最小二乘配置模型的参数估计

利用罚最小二乘原理构造加权惩罚平方和,导出了最小二乘配置模型中正规化矩阵正定时参数平差的计算方法,用直接法得到了参数和信号的估计量,给出了相应的公式.通过选取合适的平滑因子,能使残差的分布更接近其真实分布,提出了回归系数的检验方法,用实例说明了其有效性.     

An edge-based strain smoothing particle finite element method for large deformation problems in geotechnical engineering

To solve large deformation geotechnical problems, a novel strain-smoothed particle finite element method (SPFEM) is proposed that incorporates a simple and effective edge-based strain smoothing method within the framework of original PFEM. Compared with the original PFEM, the proposed novel SPFEM can solve the volumetric locking problem like previously developed node-based smoothed PFEM when lower-order triangular element is used. Compared with the node-based smoothed PFEM known as “overly soft” or underestimation property, the proposed SPFEM offers super-convergent and very accurate solutions due to the implementation of edge-based strain smoothing method. To guarantee the computational stability, the proposed SPFEM uses an explicit time integration scheme and adopts an adaptive updating time step. Performance of the proposed SPFEM for geotechnical problems is first examined by four benchmark numerical examples: (a) bar vibrations, (b) large settlement of strip footing, (c) collapse of aluminium bars column, and (d) failure of a homogeneous soil slope. Finally, the progressive failure of slope of sensitive clay is simulated using the proposed SPFEM to show its outstanding performance in solving large deformation geotechnical problems. All results demonstrate that the novel SPFEM is a powerful and easily extensible numerical method for analysing large deformation problems in geotechnical engineering.     

Smoothing of digital elevation models and the alteration of overland flow path length distributions

DEM smoothing is a common pre-processing technique used to remove undesirable roughness from a DEM. However, it is hypothesized that smoothing straightens and reduces the length of overland flow paths, which is an important factor controlling modelled time-to-peak flow. Currently, there is a lack of research comparing how different smoothing techniques alter the distribution of overland flow path length. Four low-pass filtering techniques were applied to three fine-resolution LiDAR DEMs of varying relief: the mean filter, the median filter, the Gaussian filter, and the feature-preserving DEM smoothing (FPDEMS) filter, each with different degrees of smoothing. Downslope-distance-to-stream distributions were then derived using D8 and D∞ flow directions and statistically compared to distributions derived from the unsmoothed DEM for each study site. The results indicate that the alteration of flow path length distributions as a result of smoothing is complex. Mean flow path lengths may decrease or increase in response to smoothing, depending on landscape relief and the derivation of flow directions, and generalized flow paths may become longer. The largest increase in mean flow path lengths was 19.2 m using the 21 × 21 median filter and D8 flow directions in the high-relief study site, relative to an unsmoothed mean length of 138.6 m in this site. The largest decrease in mean flow path length was 48.9 m using the 21 × 21 mean filter and D∞ flow directions in the low-relief study site, relative to an unsmoothed mean length of 290.9 m in this site. Furthermore, minimal flow path length alterations were achieved with the Gaussian filter when gentle smoothing is required, and with the FPDEMS filter when moderate to aggressive smoothing is required. These results suggest that an appropriate smoothing method should be chosen based on the relief of the landscape and the degree of smoothing required.     

多面函数法在确定局部似大地水准面中的应用研究

在局部区域似大地水准面的确定中,应用数学模型来求取高程异常,是工程中常用的方法。对正双曲面、倒双曲面、三次曲面三种不同核函数的多面函数拟合法最佳光滑因子的选取问题进行了比较研究。通过对地形复杂矿区工程实例分析,表明了三种方法在地形较复杂区域似大地水准面确定中的可行性。     

GPS单频伪距相位平滑及其单点定位的精度分析

本文基于Hatch滤波方法进行GPS单频伪距相位平滑及其单点定位的研究,针对单频伪距相位平滑的离散性,给出了移动窗口分段平滑方法的具体处理方案,并研制了相应的软件模块。采用自编软件,利用IGS跟踪站观测数据,以静态模拟动态的方式,对GPS单频伪距进行了相位平滑处理和动态单点定位计算,并对单频相位平滑伪距及其单点定位的精度进行了分析。计算结果验证了本文基于Hatch滤波和移动窗口分段平滑的单频伪距相位平滑方法的可行性和有效性。     

中强地震活动区地震年平均发生率确定方法的比较

目前确定地震活动性参数的方法有2种,即潜在震源区划分法和格点空间光滑法.本文针对格点空间光滑法,重点介绍了高斯空间光滑法及其改进后的方法,并对比分析了这些方法的优缺点及适用性;然后以华中为研究区,分别采用高斯空间光滑法和潜在震源区法建立地震活动性模型计算地震年平均发生率,并利用概率地震危险性分析方法计算地震危险性,对比两种方法所得区划结果的差异并分析了引起差异的原因.结果表明:空间光滑法适用于中强地震活动区地震危险性或由背景地震引起的地震危险性的计算;潜在震源区划分法适用于考虑明确的发震构造的地震危险性.将2种方法相结合,综合考虑地震和已知构造信息是判断中强地震活动区地震危险性的可行方法.     

非开挖钻进工程最优穿越曲线的计算

在非开挖钻进工程中,穿越曲线的设计是第一个关键的工作,而只有根据现场条件设计计算出合适的穿越曲线,才能保证整个钻进穿越工程的顺利进行和完成。本文在满足相关规范要求的基础上,建立了穿越曲线的计算模型,并利用MATLAB计算程序对其进行优化计算,确定最短穿越距离,使得穿越工程费用最经济。通过现场工程的验证,该计算模型对现场施工有一定的指导意义。     

曲线拟合背景场在提取大气重力波参数中的缺陷

利用一次东亚副热带高空急流演变过程的高分辨率数值模拟结果,采用Morlet小波分析和Fourier功率谱分析方法,以3阶和4阶曲线拟合为例,研究了提取大气重力波参数时常用的曲线拟合背景场获取方法的缺陷.结果表明:虽然4阶拟合对原始风廓线的拟合程度高于3阶拟合,但基于4阶拟合背景场得到风速扰动垂直廓线后,所提取的重力波参数和实际情况的差异大于3阶曲线拟合方法的结果.因此,不能将背景场对原始风廓线的拟合程度作为判断重力波参数提取准确率的依据.曲线拟合方法在大多数情况下会使扰动场中包含背景场信号,且所包含的背景场信号强度差异很大,同时还会引入虚假波信号.所以在提取大气重力波参数时,采用曲线拟合方法获取背景场存在缺陷,需要设计更合理的背景场获取方法.     

利用无人机激光点云数据更新地形级实景三维地理场景

随着实景三维建设工作的不断推进,对地形级实景三维地理场景的现势性要求日益提高。为解决地理场景更新的及时性和高效性,本文利用无人机获取遥感卫星监测变化图斑点云数据,通过TerraScan点云分类滤波算法批量提取地面点,并采用CloudCompare拉普拉斯平滑算法进行平滑处理,进一步消除离散噪点,输出数字高程模型,最终实现地形级实景三维地理场景更新。试验结果表明,该方法自动化程度高,精度可靠,更新后的实景三维地理场景准确、自然真实。     

用GPS观测值对推断数据进行非线性平滑的模型建立

通过对全球定位系统（GPS）与推断系统（DRS）的联合系统中影响DRS观测值的主要误差来源进行分析，建立了一个表示这些误差的数学模型。并将该模型用于建立一个在DRS观测值存在的情况下，状态向量估计的非线性平滑器。