AN ASSESSMENT OF THE MESHLESS WEIGHTED LEAST-SQUARE METHOD

The meshless weighted least-square (MWLS) method was developed based on the weighted least-square method. The method possesses several advantages, such as high accuracy, high stability and high e?ciency. Moreover, the coe?cient matrix obtained is symmetric and semi- positive de?nite. In this paper, the method is further examined critically. The e?ects of several parameters on the results of MWLS are investigated systematically by using a cantilever beam and an in?nite plate with a central circular hole. The numerical results are compared with those obtained by using the collocation-based meshless method (CBMM) and Galerkin-based meshless method (GBMM). The investigated parameters include the type of approximations, the type of weight functions, the number of neighbors of an evaluation point, as well as the manner in which the neighbors of an evaluation point are determined. This study shows that the displacement accuracy and convergence rate obtained by MWLS is comparable to that of the GBMM while the stress accuracy and convergence rate yielded by MWLS is even higher than that of GBMM. Furthermore, MWLS is much more e?cient than GBMM. This study also shows that the instability of CBMM is mainly due to the neglect of the equi- librium residuals at boundary nodes. In MWLS, the residuals of all the governing equations are minimized in a weighted least-square sense.

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-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。

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。

Prediction of earth rotation parameters based on improved weighted least squares and autoregressive model

In this paper, an improved weighted least squares （WLS）, together with autoregressive （AR） model, is proposed to improve prediction accuracy of earth rotation parameters（ERP）. Four weighting schemes are developed and the optimal power e for determination of the weight elements is studied. The results show that the improved WLS-AR model can improve the ERP prediction accuracy effectively, and for different prediction intervals of ERP, different weight scheme should be chosen.

基于APSO–WLS–SVM的含瓦斯煤渗透率预测模型

为了较准确预测含瓦斯煤渗透率,有效预防瓦斯安全事故,提出自适应粒子群算法(APSO)优化的加权最小二乘法支持向量机(WLS–SVM)算法。根据对含瓦斯煤渗透率的相关理论及文献研究分析,选取有效应力、瓦斯压力、温度和抗压强度作为主要特征指标,采用APSO算法对WLS–SVM模型的组合参数(C、σ)寻优,建立APSO–WLS–SVM含瓦斯煤渗透率预测模型。结合现场实测资料中的40组数据作为训练样本,其余10组为预测样本,对该模型进行训练与检验,并将其预测结果与利用PSO–WLS–SVM和WLS–SVM模型的预测结果进行对比。结果表明:APSO-WLS-SVM模型的预测效果优于另外2个模型,提高了煤体渗透率的预测性能与泛化能力。

对基于贝叶斯证据框架下WLS-SVM中期负荷预测的研究

本文提出了一种基于贝叶斯证据框架下加权最小二乘支持向量机(Weighted Least Squares Support Vector Machine,WLS-SVM)的短期负荷预测模型和算法。在对历史负荷数据进行完预处理基础上,分析影响负荷变化的重要因素,然后选择最佳的输入数据作为LS-SVM训练模型的输入向量。通过贝叶斯证据三层推断寻找到模型的最佳参数:第一层推断确定LS-SVM的权向量w和偏置值b,第二层推断确定模型的超参数γ,第三层推断确定核函数的超参数σ。为了提高模型的鲁棒性,赋予了每个样本误差不同的权系数,建立了具有良好泛化性能的WLS-SVM回归模型,从而进一步提高了模型预测的精度。采用上述方法对一固定预测区电网中期负荷进行了预测,结果证明了该方法具有良好的预测效果。

WLS filter for reducing atmospheric effects in spaceborne SAR tomography

A new approach was presented to eliminate the atmosphere-induced phase error utilizing only the single look complex(SLC) synthetic aperture radar(SAR) image set. This method exploited the space-invariance characteristic of phase error components contained in image pixels and estimates the phase error using the weighted least-squares(WLS) filter. Actually, this sort of method can be classified as autofocus algorithm which was generally applied in airborne SAR 2-D imaging to compensate the phase error introduced by airplane's nonideal motion. Real data processing, which is relevant to Honda center and Angel stadium of Anaheim test-sites and acquired by Envisat-ASAR during the period from June 2004 to October 2007, was carried out to evaluate this WLS estimation algorithm. Experimental results show that the phase error estimated from WLS filter is very accurate and the focusing quality along NSR dimension is improved prominently via phase correction, which verifies the practicability of this new method.

观测站误差下外辐射源雷达TS-WLS定位算法

多基外辐射源定位系统中,观测站位置误差严重影响目标定位精度。为此,提出一种改进的两步加权最小二乘的单站外辐射源雷达到达时差定位算法。首先,通过引入辅助变量将非线性量测方程线性化,将观测站位置量测噪声统计特性融入定位算法中从而获得目标的位置估计;在此基础上,根据辅助变量与目标位置之间的关联性构建关联最小二乘估计模型进一步提高目标的定位精度;最后,推导该算法的理论估计误差和克拉美罗下界。理论分析和仿真结果均表明:在较高噪声时,改进算法对近场目标和远场目标的定位精度均可达到克拉美罗下界。

基于观测站精确距离信息的多站时差定位方法

对于空中机动平台,观测站位置误差的存在,使得传统时差定位方法的精度不能满足高精度定位需求。针对观测站位置误差下的多站时差定位问题,提出一种基于观测站精确距离信息的高精度时差定位方法。不同于传统的两步加权最小二乘(two step weighted least squares,TS-WLS)算法,该算法在加权最小二乘时直接对目标位置估计的误差进行估计,避免了开方、平方等非线性运算。仿真实验结果表明,引入观测站精确距离信息能够大幅提升目标定位精度,所提算法具有较强的噪声适应能力,能够在观测站位置误差较大的情况下实现高精度时差定位。

基于5G+UWB的室内定位算法研究

第五代通信技术(5th-Generation,5G)为室内定位领域带来了新的可能性,超宽带(ultra wide band,UWB)定位技术与5G定位技术都具有带宽大、频率高的特性,但是定位性能却略有差异.针对单一传感器定位的准确性、稳定性差的问题,本文提出了5G+UWB的融合定位算法,构建了基于到达时间差(time difference of arrival,TDOA)的5G室内定位、基于三边定位算法的UWB室内定位以及基于融合定位算法的5G+UWB室内定位模型.首先验证了通过加权最小二乘(weighted least squares,WLS)算法得到的各单系统的初步定位结果,之后验证了结合Taylor级数展开法得到的改进后定位结果.在此基础上,进一步对通过融合算法将两个单系统定位结果进行融合后的组合定位结果进行实验验证.实验结果表明:UWB单系统定位结果呈现准确性较低、稳定性较高的特点,5G单系统定位结果呈现准确性较高、稳定性较低的特点,二者组合后可得到准确性和稳定性都相对较好的定位结果,组合系统定位精度最高可达0.22 m,最低可达0.73 m,可实现亚米级定位.

A two-step weighted least-squares method for joint estimation of source and sensor locations: A general framework

It is well known that the Two-step Weighted Least-Squares(TWLS) is a widely used method for source localization and sensor position refinement. For this reason, we propose a unified framework of the TWLS method for joint estimation of multiple disjoint sources and sensor locations in this paper. Unlike some existing works, the presented method is based on more general measurement model, and therefore it can be applied to many different localization scenarios.Besides, it does not have the initialization and local convergence problem. The closed-form expression for the covariance matrix of the proposed TWLS estimator is also derived by exploiting the first-order perturbation analysis. Moreover, the estimation accuracy of the TWLS method is shown analytically to achieve the Cramér-Rao Bound(CRB) before the threshold effect takes place. The theoretical analysis is also performed in a common mathematical framework, rather than aiming at some specific signal metrics. Finally, two numerical experiments are performed to support the theoretical development in this paper.

Defect detection on button surfaces with the weighted least-squares model

Defect detection assurance on production lines machine-vision-based surface is important in quality This paper presents a fast defect detection method using the weighted least-squares model. We assume that an inspection image can be regarded as a combination of a defect-free template image and a residual image. The defect-free template image is generated from training samples adaptively, and the residual image is the result of the subtraction between each inspection image and corresponding defect-free template image. In the weighted least-squares model, the residual error near the edge is suppressed to reduce the false alarms caused by spatial misalignment. Experiment results on different types of buttons show that the proposed method is robust to illumination vibration and rotation deviation and produces results that are better than those of two other methods.

A novel adaptive image zooming scheme via weighted least-squares estimation

A critical issue in image interpolation is preserving edge detail and texture information in images when zooming. In this paper, we propose a novel adaptive image zooming algorithm using weighted least-square estimation that can achieve arbitrary integer-ratio zoom （WLS-AIZ） For a given zooming ratio n, every pixel in a low-resolution （LR） image is associated with an n x n block of high-resolution （HR） pixels in the HR image. In WLS-AIZ, the LR image is interpolated using the bilinear method in advance. Model parameters of every n×n block are worked out through weighted least-square estimation. Subsequently, each pixel in the n × n block is substituted by a combination of its eight neighboring HR pixels using estimated parameters. Finally, a refinement strategy is adopted to obtain the ultimate HR pixel values. The proposed algorithm has significant adaptability to local image structure. Extensive experiments comparing WLS-AIZ with other state of the art image zooming methods demonstrate the superiority of WLS-AIZ. In terms of peak signal to noise ratio （PSNR）, structural similarity index （SSIM） and feature similarity index （FSIM）, WLS-AIZ produces better results than all other image integer-ratio zoom algorithms.

基于误差因子的改进WLS超宽带定位算法

为提高非视距场景下超宽带(ultra‑wideband,UWB)定位精度,本文提出一种基于误差因子的改进加权最小二乘(weighted least square,WLS)算法.该算法利用测距值和实时信道冲激响应特征训练1维卷积神经网络,实现误差因子的准确预测;基于预测得到的误差因子设计改进WLS算法的加权矩阵,赋予不同基站合理的权重,以改善非视距场景下UWB定位性能.通过实测采集静态和动态定位数据对改进WLS算法进行性能验证.实验结果表明:视距场景下,改进WLS算法与最小二乘(least square,LS)算法、WLS算法定位性能相近;非视距场景下,改进WLS算法明显优于LS算法、WLS算法,能够有效抑制非视距误差.

基于迭代最小二乘的水下三维高鲁棒性定位算法

为解决基于空间角信息水下3维定位中,闭式解算法中定位性能无法达到克拉默-拉奥界(CRLB)和牛顿迭代算法初始值选取问题,该文利用一种基于迭代最小二乘的高鲁棒性算法修正闭式解的残差项与选取迭代算法的初始值。利用伪线性加权最小二乘算法得到闭式解作为正则化修正迭代法的初始值,将迭代结果修正闭式解算法的残差项,通过迭代最小二乘法的交替运算,得到稳定精确的解。通过仿真验证了基于迭代最小二乘算法的高鲁棒性,消除伪线性加权最小二乘算法中残差项选取的不利影响,解决了迭代法初始值选取问题,得到与收敛情况下迭代法相近的定位性能。