基于粒子群优化算法的 AR模型参数估计

利用粒子群优化算法对模型AR（ P）参数进行优化,提高了模型的预测精度。采用AIC准则判断出模型的最佳阶数。该估算方法优于传统的基于最小二乘估计和基于灰色理论估计,为此类模型的参数估计提供了一种新思路。     

基于复合分位数高斯核基函数的非参数回归模型及应用

波动性大、规律性和整体性较差的建筑物变形数据,难以用参数回归模型描述其变化规律,为此建立了一种基于高斯核基函数的非参数回归模型,利用复合分位数和模拟退火算法估算模型系数。工程实例表明,复合分位数估算的高斯核基非参数回归模型具有较高的精度,能够满足工程需要,用该模型对建筑物变形数据进行预测分析是可行的。     

基于最小二乘支持向量机的小样本威布尔可靠性分析

在图估法的基础上,提出了基于最小二乘支持向量机的威布尔可靠性分析方法,在MATLAB平台上绘制了威布尔概率纸,通过程序化的方式分析估计威布尔概率参数;进行了可靠性寿命分析,并对比分析了基于最小二乘支持向量机、支持向量机和最小二乘法威布尔可靠性分析的效果。实例分析结果显示,在威布尔可靠性分析中,最小二乘支持向量机的拟合精度不仅优于传统的最小二乘法的拟合精度,而且优于支持向量机的拟合精度,表明该方法可以提高可靠性分析效率和精度,可作为威布尔可靠性分析的一种新方法,特别适用于小样本的情况。     

基于提升核偏最小二乘回归的色彩校正

为进一步提高回归算法的色彩校正精度,提出一个基于核偏最小二乘回归的局部迭代算法.该算法首先将源色彩空间中校正样本的邻域样本经核函数映射到一个高维的线性特征空间,然后在提升的迭代过程中通过偏最小二乘回归消除映射数据的多重共线性,最终达到色彩校正的目的.实验证明算法引入的特征空间提供了额外的校正信息,提升方法增强了核偏最小二乘回归性能,算法在精度和鲁棒性上均优于传统的多重回归和基于分区的回归校正方法.     

偏最小二乘法在鱼雷出管速度预测中的应用

采用偏最小二乘回归方法,经交叉有效性检验建立了鱼雷出管速度的回归方程.通过与实验数据比较,该模型拟合精度较强,说明偏最小二乘回归是估算舰艇鱼雷发射内弹道特征参数的一种有效方法.     

异方差回归-时序模型

提出一种异方差回归一时序模型，通过建立回归分析残差的标准差自回归方程，给出回归系数、自回归系数和滑动平均系数的最小二乘估计和极大似然估计。该模型能够在小样本情况下充分发挥回归分析和时间序列各自的优点，对回归模型的残差项进行有效补偿，提高回归分析的精度。文中对回归模型残差相互独立和自相关两种情况分别进行讨论。大量计算表明，该方法具有较高的分析和预测精度。     

基于局部加权偏最小二乘法的冷凝器污垢预测

提出了基于局部加权偏最小二乘回归算法的污垢预测算法,通过在训练集的污垢数据局部模型内对新测得的数据进行偏最小二乘回归分析,并应用自适应算法对模型参数、各模型之间的加权系数进行自动优化调整。算法能很好地解决新旧数据相互影响问题,以适应冷凝器水质及工况参数的动态变化,具有学习速度快、泛化能力强及鲁棒性强的特点。通过与各种工况下的污垢预测值比较,实验结果说明基于局部加权偏最小二乘回归学习算法的污垢模型预测精度比神经网络模型、渐近污垢模型有显著提高。     

基于高阶累积量的OFDM信道估计算法研究

基于高阶累积量与LS准则联合估计信道参数的思想,在数据相关条件下,提出采用加权最小二乘法进行信道估计.算法提升了LS算法信道估计的精度,降低了信道估计算法的复杂度.仿真结果表明,该算法性能接近于传统MMSE和ML算法性能.     

支持向量机分类与回归联合建模方法及其在拉曼光谱分析中的应用

多元校正分析模型的精度不仅依赖于模型的结构和参数,还很大程度上取决于训练样本的分布。实际过程中,训练样本通常呈现不均匀分布,导致基于全体样本的回归模型预测性能不理想。本文针对该问题提出了支持向量机分类与回归联合建模方法:首先使用最小二乘支持向量机(LS-SVM)分类器构建分类决策树,然后对每一类样本分别建立最小二乘支持向量机回归模型;对未知样本进行定量分析时,首先经过分类决策树分类,再根据分类信息选择相应的回归模型进行计算。针对汽油辛烷值拉曼光谱分析问题,基于全体样本建模的LS-SVM回归模型的标准预测误差为0.54,而采用本文方法所得的模型预测误差为0.22,大幅度地提高了分析精度。     

故障时间观测的机电系统可靠性估计

根据系统发生故障时间的统计数据,应用KM方法估计系统可靠度,并利用威布尔分布模型拟合可靠度估计结果。分别用最小二乘和支持向量回归机两种方法估计威布尔分布模型参数,从而得到基于这两种方法的威布尔分布模型。利用所研究的方法,分析了卫星机电系统发生故障时间的统计数据,给出了系统可靠度估计结果,并进行了结果对比分析。     

基于稳健回归分析的转子系统不平衡量识别

不平衡是造成转子系统振动过大、影响其安全运行的重要因素。传统的最小二乘算法(least squares,简称LS)在不平衡量识别过程中存在对外界干扰或异常值敏感的问题,改进的加权最小二乘算法(weighted least squares,简称WLS)虽然能够降低异常值的影响,但需要经验积累并对振动数据进行深入分析。提出一种基于稳健回归分析的转子系统不平衡量识别方法,通过构建优化的目标函数自动消除异常值的影响,得到正常状态下转子系统不平衡量的最佳估值。实验结果表明,该方法能够有效消除外界干扰和异常值的影响,准确识别出转子系统不平衡量。     

Bayesian and least-squares algorithms for estimating signal harmonics: A comparative study

Two algorithms for estimating signal harmonics are described and their performances are compared for waveform metrology applications: least squares and Bayesian harmonic analysis. It is confirmed that the estimates provided by them practically coincide. It is also shown that the least squares algorithm is faster than the Bayesian one.     

Nonlinear least squares regression for single image scanning electron microscope signal‐to‐noise ratio estimation

A new method based on nonlinear least squares regression (NLLSR) is formulated to estimate signal‐to‐noise ratio (SNR) of scanning electron microscope (SEM) images. The estimation of SNR value based on NLLSR method is compared with the three existing methods of nearest neighbourhood, first‐order interpolation and the combination of both nearest neighbourhood and first‐order interpolation. Samples of SEM images with different textures, contrasts and edges were used to test the performance of NLLSR method in estimating the SNR values of the SEM images. It is shown that the NLLSR method is able to produce better estimation accuracy as compared to the other three existing methods. According to the SNR results obtained from the experiment, the NLLSR method is able to produce approximately less than 1% of SNR error difference as compared to the other three existing methods.     

Outlier-resistant methods for estimation and model fitting

Least squares is perhaps the most widely used technique for model fitting. In this article, we illustrate the poor performance of least squares when there are spurious values, or outliers, in a sequence of measurements. A brief overview of three well-known classes of robust alternatives to the least-squares mean is presented. For robust regression, a recent proposal called least median squares (LMS) is decribed. LMS regression is compared to least-squares regression in an example involving the estimation of optical fiber geometry. References are provided for software that is available for robust estimation techniques surveyed in this article.     

Estimating the parameters of regression dependences using the Gramm-Charlier approximation

Estimation of the regression model parameters is considered. A new approach to estimating the parameters for random error distributions that differ from the normal one and may be represented as the A-type Gramm-Charlier series is proposed. The developed approach is compared with the traditional least squares method and the sign method by means of computing experiments.     

Best-fit criterion within the context of likelihood maximization estimation

This article presents an approach toward surface best-fit based on Bayesian inference statistics. The objective is to propose a best-fit criterion which integrates the distribution of points around the best-fit feature. This approach is used to guarantee a better estimate of the best-fit feature parameters. The best-fit criterion proposed in this article accounts for varied distributions that are not necessarily symmetric, such as those generated by turning and milling processes. It forms a generalization of least squares and enables the user to add information concerning the expected residual distribution shape. Therefore it provides the same results as the least squares method when the hypothesis of normal distribution is chosen. This article shows that using the proposed criterion will bring about a better estimate of the orientation of the best-fit feature and will lead to an evaluation of the form defect which is the closest to actual fact.     

Excel在光学实验数据处理中的应用

回归分析是一类数学模型,其研究对象是一个随机变量同一个或多个非随机变量的关系问题,在提出一元和多元线性回归的基础上,通过比较最小二乘法解法和Excel函数解法,指出Excel函数解法可以简化复杂的数学运算,并配以图表,给求解过程带来方便.