Unified displacement boundary constraint formulation for discontinuous deformation analysis (DDA)

Displacement boundary constraints in discontinuous deformation analysis (DDA) are applied using stiff penalty springs. A co‐ordinate‐free formulation for displacement boundary constraints is presented here for DDA, which unifies previous derivations for points of fixity, and for points constrained to induce or prohibit block motion in specified directions as a function of location or time. Examples for each type of constraint are used to illustrate the behaviour of the algorithm and provide a link with previous formulations for each case. The new, unified formulation has five benefits: (1) simple to express algorithmically; (2) easy to program and verify; (3) penalty values in different directions may be chosen to allow fixed points, lines, curves or planes; (4) formulation works for 2D and 3D; (5) displacement constraint may be a function of time or location or both. Feedback in the algorithm may induce internal resonance in homogeneously deformable discrete elements used in DDA, and resonance in block‐to‐block contact interactions. Consequently, high mass problems with insufficient damping may suffer from excessive ‘vibrational hammering’, inducing physically implausible behaviour such as elastic rebound. Copyright © 2005 John Wiley & Sons, Ltd.     

基于相对状态符号信息的分布式优化算法

针对网络化多智能体的分布式优化问题,本文讨论一种只利用邻居相对状态的符号信息的分布式算法.该算法不要求与图相关的权重矩阵是双随机矩阵.首先利用优化理论中的惩罚函数法解释该算法,然后分析算法在静态图上的收敛性以及收敛速度.与现有使用邻居相对状态的完整信息的分布式梯度下降算法相比,所提算法的收敛速度并没有本质上降低.另一方面,将所提算法扩展到确定性和随机性的时变图上,并给出相应的收敛性结论.最后,通过数值仿真实验验证算法的有效性.     

约束非负矩阵分解框架下高维自适应粒子群端元提取

传统基于约束非负矩阵分解NMF(Nonnegative Matrix Factorization)的高光谱端元提取算法一般存在两个问题:一方面,以固定惩罚系数方法处理端元提取的约束优化问题,难以较好权衡目标项与约束项间的关系,影响提取效果;另一方面,求解过程通常基于梯度算法,依赖于初始值和步长的设定,容易陷入局部最优。针对这些问题本文提出约束NMF框架下高维自适应粒子群端元提取算法HAPSO(High-dimension Adaptive Particle Swarm Optimization)。该算法在端元距离最小约束的NMF框架下,利用粒子群算法PSO替代原梯度算法以增强全局搜索能力;采用高维PSO方法解决了多波段高维问题,并结合种群信息构建自适应惩罚机制以实现端元提取中目标与约束的合理权衡。通过模拟影像和真实影像的实验,证实该算法与传统的NMF端元提取算法相比能够更合理地权衡约束和避免局部最优,具有较好的端元提取效果。     

Some numerical issues using element‐free Galerkin mesh‐less method for coupled hydro‐mechanical problems

A new formulation of the element‐free Galerkin (EFG) method is developed for solving coupled hydro‐mechanical problems. The numerical approach is based on solving the two governing partial differential equations of equilibrium and continuity of pore water simultaneously. Spatial variables in the weak form, i.e. displacement increment and pore water pressure increment, are discretized using the same EFG shape functions. An incremental constrained Galerkin weak form is used to create the discrete system equations and a fully implicit scheme is used for discretization in the time domain. Implementation of essential boundary conditions is based on a penalty method. Numerical stability of the developed formulation is examined in order to achieve appropriate accuracy of the EFG solution for coupled hydro‐mechanical problems. Examples are studied and compared with closed‐form or finite element method solutions to demonstrate the validity of the developed model and its capabilities. The results indicate that the EFG method is capable of handling coupled problems in saturated porous media and can predict well both the soil deformation and variation of pore water pressure over time. Some guidelines are proposed to guarantee the accuracy of the EFG solution for coupled hydro‐mechanical problems. Copyright © 2008 John Wiley & Sons, Ltd.     

A Versatile Nonlinear Inversion to Interpret Gravity Anomaly Caused by a Simple Geometrical Structure

A geophysical interpretative method is proposed to depth, amplitude coefficient and geometrical shape factor determination of a buried structure from an observed gravity anomaly related to a cylinder or a sphere-like structure.The method is based on nonlinearly constrained mathematical modelling and also on stochastic optimization approaches. The proposed interpretative method first has been tested on theoretical synthetic models with different random errors at a certain depth, where a very close agreement has been observed between assumed and evaluated parameters. Subsequent field data have been considered for which the interpreted results by other methods are available for comparison. The agreement between the obtained results by the proposed technique and by other geophysical methods is good. A statistical analysis has been also carried out to demonstrate the accuracy and the precision of the suggested interpretative method.     

Estimation of hypocentral parameters of local earthquakes when crustal layers have constantP-velocities and dipping interfaces

The paper describes an algorithm for estimating the hypocentral coordinates and origin time of local earthquakes when the wave speed model to be employed is a layered one with dipping interfaces. A constrained least-squared error problem has been solved using the penalty function approach, in conjunction with the sequential unconstrained optimization technique of Fiacco and McCormick. Joint confidence intervals for the computed parameters are estimated using the approach of Bard for nonlinear problems. These results show that when a hypocentre lies outside the array of recording stations and head waves from a dipping interface are involved, then its inclination must be taken into account for dip angles exceeding 5°.     

无单元伽辽金法及其在瞬态温度场中的应用研究

无单元伽辽金法(EFGM)采用移动的最小二乘法构造形函数,和有限元相比,它只需结点信息而不需要单元信息.简述了无单元法的基础理论,推导出瞬态温度场的无单元法计算公式,采用罚函数法引入了第一类边界条件,编制了相应的计算程序.通过应用于经典的瞬态温度场例子,和有限元结果作比较,说明了无单元法具有精度高、前后处理简单等优越性,是一种具有较大发展潜力的新数值计算方法.     

附不等式约束平差的一种简单迭代算法

基于最优化计算理论中罚函数方法及传统测量平差中零权和无限权的思想,提出一种有效的迭代算法,算法过程与经典平差计算方法相同.数值实验表明,该算法简单、可行,并且具有很快的收敛速度.作者还将该模型用在大坝变形分析中,根据地形对控制点建立不等式约束,能够探测到更真实的点位位移,较之无约束平差更合理可靠.     

固结问题无单元法解的影响因素分析

无单元法是求解比奥固结问题的一种新型数值方法。在采用罚函数法处理本质边界条件的基础上,推导出无单元伽辽金法解固结问题的系统方程。并着重讨论了计算域内结点分布方式、结点影响域的形状和大小、数值积分方案、惩罚因子等因素对结点位移、超孔隙水压力等的计算结果精度的影响。通过比较、分析,分别提供出相应的取值范围,或给出了参考性建议。     

附不等式约束的总体最小二乘迭代算法

基于惩罚函数和测量平差中权的思想,提出了附不等式约束的总体最小二乘平差模型,即利用惩罚函数对不等式约束方程构造约束权,通过零权和无限权将不等式约束转换为等式约束,从而将不等式约束平差准则转化为传统的测量平差准则。同时,根据非线性最小二乘平差理论,用构造结构矩阵的方法来顾及系数矩阵的结构性,推导了附不等式约束的总体最小二乘迭代算法。该算法迭代格式与传统的间接平差类似,只需经过若干次迭代便能得到最优解。