Preconditioned iterative methods for solving weighted linear least squares problems

A class of preconditioned iterative methods, i.e., preconditioned generalized accelerated overrelaxation （GAOR） methods, is proposed to solve linear systems based on a class of weighted linear least squares problems. The convergence and comparison results are obtained. The comparison results show that the convergence rate of the preconditioned iterative methods is better than that of the original methods. Furthermore, the effectiveness of the proposed methods is shown in the numerical experiment.

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.

Recursive weighted least squares estimation algorithm based on minimum model error principle

Kalman filter is commonly used in data filtering and parameters estimation of nonlinear system,such as projectile's trajectory estimation and control.While there is a drawback that the prior error covariance matrix and filter parameters are difficult to be determined,which may result in filtering divergence.As to the problem that the accuracy of state estimation for nonlinear ballistic model strongly depends on its mathematical model,we improve the weighted least squares method(WLSM)with minimum model error principle.Invariant embedding method is adopted to solve the cost function including the model error.With the knowledge of measurement data and measurement error covariance matrix,we use gradient descent algorithm to determine the weighting matrix of model error.The uncertainty and linearization error of model are recursively estimated by the proposed method,thus achieving an online filtering estimation of the observations.Simulation results indicate that the proposed recursive estimation algorithm is insensitive to initial conditions and of good robustness.

STUDY ON FREQUENCY ESTIMATION BASED ON WEIGHTED LEAST SQUARE METHOD WITH THREE FOURIER COEFFICIENTS

In this paper,a sinusoidal signal frequency estimation algorithm is proposed by weighted least square method.Based on the idea of Provencher,three biggest Fourier coefficients in the maximum periodogram are considered,the Fourier coefficients can be written as three equations about the amplitude,phase,and frequency,and the frequency is estimated by solving equations.Because of the error of measurement,weighted least square method is used to solve the frequency equation and get the signal frequency.It is shown that the proposed estimator can approach the Cramer-Rao Bound(CRB)with a low Signal-to-Noise Ratio(SNR)threshold and has a higher accuracy.

基于改进灰狼算法优化WLSSVM的短期风功率预测

为提高风功率短期预测的准确率,提出一种基于改进灰狼算法优化加权最小二乘支持向量机(Weighted Least Squares Support Vector Machine,WLSSVM)的短期风功率预测方法。采用C-C法对风功率时间序列的嵌入维数进行了计算,根据计算结果确定短期风速预测输入量与输出量的关系。利用Tent映射和参数非线性调整策略对灰狼算法进行改进,得到了优化性能更强的改进灰狼优化(Improved Grey Wolf Optimization,IGWO)算法,并利用测试函数验证了IGWO算法能够加快迭代收敛,提高计算精度。采用IGWO算法对WLSSVM的惩罚系数和核参数进行优化,建立基于IGWO-WLSSVM的短期风功率预测模型。采用某风电场春夏两个不同季节的风功率数据进行算例分析,结果表明,所提短期风功率预测结果的平均相对误差、均方根误差和最大相对误差更小,风功率预测精度和预测结果的稳定性均优于其他方法,验证了所提方法的有效性和实用性。

A STUDY ON THE WEIGHT FUNCTION OF THE MOVING LEAST SQUARE APPROXIMATION IN THE LOCAL BOUNDARY INTEGRAL EQUATION METHOD

The meshless method is a new numerical technique presented in recent years.It uses the moving least square(MLS)approximation as a shape function.The smoothness of the MLS approximation is determined by that of the basic function and of the weight function,and is mainly determined by that of the weight function.Therefore,the weight function greatly affects the accuracy of results obtained.Different kinds of weight functions,such as the spline function, the Gauss function and so on,are proposed recently by many researchers.In the present work,the features of various weight functions are illustrated through solving elasto-static problems using the local boundary integral equation method.The effect of various weight functions on the accuracy, convergence and stability of results obtained is also discussed.Examples show that the weight function proposed by Zhou Weiyuan and Gauss and the quartic spline weight function are better than the others if parameters c and α in Gauss and exponential weight functions are in the range of reasonable values,respectively,and the higher the smoothness of the weight function,the better the features of the solutions.

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.

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.

结合WLS滤波与还原控制因子的图像去雾

雾天退化图像的复原过程中,针对大气光幕和大气亮度估计不准确导致光晕效应、偏色现象和对比度不足等问题,提出一种结合WLS(weighted least square)滤波与还原控制因子的去雾算法.首先分析WLS滤波器的原理和性能,并用于大气光幕的有效提取;其次利用Sobel算子检测二值化图像边缘,将边缘数目与像素均值同时作为四叉树空间索引的依据,提高大气亮度的估计准确性;最后分析天空出现颜色失衡现象的原因,引入还原控制因子改善视觉效果.实验结果表明,去雾后图像的平均梯度整体提高58.03%,信息熵提高2.88%,运行时间节省50%以上.该方法对含有浓雾、薄雾以及天空等深度复杂的远景图像、近景图像均能得到高对比度、可视度和色彩保真度的恢复效果.

基于MPSO-WLS-SVM的矿井瓦斯涌出量预测模型研究

为有效预防瓦斯灾害,以预测矿井瓦斯涌出量为研究目的,提出经改进的粒子群算法(MPSO)优化的加权最小二乘支持向量机(WLS-SVM),并用其预测非线性动态瓦斯涌出量。算法通过对WLS-SVM的正则化参数C和高斯核参数σ寻优,建立基于MPSO优化的WLS-SVM的瓦斯涌出量预测模型,并利用某矿井监测到的各项历史数据进行实例分析。试验结果表明:该预测模型预测的最大相对误差为5.99%,最小相对误差为0.43%,平均相对误差为2.95%,较其他预测模型有更强的泛化能力和更高的预测精度。

基于多准则分区和WLS-PDIPM算法的有源配电网状态估计

针对复杂有源配电网三相不平衡状态估计计算速度较慢与计算精度较低的问题,提出了一种基于多准则分区和基本加权最小二乘法—原对偶内点法(WLS-PDIPM)混合算法的状态估计方法。基于对有源配电网中实时量测、虚拟量测和伪量测的配置分析,建立了适用于复杂有源配电网状态估计的多准则分区优化模型,该模型综合考虑了分区后各子区域规模均衡、量测冗余度均衡及伪量测平均误差均衡。通过高级量测体系(AMI)全量测点实现各子区域完全解耦,有效减小了系统规模和雅可比矩阵阶数。所提方法将WLS与PDIPM的优点相结合,在提高算法精度的同时减少了计算时间。仿真算例结果表明所提方法可实现对复杂有源配电网的合理分区,有效提高了状态估计的计算速度与求解精度。

基于WLS-ABC算法的工业机器人参数辨识

针对工业机器人在不带负载时的动力学参数辨识问题,提出了一种基于加权最小二乘法与人工蜂群算法(WLS-ABC)的辨识算法.首先计及关节摩擦特性,推导出机器人动力学模型的线性形式;接着设计五阶傅里叶级数作为激励轨迹,采集辨识实验数据;然后根据文中辨识算法,采用加权最小二乘法得到待辨识参数初始解,并以蜂群为搜索单位,通过群体之间的信息交流与优胜劣汰机制找到全局最优参数;最后对得到的模型进行验证与分析.实验结果表明,通过文中辨识算法得到的预测力矩与测量力矩有较高的匹配度,所建立的模型能够反映机器人的动力学特性.

含未知输入非线性系统的扩展平方根容积卡尔曼滤波算法

针对工程实际应用中存在的未知输入会导致经典的非线性滤波器状态估计精度下降甚至滤波发散的问题,提出了一种基于最小方差无偏估计(minimum variance unbiased estimation,MVUE)准则的扩展平方根容积卡尔曼滤波(extended square-root cubature Kalman filter,ESRCKF)算法。首先,结合上一时刻未知输入估计值对状态一步预测值进行修正,得到含未知输入条件下的状态预测值。其次,设计新息并采用加权最小二乘(weighted least squares,WLS)法获取当前时刻未知输入的无偏估计。最后,通过最小化协方差矩阵的迹,同时采用拉格朗日乘子法和舒尔补引理得到系统状态的最小方差无偏估计。仿真结果表明,相比于现有的非线性滤波算法,ESRCKF算法提高了在处理含未知输入非线性系统时的状态估计精度,并能同时实现系统状态和未知输入的最优估计,验证了该算法的有效性。

基于WLS-SVM回归模型的电力负荷预测

针对电力系统年用电量增长的特点,提出一种基于加权最小二乘支持向量机(LS-SVM)的电力负荷预测模型。与标准LS-SVM的电力预测方法比较,该模型能通过设置训练样本权重比例,实现样本优化选择,达到历史数据"重近轻远"的学习效果,从而能有效提高预测精度。通过具体实例验证,WLS-SVM模型预测精度明显优于标准LS-SVM模型,说明本文模型实现容易,鲁棒性好,预测精度高。

未知信号传播速度的TDOA定位方法研究

研究了未知信号传播速度时的到达时间差(Time-Difference-Of-Arrival,TDOA)定位问题,提出两种联合估计信号传播速度和目标位置的定位方法。第一种方法为两步加权最小二乘方法。在该方法中,首先不考虑变量之间关系,得到一个关于未知变量的初始加权最小二乘估计。为改进第一步估计的性能,第二步考虑第一步估计中变量之间的关系,将其转换为一个标准的广义信赖域子问题,最终获得更高精度的估计性能。第二种方法为半正定松弛方法,通过构建非线性非凸加权最小二乘问题,然后利用半正定松弛技术将其松弛为凸的半正定规划问题,容易求解。仿真结果表明,所提两种方法均能够在高斯噪声下,且噪声不太大时达到克拉美-罗界。

基于WLS-SVM的加速度计动态模型参数辩识

提高加速度计动态模型参数辨识精度,对研究和改善加速度计动态特性有重要作用。针对加速度计的非线性影响其动态模型参数辨识精度的问题,提出了一种基于加权最小二乘(WLS)和支持向量机(SVM)的加速度计动态模型参数辩识方法,该方法针对包含线性部分和非线性项的加速度计二阶非线性动态模型,利用WLS辩识加速度计动态模型的线性部分参数,并采用SVM估计加速度计动态模型的非线性特性,通过迭代和最小化所构建的误差准则函数,实现加速度计动态模型参数最优辨识。仿真实验和加速度计绝对法冲击激励校准实验表明,该方法能够减小加速度计非线性对动态模型参数辩识精度的影响,所得加速度计动态模型参数辨识结果具有较高的精度。

基于WLS-SVM标准差σ预测的产品过程质量控制方法研究

及时、准确地预测加工过程产品质量标准差σ,对于及时判断工序状态、调整加工过程因素,进而提高产品过程质量等具有重要意义。文章提出了一种基于加权最小二乘支持向量机(WLS-SVM)的时间序列预测新方法,该方法采用了结构风险最小化原则,较好地避免了人工神经网络等智能方法在小样本学习、预测过程中存在的过学习、泛化能力弱等缺点;并采用"重近轻远"的权重设置原则,提高了预测的精度。实验表明,采用该方法对产品过程质量标准差σ进行预测切实可行,对于产品过程质量控制具有重要意义。

基于WPA与WLS-SVM方法的化工过程故障诊断

化工过程存在变量多,系统复杂,非线性等特点,这使得常规的故障诊断方法具有模型难以建立、参数难以调整、收敛速度慢、多故障无法正确识别等局限性。以标准化模型TE过程为实验平台,结合模型特点以及在故障诊断中的难点,采用小波包算法(WPA)滤除过程数据噪声,恢复原始信号,数据缩放统一数据量度,最小二乘支持向量机(WLS-SVM)为模型,K聚类方法确定权值系数,交叉验证来选择模型参数,提出了一系列具体的解决方案。通过仿真实验,验证了算法的有效性,以及在过程故障诊断中的可行性,并在最后提出了一些展望。

基于时序聚类及改进Pettitt的系统谐波阻抗估计

针对谐波电压与电流数据出现严重无序性,导致常规非干预式方法难以对系统谐波阻抗进行准确的实时估计,提出一种基于时序聚类及改进Pettitt的系统谐波阻抗估计方法。首先,运用时序聚类中互相关系数原理使谐波电压和电流序列平移对齐并筛选出强相关性的数据。然后,为了规避阻抗突变的影响,提出基于二元分割的Pettitt方法对阻抗突变点进行检验。最后,使用再生权最小二乘法,通过赋权重系数进一步减小异常值对结果的影响。仿真与实例结果表明,本文方法可以有效降低背景谐波波动和阻抗突变对系统谐波阻抗估计带来的误差。

岩石抗剪强度参数的加权线性回归估计与验证

研究了岩石抗剪强度参数的优化估计方法,针对岩石抗剪强度数据中存在的异方差问题,引入了加权线性回归方法。在岩石抗剪强度的线性回归分析中,一般假定因变量观测值的观测误差都服从同一正态分布,但忽略了三轴强度数据中所存在的异方差问题。利用位于四川省西南地区的露天砂岩为研究对象,获取砂岩在不同围压下的三轴强度数据并应用加权线性回归方法进行分析并解决了数据的异方差问题。首先介绍了岩石抗剪强度的理论基础和相关的统计方法,然后详细阐述了加权线性回归的概念及应用范围。提出了加权线性回归的理论公式和检验方法,并解释了加权回归中的权重定义和计算方法。最后通过位于四川省西南地区的露天砂岩的试验数据进行验证,研究结果证明了加权最小二乘法在岩石抗剪强度参数估计中的有效性,研究成果可为抗剪强度参数的选取提供相关的理论依据。