severe precipitation, which has qualitative indicating significance for the nowcasting of short-time heavy precipitation. A quantitative analysis of the radar echo parameters suggests that the“sudden drop”of FV40was a precursor signal of cells’ coalescence and rapid development to the mature stage. The areal change of the echo core at the 6 km height was highly subject to the merging and developing of cells, the rapid change of hydrometeor particles in clouds and the precipitation intensity. Changes in the cross-sectional area of convective cells at different heights can indirectly reflect the changes of liquid particles and ice particles in clouds, which is indicatively meaningful for predicting the coalescing and developing-to-maturing of cells and heavy precipitation 30-45 min earlier.A comprehensive echo parameter prediction model constructed by the random forest principle can predict the magnitude of short-time heavy precipitation 40-50 min in advance. Numerical simulation reveals that large amounts of water vapor existed in the near-surface atmosphere, and that the cells rapidly obtained moisture from the ambient atmosphere and developed rapidly through maternal feeding. The cold cloud zone was narrow, upright and had a high stretch height. The upward motion in clouds was strong and deep, and very rich in liquid water content. The graupel particles had a large vertical distribution range, the coexistence area of graupel and snow was large, the height of raindrops was close to the surface with a wide horizontal scale, and the precipitation efficiency was high. These may be the important elements responsible for the occurrence of the short-time heavy precipitation that exceeded historical extreme values. On the basis of the above analyses, a comprehensive parameter(CP) prediction model is worked out, which can estimate the developing trend of supercells and the intensity of short-time heavy precipitation about 1 h in advance.

Characteristics Analysis on Short-Time Heavy Rainfall during the Flood Season in Shanxi Province, China

In order to provide a reference for the correct forecasting of short-term heavy rainfall and better disaster prevention and mitigation services in Shanxi Province, China, it is very important to carry out systematic research on short-term heavy precipitation events in Shanxi Province. Based on hourly precipitation data during the flood season (May to September) from 109 meteorological stations in Shanxi, China in 1980-2015, the temporal and spatial variation characteristics of short-time heavy rainfall during the flood season are analyzed by using wavelet analysis and Mann-Kendall test. The results show that the short-time heavy rainfall in the flood season in Shanxi Province is mainly at the grade of 20 - 30 mm/h, with an average of 97 stations having short-time heavy rainfall each year, accounting for 89% of the total stations. The short-time heavy rainfall mainly concentrated in July and August, and the maximal rain intensity in history appeared at 23 - 24 on June 17, 1991 in Yongji, Shanxi is 91.7 mm/h. During the flood season, the short-time heavy rainfalls always occur at 16 - 18 pm, and have slightly different concentrated time in different months. The main peaks of June, July and August are at 16, 17 and 18 respectively, postponed for one hour. Short-time heavy rainfall overall has the distribution that the south is more than the north and the east less than the west in Shanxi area. In the last 36 years, short-time heavy rainfall has a slight increasing trend in Shanxi, but not significant. There is a clear 4-year period of oscillation and inter-decadal variation. It has a good correlation between the total precipitation and times of short-time heavy rainfall during the flood season.

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.

Short-Time Decoherence of Solid-State Qubit at Optimal Operation Points

We investigate the short-time decoherence of a solid-state qubit under Ohmic noise at optimal operation points. The decoherence is analyzed by maximum norm of the deviation density operator. It is shown that at the temperature T = 3 mK, the loss of the fidelity due to decoherence is much smaller than the DiVincenzo low decoherence criterion, which means that the mode/may be an optimal candidate of qubit for quantum computation.

Short-Time Dynamics of the Random n-Vector Model

Short-time critical behavior of the random n-vector model is studied by the theoretic renormalization-group approach.Asymptotic scaling laws are studied in a frame of the expansion in e = 4 - d for n ≠ 1 and for n = 1respectively.In d ＜ 4,the initial slip exponents θ′ for the order parameter and θ for the response function are calculated up to the second order in e ＝ 4 - d for n ≠ 1 and for n ＝ 1 at the random fixed point respectively.Our results show that the random impurities exert a strong influence on the short-time dynamics for d ＜ 4 and n ＜ nc.

Spatial and Temporal Distribution of Different Grades of Short-time Precipitation in Xining City

Based on the hourly precipitation data from 4 observation stations of Xining City from June to September during 2005-2011,the temporal and spatial distribution characteristics of short-time precipitation were analyzed.The results show that the precipitation distribution in Xining region exhibited the less-more-less trend from southwest to northeast,while the torrential rain gradually increased from the northwest and southwest to the middle.The hourly general precipitation in Xining region had obviously seasonal characteristics,and its annual distribution showed wavy changes,but the annual variation of short-time heavy precipitation and rainstorm was very obvious.Furthermore,short-time heavy precipitation was concentrated from 18:00 to 24:00,followed by 03:00-07:00 on the following day.The occurrence time of short-time rainstorm accorded with short-time heavy precipitation.It offers a useful reference for the accurate and timely short-term forecast.

Comparative Analysis of Two Short-time Strong Precipitation Processes

By means of conceptual model prediction, two short-time strong precipitation processes in Xiamen on June 12th and 14th, 2008 were analyzed from the aspects of real precipitation, weather situation, physical parameter and radar echo. The results showed that two short-time strong precipitation processes had complete different weather backgrounds, so physical quantities which could reflect atmospheric thermal and dynamic characteristic were different, as well as the characteristic and evolution process of radar echo, and it revealed that two short-time strong precipitation processes in Xiamen had various formation mechanisms and evolution processes. Therefore, many data should be combined to grasp different vantage points in precipitation forecast.

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.

分数阶Fourier变换的测不准原理

该文参考Fourier变换的性质研究了离散分数阶Fourier变换的测不准原理以及连续分数阶Fourier变换在Lebesgue测度下的测不准原理,使得分数阶Fourier变换的测不准原理性质更一般化.

周期边界条件下四阶特征值问题的一种有效的Fourier谱逼近

文章提出了周期边界条件下四阶特征值问题的一种有效的Fourier谱逼近方法.首先,根据周期边界条件引入了适当的Sobolev空间和相应的逼近空间,建立了原问题的一种弱形式及其离散格式,并推导了等价的算子形式.其次,定义了正交投影算子,并证明了其逼近性质,结合紧算子的谱理论证明了逼近特征值的误差估计.另外,构造了逼近空间中的一组基函数,推导了离散格式基于张量积的矩阵形式.最后,文章给出了一些数值算例,数值结果表明其算法是有效的和谱精度的.

Fourier正则化同时反演热传导方程的初值和源项

研究边值问题中从已知的给定数据中同时识别初始条件和未知源的问题。用Fourier变换求出问题的精确解,发现该反问题是严重不适定的。为了解决所提出的问题,本文中用Fourier正则化方法构造出正则化解近似解,并在边界条件的假设下,得到先验参数选取下的精确解与其正则化近似解之间的对数型误差估计。

Sufficient variable selection of high dimensional nonparametric nonlinear systems based on Fourier spectrum of density-weighted derivative

The variable selection of high dimensional nonparametric nonlinear systems aims to select the contributing variables or to eliminate the redundant variables.For a high dimensional nonparametric nonlinear system,however,identifying whether a variable contributes or not is not easy.Therefore,based on the Fourier spectrum of densityweighted derivative,one novel variable selection approach is developed,which does not suffer from the dimensionality curse and improves the identification accuracy.Furthermore,a necessary and sufficient condition for testing a variable whether it contributes or not is provided.The proposed approach does not require strong assumptions on the distribution,such as elliptical distribution.The simulation study verifies the effectiveness of the novel variable selection algorithm.

Super-Fast Approximation Algorithms Using Classical Fourier Tools

In the author’s recent publications, a parametric system biorthogonal to the corresponding segment of the exponential Fourier system was unusually effective. On its basis, it was discovered that knowledge of a finite number of Fourier coefficients of function f from an infinite-dimensional set of elementary functions allows f to be accurately restored (the phenomenon of over-convergence). Below, parametric biorthogonal systems are constructed for classical trigonometric Fourier series, and the corresponding phenomena of over-convergence are discovered. The decisive role here was played by representing the space L2 as an orthogonal sum of two corresponding subspaces. As a result, fast parallel algorithms for reconstructing a function from its truncated trigonometric Fourier series are proposed. The presented numerical experiments confirm the high efficiency of these convergence accelerations for smooth functions. In conclusion, the main results of the work are summarized, and some prospects for the development and generalization of the proposed approaches are discussed.