显著性加权最小二乘图像匹配跟踪方法

针对复杂背景下运动目标跟踪这类问题,提出了一种显著性加权最小二乘图像匹配跟踪算法.新方法首先根据目标上不同区域和背景的差别大小,给每个目标区域赋予不同的权值.然后将权值与最小二乘图像匹配算法结合起来对目标进行跟踪.实验中将本文算法与三种经典跟踪算法进行比较,实验结果表明,在复杂背景下,新算法仍然可以有效、准确地跟踪运动目标,而经典算法均出现问题.新算法的单帧处理时间也可以满足实时处理要求.     

包装复合膜中丙酮校准回归方程模型与评价

目的为了提高包装复合膜中丙酮检测结果的准确性,拟建立包装复合膜中丙酮校准回归方程模型。方法针对溶剂残留丙酮,以《包装材料溶剂残留量测定方法》YBB00312004—2015中溶剂残留测定方法为基础,采用加权最小二乘法,建立了包装复合膜中丙酮校准回归方程模型,并通过异常值检验、相关分析、参数估计、同方差性的判定等指标对校准回归方程模型进行综合评价,并与普通最小二乘法校准回归方程进行了对比分析。结果加权最小二乘法能有效消除异方差对校准回归方程的影响,且加权最小二乘法校准回归方程线性显著,拟合程度高,检测结果准确度高。结论加权最小二乘法校准回归方程模型适用于包装复合膜中丙酮质量检测。     

主动全向浮标阵的定位解算方法

推导出一种利用加权最小二乘法解算多枚浮标的定位结果的方法,对其性能进行了数值仿真分析,并与最小二乘法进行了比较。仿真结果表明,加权最小二乘法的性能较最小二乘法的性能有所提高,证明了算法的有效性。     

加权最小二乘法线性回归模型参数的理论推导与计算实例

利用数学方法从理论上得到加权最小二乘法回归方程的斜率和截距,进而推导出加权相关系数,用柯西不等式对加权相关系数进行了证明。采用加权最小二乘法建立了赭曲霉毒素液相分析的工作曲线,通过比较证明加权最小二乘法能提高低浓度范围测量的准确度。     

删失数据下一类回归模型的参数估计

考虑一类回归模型,在右删失数据下构造了参数的最小二乘估计和加权最小二乘估计,证明了估计量具有渐近正态性。模拟结果表明加权最小二乘估计比最小二乘估计有优良的性质。     

用考虑置信区间长度影响的最小二乘法拟合S－N曲线

S－N曲线是用名义应力法预测结构疲劳寿命的基础。基于试验疲劳寿命分散的物理机制,提出了一个S－N曲线试验数据处理的加权最小二乘法,此方法中每组数据的权重与该组数据的置信区间成反比。计算结果表明用考虑置信区间长度影响的最小二乘法拟合得到的S－N曲线比用一般最小二乘法得到的S－N曲线具有更高的可靠度,给出的寿命预测结果也更安全。     

溶剂残留（甲苯）校准回归方程的建立及评价

目的为了提高溶剂残留检测水平,以溶剂残留中的甲苯为例详细说明校准回归方程的建立以及评价方法。方法以GB/T 10004—2008中溶剂残留分析方法为基础,建立甲苯加权最小二乘法校准回归方程,并通过判定系数、标准差、统计检验、置信区间、控制限、线性范围、不确定度对加权校准回归方程进行系统综合评价,对普通与加权最小二乘法得到的校准回归方程的实际回归效果进行比较。结果加权校准回归方程模型恰当、线性显著、拟合程度高,能有效消除异方差对校准回归方程的影响,显著降低低浓度测定时的相对误差,保证测量结果的精确性、可靠性。结论文中方法对于实验室进行校准回归方程的建立和评价、质量控制以及数据处理和分析具有一定的指导意义。     

线性振动系统加权递推最小二乘法时域参数识别

本文给出了加权最小二乘法的递推形式，并利用该方法根据自由响应的信噪比随时间逐渐降低的性质加不同的权项。在时域识别了粘性阻尼线性振动系统的复频率，并与递推最小二乘法进行了对比。通过计算机仿真和实际应用表明本文提出的方法是可靠和有效的。     

加权最小二乘法建立板材中游离甲醛含量分析标准曲线的研究

化学分析工作中，两个变量之间的关系普通采用最小二乘法建立标准曲线，如果分析测定的变量范围宽，在低浓度区域则分析结果的相对误差较大，本文主要讨论了以加权最小二乘法建立标准曲线的优越性，并以GB／T 17657—1999乙酰丙酮法测板材中游离甲醛为应用实例，介绍了加权最小二乘法的原理、计算公式、权重因子在提高低浓度测定相对误差的作用。     

基于遗传算法的圆度误差评价

为了在全局范围正确评价圆度误差 ,本文采用遗传算法对圆度测量数据进行最小二乘法评价 ,克服了传统圆度最小二乘法评价的局部收敛问题。计算结果表明 ,本文介绍的方法可以在设计变量的全局范围内有效、正确地评价圆度误差     

Investigation on the use of chemical mass balance receptor model: Numerical computations

Cheng, M.D. and Hopke, P.K., 1986. Investigation on the use of chemical mass balance receptor model: numerical computations. Chemometrics and Intelligent Laboratory Systems, 1: 33–50.The use of various numerical techniques in the chemical mass balance receptor model leads to different estimations of mass contributions by the identified sources for an ambient air quality data set. Weighted-constrained L₁ (called least absolute deviations in statistics), ordinary weighted least squares, effective variance weighted least squares, and two variants of standard linear programming methods based on the maximized allocation of aerosol mass were studied. The data sets used in this study were the simulated aerosol composition data generated by the National Bureau of Standards for the EPA workshop on mathematical and empirical receptor modeling held at Quail Roost, NC, U.S.A. in 1982. The ensemble reliability of the numerical solutions for these test data sets were evaluated. The weighted-constrained L₁ solutions were found highly stable compared to those from the least-squares methods subject to various complexities of the simulated data sets. The effective variance weighted least squares was found to be ineffective in improving the quality of aerosol mass apportionment by the chemical mass balance model. The results of the standard linear programming methods were insensitive to the lognormal random variations present in the source compositions in Set 3, but gave less precise results than those obtained with the L₁ or least squares methods.     

Application of weight functions to the magnetic localization of anobject

A method to localize a magnetized object from the readings of simple array of magnetometers that is selected to the advantage of magnetic field measurement is applied. In the method the dipole field curve is fit to the readings by weighted least squares, where the weight function that is proportional is applied to the sixth power of the distance between the assumed location of the object and the point for measurement to ensure convergence of the iteration. By an experiment using a ship's magnetic model, it was ascertained that the convergence could be ensured if the initially approximated location is taken farther than the real one     

Advantages of soft versus hard constraints in self-modeling curve resolution problems. Penalty alternating least squares (P-ALS) extension to multi-way problems

An extension to the penalty alternating least squares (P-ALS) method, called multi-way penalty alternating least squares (NWAY P-ALS), is presented. Optionally, hard constraints (no deviation from predefined constraints) or soft constraints (small deviations from predefined constraints) were applied through the application of a row-wise penalty least squares function. NWAY P-ALS was applied to the multi-batch near-infrared (NIR) data acquired from the base catalyzed esterification reaction of acetic anhydride in order to resolve the concentration and spectral profiles of l-butanol with the reaction constituents. Application of the NWAY P-ALS approach resulted in the reduction of the number of active constraints at the solution point, while the batch column-wise augmentation allowed hard constraints in the spectral profiles and resolved rank deficiency problems of the measurement matrix. The results were compared with the multi-way multivariate curve resolution (MCR)-ALS results using hard and soft constraints to determine whether any advantages had been gained through using the weighted least squares function of NWAY P-ALS over the MCR-ALS resolution.     

样条加权残数法分析薄壳

本文用加权残数法分析薄壳,以五次样条函数构造试函数。我们用离散型最小二乘法分析了扁壳和变厚度圆柱壳的轴对称弯曲问题,对等厚度圆柱壳的轴对称弯曲问题分别采用了配点和配线法进行计算此较。各个问题都编制了程序,通过实例计算并与精确解比较,证明上述方法程序编制简单,输入数据少,耗用机时少,计算精度高,较为经济、实用。     

Weighted radial basis collocation method for boundary value problems

This work introduces the weighted radial basis collocation method for boundary value problems. We first show that the employment of least‐squares functional with quadrature rules constitutes an approximation of the direct collocation method. Standard radial basis collocation method, however, yields a larger solution error near boundaries. The residuals in the least‐squares functional associated with domain and boundary can be better balanced if the boundary collocation equations are properly weighted. The error analysis shows unbalanced errors between domain, Neumann boundary, and Dirichlet boundary least‐squares terms. A weighted least‐squares functional and the corresponding weighted radial basis collocation method are then proposed for correction of unbalanced errors. It is shown that the proposed method with properly selected weights significantly enhances the numerical solution accuracy and convergence rates. Copyright © 2006 John Wiley & Sons, Ltd.     

Transient analysis of electro‐osmotic transport by a reduced‐order modelling approach

Transient behaviour of electro‐osmotic transport in typical electrokinetic channels is studied in this paper. The time needed for the electro‐osmotic flow to reach steady‐state exhibits multiple time scales depending on whether the flow is governed by either a viscous force, electrokinetic force or by a combination of both. When an intersection is present in the electrokinetic channel, such as in a cross or a T‐channel, the flow in the main channel and in the intersection gets to steady‐state at different times. A weighted Karhunen–Loève (KL) decomposition method is proposed in this paper to generate the global basis function for reduced‐order simulation. The key idea in a weighted KL approach is that, instead of minimizing a least‐squares measure of ‘error’ between the linear subspace spanned by the basis functions and the observation space, we minimize the weighted ‘error’ between the two spaces. The global basis functions in a weighted KL approach can be generated by computing the singular value decomposition (SVD) of the matrix containing the weighted snapshots. We show that the weighted KL decomposition based reduced‐order model is computationally more efficient and can capture the multiple time scales encountered in electro‐osmotic transport much more effectively compared to the classical KL decomposition based reduced‐order model. Copyright © 2003 John Wiley & Sons, Ltd.     

一种基于变尺度积分滑动平均的载荷识别方法

首先,基于积分滑动平均思想构造了变尺度加权积分函数,提出了最小二乘意义下加权积分滑动平均最佳近似响应函数模型。其次,利用形函数方法构造最佳近似载荷模型,组合近似载荷及响应得到实际情况下的Duhamel积分方程,对Duhamel积分离散化得到用于载荷识别的离散线性系统方程。再次,使用正则化方法进行载荷识别。利用正则化方法中最小二乘解构造以正则化参数为自变量的函数,提出了一种选取最优正则化参数的新方法。最后,数值仿真及试验验证将该文提出方法与传统方法进行了比较,结果说明新方法能够得到精度较好的近似稳定解,并且具有较好的抗噪性。     

Problems of Nonnormality and Multicollinearity for Forecasting Methods Based on Least Squares

Many popular forecasting and time-series analysis methods assume that the variable to be forecast can be expressed as a linear function of a set of predictors. The predictors may include variables related in either a correlative or causal fashion to the response variable, lagged values of this variable, or known mathematical functions of time. The method of least squares is used almost exclusively to estimate the parameters in these models. This paper discusses two hazards in the indiscriminant use of least squares; nonnormality of the observations on the variable of interest and multicollinearity among the predictors. Robust estimation methods are suggested as alternatives to least squares for nonnormal data, and a robust version of exponential smoothing is developed. A small Monte Carlo study indicates that the robust procedure can be superior to ordinary exponential smoothing in many situations. The sources and effects of multicollinearity are discussed, and several diagnostic statistics are presented. Methods for dealing with multicollinearity are reviewed, including collecting additional data, variable selection, and biased estimation. An example of ridge regression is included.     

Estimation of the Shape Parameter of the Weibull Distribution Using Linear Regression Methods: Non‐Censored Samples

The two‐parameter Weibull distribution is one of the most widely applied probability distributions, particularly in reliability and lifetime modelings. Correct estimation of the shape parameter of the Weibull distribution plays a central role in these areas of statistical analysis. Many different methods can be used to estimate this parameter, most of which utilize regression methods. In this paper, we presented various regression methods for estimating the Weibull shape parameter and an experimental study using classical regression methods to compare the results of the methods. A complete list of the parameter estimators considered in this study is as follows: ordinary least squares (OLS), weighted least squares (WLS, Bergman, F&T, Lu), non‐parametric robust Theil's (Theil) and weighted Theil's (WeTheil), robust Winsorized least squares (WinLS), and M‐estimators (Huber, Andrew, Tukey, Cauchy, Welsch, Hampel and Logistic). Estimator performances were compared based on bias and mean square error criteria using Monte‐Carlo simulations. The simulation results demonstrated that for small, complete, and non‐outlier data sets, the Bergman, F&T, and Lu estimators are more efficient than the others. When the data set contains one or two outliers in the X direction, Theil is the most efficient estimator. Copyright © 2012 John Wiley & Sons, Ltd.