Power spectral density analysis for nonlinear systems based on Volterra series

A consequence of nonlinearities is a multi-harmonic response via a monoharmonic excitation.A similar phenomenon also exists in random vibration.The power spectral density(PSD)analysis of random vibration for nonlinear systems is studied in this paper.The analytical formulation of output PSD subject to the zero-mean Gaussian random load is deduced by using the Volterra series expansion and the conception of generalized frequency response function(GFRF).For a class of nonlinear systems,the growing exponential method is used to determine the first 3 rd-order GFRFs.The proposed approach is used to achieve the nonlinear system’s output PSD under a narrow-band stationary random input.The relationship between the peak of PSD and the parameters of the nonlinear system is discussed.By using the proposed method,the nonlinear characteristics of multi-band output via single-band input can be well predicted.The results reveal that changing nonlinear system parameters gives a one-of-a-kind change of the system’s output PSD.This paper provides a method for the research of random vibration prediction and control in real-world nonlinear systems.

A robust power spectrum split cancellation-based spectrum sensing method for cognitive radio systems

Spectrum sensing is an essential component to realize the cognitive radio, and the requirement for real-time spectrum sensing in the case of lacking prior information, fading channel, and noise uncertainty, indeed poses a major challenge to the classical spectrum sensing algorithms. Based on the stochastic properties of scalar transformation of power spectral density（PSD）, a novel spectrum sensing algorithm, referred to as the power spectral density split cancellation method（PSC）, is proposed in this paper. The PSC makes use of a scalar value as a test statistic, which is the ratio of each subband power to the full band power. Besides, by exploiting the asymptotic normality and independence of Fourier transform,the distribution of the ratio and the mathematical expressions for the probabilities of false alarm and detection in different channel models are derived. Further, the exact closed-form expression of decision threshold is calculated in accordance with Neyman–Pearson criterion. Analytical and simulation results show that the PSC is invulnerable to noise uncertainty,and can achive excellent detection performance without prior knowledge in additive white Gaussian noise and flat slow fading channels. In addition, the PSC benefits from a low computational cost, which can be completed in microseconds.

Modeling of Noise Power Spectral Density Analysis for GaN/AlGaN HEMT

Nano Technology is the branch of technology that deals with dimensions and tolerances in terms of nanometers. In this paper, the electrical characteristics analysis is determined for the Nano-GaN HEMT and Micro-GaN HEMT and also power spectrum density is determined for GaN Nano-HEMT by reducing the gate length Lg in nm range. The GaN Nano HEMT is producing high current comparing to Micro GaN HEMT. Accuracy of the proposed analytical model results is verified with simulation results.

地震背景噪声功率谱密度及概率密度函数的计算及其Matlab实现

介绍了地震背景噪声功率谱密度及概率密度函数计算方法及涉及的一些概念,以台站实际数据为例,给出了应用Matlab计算噪声功率谱密度及其概率密度函数的程序算法,该方法直接输入文本格式数据,计算台基噪声功率谱概率密度函数;以洛阳地震台24小时的连续波形记录为例,详细叙述了原始数据去仪器响应、计算功率谱密度、倍频程计算和噪声功率谱密度的概率密度函数计算实现的全过程。该方法编程简单,适用于单台噪声水平评估,在野外台站的快速勘选中具有潜在应用价值。

乌鲁木齐及周边地区重力场及视密度变化特征

文中基于2019年4月—2022年4月乌鲁木齐及周边地区流动重力观测资料,采用绝对重力控制进行经典平差计算,获取研究区重力场时空演化特征图像。针对0.5a尺度和1a尺度重力场变化并结合构造地质部位分析重力剖面变化图像,分析了乌鲁木齐及周边地区的重力场变化特征。此外,文中采用小波多尺度分析方法,对乌鲁木齐及周边地区2019—2020年、2020—2021年和2021—2022年3a的重力场动态变化数据进行处理,分解不同场源异常,并对分离出的异常信息进行解释和分析,以此提升地震前兆重力异常的可信度。结果表明,研究区重力场具有明显的分区特征,整体以负值变化为主,正、负重力变化交替出现;小波重力细节反映异常区域与地质构造吻合,功率谱估算的近似场源深度与crust1.0模型相近;此外,基于流动重力观测资料反演得到研究区地壳内部等效视密度变化特征。文中的研究成果将为研判乌鲁木齐及周边地区未来的重力场变化趋势提供初步依据。

功率谱密度消频散变换被动估计脉冲声源距离

浅海中传播的低频声波具有多模态特征和频散效应。对接收声信号消频散变换(DDT)可以消除频散效应,实现被动估计声源距离。针对消频散变换存在的测距多值问题,该文提出一种利用功率谱密度消频散变换的被动测距方法(PSD-DDT)。首先使用声场模型KRAKEN计算模态的水平波数;其次在只知道波导不变量大概范围的情况下,估计两个模态之间的频散常数;然后对保留了模态间干涉项的功率谱密度进行消频散变换;最后获得目标距离的估计值为PSD-DDT极大值对应的自变量与频散常数的比值。另外,当海洋参数未知时,需要分别对待测声源和引导声源进行PSD-DDT,利用自变量的比值确定声源距离,这种方法不需要估计频散常数。通过仿真和海试验证了PSD-DDT方法被动测距的有效性,并分析了波导不变量、模态阶数、噪声等因素对距离估计结果的影响。基于黄海试验结果,与DDT方法相比,PSD-DDT的测距误差下降了约49.2%。在35 km范围内最优波导不变量对应的平均相对误差约2.55%,被动测距精度较高。

中低速磁浮轨道不平顺功率谱研究

轨道不平顺作为中低速磁浮列车主要的外部激励源,是造成磁浮列车-轨道耦合振动的重要原因。由于弦测值幅频特性存在畸变,通常不能作为实际轨道不平顺应用于工程实践中。基于实测长达4 km的长沙磁浮快线F轨高低和轨向10 m弦测数据,分析实测数据的传递特性,利用“以小推大”逆推算法扩大轨道不平顺波长的有效检测范围,并采用“逆滤波”算法对轨道不平顺进行复原,得到0.5~100 m波长的轨道不平顺。结果表明:实测F轨10 m弦测数据存在畸变,总体趋势与传递函数相符,不能对实际轨道几何状态正确表达;修正后的轨道不平顺功率谱具有很好的平顺性,无明显周期性成分;对轨道不平顺功率谱进行分段拟合,确定中低速磁浮轨道不平顺表达式的各项参数;将拟合的中低速磁浮轨道谱与国内外成熟铁路轨道谱进行对比,高低轨道不平顺与德国高干扰谱较为接近,在1.5~100 m波长范围内,处于德国高干扰谱与德国低干扰谱之间,在0.5~1 m波长范围内,处于美国五级谱与美国六级谱之间;轨向不平顺与高速铁路标准谱较为接近,在波长7~100 m波长范围内,高于高速铁路标准谱,在波长0.5~7 m波长范围内,低于高速铁路标准谱。

高速列车轴箱振动特性及功率谱密度归纳研究

针对我国动车组轴箱振动特性及实测加速度功率谱密(Power Spectral Density,PSD)不明确等问题,在我国多条线路上开展轴箱振动试验,获取各个线路轴箱振动加速度数据。通过滑窗计算并拟合峭度、偏斜度两个非高斯参数的分布形式。采用约翰逊拟合对非正态分布的PSD样本进行谱归纳,获得轴箱实测功率谱密度,与IEC 61373标准进行对比分析。结果表明:轴箱振动加速度信号有着明显的超高斯特性,其中峭度分布符合对数正态分布,且进行曲线平移后拟合效果较好;高斯混合模型对偏斜度分布有着较好的拟合。通过对5条线路实测功率谱密度的统计结果可知,标准值与实测功率谱密度差异较大,各线路在500~1000 Hz高频振动能量大于标准值;在5~300 Hz低频振动能量小于标准值。将统计结果作为轴箱附属部件的载荷输入,为轴箱附属部件进行考虑线路非高斯特性的疲劳可靠性设计和振动试验提供理论指导。

非道路特种车辆耐久性载荷谱的高置信度最少采集样本量

针对特种车辆的耐久性开发时服役载荷获取问题,提出服役载荷谱的特征参数服从威布尔分布的高置信度(90%以上)最少采集样本量模型。基于全面表征载荷谱能量分布和损伤分布的累积功率谱密度,开展该特征参数的威布尔分布及参数估计研究,并构建耐久性载荷谱高置信度最少采集里程模型。以非道路条件下特种车辆在两段路程下采集的轮端六分力信号为对象,基于所构建的载荷谱采集最小子样容量模型,同时指定采集载荷谱的样本与总体之间的精度指标和置信度要求,分别获取特种车辆在典型工况下载荷谱的最少采集里程,并相互验证。研究结果表明:提出的服役载荷谱特征参数服从威布尔分布的高置信度最少采集里程模型,能够有效地实现高置信度、高精度载荷谱采集的最少里程计算。

基于大涡模拟方法的可压缩空化流流场数值模拟分析

针对可压缩空化流流场细节特征,对空化的回射流机制与凝结激波机制下的空化云演化过程进行大涡模拟。通过对比文献实验数据验证了可压缩空化流数值模拟方法的可靠性,并分析了空化数σ、CN空化数、St数和压力损失系数K等无量纲参数,发现数值模拟对空化流压力-速度耦合计算的准确性方面还有待进一步提升。两种空化机制情况下,涡环生长是空化云脱落后耗散过程,涡环溃灭成游离涡是耗散结果;通过大涡模拟实现两种机制下的空化模拟,对比发现回射流机制的空化的无量纲参数偏差较少,凝结激波具有一定偏差;凝结激波的功率谱密度分析发现满足-7/3标度律,回射流满足-5/3标度律。

新疆达坂城风区顺风向脉动风功率谱

为研究新疆乌鲁木齐所处达坂城风区的复杂脉动风环境,基于实测风场风速数据分析并拟合了该风区的顺风向脉动风功率谱。结果表明:以反比例函数拟合山区峡谷地形平均风速与湍流强度的关系误差较小;山区峡谷地形湍流积分尺度分布较离散,但整体随平均风速的增大而增大;考虑地形系数的Kaimal修正谱在含能区和惯性子区间能较好地表征实测谱,在耗能区选用三参数拟合描述实测谱效果良好;选用过渡函数来描述惯性子区间与耗能区接触区域的功率谱,拟合效果较为理想。可见达坂城风区具有特殊顺风向脉动风特性,以修正谱和拟合谱分段构成的函数模型可用于表征该风区顺风向脉动风功率谱。

内蒙古基准站噪声特征与监测能力

选取2022年1月内蒙古预警区域内22个基准站的三分量连续波形数据,计算了波形数据PSD、PDF分布,统计了0.01~50Hz频率下的PSD分布,对RMS和异常台站进行分析,并对不同频率和区域下背景噪声的变化特征按照高频段(≤1s)、微震频段(1~20s)、长周期段(≥20s)予以研究,同时对测震台网监测能力进行分析。结果表明:地震预警台站的高频段背景噪声水平与人口、工业密度有一定关联;第二类地脉动噪声水平整体较为一致,第一类地脉动观测到的噪声能量较弱,地理空间分布的噪声水平差异小;在20s以上的长周期部分,背景噪声主要受到温度湿度等自然环境影响并且有一定的区域差异,将地震计安置在山洞和井下,可以有效地降低台站周围人类活动干扰源、温度和压强等对高频段和长周期观测的影响,使其在高频段和长周期观测的噪声水平低于地表安装方式;微震频段相比高频和长周期频段背景噪声分析可以更有效、更准确地对台站仪器如靠摆、参数错误等状态进行评估;故障台站修复后,内蒙古地震预警区域台站背景噪声均优于Ⅱ级,使预警区测震台网监测能力有了显著提升,对预警工程起到了良好的保障作用。

基于便携式三维激光扫描仪的路面平整度测评

针对当前公路路面测量评定方法结构复杂、成本高昂的问题,构建了基于便携式三维激光扫描仪的测量评定方法。采用三维激光扫描仪对沥青公路路面数据进行测量,获取路面三维点云数据,经分析处理得到路面的三维高程曲面,使用RegularizeData3D算法和经验模态分解等方法对数据进行预处理,重构区域路面不平度,获取路面相应等级的路面平整度数据序列,最后求解和分析试验路面功率谱密度,并根据统计结果对整个试验路面状况进行评价。结果表明:系统能较好地重建所测区域路面的特征信息,路面平整度大部分集中在A级和B级,整体路面平整度在B级以上。

基于响应谱传递比估计误差的结构模态参数识别精度分析

为了研究响应谱估计误差及其传递对振动响应功率谱密度传递比(Power Spectrum Density Transmissibility,PSDT)估计的影响,基于摄动理论和统计矩定义,推导了两个变量比例函数的均值和方差近似表达式;将响应谱估计统计矩代入,可以推导出由响应相干函数、谱估计中信号平均分段数,近似表征的PSDT估计幅值的均值和方差解析公式.基于此,揭示了共振频率处PSDT估计幅值误差规律,并实现了模态振型幅值的精度度量.研究发现,共振频率处PSDT幅值方差存在极小值,且变异系数小于相关响应谱.通过数值框架数据验证了文中误差公式的准确性.此外,还研究了参考响应的选择、响应时长、窗函数类型对PSDT和模态振型估计的影响.结果表明,以PSDT两组响应作为参考响应,能得到较好PSDT和模态分析结果;同时模态振型估计标准差随测试数据时长的增加,也随之降低至一定水平.

更快速度下周期性短波不平顺引起的轮轨高频振动特性及控制限值

随着列车运行速度的不断加快,轮轨高频振动引起的车辆、轨道部件伤损问题更加突出,尤以周期性的短波不平顺最为常见。为了掌握轮轨高频振动自下而上的传递衰减规律以及制定合理的钢轨打磨策略,有必要针对车辆系统在高频激励条件下的耦合振动特性开展深入的理论研究。本文通过对大量实测数据的拟合,得到了更宽频段范围内的轨道高低不平顺谱拟合公式,并通过反演得到了0.002~100 m波长范围内的高低不平顺样本;在此基础上建立了高速动车组-轨道刚柔耦合动力学模型,其中对轮对、钢轨均考虑了弹性体振动模态,仿真分析了周期性短波不平顺引起的轮轨高频振动特性。结果表明,车辆各部件的振动频率分布范围为30~1390 Hz,且自下至上呈逐层衰减趋势。通过提取周期性短波不平顺幅值变化对轮轨相互作用的影响规律,进一步提出了适应400 km/h高速铁路的典型波长周期性短波不平顺的量化控制限值要求。

不同场地下大跨斜拉桥多维多点随机地震响应分析

为了研究不同场地下大跨斜拉桥随机地震响应,该文采用场地传递函数评估不同场地条件对地震动传播的影响,综合考虑行波效应及相干效应,生成了不同场地条件的多点功率谱,运用绝对位移求解的虚拟激励法对斜拉桥在不同场地下的一致激励及多点多维的地震响应进行对比分析。选取一大跨斜拉桥作为工程实例,采用Ansys有限元软件进行随机地震响应分析;考虑场地条件对地震功率谱的影响,计算桥梁结构在不同激励方式下的随机响应,提取桥梁各单元响应的功率谱,并计算功率谱响应的均方根极值。研究结果表明:软土场地对桥梁随机响应的放大效应约为硬土场地的3倍;多点激励对桥梁随机响应的放大影响约为一致激励的1.5倍。因此,场地效应对大跨斜拉桥梁的随机地震响应影响极大,在抗震设计时不能忽略其影响。

小泉沟地震台台基背景噪声特征分析

运用Welch算法计算小泉沟地震台功率谱密度PSD,得到垂直向1/3倍频程带宽1—20 Hz各段的平均地动噪声RMS值为2.88×10^(-9)m/s,小于3.16×10^(-8)m/s,符合Ⅰ类台基标准。通过计算概率密度函数PDF,得到小泉沟地震台台背景噪声日变特征为,12—20时明显增大,夜间明显降低,背景噪声受人为活动影响较大;背景噪声年变特征受气温、气压影响较大,呈现夏低冬高的变化趋势。

Analysis of vibration and frequency transmission of high speed EMU with flexible model

When the operation speed of the high-speed train increases and the weight of the carbody becomes lighter,not only does the sensitivity of the wheel/rail contact get higher,but also the vibration frequency range of the vehicle system gets enlarged and more frequencies are transmitted from the wheelset to the carbody.It is important to investigate the vibration characteristics and the dynamic frequency transmission from the wheel/rail interface to the carbody of the high-speed electric multi-uint（EMU）.An elastic highspeed vehicle dynamics model is established in which the carbody,bogieframes,and wheelsets are all dealt with as flexible body.A rigid high-speed vehicle dynamics model is set up to compare with the simulation results of the elastic model.In the rigid vehicle model,the carbody,bogieframes and wheelsets are treated as rigid component while the suspension and structure parameters are the same as used in the elastic model.The dynamic characteristic of the elastic high speed vehicle is investigated in time and frequency domains and the di ff erence of the acceleration,frequency distribution and transmission of the two types of models are presented.The results show that the spectrum power density of the vehicle decreases from the wheelset to the carbody and the acceleration transmission ratio is approximately from 1%to 10%for each suspension system.The frequency of the wheelset rotation is evident in the vibration of the flexible model and is transmitted from the wheelset to the bogieframe and to thecarbody.The results of the flexible model are more reasonable than that of the rigid model.A field test data of the high speed train are presented to verify the simulation results.It shows that the simulation results are coincident with the field test data.

A new spatial coherence model and analytical coeffi cients for multi-support response spectrum combination

In this paper, a new spatial coherence model of seismic ground motions is proposed by a fitting procedure. The analytical expressions of modal combination （correlation） coefficients of structural response are developed for multi-support seismic excitations. The coefficients from both the numerical integration and analytical solutions are compared to verify the accuracy of the solutions. It is shown that the analytical expressions of numerical modal combination coefficients are of high accuracy. The results of random responses of an example bridge show that the analytical modal combination coefficients developed in this paper are accurate enough to meet the requirements needed in practice. In addition, the computational efficiency of the analytical solutions of the modal combination coefficients is demonstrated by the response computation of the example bridge. It is found that the time required for the structural response analysis by using the analytical modal combination coefficients is less than 1/20 of that using numerical integral methods.

Bispectrum Feature Extraction of Gearbox Faults Based on Nonnegative Tucker3 Decomposition with 3D Calculations

Nonnegative Tucker3 decomposition（NTD） has attracted lots of attentions for its good performance in 3D data array analysis. However, further research is still necessary to solve the problems of overfitting and slow convergence under the anharmonic vibration circumstance occurred in the field of mechanical fault diagnosis. To decompose a large-scale tensor and extract available bispectrum feature, a method of conjugating Choi-Williams kernel function with Gauss-Newton Cartesian product based on nonnegative Tucker3 decomposition（NTD_EDF） is investigated. The complexity of the proposed method is reduced from o（nNlgn） in 3D spaces to o（RiR2nlgn） in 1D vectors due to its low rank form of the Tucker-product convolution. Meanwhile, a simultaneously updating algorithm is given to overcome the overfitting, slow convergence and low efficiency existing in the conventional one-by-one updating algorithm. Furthermore, the technique of spectral phase analysis for quadratic coupling estimation is used to explain the feature spectrum extracted from the gearbox fault data by the proposed method in detail. The simulated and experimental results show that the sparser and more inerratic feature distribution of basis images can be obtained with core tensor by the NTD EDF method compared with the one by the other methods in bispectrum feature extraction, and a legible fault expression can also be performed by power spectral density（PSD） function. Besides, the deviations of successive relative error（DSRE） of NTD_EDF achieves 81.66 dB against 15.17 dB by beta-divergences based on NTD（NTD_Beta） and the time-cost of NTD EDF is only 129.3 s, which is far less than 1 747.9 s by hierarchical alternative least square based on NTD （NTD_HALS）. The NTD_EDF method proposed not only avoids the data overfitting and improves the computation efficiency but also can be used to extract more inerratic and sparser bispectrum features of the gearbox fault.