多元线性过程回归分析

提出多元线性过程的定义及其回归模型,建立多元线性过程回归分析方法,给出其回归方程和高置信水平、高可靠度的置信上、下限曲线.多元线性过程是具有线性函数均值和二次函数方差的独立增量随机过程,也是性能曲线测试和可靠性评估中常见的一类随机过程.传统方法在测定不同条件下产品的性能曲线时,要求在每一种条件下都测得一组样本函数,并对...     

相关系数平稳过程方法

工程实际中遇到的随机过程,其均值和方差多数都随时间而变化,因此,无法用传统的平稳随机过程理论描述。文中通过对大量随机过程实测数据的分析研究,发现它们的相关系数函数基本上不随时间平移而改变,即相关系数函数是平稳的。在此基础上建立一种新的相关系数平稳随机过程理论和方法,并给出相关系数平稳正态过程的极大似然估计。从而在性能测试中,采用本文方法只要测定一个样本函数就能够对产品性能的均值和方差进行估计,与传统的需要测定一组样本函数的成组试验法相比,可以节省大量试验。     

基于函数型数据分析的半导体生产过程监控

提出一种基于函数型数据分析的非平稳生产状态下的多批次生产过程监控方法。引入函数型数据分析方法将三维数据中的每个变量沿时间方向进行函数拟合,从而将三维离散数据矩阵转化为二维函数矩阵。对各个变量曲线求取二阶导数,消除非平稳生产状态所导致的均值波动现象,增加建模的准确性。在此基础上,利用函数型主成分分析方法对各个变量的导数曲线进行特征提取,并使用基于权重的主成分融合方法,获得函数型主成分矩阵。利用支持向量数据描述方法对函数型主成分矩阵进行监控,并将其应用于工业半导体生产过程的监控中。结果表明,基于函数型数据分析的监控方法与传统方法相比,具有更低的漏检率,验证了新方法的有效性。     

非线性结构平稳随机过程数值仿真分析

平稳随机过程数值仿真分析因结构高度非线性因素而成为平稳随机振动分析中的难点,通常采用振型叠加法,将非线性结构简化为线性结构进行平稳随机过程数值仿真分析.为克服这一难点,文中以某一非线性预应力结构为例,首先采用谐波叠加法,将已知的频域内功率谱密度曲线转化为时域内的加速度曲线,然后通过中心差分法,对非线性结构进行平稳随机过程数值仿真分析,并对数值仿真分析中存在的关键性技术进行探讨.结果表明,对具有预应力的非线性结构,振型叠加法在一定程度上能够反映结构的动力学特性,但不能反映结构的非线性特性,而中心差分法能更精确地反映非线性结构在随机激励下的动力学特性.通过分析,文中针对非线性结构平稳随机过程数值仿真分析,提出一种综合振型叠加法和中心差分法的有限元分析方法,目的在于解决平稳随机过程数值仿真分析中结构的高度非线性因素,为高度非线性预应力结构的平稳随机过程数值仿真分析提供一种新思路.     

固支矩形薄板通入非平稳随机电流的磁弹性随机振动

针对四边固支矩形薄板,以连续体的随机振动理论及板壳磁弹性基本理论为基础,导出了在外加磁场中通入非平稳随机电流情形下矩形薄板的磁弹性随机振动方程。将洛伦兹力耦合项中的一部份假设为薄板的一种阻尼,另一部分假设为非平稳随机均匀分布载荷,分别得到了外加磁场中通入非平稳随机电流时板的随机位移响应的均值、功率谱密度函数等数字特征。针对具体算例,在通以非平稳随机电流的情形下,计算了其位移响应的功率谱密度函数和均方值函数,并绘出了板中心点的位移响应功率谱密度图、速度功率谱密度图及加速度功率谱密度图,并讨论了磁场强度及洛伦兹力耦合项对在非平稳随机电流下的随机位移响应的影响。     

最佳无偏整体估计方法

提出一种最佳无偏整体估计方法,给出整体参数的估计量及其协方差公式,建立正态分布、Weibull分布和极值分布等位置-尺度分布族的点估计与区间估计。传统的回归分析只适用于正态分布和完全数据,最佳无偏整体估计方法则将回归分析推广到工程中常见的位置-尺度分布族和截尾数据的情况。该方法可以将不同条件(状态)下的试验数据作为一个整体进行统计推断,能够全面开发利用不同条件下试验数据之间的横向信息,使其可利用的信息量远远大于只能分别在各自条件下对试验数据进行处理的传统最佳线性无偏估计方法。最佳无偏整体估计方法对一种条件下只有一个失效数据的情况也能进行分析,传统最佳线性无偏估计方法则要求在一种条件下有较多的失效数据,因此前者具有小样本性质;并且前者的参数估计量是所有条件下顺序统计量的线性函数,后者的参数估计量只是一种条件下顺序统计量的线性函数,所以前者的参数估计量具有更好的正态分布特性。大量Monte Carlo模拟和工程应用表明,在试样数相同的情况下,文中方法比传统方法具有更高的精度,而在精度相同的情况下,则可节省大量试样。     

线性过程回归分析

提出线性过程的定义及其回归分析方法,建立线性过程回归模型、回归方程和高置信水平、高可靠度的置信上、下限曲线。线性过程是具有线性函数均值和二次函数方差的独立增量随机过程,工程中的蠕变、松弛、刚度降、裂纹扩展、性能退化等许多随机过程均可变换为线性过程。传统回归分析只能对数据点进行处理,文中方法则能对过程进行回归分析,可以将线性过程作为一个整体进行统计推断,充分开发利用不同时刻试验数据之间的纵向信息,增大了信息量。从而在精度相同的情况下可节省大量试样,在试验量相同的情况下则能显著提高估计精度。     

分散性和落入概率整体推断方法

针对正态分布均值为零或已知（包括均值能被正确仿真）的情况，提出一种分散性和落入概率整体推断方法。该方法通过仿真结果与试验数据的结合，将多个不同状态下的试验数据作为一个整体进行统计分析，给出正态分布方差和落入概率的整体估汁与置信区间估计。与传统方法相比，该方法不但具有更高的精度，而且解决了一种状态下只有一个试验数据时分散性和落入概率评定的难题。文中还给出一种方差仿真结果的极小子样检验方法。     

基于HHT的非平稳信号分析仪的研究

本文介绍了希尔伯特-黄变换（HHT）的原理，首先通过经验模态分解（EMD），信号被分解成一系列固有模态函数（IMF），再通过Hilbert变换得到每个IMF的瞬时频率（IF）和瞬时幅值函数，最终得到原始信号的IF分布和Hilbert谱。Hilbert谱是信号的时间-频率-能量分布。为使HHT能有效分析非平稳信号，引入了改进HHT的方法，即在HHT过程中，将小波包变换（WPT）作为预处理器，外加IMF的筛选。采用虚拟仪器开发技术研制了一台基于HHT的非平稳信号分析仪。最后以HHT去噪为例，介绍了基于HHT的非平稳信号分析仪的应用。     

基于多特征参数和概率神经网络的滚动轴承故障诊断方法

针对滚动轴承故障振动信号的非平稳特性,提出了一种基于多特征参数和概率神经网络的滚动轴承故障诊断方法。首先利用经验模态分解（EMD）方法将采集到的滚动轴承原始振动信号分解为有限个固有模式函数（IMF）之和,然后提取表征故障信息的若干个IMF的能量、峭度和偏度作为概率神经网络的输入参数来进行故障分类。试验结果表明,该方法可以准确、有效地识别滚动轴承的工作状态和故障类型,是一种可行的滚动轴承故障诊断方法。     

Nonstationary random analysis of structures with hybrid mass damper system

The building structure is modeled as a linear single-degree-of-freedom system, and an active mass damper (AMD) is also adopted as the control device in order to reduce the structural response due to the external random load. In addition, suppose that the input acceleration of earthquake can be modeled as the product of nonstationary envelope function and narrow-band stationary random process with Kanai-Tajimi spectrum. In order to obtain the nonstationary stochastic response of control system due to the narrow-band nonstationary random process, in consideration of exchanging the active control mode for the passive one, considerable efforts are generally required in the analytical formulation. This paper, therefore, proposes an analytical technique to acquire the response covariance matrix by utilizing the state transition matrix method in state space. The proposed technique is evaluated by comparing the analytical results with those from numerical simulations.     

制造过程质量控制中误差流理论的研究

基于平稳随机过程正态分布假定和手工计算的传统统计过程控制法与控制图已经不满足现代制造过程质量控制与保障的要求。为提高产品质量必须研究与质量形成过程相关的几个误差流理论问题：误差流的跟踪与监视控制，误差流控制图，三维误差模型及其失稳自组织恢复原理。介绍了上述问题的研究结果与模型，并报道单／多工序车削加工误差流跟踪和误差流控制图的试验研究结果。     

网格曲面上的样条曲线阵列

提出一种流形网格曲面上曲线阵列复制方法,达到曲线重用与再设计的目的。网格曲面上的曲线用测地B样条表示,使对曲线的操作可以转换为对曲线控制顶点的操作;引入离散指数映射理论将给定的源曲线控制顶点映射到切空间,获得它们的法坐标,按照曲线阵列前后控制顶点法坐标保持不变的原则,建立曲线阵列前后控制顶点的对应关系,实现曲线的有规律多重复制。法坐标很好地保持了控制顶点之间的测地距离和相对位置关系,因而也保证了曲线阵列重用过程中的形状保持性。将曲线阵列时的位置与形状分开处理,使曲线生成仅与其所在的局部区域有关而与曲面的整体大小无关,既便于保证曲线的形状保持性,也减少了计算量。试验结果表明,所介绍方法健壮、有效,能满足曲面上曲线的交互设计要求。     

基于混沌关联积分的暂态电能质量扰动分类

关联积分曲线基于时间序列重构,能够更全面反映时间序列扰动变化,并且作为扰动识别的特征量,可以避开关联维无标度区间确定这一问题。根据暂态电能质量信号在不同扰动下其关联积分曲线所呈现出的特有形态特征,将关联积分曲线作为扰动识别的特征量。不同扰动信号的关联积分曲线区别较大,直观明了。该方法操作简单方便,可以省去烦琐的数值分析,且具有较高的精确度和实用性。对几种典型的暂态扰动信号进行识别和分类,仿真结果证明了其有效性和优越性。     

时频非平稳地震动模型及结构随机振动应用

地震动具有显著的时域和频域非平稳性,传统的均匀调制地震动模型不能充分表征时频两域的非平稳性,并影响结构随机振动分析的精准度。为了克服上述不足,建立由多峰平滑包络和非平稳噪声信号点乘而成的非均匀调制地震动模型,该模型能够在时域上充分反映地震动的波动和衰减特性,同时其频谱特征也与真实信号相接近。在此基础上,建立同时以时间和频率为变量的非平稳地震动演变谱随机模型。分析结果表明,以上两种模型在时域和频域的合成精度上均优于均匀调制模型。针对以上地震动随机模型的形式和特点,对传统结构随机振动响应求解方法进行改进。通过算例证明,按照均匀调制模型计算结构随机响应不能充分获得结构时频域的非平稳特性且结果偏于不安全,而利用两种改进模型可以获得更精确的结构响应概率特征和更细致的非平稳性演变过程。     

A spline-based method for stability analysis of milling processes

Based on the idea of collocation methods, a spline-based integration method for the stability prediction of systems governed by time-periodic delay differential equations (DDEs) is presented. A B-spline curve is adopted to approximate the solution of the DDEs using the direct integration technique. The stability of the dynamic system is then predicted using the Floquet theory based on the established state transition matrix. The proposed method can apply to time-periodic DDEs where the delay and the period are incommensurate, and the proposed method is extended to study the stability of milling processes as well. For stability analysis of variable pitch cutters, the proposed method use one or multiple B-spline curves to approximate the solution of the DDEs according to the relationship between the cutter angles and the radial immersion, which can describe exactly the free vibration of the cutter. Compared with the numerical integration method and the Chebyshev collocation method, the simulation results demonstrate that the proposed technique is more efficient and accurate for stability prediction at low radial immersion cases in milling processes with variable pitch cutters.     

Bilateral prediction and intersection calculation autofocus method for automated microscopy

In this paper, a bilateral prediction and intersection calculation autofocus method for automated microscopy, which obtains the in‐focus position by calculating the intersection of the predicted left and right focus measure curves located respectively in the left and right sides of the peak position of the focus measure curve, is proposed and performed. According to the autofocus method, the area including the peak position of the focus measure curve and its left and right neighbourhoods should be determined firstly, and the left and right neighbourhoods are considered as the left and right sampling areas. The left and right focus measure curves are predicted by appropriate predicting models according to the two sample sequences, which comprise the focus values by evaluating the sampled images in the left sampling area and right sampling area, respectively and their corresponding sampling positions. The intersection of the predicted left and right focus measure curves is calculated and can be considered as the in‐focus position. The autofocus can be realized by moving the focus plane of the microscope to the intersection of the predicted left and right focus measure curves. The proposed bilateral prediction and intersection calculation autofocus method is experimentally verified in an automated light microscopy for implementing microassembly and micromanipulation. The theoretical analyses have shown that the proposed bilateral prediction and intersection calculation autofocus method can not only effectively avoid the principle error caused by assuming the symmetrical focus measure curve in the autofocus methods based on curve fitting, but also eliminate the possible waver search near the peak position in the modified fast climbing servo method. The experimental results have shown that the proposed bilateral prediction and intersection calculation autofocus method possesses the merits as follows: (1) the focusing accuracy is high and slightly affected by the sampling step size and (2) the focusing speed is higher than those of the 7‐point hill‐climbing search method and the quadratic curve fitting method with a determinate focusing accuracy.     

Response-only modal identification using random decrement algorithm with time-varying threshold level

Modal Identification from response data only is studied for structural systems under nonstationary ambient vibration. The topic of this paper is the estimation of modal parameters from nonstationary ambient vibration data by applying the random decrement algorithm with time-varying threshold level. In the conventional random decrement algorithm, the threshold level for evaluating randomdec signatures is defined as the standard deviation value of response data of the reference channel. The distortion of randomdec signatures may be, however, induced by the error involved in noise from the original response data in practice. To improve the accuracy of identification, a modification of the sampling procedure in random decrement algorithm is proposed for modal-parameter identification from the nonstationary ambient response data. The time-varying threshold level is presented for the acquisition of available sample time history to perform averaging analysis, and defined as the temporal root-mean-square function of structural response, which can appropriately describe a wide variety of nonstationary behaviors in reality, such as the time-varying amplitude (variance) of a nonstationary process in a seismic record. Numerical simulations confirm the validity and robustness of the proposed modal-identification method from nonstationary ambient response data under noisy conditions.     

A practical sampling method for profile measurement of complex blades

Blade is one of the most important parts in turbine machinery. The complex geometry of blades not only makes them difficult to fabricate, but also leads them difficult to inspect. Typically, the surface of blades is measured by using coordinate measuring machine (CMM). Since the measurement time and cost increase proportionally as the increase of measurement points, it is essential to sample measurement points which can represent entire blade with sufficient confidence and accuracy. In order to achieve a certain allowable deviation with a suitable set of points, a practical sampling method for surface measurement of blades was studied. Firstly, the leading edge curve and trailing edge curve were supposed to represent the twisted and bend information of blades. A sampling method based on maximum chordal deviation for leading edge curve and trailing edge curve was researched. Further, a fusion approach for sampling points on both edge curves, which determine the cross-sections, was proposed. Secondly, the inspection points sampling method for sectional curves were investigated. Finally, two simulation and one experimental examples were used to demonstrate the sampling methodology. The results indicated that the approach of this study can ensure the measurement precision at high curvature potion by measuring a small number of points.     

包含颈缩失稳的中厚钢板应力应变关系

为弥补传统引伸计在颈缩区域测量方面的不足,提出一种基于三维数字图像相关(3D-DIC)技术的截面分析方法。以轧制方向为0°的QStE700中厚钢板为研究对象,采用截面分析方法获得单向拉伸过程中截面几何形貌及面积,确定颈缩失稳发生时刻,并分析包含颈缩失稳的应力-应变演化过程及截面积变化规律。利用改进的Bridgeman方程对颈缩失稳后的真实应力-应变曲线进行校正,获得包含颈缩失稳的中厚钢板等效应力-应变曲线。分别以传统的幂指硬化曲线和改进的等效应力-应变曲线为本构模型,建立中厚钢板单向拉伸有限元仿真模型,获得截面积随时间变化曲线及载荷与位移关系曲线。结果表明,以改进的等效应力-应变曲线为本构模型的仿真结果与试验结果吻合较好,验证了基于3D-DIC技术的截面分析方法的正确性。此方法可用于描述包含颈缩失稳的整个拉伸过程。