基于最小二乘原理的分段曲线拟合法

在最小二乘原理的基础上，运用实测数据点的分段曲线拟合法，探讨相应的模型以及用不同类型的曲线同时拟合数据点的具体应用；对一实例，应用MATLAB编程设计，完成模型的求解、显著性检验等，可以得到拟合精度比较高的拟合曲线。该方法原理简便，其模型易用MATLAB编程求解。     

无网格方法的应用前景

无网格方法是近年来出现的一种比较新的数值方法，它只需节点信息，不需将节点连成单元。本文介绍了其基本思想以及发展进程，着重分析了当前主要的几种无网格方法的发展情况及特点，通过典型算例的计算和比较，反映了无网格方法具有较好的精度，并对无网格方法的前景进行了展望。     

声学法二维温场重建算法及仿真分析

阐述了声学法二维温场重建思想，并且应用最小二乘法和声波折射效应在matlab环境下对工业炉二维温场进行了重建仿真，最后分析了重建结果。     

椭圆边值问题的Galerkin法及最小二乘法处理

研讨椭圆边值问题的Galerkin法，并对导数作出最小二乘法处理从而得到超收敛结果。     

抛物问题的Galerkin法及最小二乘处理

讨论了抛物问题的Galerkin法，并应用最小二乘法处理有限元解，得到超收敛结果。     

用最小二乘拟合法量化手臂运动控制中肌电与力的动态对应关系

肌肉等长收缩时肌电积分与肌力间已被认定存在着线性关系。肌肉非等长收缩过程中肌电与肌力间的对应关系则难以定量表达。然而，为了探入我们对人体运动神经控制内在机制的量化分析，不可避免地我们要对肌肉动态收缩中肌电与肌力间的对应关系有定量的了解。本文介绍作者在手臂指点动作的神经-运动控制研究中建立起以环节转动方向为参照的协同肌-对抗肌共同活动的肌力模型，用数理统计方法中之最小二乘拟合法求解肌电与肌力间动态对应关系的过程。     

Characterizing and estimating rice brown spot disease severity using stepwise regression,principal component regression and partial least-square regression

Detecting plant health conditions plays a key role in farm pest management and crop protection. In this study, measurement of hyperspectral leaf reflectance in rice crop (Oryzasativa L.) was conducted on groups of healthy and infected leaves by the fungus Bipolaris oryzae (Helminthosporium oryzae Breda. de Hann) through the wavelength range from 350 to 2 500 nm. The percentage of leaf surface lesions was estimated and defined as the disease severity. Statistical methods like multiple stepwise regression, principal component analysis and partial least-square regression were utilized to calculate and estimate the disease severity of rice brown spot at the leaf level. Our results revealed that multiple stepwise linear regressions could efficiently estimate disease severity with three wavebands in seven steps. The root mean square errors (RMSEs) for training (n=210) and testing (n=53) dataset were 6.5% and 5.8%, respectively. Principal component analysis showed that the first principal component could explain approximately 80% of the variance of the original hyperspectral reflectance. The regression model with the first two principal components predicted a disease severity with RMSEs of 16.3% and 13.9% for the training and testing dataset, respec-tively. Partial least-square regression with seven extracted factors could most effectively predict disease severity compared with other statistical methods with RMSEs of 4.1% and 2.0% for the training and testing dataset, respectively. Our research demon-strates that it is feasible to estimate the disease severity of rice brown spot using hyperspectral reflectance data at the leaf level.     

某连续梁桥预应力孔道摩阻损失试验研究

结合某连续梁桥的孔道摩阻损失试验,介绍了预应力摩阻试验的内容和方法,并利用最小二乘法计算出合理的孔道摩阻系数和偏差系数值,其结果表明试验原理与计算方法是有效的,可以为预应力张拉质量提供正确的依据。     

A HIERARCHICAL IDENTIFICATION ALGORITHM FOR THE EXTENDED EXPONENTIAL MODEL

A new hierarchical identification algorithm is proposed for solving the identi-fication problem of the extended exponential model,which is used frequently in ecological,social and economical systems.By using the zero character of the optimal Lagrangianmultipliers of the equivalent identification problem,a two-level structure of the algorithmis derived first.Then,the convergence and the correspondence with the conventionalnonlinear approaches of the algorithm are proved.The results of simulation and applica-tion show that its convergent rate is greatly higher than that of the L-Mmethod.     

残差在数学建模中的应用

文章在线性系数的最小二乘法处理的基础上,通过对残差的分析,选择合适的非线性周期函数对残差进行再次拟合。该方法弥补了线性系数最小二乘法的不足,获得了周期性系统误差的信息,提升了电涡流传感器的精度。