Accuracy and robustness of four basic single degree of freedom methods for determining the modal parameters of non-lightly damped systems

An adequate measurement strategy (the combination of measurement method, response parameter, and where applicable, damping estimator) should be used for accurate determination of the natural frequency and damping of non-lightly damped single degree of freedom (SDOF) systems, otherwise, significant measurement bias errors can exist. The accuracy of four commonly used methods is studied and the measurement strategies that are exact are identified. This can depend on the damping mechanism, which if not known can be gleaned from patterns of bias errors between frequency estimations from different strategies. Since in practice a SDOF system rarely exists, or as SDOF techniques are knowingly applied to multiple degree of freedom (MDOF) systems, the robustness of the strategies in the presence of a secondary mode is studied, and the more robust (and therefore preferable) strategies are identified. The measurement method based on the real spectral part is advantageous as it evaluates the damping exactly and is independent of the damping mechanism, in addition the natural frequency obtained is independent of the response parameter. However, this method is not a relatively robust one, and is also sensitive to phase changes accrued during measurements.     

Practical improvements to real and imaginary spectral based modal parameter measurements of SDOF systems

For a single degree of freedom system, especially with non-light damping, the use of the real spectral part of either the displacement or velocity responses (or the transfer functions based on them) has the advantages of determining the natural frequency (f_n) directly, independent of the response parameter, and providing an accurate measurement for damping (ζ). However, this method is sensitive to spectral phase errors due to temporal misalignment of the signal or due to net inter-channel delay differences caused by signal filtering. Two techniques are presented to correct for these errors; one based on the correct temporal alignment of the impulsive part, and the other on the infimum of the imaginary spectral part. These are first demonstrated using a numerical model, and are shown to facilitate the correct measurement of f_n and bring ζ within the expected error limits due to quantisation. Secondly, they are applied to an experimental system and are seen to greatly improve the consistency between measurements using different methods.     

An efficient method for determining the effects of mass modifications in damped systems

An analytical procedure is presented for determining the effects of mass modifications in viscously damped vibratory systems. A very general but straightforward formulation is given which simplifies considerably for positive definite systems with distinct eigenvalues, the most common case. The procedure permits successive modifications, is reversible, provides accurate results, and significantly reduces computation time. The complete solution of the unmodified system is not a prerequisite for applying the method, although if it is available an exact solution for the modified system can be obtained. A stable numerical scheme for locating the complex roots of the characteristic equation is given, and numerical results are provided to demonstrate the theory.     

用曲线拟合方法测量空气阻尼常量

以物体在气垫导轨上做一维阻尼运动为例,用曲线拟合方法推导出空气的阻尼常量的计算公式,利用与计算机相连的数码照像机采集数据,画出拟合曲线,从而得出了空气的阻尼常量.     

颗粒离散元模拟中的阻尼系数标定

离散元模型中所采用的阻尼系数是不确定的,经常凭主观经验设定.为了使得物理模型与现实中的颗粒动力学属性符合更好,通过采用声频采样技术对物理模型中的阻尼系数进行标定,得出与实验符合的阻尼系数应为0.5左右.利用标定后的阻尼系数模拟了一元颗粒在圆柱形容器里的随机堆积过程,得到最终的堆积密度为0.625,与经典的实验结果一致.研究证明,在得到模型阻尼系数的同时,也确认了数值模型的正确性和用声频采样技术进行高精度碰撞时间检测的可行性. 关键词： 颗粒堆积 阻尼系数标定 声频采样 离散元法     

General method for determining the sensor readings of motion measurement systems by using skew-ray tracing method

High-accuracy laser-based optoelectronic motion- and position-measuring systems typically utilize light rays that travel from one optical boundary surface to another to perform motion and/or position measurements. It is not a simple task to accurately determine the equations of these sensor readings in terms of positional/angular motions. This problem is addressed in this paper by application of the analytic skew-ray tracing methodology as computed by the finite-difference methodology. An illustrative example of a motion-measurement system and comparison of the position-sensing detector (PSD) readings are given to validate the proposed methodology. It is shown that the proposed methodology can provide accurate expressions of PSD readings. It is also shown that the performance of a corner-cube retro-reflector is better than a cat's eye retro-reflector in positional/angular motion measurement systems.     

位阻效应对受阻酚杂化体系阻尼机理的影响

针对尚未解决的受阻酚结构变化与杂化体系阻尼机理间关系的问题,本文采用分子动力学模拟方法构建了三种受阻程度不同的受阻酚/聚合物杂化体系,从理论上探讨了位阻效应对阻尼机理的影响.对体系氢键相互作用、结合能、相对自由体积及扩散系数进行模拟分析表明,位阻效应对受阻酚分子内氢键相互作用有显著的弱化效果,可减少小分子团聚倾向,有利于小分子与聚合物分子间氢键相互作用的形成.但是,过高的位阻对小分子运动有阻碍作用,不利于小分子与聚合物形成强烈的氢键键合,也即不利于杂化体系阻尼性能的提高.因此,如何选择受阻程度适中的受阻酚是制备高阻尼杂化材料的一关键要素.     

一种工业CT测量精度评估方法

为了验证工业CT系统对检测件的测量精度,设计了一套评估方法,针对由国家X射线数字化成像仪器中心自主研发的9 MeV 高能工业CT系统和450 kV工业CT系统,设计制作了标准测量试块,以三坐标测量机为辅助测量手段,对CT图像的线性尺寸、球面尺寸、角度尺寸、孔径尺寸和定位尺寸等进行对比测量,得到不同尺寸类型的测量误差。在不考虑尺寸类型的影响下,分别对铝、不锈钢和尼龙三种材料做了CT测量误差对比,结果表明,对于这三种材料来说,材料密度越大测量精度越高。实验结果表明,可验证工业CT系统对不同类型尺寸测量的精度,工业CT系统可完成精度较高的尺寸测量工作,特别对复杂结构的内部尺寸测量有一定的优势。     

一种工业CT测量精度评估方法

为了验证工业CT系统对检测件的测量精度,设计了一套评估方法,针对由国家X射线数字化成像仪器中心自主研发的9 MeV 高能工业CT系统和450 kV工业CT系统,设计制作了标准测量试块,以三坐标测量机为辅助测量手段,对CT图像的线性尺寸、球面尺寸、角度尺寸、孔径尺寸和定位尺寸等进行对比测量,得到不同尺寸类型的测量误差。在不考虑尺寸类型的影响下,分别对铝、不锈钢和尼龙三种材料做了CT测量误差对比,结果表明,对于这三种材料来说,材料密度越大测量精度越高。实验结果表明,可验证工业CT系统对不同类型尺寸测量的精度,工业CT系统可完成精度较高的尺寸测量工作,特别对复杂结构的内部尺寸测量有一定的优势。     

A new method for determining excited states of quantum systems

Summary A new method for computing excited states of a given operatorH is here presented. Our procedure is of particular value when its representation requires an orthonormal basis set of large dimension. In order to obtain the excited state ofH nearest in energy to any chosen trial energyE _t, we consider the auxiliary operatorA=(H−E _t)². We show that a reasonable number of relaxations on appropriately generated low-order Krylov subspaces forA is sufficient to produce better and better approximations of its ground state; a high-accuracy final refinement of the ground state ofA is then possible through the standard Lanczos procedure. An important feature of our method is that storage memory limitations, encountered in the conventional determination of all eigenvalues of large systems, are here overcome. As an illustration of the method two significant examples are discussed. In honour of Prof. Fausto Fumi on the occasion of his retirement from teaching.     

Parameter accuracy analysis of weak-value amplification process in the presence of noise

We theoretically introduce the statistical uncertainty of photon number and phase error to discuss the precision of parameters to be measured based on weak measurements. When the photon counting scheme is used, we discuss the relative accuracy of the system in the presence of phase error by using the orthogonal and nonorthogonal pre-and postselected states, respectively. When using the measurement scheme of pointer shift, we discuss the measurement accuracy in the presence of phase error, pointer resolution, and statistical uncertainty. These results give a guide way to get the smallest relative precision and deepen our understanding about weak measurement.     

Novel method for high accuracy figure measurement of optical flat

Phase Measuring Deflectometry (PMD) is a non-contact, high dynamic-range and full-field metrology which becomes a serious competitor to interferometry. However, the accuracy of deflectometry metrology is strongly influenced by the level of the calibrations, including test geometry, imaging pin-hole camera and digital display. In this paper, we propose a novel method that can measure optical flat surface figure to a high accuracy. We first calibrate the camera using a checker pattern shown on a LCD display at six different orientations, and the last orientation is aligned at the same position as the test optical flat. By using this method, lens distortions and the mapping relationship between the CCD pixels and the subaperture coordinates on the test optical flat can be determined at the same time. To further reduce the influence of the calibration errors on measurements, a reference optical flat with a high quality surface is measured, and then the system errors in our PMD setup can be eliminated by subtracting the figure of the reference flat from the figure of the test flat. Although any expensive coordinates measuring machine, such as laser tracker and coordinates measuring machine are not applied in our measurement, our experimental results of optical flat figure from low to high order aberrations still show a good agreement with that from the Fizeau interferometer.     

利用光测影像测量飞行目标姿态方法的误差分析

针对一种利用光测图像获取飞行目标空中姿态的方法,建立数学模型,并基于该模型,深入研究了目标姿态角的测量误差问题.结论：像面直线的截距提取误差对交会结果影响很小,倾角提取误差影响较大;两交会平面之间夹角过小将大大降低交会结果的可靠程度,实际测量时必须保证交会角足够大.考虑了该方法使用中的一些细节,为该方法的具体实现提供了依据.     

声学立靶弹着点测试数学模型与误差分析

本文根据空气动力学理论和超音速弹丸的激波特性，建立了在使用L型立靶基础上正向射击和任意角度射击时的数学模型，并进行了误差分析，提出了减小误差的修正方法。     

Effect of viscous damping on power transmissibility for the vibration isolation of building services equipment

Vibration isolation plays an important role in both the vibration and noise control of building services equipment. To evaluate vibration isolation performance, the force transmissibility method is commonly adopted. However, increasing the damping effect in the force transmissibility method reduces both the resonance peak value and the isolation performance in the “isolation region”. The limitation of the method is that the transmitted displacement of a floor structure and the interaction of mounting points are neglected. To include the floor displacement and the interaction of mounting points, Mak and Su recently proposed the power transmissibility method to assess the performance of vibration isolation. In this paper, the effect of viscous damping on power transmissibility is investigated. A practical procedure for experimentally determining the damping ratio is also given.     

基于FICP算法提高对低频噪声时延的估计精度

针对非平稳随机噪声（直升机飞行声音，导弹喷流噪声）信号，研究了提高时延估计计算精度的方法，通过计算信号的细化频谱，并避免了标准FFT计算带来的栅栏效应，从而使得对于超短取样信号的频谱计算精度与信号长度无关，采用快速计算方法FICP由N点互谱计算2N点相关波形，提高了相关波形的分辨率，使得时延估计精度得以提高。对实测直升机飞行噪声和导弹噪声计算了不同取样长度和不同采样率下的时延估计，得出了谱分辨率越高，时延估计精度越高的结论。     

X-ray fluorescence method for determining the mass absorption coefficient in two-layer thin-film Ti/Ge and Ni/Ge systems

We propose a new method for determining the mass absorption coefficient in x-ray fluorescence analysis of two-layer thin-film Ti/Ge and Ni/Ge systems using easily made standardized film layers obtained by deposition of titanium or nickel on a polymer film substrate. We calculate correction factors taking into account absorption of primary emission from the x-ray tube and absorption of the analytical line for an element of the bottom layer in the top layer.     

光电经纬仪动态测角精度随机误差检测方法研究

为了实现光电经纬仪动态测角精度随机误差的检测,进一步提高光电经纬仪的检测能力,进行了光电经纬仪动态测角精度随机误差的研究。基于布尔萨坐标转换原理,通过严格理论推导,得到动靶标方位值和俯仰值的理论公式。以光电经纬仪的方位角A、俯仰角E以及采样时间t等基本参数为基础,结合动靶标方位值和俯仰值的理论公式,得到A和E的理论真值,再与光电经纬仪测得值A和E进行比较,得到光电经纬仪动态测角精度随机误差。提出一种检测光电经纬仪的动态测角精度随机误差的新方法,为光电经纬仪动态测角精度随机误差的测量提供了新的思路。     

光学系统受迫振动的激光测量方法

将激光信号与高帧频CCD结合,解决了光学系统中振动信号和激光信号之间的转换问题,不仅能够测量振动对系统光束指向稳定性的影响,而且能够得到振动信号本身的频率特性。利用该方法对振源为150 Hz和200 Hz两种条件下的光学系统受迫振动进行测量,得到了与输入信号相吻合的振动信号属性。通过实验与分析得知:时域振幅测量精度为6.25 m,频域分辨力为2 Hz,方法简便高效,测量结果准确,已应用于角多路准分子激光主振荡功率放大器系统打靶试验平台光束指向稳定性的研究中。