Data point selection for weighted least square fitting of cavity decay time constant

For the accurate extraction of cavity decay time, a selection of data points is supplemented to the weighted least square method. We derive the expected precision, accuracy and computation cost of this improved method, and examine these performances by simulation. By comparing this method with the nonlinear least square fitting （NLSF） method and the linear regression of the sum （LRS） method in derivations and simulations, we find that this method can achieve the same or even better precision, comparable accuracy, and lower computation cost. We test this method by experimental decay signals. The results are in agreement with the ones obtained from the nonlinear least square fitting method.

Weighted Least-Squares for a Nearly Perfect Min-Max Fit

In this note, we experimentally demonstrate, on a variety of analytic and nonanalytic functions, the novel observation that if the least squares polynomial approximation is repeated as weight in a second, now weighted, least squares approximation, then this new, second, approximation is nearly perfect in the uniform sense, barely needing any further, say, Remez correction.

ADAPTIVE FUSION ALGORITHMS BASED ON WEIGHTED LEAST SQUARE METHOD

Weighted fusion algorithms, which can be applied in the area of multi-sensor data fusion, are advanced based on weighted least square method. A weighted fusion algorithm, in which the relationship between weight coefficients and measurement noise is established, is proposed by giving attention to the correlation of measurement noise. Then a simplified weighted fusion algorithm is deduced on the assumption that measurement noise is uncorrelated. In addition, an algorithm, which can adjust the weight coefficients in the simplified algorithm by making estimations of measurement noise from measurements, is presented. It is proved by emulation and experiment that the precision performance of the multi-sensor system based on these algorithms is better than that of the multi-sensor system based on other algorithms.

Least squares fitting of coordinate parameters model

This paper starts with untime-diversification of the time-diversification deformation model and gives displacement distribution model of untime-diversification and simplifies further the study of deformation model. The paper discusses the problem of least squares fitting of coordinate parameters model—parameters of deformation model. During discussion, the basic means of cubic B splines and two steps of multidimensional disorder datum fitting are adopted which can make fitting function calculated mostly approximate coordinate parameters model and it can make calculation easier.

Visualising data distributions with kernel density estimation and reduced chi-squared statistic

The application of frequency distribution statistics to data provides objective means to assess the nature of the data distribution and viability of numerical models that are used to visualize and interpret data.Two commonly used tools are the kernel density estimation and reduced chi-squared statistic used in combination with a weighted mean.Due to the wide applicability of these tools,we present a Java-based computer application called KDX to facilitate the visualization of data and the utilization of these numerical tools.

Large Scattered Data Fitting Based on Radial Basis Functions

Solving large radial basis function （RBF） interpolation problem with non-customized methods is computationally expensive and the matrices that occur are typically badly conditioned. In order to avoid these difficulties, we present a fitting based on radial basis functions satisfying side conditions by least squares, although compared with interpolation the method loses some accuracy, it reduces the computational cost largely. Since the fitting accuracy and the non-singularity of coefficient matrix in normal equation are relevant to the uniformity of chosen centers of the fitted RBE we present a choice method of uniform centers. Numerical results confirm the fitting efficiency.

Research on the Model of Linear Data Fitting Method

By using the method of least square linear fitting to analyze data do not exist errors under certain conditions, in order to make the linear data fitting method that can more accurately solve the relationship expression between the volume and quantity in scientific experiments and engineering practice, this article analyzed data error by commonly linear data fitting method, and proposed improved process of the least distance squ^re method based on least squares method. Finally, the paper discussed the advantages and disadvantages through the example analysis of two kinds of linear data fitting method, and given reasonable control conditions for its application.

Criteria for Weighted Moving-Mean Method

The moving-mean method is one of the conventional approaches for trend-extraction from a data set. It is usually applied in an empirical way. The smoothing degree of the trend depends on the selections of window length and weighted coefficients, which are associated with the change pattern of the data. Are there any uniform criteria for determining them? The present article is a reaction to this fundamental problem. By investigating many kinds of data, the results show that: 1) Within a certain range, the more points which participate in moving-mean, the better the trend function. However, in case the window length is too long, the trend function may tend to the ordinary global mean. 2) For a given window length, what matters is the choice of weighted coefficients. As the five-point case concerned, the local-midpoint, local-mean and global-mean criteria hold. Among these three criteria, the local-mean one has the strongest adaptability, which is suggested for your usage.

基于幂加权最小二乘拟合的红外相机辐射定标方法

分析了现有线性度计算方法的不足,提出基于偏差/测量值的新线性度评价方式,通过该方式最小二乘拟合的低端温度偏差比高端大一个数量级,并采用加权拟合提高系统响应线性度。在分析不同光谱的温度和辐亮度拟合函数基础上,提出一种基于辐亮度倒数幂加权最小二乘线性拟合的地面和星上辐射定标方法,确认最佳权重幂次,建立了幂次n=1的加权最小二乘拟合外黑体线性定标方程、内黑体线性定标方程、内外黑体辐亮度转换模型。针对星上内黑体高精度两点定标建立了基于加权最小二乘拟合内外黑体辐亮度转换模型;针对星上黑体发射率退化提出了基于恒星定标的红外相机星上内黑体辐亮度定标修正方法,建立了外黑体辐亮度、内黑体辐亮度和恒星辐亮度转换模型。采用加权线性拟合后,积分时间10 ms的低温端外黑体反演偏差由1.63 K下降到0.52 K,内黑体偏差反演温度偏差由0.83 K下降到0.39 K,系统响应线性度明显提升。

曲线曲面局部最小二乘渐进迭代逼近

作为一种有效的大数据拟合方法,曲线曲面最小二乘渐进迭代逼近方法(LSPIA)吸引了众多研究者的关注,并获得了广泛的应用。针对LSPIA算法拟合局部数据点效果较差的问题,提出了一种局部的LSPIA算法,称为LOCAL-LSPIA。首先,给定初始曲线(曲面)并从给定的数据点中选择部分数据点;然后在初始曲线(曲面)上选择需要调整的控制点;最后,LOCAL-LSPIA通过迭代调整这一部分控制点来生成一系列局部变化的拟合曲线(曲面),并且保证生成的曲线(曲面)的极限是在仅调整这部分控制点的情况下拟合部分数据点的最小二乘结果。在多个曲线曲面拟合上的实验结果表明,为达到相同的拟合精度,LOCAL-LSPIA算法比LSPIA算法需要的步骤和运算时间更少。因此,LOCAL-LSPIA是有效的,而且在拟合局部数据的情况下比LSPIA算法的收敛速度更快。

融合IMR-WGAN的时序数据修复方法

工业数据由于技术故障和人为因素通常导致数据异常,现有基于约束的方法因约束阈值设置的过于宽松或严格会导致修复错误,基于统计的方法因平滑修复机制导致对时间步长较远的异常值修复准确度较低.针对上述问题,提出了基于奖励机制的最小迭代修复和改进WGAN混合模型的时序数据修复方法.首先,在预处理阶段,保留异常数据,进行信息标注等处理,从而充分挖掘异常值与真实值之间的特征约束.其次,在噪声模块提出了近邻参数裁剪规则,用于修正最小迭代修复公式生成的噪声向量.将其传递至模拟分布模块的生成器中,同时设计了一个动态时间注意力网络层,用于提取时序特征权重并与门控循环单元串联组合捕捉不同步长的特征依赖,并引入递归多步预测原理共同提升模型的表达能力;在判别器中设计了Abnormal and Truth奖励机制和Weighted Mean Square Error损失函数共同反向优化生成器修复数据的细节和质量.最后,在公开数据集和真实数据集上的实验结果表明,该方法的修复准确度与模型稳定性显著优于现有方法.

引入神经网络极限学习机的关键数据查询模型

网络空间数据的结构具有较高相似性,海量数据的不断增量更新,导致关键数据查询结果存在冗余和偏离问题。因此提出基于神经网络极限学习机的关键数据查询方法。建模描述关键数据查询问题。基于此引入神经网络极限学习机,建立关键数据查询模型。预处理数据库中无用数据和重复数据做,通过输出权值范数的最小二乘解,避免算法陷入局部最优。结合输出矩阵,训练查询模型,输出结果结果即为关键数据查询结果。为证明上述方法的性能优势,设计对比实验,结果表明提出的方法应用于关键数据查询的均方根误差不超过1.2,平均绝对百分比误差最高为4.1%,关系数F可达0.6,网络节点的使用率低于20%。以上实验数据验证了上述方法数据查询精度较高,可应用性更强。

Iterative weighted partial spline least squares estimation in semiparametric modeling of longitudinal data

In this paper we consider the estimating problem of a semiparametric regression modelling whenthe data are longitudinal. An iterative weighted partial spline least squares estimator (IWPSLSE) for the para-metric component is proposed which is more efficient than the weighted partial spline least squares estimator(WPSLSE) with weights constructed by using the within-group partial spline least squares residuals in the senseof asymptotic variance. The asymptotic normality of this IWPSLSE is established. An adaptive procedure ispresented which ensures that the iterative process stops after a finite number of iterations and produces anestimator asymptotically equivalent to the best estimator that can be obtained by using the iterative proce-dure. These results are generalizations of those in heteroscedastic linear model to the case of semiparametric regression.

HERMITE SCATTERED DATA FITTING BY THE PENALIZED LEAST SQUARES METHOD

Given a set of scattered data with derivative values. If the data is noisy or there is an extremely large number of data, we use an extension of the penalized least squares method of von Golitschek and Schumaker [Serdica, 18 （2002）, pp.1001-1020] to fit the data. We show that the extension of the penalized least squares method produces a unique spline to fit the data. Also we give the error bound for the extension method. Some numerical examples are presented to demonstrate the effectiveness of the proposed method.

路面表层土壤承压特性试验研究

不同类型可变形软土路面表层土壤在其不同含水状态下的承压特性是军用车辆行驶于其上行驶阻力及沉陷深度的关键影响因素,决定了军用车辆行驶于其上的通过能力。为了得到不同类型可变形软土路面及其不同含水状态下表层土壤的承压特性,基于改进的高精度万能试验机对军用车辆行驶典型路面-起伏土路、碎石子路、河滩路和戈壁路采集得到土壤样本进行压板试验,得到土壤承压特性基础数据,通过加权最小二乘法获得土壤Bekker承压模型特征参数。研究结果为军用车辆行驶系统设计、仿真及通过性分析积累了有效基础数据,具有参考意义。

船舶操纵性约束模测量系统设计与分析

为解决实验室船舶操纵性约束模实验中的测量及数据分析处理技术问题,开发组建实验测量系统,推导数据分析处理方法,以期实现约束模实验的测量与数据在线分析处理;根据前期研究经验,设计了较为完善的测量硬件系统方案;为实现约束模中精确的零相位整周期测量要求,采用光电开关利用数据采集卡的硬件触发启动功能,并给出了整数周期测量的方案;利用最小二乘拟合及傅里叶分析等方法推导给出各船舶水动力导数数据处理方法;在此基础上,作为重点编写了完整的在线测量与数据在线分析程序,主要功能内部独立实现;该系统手工介入频度低,基本实现了测量的自动化,效率得到大幅提高;最后进行实际测量验证,数据的拟合结果与测量结果符合良好,验证了该系统的可靠性;同时处理结果显示船舶附加质量导数Y同船舶惯性质量很接近,而导数Y′r,N′数值很小,近于零。

基于向量自回归模型的电网虚假数据注入攻击检测

虚假数据注入攻击(false data injection attack,FDIA)是威胁电网运行安全的主要因素之一,其主要通过攻击电网中的一些通信环节,误导电力系统的状态估计结果,给电网安全运行带来巨大威胁。针对FDIA难以有效检测及电力系统状态估计中过程噪声与量测噪声两者协方差矩阵非正定问题,将向量自回归(vector auto regression,VAR)模型引入电力系统状态估计,提出一种基于VAR和加权最小二乘法(weighted least squares,WLS)的FDIA检测方法。首先,建立VAR状态估计模型,将量测噪声视为稳定量,只对过程噪声进行估计,解决两者协方差矩阵的非正定问题;其次,分别采用VAR与WLS对电力系统进行状态估计,采用一致性检验与量测量残差检验对2种方法的结果进行检测,以判定是否存在FDIA;最后,IEEE 14节点和IEEE 30节点仿真结果表明,本文所提检测方法能够成功检测到FDIA,且检测成功率较高,从而验证了该方法的可行性及有效性。

多信源无线传感网络带宽时延感知数据汇聚方法

为提高多信源无线传感网络的传输效率,设计了一种多信源无线传感网络带宽时延感知数据汇聚方法。该方法构建三类虚拟队列,并根据带宽时延数据判断阈值进行端到端计算,以针对不同类型的数据流计算相应的带宽时延阈值。使用卡方拟合检验方法对当前时延感知数据的信任度进行判定,在此基础上排除异常或偏离分布模型的数据样本。对高卡方统计量的数据进行压缩或信息提取,并通过聚类权值实现感知数据汇聚。仿真结果显示,该方法在高斯噪声或莱斯噪声环境下,能将传输时延控制在50 ms以内,网络带宽数据汇聚结果较高,且网络数据传输耗能低于100 J。这表明多信源无线传感网络带宽时延感知数据汇聚可减少传输时间和资源浪费。

基于车载扫描点云的地铁盾构隧道椭圆度分析

椭圆度是衡量地铁盾构隧道管片变形的重要指标之一,由于地铁隧道中存在道床管线,导致隧道点云中会存在大量到内壁距离不等的非隧道内壁点,会对椭圆度分析产生影响。对于道床一般利用直通滤波来处理,但轨道超高时处理效果不佳;对于其他附属物通过设置距离阈值方法来处理,但阈值难以预先准确确定。为解决以上问题,依据盾构隧道点云分布特点,提出一种道床点距离阈值剔除、附属物点分级定权剔除算法。结果表明,算法给出的椭圆度MAE为0.085‰,优于直接最小二乘法和RANSAC算法。基于某地铁隧道56个单环隧道的激光点云,对算法性能进行测试,各环椭圆度MAE均值为0.174‰、各环椭圆度标准差均值为0.216‰,较RANSAC算法分别提升19.1%、19.7%,证明该方法能够有效消除地铁隧道点云中非隧道内壁点的影响,椭圆度计算结果具有较好的稳健性。

一种基于PEIV模型的GNSS高程拟合解法

采用二次曲面函数拟合全球卫星导航系统(GNSS)高程时,系数矩阵中含有观测坐标,所以系数矩阵同样存在误差,故采用总体最小二乘拟合GNSS高程更加合理。但系数矩阵不同位置有相同的元素,为保证这些相同元素有相同的改正数,本文提出了基于部分变量含误差(PEIV)模型的GNSS高程拟合解法,该方法可以保证相同元素的改正数一致。最后通过模拟算例和实例算例分析发现,本文解法与加权总体最小二乘(WTLS)解算结果一致,验证了本文解法的可行性。