椭球面三角形外接大地圆圆心测地坐标的另一种解法

为了在测地坐标系中确定外接大地圆圆心,采用了解非线性方程组的牛顿迭代法,解法简便,易于理解.数据验证表明,由该数值法求解的结果与由解析公式获得的结果完全一致.由此亦表明,一些繁难的大地测量计算也可改用数值法来进行.     

广义非线性动态处理模型及其解算方法

本文针对当今各国高层领导和科学家十分关注并大力倡导的“数字地球”、“数字国家”、“数字城市”、“数字矿山”等科学工程构建中遇到的大量的多源、多维、多类型、多时态、多精度并具有非线性特征的联合数据处理问题的特点,建立了一个广义非线性动态联合数据处理模型及其相应的广义非线性最小二乘模型。针对该模型规模大、维数高的特点,借鉴多变量函数寻优的“变量轮换法”或“因素交替法”的思想、结合无记忆牛顿法,建立了一个解算算法,该算法将大规模的优化问题分解为两个较低规模的优化问题进行解算,降低了问题的规模,借助无记忆牛顿法,减少了存储量,特别适合大规模问题的解算。     

Improved hybrid iterative optimization method for seismic full waveform inversion

In full waveform inversion (FWI), Hessian information of the misfit function is of vital importance for accelerating the convergence of the inversion; however, it usually is not feasible to directly calculate the Hessian matrix and its inverse. Although the limited memory Broyden-Fletcher-Goldfarb-Shanno (L-BFGS) or Hessian-free inexact Newton (HFN) methods are able to use approximate Hessian information, the information they collect is limited. The two methods can be interlaced because they are able to provide Hessian information for each other; however, the performance of the hybrid iterative method is dependent on the effective switch between the two methods. We have designed a new scheme to realize the dynamic switch between the two methods based on the decrease ratio (DR) of the misfit function (objective function), and we propose a modified hybrid iterative optimization method. In the new scheme, we compare the DR of the two methods for a given computational cost, and choose the method with a faster DR. Using these steps, the modified method always implements the most efficient method. The results of Marmousi and over thrust model testings indicate that the convergence with our modified method is significantly faster than that in the L-BFGS method with no loss of inversion quality. Moreover, our modified outperforms the enriched method by a little speedup of the convergence. It also exhibits better efficiency than the HFN method.     

基于插值理论的GRACE卫星精密轨道内插的研究

利用GRACE卫星高采样率精密轨道,进行了拉格朗日插值、牛顿插值和线性插值方法的研究,并对插值结果进行了比较和分析,探讨了插值方法的插值精度及其应用于低轨卫星轨道内插的适用性。     

不等式约束Partial EIV模型的WHP拟牛顿修正解法及其精度评定的SUT法

提出一种确定不等式约束Partial EIV模型解及精度评定的新方法,在总体最小二乘准则下,将附有不等式约束的Partial EIV模型转换为标准最优化问题。采取WHP拟牛顿修正的SQP方法求解,并利用SUT法对参数估值进行精度评定,可以减小迭代次数、提高收敛速度,且精度评定方法简单有效。     

港口工程中非均质层状地基承载力计算方法

在深水码头、防浪堤等大型港口工程建设中常常会遇到构筑物下覆地基由非均质的层状土构成的情况。对于这类非均质层状地基,我国港口工程地基规范推荐采用Hansen 61公式、Hansen 69公式和Sokolovskii数值解法3种方法计算地基的极限承载能力。然而,工程实践中由这3种方法计算得出的地基极限承载力数值往往有较大的差别。考虑到规范的继承性,基于牛顿迭代法,针对3个理论计算公式编制了计算程序,根据长江口深水治理二期工程地质实测资料,运用该计算程序对该地区地基的极限承载能力进行了计算比较。计算结果表明,对于非均质层状地基,在相同地质条件、相同荷载条件下Sokolovskii数值解法得到的承载力数值最大,Hansen 69公式得到的承载力数值最小。     

滑坡动态力学监测及破坏过程案例分析

边坡临滑预警一直是地灾研究的难点与热点问题。本文采用一种力学监测方法(牛顿力监测)对雅安宝兴县某傍山公路边坡进行监测,该边坡位于唐包滑坡老滑坡体下缘边界处。经过4个月的连续监测,获取了大量监测数据,并成功预报了两次局部滑坡。本文首先整合牛顿力监测数据和降雨量监测数据,再将监测曲线与滑坡演化过程进行对比分析,揭示滑坡过程中的力学演化规律,对降雨条件下诱发滑坡的原因进行了分析。然后对牛顿力监测预警成功的案例其临滑预警时长与滑坡体量间的关系进行拟合,发现存在明显的正相关关系。最后讨论了牛顿力监测方法与斋藤模型之间的关联性以及优劣势,并根据各自的特点提出了由面到点的监测预警思路。通过分析,牛顿力监测曲线与滑坡演化过程能较好对应,并可将土质滑坡分为3阶段:(1)牛顿力上升阶段; (2)牛顿力突降阶段; (3)滑坡阶段。本文为牛顿力监测系统的推广提供了实践经验,并为力学监测与位移监测结合的研究提供一个新的思路。     

重力卫星加速度数据的插值算法研究

阐述拉格朗日插值法和牛顿插值法的原理,详细地推导其一次、二次微分通用公式,并分别利用推导出来的微分公式对卫星星历模拟数据进行了相应的插值计算,得到对应的卫星加速度数据。通过比较不同公式的计算结果,验证一次、二次微分公式的正确性,并得到一些有益的结论。     

On Newton-like methods for solving nonlinear equations

Introduction Manymethodsforsolvingnonlinearequations aredescribedindetail[1,2].TheNewtonmethod fortheapproximationofarootofnonlinear equationf(x)=0isanimportantandbasic method,whichconvergesquadratically.The Newtonmethodanditsdeformationsarefocused onallt…     

The Terrain Correction in a Moving Tangent Space

Conventionally the terrain/topographic reduction is based on the Bouguer Plate, which is flat and extends in the local tangent plane/horizontal plane to infinity. Here we aim at an error estimate of such a planar approximation of the Newton integral of the type of a disturbing potential and gravitational disturbance as linearized forms of the gravitational potential and the modulus of gravitational field intensity. To effect this quality control of the conventional terrain reduction, we first transform the spherical Newton functional from an equatorial frame of reference to an oblique meta-equatorial frame of reference with the evaluation point as a meta-North pole, and then by means of an oblique equiareal map projection of the azimuthal type to a tangent plane which moves at the evaluation point. The first term of these transformed Newton functionals is the planar approximation. The difference between the exact Newton kernels and their planar approximation are plotted and tabulated in Tables 1-3. Three configurations are studied in detail: for points at radius r = 10 km around the evaluation point the systematic error varies from 0.26% for a spherical height difference of the order of H – H* = 5 km, more than 0.80% for a spherical height difference of the order of H – H* = 1 km, and more than 1.60% for a spherical height difference of H – H* = 500 m. In contrast, the systematic error for spherical height difference H – H* = 1 km at a distance of r = 1000 km from the evaluation point increases to 44%. Indeed, the newly derived exact Newton kernels which are of the convolution type and are represented in the tangent space moving with the evaluation point can be preferably used with little extra computational effort.