用主成分法求解秩亏自由网的研究

结合多数平差和主成分估计理论,导出误差方程中含多重共线性关系时求解未知数的公式,并证明主成分估计的解是最小二乘最小范效解。由此,将主成分估计推广到秩亏自由网平差中,导出求解未知多数及其协因数的公式,并据主成分估计演绎出用附有条件的参数平差法求解秩亏自由网的条件方程（基准在达式）。     

DETECTING AND ADJUSTING FOR NON-LINEARITIES IN CALIBRATION OF NEAR-INFRARED DATA USING PRINCIPAL COMPONENTS

A new regression method for non-linear near-infrared spectroscopic data is proposed.The technique isbased on a model which is linear in the principal components and simple functions(squares and products)of them.Added variable plots are used to determine which squares and products to incorporate into themodel.The regression coefficients are estimated by a Stein estimate which shrinks towards the estimatedetermined by the first several principal components and the selected non-linear terms.The technique isnot computationally intensive and is appropriate for routine predictions of chemical concentrations.Themethod is tested on three data sets and in all cases gives more accurate predictions than does linearprincipal components regression.     

稳健估计在人卫激光测距资料预处理中的应用

本文提出一种稳健估计的方法，作为对现有最小二乘方法的改进，对人造卫星激光测距资料进行预处理，判别异常值，估计中误差。该方法将使异常值的剔除更加稳定可靠；在多数情况下，可不借助人工屏幕处理，实现自动化，该方法有５０％崩溃点，且不受端点效应的影响。     

论三角测量单位权方差的先验估计与后验估计

三角洲量单位权方差的先验估值一般用经典菲列罗公式计算。实践中，经常出现三角测量单位权方差的先验估值不等于后验估值的情形．本文根据条件平差的原理，证明了单位权方基的先验估值是有偏估计，经典菲列罗公式是后验估计公式的特殊形式，并推导出了广义菲列罗公式。     

Comparative performance of indicator algorithms for modeling conditional probability distribution functions

This paper compares the performance of four algorithms (full indicator cokriging. adjacent cutoffs indicator cokriging, multiple indicator kriging, median indicator kriging) for modeling conditional cumulative distribution functions (ccdf).The latter three algorithms are approximations to the theoretically better full indicator cokriging in the sense that they disregard cross-covariances between some indicator variables or they consider that all covariances are proportional to the same function. Comparative performance is assessed using a reference soil data set that includes 2649 locations at which both topsoil copper and cobalt were measured. For all practical purposes, indicator cokriging does not perform better than the other simpler algorithms which involve less variogram modeling effort and smaller computational cost. Furthermore, the number of order relation deviations is found to be higher for cokriging algorithms, especially when constraints on the kriging weights are applied.     

A FUSING TECHNIQUE WITH SATELLITE PRECIPITATION ESTIMATE AND RAINGAUGE DATA*

Satellite rainfall estimate can provide rainfall information over large areas,and raingauge can provide point-based ground observations with high accuracy.With the combination of satellite and raingauge data together,the estimated rainfall fields are greatly improved.This combination method,called "fusing technique",is discussed in this paper,and the validation for this technique is accomplished with HUBEX IOP data.     

半参数回归模型中非参数信号的推估--三次样条函数插值法

对于半参数回归模型yi=Xi^Tβ s(ti) e，在文献[1]的基础上考虑其非参数信号s(f)的推估j(f)，从而有利于研究非参数信号；接着给出了s(t)与s^-(t)的偏差大小，从而为推估的准确性提供理论依据；并以实例加以证明。     

SVD方法在场的定量预测中的应用

经SVD分析,截取足够多的预报场和因子场时间系数,使其相互关系代表两场的大尺度联系,预报场时间系数与其奇异向量线性组合估计场能反映原场主要特征.利用最小二乘法得到数值上最接近原场的初值,借助最优化技术,确定合理的系数,建立预测公式,由因子场时间系数预测预报场时间系数,同时订正预报场时间系数a1,a2,……,aN本身的误差和反演过程中分析误差造成的场格点趋势预测的误差.最后将预测的预报场时间系数和对应奇异向量反演为整个场的预报.预报过程重点考虑可预报的大尺度变化,滤去不可预报的小扰动,依据两场主要耦合关系,预测预报场未来的主要变化.     

GMS5红外卫星云图参数化及在降水预测中的应用

从大气探测的基本原理出发,利用2001—2002年4—10月逐时的气象卫星红外云图和地面观测资料,对云图进行参数化估计,得到一些参数化估计结果,分析了不同视场条件下各类参数与降雨强度的关系,发现测站降水强度和其上空一定视场范围内的平均亮温、亮温方差、等效云量、亮温面积指数(1级、5级、6级)关系较明显,并利用最优子集回归方法建立小区域降水强度的预测方程,检验结果表明:利用红外资料估算未来6h的降雨强度其平均准确率在80%以上,分析视场大小对预测效果影响不大。     

H-adaptivity applied to liquefiable soil in nonlinear analysis of soil–pile interaction

This paper is concerned with application of the h-adaptive finite element method to dynamic analysis of a pile in liquefiable soil considering large deformation. In finite element analysis of pile behavior in liquefiable soil during an earthquake, especially considering large deformation of liquefied ground, error due to discretization in the zone near the pile becomes very large. Our purpose was to refine the approximation of the finite element method. The updated Lagrangian formulation and a cyclic elasto-plastic model based on the kinematic hardening rule were adopted to deal with the nonlinearity of the soil. The mixed finite element and finite difference methods together with the u-p formulation and Biot's two-phase mixture theory were used. To improve the accuracy and increase the efficiency of finite element analysis, an h-adaptive scheme that included a posteriori error estimation and h-version mesh refinement was applied to the analysis. The calculated results of effective stress were smoothed locally by the extrapolation method and smoothed stress was used to calculate the L₂ norm of the effective stress error in the last step of the calculation of each time increment. The mesh was refined by a fission procedure based on the indication of the error estimate As a numerical example, a soil–pile interaction system loaded cyclically was analyzed by our method.