GPS高程拟合的方式及可靠性分析

在范围不大的区域中，高程异常具有一定的几何相关性，GPS高程拟合就是利用这一原理，求解正常高。在解析法求解过程中，首先用最小二乘法确定拟合数学模型的系数，在此基础上计算出待测点的高程异常值。通过实例验证：GPS高程拟合的精度主要取决于GPS大地高的精度、重合点正常高的精度、重合点的分布及拟模型的选择。一般在重合点数量充足且分布均匀的情况下，GPS高程拟合的精度可达到四等水准网的精度要求。     

圆形标志中心子像素定位方法的研究与实现

采用回光反射材料制作圆形回光反射标志，经摄影后得到标志的“准二值影像”；对标志的椭圆影像进行亚像素边缘提取，经最小二乘椭圆拟合后得到标志中心的子像素级位置。试验表明，可以达到0．02像素的定位精度。     

A non-linear stress-stiffness model for geomaterials at small to intermediate strains

A double exponential fitting model (DEFM) capable of expressing the non-linear stress-stiffness relationship of geomaterials has been proposed by Shibuya et al. (1997). The model comprises two material constants; the elastic stiffness at very small strains and the strength, together with other free parameters to determine the complete stress-stiffness relationship. In this paper, the capability of the original function used for DEFM in simulating the tangent stiffness-stress relationship of geomaterials is first discussed. Second, the methods for determining the free model parameters, as well as its conversion to obtain a stress-strain relationship are proposed. The applicability of DEFM to predicting non-linear stress-stiffness relationship is examined in detail in a total of forty-nine fitting cases of compression test data on sedimentary rock, artificial soft rock and soft clay. It is found that the DEFM is effective in expressing the non-linear stress-stiffness relationship of various kinds of geomaterials at small to intermediate strains, say less than 0.5%. The superiority of this model compared to other fitting models currently in use is also demonstrated in some of the fitting cases.     

地图投影的最小二乘二元多项式拟合的误差估计

探讨了在地图投影的最小二乘二元多项式拟合中参考点的分布对拟合误差的影响,提出了一种基于矩阵的秩亏的方法来判断参考点是否在指定次数的二元多项式空间的代数曲线上,并导出在极小范数最小二乘意义下的拟合多项式的误差估计式,公式表明拟合误差和参考点的最小二乘误差无关。     

关于O3层垂直剖面遥感的逆转曲线的数学拟合模式

逆转遥感是当前获得大气O₃层垂直剖面资料的重要方法之一，而逆转曲线的质量对遥感结果的精度至关重要．本文在最小二乘法的基础上，结合逆转曲线的特征，加以适当处理，建立了逆转曲线的拟合数学模式．其性能良好，对研究O₃层垂直剖面的长期演变趋势具有重要意义．     

Pall型摩擦阻尼支撑内力计算方法

从Pall摩擦阻尼器四连杆机构的几何非线性变形特征出发，分析框架位移、支撑刚度、阻尼器摩擦力、阻尼器大小、支撑倾角、支撑屈曲力等对一种改进的Pall摩擦阻尼器-T形芯板摩擦阻尼器支撑的受力特点，拟合出可供设计人员使用的实用计算公式。     

Testing a statistical curve‐fitting procedure for quantifying sediment populations within multi‐modal particle‐size distributions

This paper describes a series of tests designed to evaluate the capacity of a personal computer (PC) based statistical curve‐fitting program called MIX to quantify composite populations within multi‐modal particle‐size distributions. Three natural soil samples were analysed by a Coulter Multisizer, and their particle‐size distributions analysed using MIX software to identify the modes, standard deviations and proportions of their composite populations. The particle‐size distributions of the three natural soil samples were then numerically combined in equal proportions using a spreadsheet program to create synthetic particle‐size distributions of known populations. MIX was then tested on the synthetic particle‐size distributions to see if the modes and proportions it identified were similar to those modes and proportions known to characterize the synthetic particle‐size distributions. The main outcome is that MIX can very accurately describe the modal particle size and proportions of the major composite populations within a particle‐size distribution. However MIX has difficulty in identifying small populations (those contributing <10 per cent of a total particle‐size distribution), particularly when they are located in the central sections of particle‐size distributions, overlain by larger populations, or when positioned in the fine tails of distributions. Despite these minor shortcomings, MIX is a valuable tool for the examination and interpretation of particle‐size data. Copyright © 2005 John Wiley & Sons, Ltd.     

Evaluating soil moisture estimation from ground-penetrating radar hyperbola fitting with respect to a systematic time-domain reflectometry data collection in a boreal podzolic agricultural field

The upper 30 cm of the soil profile, which hosts the majority of the root biomass, can be considered as the shallow agricultural root zone of most temperate crops. The electromagnetic wave velocity in the soil obtained from reflection hyperbolas in ground-penetrating radar (GPR) data can be used to estimate soil moisture (SM). Finding shallow hyperbolas in a radargram and minimizing the subjective error associated with the hyperbola fitting are the main challenges in this approach. Nevertheless, we were motivated by the recent improvements of hyperbola fitting algorithms, which can reduce the subjective error and processing time. To overcome the difficulty of finding very shallow hyperbolas, we applied the hyperbola fitting method to reflections ranging from 27- to 50-cm depth using a 500-MHz centre-frequency GPR and compared the estimated moisture with vertically installed, 30-cm-long time-domain reflectometry (TDR) sensors. We also compared TDR and GPR sample areas in a 2-D plane using different GPR survey types and different hyperbola depths. SM measured with TDR and GPR were not significantly different according to Mann–Whitney's test. Our analyses showed that a root mean square error of 0.03 m³ m⁻³ was found between the two methods. In conclusion, the proposed method might be suitable to estimate SM with an acceptable accuracy within the root zone if the soil profile is fairly uniform within the application depth range.     

Dynamic response of a pile considering the interaction of pile variable cross section with the surrounding layered soil

Assuming that the pile variable cross section interacts with the surrounding soil in the same way as the pile toe does with the bearing stratus, the interaction of pile variable cross section with the surrounding soil is represented by a Voigt model, which consists of a spring and a damper connected in parallel, and the spring constant and damper coefficient are derived. Thus, a more rigid pile–soil interaction model is proposed. The surrounding soil layers are modeled as axisymmetric continuum in which its vertical displacements are taken into account and the pile is assumed to be a Rayleigh–Love rod with material damping. Allowing for soil properties and pile defects, the pile–soil system is divided into several layers. By means of Laplace transform, the governing equations of soil layers are solved in frequency domain, and a new relationship linking the impedance functions at the variable‐section interface between the adjacent pile segments is derived using a Heaviside step function, which is called amended impedance function transfer method. On this basis, the impedance function at pile top is derived by amended impedance function transfer method proposed in this paper. Then, the velocity response at pile top can be obtained by means of inverse Fourier transform and convolution theorem. The effects of pile–soil system parameters are studied, and some conclusions are proposed. Then, an engineering example is given to confirm the rationality of the solution proposed in this paper. Copyright © 2017 John Wiley & Sons, Ltd.