功率谱密度的数值计算方法

张蓉竹[1] 蔡邦维[1] 杨春林[1] 许乔[2] 顾元元[2]

采用功率谱密度PSD(Power Spectral Density)作为大尺寸光学元件表面质量的评价标准，对其定义及计算普适公式及方法进行了详细的分析推导，给出了被测样品的计算结果，并就在不同条件下计算平均PSD的方法和结果进行了分析比较和讨论。

数字超宽带信号的功率谱密度

Power Spectral Density of Digital Ultra Wide-band Signals

马晓慧 邹传云

该文根据各种超宽带（UWB）信号的调制特点,给出了统一的随机脉冲信号模型,并应用随机理论计算得出相应的功率谱密度（PSD）函数表达式,此PSD表达式应用范围广,适用于各种调制方式、多址方式、进制下的UWB信号.该文举例分析比较了几种典型调制下带有均匀分布的随机时间抖动（timing jitter）及理想情况下的信号PSD,结果表明,时抖动的存在平滑了信号功率谱,降低了对其他窄带通信系统的干扰.而且,文中给出的PSD函数表达式可以用来估计信号各参量的变化对PSD函数的影响,而不需要考虑脉冲序列的详细设计过程.[著者文摘]

In this paper, a unified model of the random impulse radio signals is presented based on the characters of a variety of UWB modulation signals. The Power Spectral Density（PSD）for the signals is carried out using stochastic theory. This PSD expression is used widely, such as for various modulation forms, various multi-access forms, either binary or M-ary systems. The PSD expressions for several typical modulation signals with or without the uniformly distributed timing jitter are taken for example and analyzed in details. The results show that the timing jitter smoothes the spectrum and alleviates the interferences on other narrowband communication systems. Furthermore, the results can be used to estimate the effect of changes in various parameters on PSD of transmitted signal, without going through the detailed design procedure.[著者文摘]

LabVIEW在货运车箱振动自功率谱密度函数分析中的应用

Application of LabVIEW in the PSD analysis of truck car compartment vibration

穆立茂 黄海英 张靖

在实验室内对车载物资和装备进行随机振动试验具有很大的经济意义，目前国际上普遍采用的一种试验方法是在频域内再现功率谱密度和随机波形，而功率谱密度通常是由实测振动数据经过自功率谱密度函数分析后得到。LabVIEW可以很好的完成自功率谱密度函数分析。首先介绍了LabVIEW中有关自功率谱密度函数的基本理论和算法，对待处理原始数据进行了简要介绍，然后详细叙述了自功率谱密度函数的计算步骤，最后开发出集数据输入、计算以及显示保存结果等功能于一体的虚拟仪器。经实践检验证明该虚拟仪器实用且效率高。[著者文摘]

Random vibration test of the commodity and the equipment in the laboratory have the very big economical significance. At present one testing method used on international is reappearing the power spectral density and the stochastic profile in the frequency range. But the power spectral density is usually obtained from the actual vibration data through the power spectral density function analysis. Lab VIEW may very good complete the power spectral density function analysis. It first introduces the basic knowledge and computing method about PSD in labVIEW. And simply introduces the original data waiting for processing. And then illustrates the steps of computing Power Spectral Density. In the end develops a VI integrating the functions such as data input, computing, show and storage of the result. The practice examination proves that this virtual instrument is practical and the efficiency is high.[著者文摘]

用功率谱密度坍陷评价光学元件波前中频误差特性

Evaluating intermediate frequency error property of wavefront of optical components with PSD collapse

程晓锋 郑万国 蒋晓东 任寰 钟伟 许华 景峰

扼要介绍了光学元件波前二维功率谱密度的计算方法，并引入功率谱密度坍陷的概念描述光学元件波前频谱特性。功率谱密度坍陷是对二维功率谱密度在不同角度上进行Radon变换得到的投影。它既利用了光学元件波前的所有有效数据，又沿袭了一维功率谱密度简明直观的特点。虽然功率谱密度坍陷在结果的表现形式和量纲方面与一维功率谱密度相同，但功率谱密度坍陷在评价光学元件波前频谱特性方面比用一维功率谱密度和二维功率谱密度更具优越性。[著者文摘]

Arithmetic of two-dimensional power spectral density （2-D PSD） of large optics wavefront was briefly described and PSD collapse was introduced to evaluate the intermediate frequency error property of wavefront. As the PSD collapse is radon transform projection of 2-D power spectral density at any angle, all valid data of wavefront of optics were used in calculation of the PSD collapse and the features of 1-D PSD were inherited in PSD collapse. Although the PSD collapse is the same as 1-D PSD in unit and behaving style, it is better in evaluating intermediate frequency error property of optics wavefront than 1-D PSD or 2-D PSD. As PSD collapse calculation uses all valid data of evaluated optics wavefront and can be directly perceived through its profile, the PSD collapse is possibly the standard evaluating method of PSD.[著者文摘]

波前功率谱密度函数评价方法探讨

任寰 卓志云 等

波前功率谱密度PSD（PowerSpectralDensity)能定量给出波前畸形的空间频率分布，限定波纹和粗糙度指标，全面反映ICF驱动器对高功率激光光学元件加工质量的特殊要求，给出了波功率谱密度PSD的定义及计算方法，并使用大口径相移干涉仪作为波前检测仪器，对光学磷酸盐钕玻璃透射波前进行了测试实验，获得波前一维PSD分布，证实功率谱密度为高功率激光光学元件波前参数的一种有效表征方式，同时，还对PSD与均方根RMS之间的关系进行了初步的讨论。

随机抖动电磁脉冲串的频域特性

Frequency-Domain Characterization for Electromagnetic Pulses with Random Timing Jitter

许建军[1,2] 廖成[1] 肖开奇[2]

针对工程实践中电磁脉冲发射机辐射的随机时间抖动周期性电磁脉冲信号，在分析随机时间抖动周期δ-函数功率谱密度的基础上，得出了随机时间抖动周期性电磁脉冲串的功率谱密度．结果表明，这类电磁脉冲串的功率谱密度由离散谱分量和连续谱分量组成，它们组成的总功率守恒．数值计算结果表明，随时间抖动范围增大和频率提高，离散功率谱分量所占比例下降。[著者文摘]

To study the periodical electromagnetic pulses with random timing jitter radiated by electromagnetic pulse transmitters, the PSD （power spectral density） of periodical electromagnetic pulses with random timing jitter was obtained based on the analysis of the δ-function of the PSD of timing jitter. The result shows that the PSD of the electromagnetic pulses consists of a continuous component and a discrete component, with the total power of the two parts being conservative. The numerical results demonstrate that the larger the zone of timing jitter and the higher the frequency, the less proportion the discrete PSD component is in the total PSD.[著者文摘]

噪声载荷作用下薄壁柱壳结构的随机振动响应的估算方法

曹茂国 李琳

给出了噪声载荷作用下薄壁柱壳结构随机振动加速度响应功率谱密度的计算公式和计算方法，并与实际测量获得的加速度响应功率谱密度进行了比较，计算的功率谱与实测的功率谱具有较好的一致性，说明这种估算噪声载荷作用下薄壁柱壳结构随机振动加速度响应功率谱密度的方法是合理可行的。用同样方法导出的Von Mises应力响应的功率谱密度及其均方值的计算公式，可直接用于疲劳强度分析。

路面功率谱密度识别的仿真

Simulation of Road Surface Power Spectrum Density Identification

张丽霞[1] 赵又群[1] 徐培民[2] 吴杰[1]

路面激励是汽车平顺性和操纵稳定性研究中的重要因素。提出了一种基于径向基函数（RBF）神经网络识别路面功率谱密度的仿真研究方法。建立了4自由度汽车振动模型，利用Matlab软件仿真得到汽车车身质心垂直加速度功率谱密度和俯仰角加速度功率谱密度。应用RBF神经网络建立了汽车车身质心垂直加速度功率谱密度、俯仰角加速度功率谱密度和路面功率谱密度之间的非线性映射模型。仿真结果表明：该方法思路明确，抗噪声能力比较强，识别的精确度高。[著者文摘]

Road surface excitation is an important factor in the research of vehicle riding and maneuver stability. Based on radial basis function （RBF） neural networks, a simulation research method of road surface power spectrum density （PSD） identification was put forward. A four-degree-of- freedom vehicle vibration model was set up and the PSDs for vertical acceleration and pitching angular acceleration of vehicle body centroid were got through Matlab simulation. The nonlinear mapping relation among the PSD of vehicle body centroid vertical acceleration, pitching angular acceleration and the road surface were found by RBF neural networks. The simulation results show that the proposed method has the feature of a good anti-noise performance and high identification accuracy.[著者文摘]

国际平整度指数与路面功率谱密度相关关系研究及验证

Study and validation of the relationship between international roughness index and power spectral density

周晓青[1] 颜利[2] 孙立军[3]

对国际平整度指数IRI与路面功率谱密度的相关关系进行研究。将路面不平整度假设为随机平稳变量而作为四分之一车模型的激励，并基于随机过程理论，通过频率响应函数求得簧上质量与簧下质量的竖向位移差的响应．由响应统计特性建立国际平整度指数IRI与簧上质量的功率谱密度均方值之间的线性相关关系。通过上海市典型路段与美国长期路面性能研究（LTPP）的纵断面实测高程数据，并利用MATLAB编程计算得到实测路段的IRI值与簧上质量谱密度的均方值，从数值上验证两者之间的线性相关关系。[著者文摘]

The relationship between International Roughness Index （IRI） and Power Spectral Density （PSD） is studied. Pavement roughness is assumed as random stationary variable and used as the exciting force of theoretical analyses of the quarter car model of IRI. From the frequency response function of the quarter car, the response function of the displacement difference between above-spring and beneath-spring mass is obtained by means of the random process theory. Then the relationship between IRI and mean square value of above-spring mass PSD is established from the statistical characteristics of the response function. Using the longitudinal road profiles of typical roads in Shanghai and the data from the Long-Term Pavement Performance （LTPP） in the US, the IRI and mean square value of above- spring mass PSD of these profiles are calculated by using MATLAB to validate the proposed model.[著者文摘]

与规范反应谱相对应的Clough—Penzien模型参数研究

Study on parameters of Clough-Penzien seismic random model corresponding to respome spectrum of GB50011 -2001

张猛[1,2] 张哲[1] 李天[1]

根据我国现行抗震规范（GB50011—2001）的反应谱曲线，对Clough—Penzien模型的参数取值进行了具体研究。采用时间包络函数考虑地震动的非平稳性，根据加速度峰值等效原则确定了谱强度因子S0的表达式，表明谱强因子不仅与地面加速度特性、场地类别有关，而且与结构的动力特性（阻尼比、自振周期）有关。最后对谱强度因子计算做了简化处理，为随机抗震计算分析提供了参考依据。[著者文摘]

A study on the parameters of Clough-Penzien seismic random model based on the response spectrum in the GB50011 -2001 is carried out. The non-stationary nature of the ground motion is considered by the envelope function. It is found that So can be determined by the equivalence principle of peak ground acceleration. The resuits show that Sois not only related to ground acceleration and site condition but also to structural dynamic property （damping ratio, natural vibration period）as well. Ultimately, a simplified method for calculating So is carried out. The parameters given in this study provide a theoretical fundamental for stochastic seismic response analysis of structures.[著者文摘]