引入模型误差的非线性回归模型

在第一类非线性回归模型中,经常出现病态问题,它严重影响计算结果的精度。提出了一种引入模型误差求解部分参数的方法,这种方法可以改变病态性质,提高对部分参数的求解精度。通过算例来检验这种方法的可行性并探讨它的使用范围。     

多视角理解约束平差法

为了深层次地揭示附有限制条件的间接平差(本文简称约束平差)的性质,以便更好地发挥约束平差在实际测量数据处理中的重要作用,从多个视角对约束平差这一基础平差方法进行理论分析。研究结果如下：给出了约束平差问题的间接平差法求解过程;推导出了结论更简单、结构更清晰的约束平差两步法算法;从“新息”角度分析了两步法约束平差与序贯平差、Kalman滤波的有趣联系;采用Fisher-Neyman分解定理证明了无约束解是原始观测的充分统计量;将无约束解视作“伪观测”,可以为理解约束平差提供新的视角;从条件正态分布的角度对两步法约束平差进行了重新推导;证明了约束解为无约束解在约束方程所定义子空间上的正交投影;介绍了一种观测方程不可解的情况下获得无约束解的新方法,从而扩展了两步法约束平差的适用范围。研究表明：拥有诸多优良性质的约束平差将在处理海量、复杂、动态的测绘数据时发挥更大作用。     

不规则重磁测线网误差模型的约束最小二乘平差

传统实用的海洋重力、磁力测线网平差方法主要为规则测线网设计,并只就线偏差进行调整,用于处理航次数据之间的拼接时效果不理想。为了解决重磁测线数据拼接和建库工作中碰到的误差难以调平的问题,设计、建立了不规则海洋重磁测线网的任意复杂误差模型的最小二乘平差方法,将线偏差纳入到任意复杂(如非线性和周期性)的误差模型中,归纳出最小二乘条件方程系数矩阵的直接构制法。针对可能出现的解不稳定,放弃不易实用的权矩阵,引入两种解决方法:先验确定部分测线误差分布的固定测线法和视误差大小实施系数矩阵对角线微扰动的泛约束法。     

基于验后方差估计原理探测与剔除粗差

将抗差估计的思想融入到粗差探测的算法中,设计出对模型误差特别是粗差具有抵抗能力的粗差探测算法。应用最小二乘法来计算观测值的参数、残差、协因数阵及单位权的初值,再根据残差和有关的参数,按所选择的权函数,计算每个观测值的权,经过迭代计算求得观测值的残差,按照统计检验的方法剔除粗差。通过实验证明,基于验后方差估计原理导出的选权迭代具有很强的粗差探测能力。     

基于LM方法的单位四元数光束法平差模型解算

以单位四元数描述遥感影像共线条件方程,建立基于单位四元数的光束法平差模型。针对共线条件方程的非线性问题,基于LM(Levenberg-Marquardt)方法解算单位四元数光束法平差模型,并引入丹麦法实现无人机影像外方位元素的抗差估计。基于仿真数据和无人机影像对该方法进行了验证,结果表明:与基于单位四元数的无初值依赖算法进行比较,LM方法具有与单位四元数法相当的可靠性;引入丹麦法方法后可消除粗差观测值对参数估计的不利影响,得到较高精度的外方位元素估值。     

基于仿射变换的数字影像内定向的误差控制分析

数字化摄影测量生产中的误差来源众多,尤其是系统误差常常很突出。针对这个问题,首先深入分析了附有未知数的仿射变换控制模型参数的误差估计,然后利用误差传播定律和误差综合原理,推导出了任意非检控点经仿射变换后输出数据精度的计算公式,并通过数值分析从理论上验证了用四个角框标进行数字影像内定向是最佳误差控制方案。     

赋双平滑参数的广义补偿最小二乘估计

基于补偿最小二乘法思想,研究推导了半参数模型解算的极小化过程中,在残差和补偿项均赋予平滑参数的广义补偿最小二乘估计解的形式及其均方误差计算公式;模拟算例表明:在这种规则下,不仅可以克服病态性对半参数模型解的影响,而且也可以正确分离系统误差。新规则下,要求赋予的两个平滑参数之和等于1,各平滑参数严格限定在区间(0,1],从而使平滑参数的选择范围得到大幅缩小,为本法的应用提供了有利条件。     

海洋重力测量中系统误差的补偿研究

本文在分析总结海洋重力测量中的主要误差源基础上,从纯数学角度建立起能够反映海洋重力观测中系统误差变化规律的误差模型及其相应的测线网平差模型,分别提出两种补偿系统误差的解算方法,即自检校平差法和验后补偿法,并详细讨论了求解过程中的秩亏现象、误差模型的选择、附加参数权的确定以及系统误差补偿效果的显著性检验等一系列应用中的具体问题,最后本文使用一个实际观测网数据验证了两种补偿方法的有效性和可靠性。     

病态半参数回归模型的岭估计求解

针对半参数回归模型求解过程可能出现的法方程病态问题,提出了用岭估计原则改进半参数模型的求解。通过模拟算例将岭估计解法和其他方法进行了比较,结果表明,岭估计解法能较好地解决半参数回归模型求解过程中的病态问题。     

条带拼接网平差参数的快速解算方法

由于多波束测深的海量数据,在基于ping的条带拼接网平差过程中,法方程的系数矩阵将会相当巨大,因此大型法方程的解算是实现条带拼接网平差的关键。结合条带拼接网中ping的分布特点,推导了按ping分段的序贯平差公式,并对此算法进行了优化。实际算例表明,此分解算法可以实现条带拼接网平差参数的快速有效解算。     

Wave deformation and vortex generation in water waves propagating over a submerged dike

The Navier–Stokes equations and the exact free surface boundary conditions are solved to simulate wave deformation and vortex generation in water waves propagating over a submerged dike. Incident waves are generated by a piston-type wavemaker set up in the computational domain. Numerical results are compared with experimental data in order to confirm the validity of the numerical model. The fast Fourier transform and a wave resolution technique are applied to decompose the transformed waves and the higher harmonics. Effects of different parameters on wave transformation and vortex generation are studied systematically. These parameters include the Ursell number, the Keulegan–Carpenter number, the water depth ratio, the Reynolds number, the length aspect ratio of the dike, and the type of dike.     

渤海海域台风风场的变分计算

本文从大气的运动方程出发,利用实测的台风气压场资料和变分调整的方法,计算了进入渤海的台风风场,模拟了台风的不对称结构。经实测资料捡验吻合程度较好。     

A finite difference solution of the shear flow over a circular cylinder

The incompressible viscous shear flow past a circular cylinder is analyzed by solving two-dimensional Navier-Stokes equations and pressure Poisson equation using a finite difference method. The shear flow is calculated for Reynolds numbers from 80 to 1000, and shear parameters up to 0.25. The numerical results indicate that the vortex shedding persists at the shear parameters up to 0.25 for the present Reynolds number range. The Strouhal number and the drag coefficient decrease as the shear parameter increases. There is a transverse force acting from the high velocity side toward the low velocity side in the shear flow.     

Further improvements to the higher-order Boussinesq equations: Bragg reflection

Enhancements for the Bragg reflection are introduced for three sets of 2D higher order Boussinesq equations to improve the prediction of the Bragg reflection. The extension of the approach to other sets of Boussinesq equations is discussed. The analytical solutions for the Bragg reflection over an infinite number of sinusoidal bars are derived for these Boussinesq models and compared to the exact theoretical solution in order to determine the optimized values of the parameters in the new enhancement terms. Numerical simulations are also carried out for the Bragg reflection over a finite number of sand bars and compared with corresponding measurements to validate the enhancements. Comparisons with other forms of Boussinesq models are made to discuss the applicability of different forms of Boussinesq models to rapidly varying topography with sand bars. The effects of the mild slope assumption on the prediction of Bragg reflection and of wave reflection on a plane self are also discussed.     

Bragg Reflection of Waves by Different Shapes of Artificial Bars

Experiments are performed in a wave flume to demonstrate the Bragg reflection of linear gravity waves by artificial bars. Three different artificial bars with rectangular, triangular and rectified cosinoidal shapes are placed discretely on the seabed for measurement of the Bragg reflection. A series of experimental conditions including the number of bars, the pe-riodic bar spacing, the water depth and various wave conditions are tested. Key parameters influencing the Bragg resonances are investigated. The experimental data are compared with the values from both theoretical and numerical models. Some key parameters have proved to be effective in describing the primary resonances. Predictive equations of the charac-teristics for the Bragg reflection are proposed in this paper.     

海洋重磁资料的最小二乘平差处理方法

海洋重磁资料的平差处理是海洋重磁资料处理过程中必不可少的环节之一。从最小二乘算法意义下的平差处理基本理论出发,建立起平羞测线网系统交点误差的方程组,给出了方程组系数矩阵的简单求取方法。理论计算和实际资料处理结果表明,该方法不仅原理简单,计算机实现方便,而且经平差处理后的系统交点误差可以达到最小二乘意义下的极小。最后讨论了实际重磁资料平差处理中任意常数的确定问题。     

Design equations of uplift capacity of circular piles in sands

Uplift capacity of circular piles in sands is one important design parameter for many pile foundations supporting important structures subjected to tensile forces. Even though a number of formulas based on the limit equilibrium or semi-empirical methods are proposed to predict the uplift capacity of piles in sands, there is a major limitation of the methods in obtaining the accurate predictions. In this paper, the computational limit analysis is employed to investigate the uplift capacity of circular piles in sands. The effects of the important variables including pile length and diameter, soil friction angle and unit weight, and roughness factor at soil-pile interface are examined extensively using the dimensionless parameters while the predicted failure mechanisms associated with the parameters are discussed and compared. Approximate statistical design equations of the uplift capacity of circular piles in sands are developed based on the numerically derived solutions and the existing experimental data. It is found that the proposed design equations provide the most accurate prediction of the uplift capacity of circular piles in sands as compared to the existing formulas.     

Numerical modelling of water transport processes in partially-connected tidal basins

In the paper two types of numerical models – a lumped-parameter model and a high-resolution two-dimensional hydrodynamic model – are used to analyse the response of a system of partially-connected tidal basins to inhomogeneous open sea forcing. The equations of the lumped-parameter model, suitable for an arbitrary number of basins with sloping walls, are formulated based on one-dimensional continuity and momentum equations. Numerical solutions to the equations are thoroughly examined, showing the influence of inhomogeneous open sea forcing and of geometrical parameters of the basins on the tidal range and the water transport through the system, with particular emphasis given to inter-basin water exchange and cumulative water transport through basins boundaries. The results of the lumped-parameter model simulations for the tidal basins of the German Wadden Sea are successfully compared with the results of calculations with the two-dimensional hydrodynamic model, which is used to investigate in more detail circulation patterns and the influence of specific local features of inlet bathymetry on the hydrodynamic processes in the study area. The influence of wind on the basins response is discussed as well.     

Statistical Distribution of Depth-Integrated Local Horizontal Momentum for Second-Order Random Ocean Waves in Finite Water Depth

Based on the second-order random wave solutions of water wave equations in tinite water depth, statistical distributions of the depth-integrated local horizontal momentum components are derived by use of the characteristic function expansion method. The parameters involved in the distributions can be all detemained by the water depth and the wavenumber spectrum of ocean waves. As an illustrative example, a fully developed wind-generated sea is considered and the parameters are calculated for typical wind speeds and water depths by means of the Donelan and Pierson spectrum. The effects of nonlinearity and water depth on the distributions are also investigated.