New approaches for error estimation and adaptivity for 2D potential boundary element methods

This work presents two new error estimation approaches for the BEM applied to 2D potential problems. The first approach involves a local error estimator based on a gradient recovery procedure in which the error function is generated from differences between smoothed and non‐smoothed rates of change of boundary variables in the local tangential direction. The second approach involves the external problem formulation and gives both local and global measures of error, depending on a choice of the external evaluation point. These approaches are post‐processing procedures. Both estimators show consistency with mesh refinement and give similar qualitative results. The error estimator using the gradient recovery approach is more general, as this formulation does not rely on an ‘optimal’ choice of an external parameter. This work presents also the use of a local error estimator in an adaptive mesh refinement procedure. This r‐refinement approach is based on the minimization of the standard deviation of the local error estimate. A non‐linear programming procedure using a feasible‐point method is employed using Lagrange multipliers and a set of active constraints. The optimization procedure produces finer meshes close to a singularity and results that are consistent with the problem physics. Copyright © 2002 John Wiley & Sons, Ltd.     

The creep experiment and theoretical model analysis of gas- containing coal

A creep experiment of preformed molding coal under different confining pressures were carried out using self-developed 3-triaxial creep loading device for gas-containing coal, which loaded by Shimadzu AGI-250 kN electrical servo-controlled stiffness testing machine. Based on the experimental results, the variation trend of axial deformation under different stress states was studied, and creep failure characteristics of gas-containing coal under different confining pressures were analyzed. The experimental results were identified with seven-component nonlinear viscoelasto-plastic creep model （Hohai model）, and the creep material parameters were obtained. The experimental result complies well with the theoretical value of this model. It indicates that creep constitutive relation of gas-containing coal can be expressed by nonlinear viscoelasto-plastic creep model correctly.     

Multiplicative Operator Splittings in Nonlinear Diffusion: From Spatial Splitting to Multiple Timesteps

Operator splitting is a powerful concept used in many diversed fields of applied mathematics for the design of effective numerical schemes. Following the success of the additive operator splitting (AOS) in performing an efficient nonlinear diffusion filtering on digital images, we analyze the possibility of using multiplicative operator splittings to process images from different perspectives.We start by examining the potential of using fractional step methods to design a multiplicative operator splitting as an alternative to AOS schemes. By means of a Strang splitting, we attempt to use numerical schemes that are known to be more accurate in linear diffusion processes and apply them on images. Initially we implement the Crank-Nicolson and DuFort-Frankel schemes to diffuse noisy signals in one dimension and devise a simple extrapolation that enables the Crank-Nicolson to be used with high accuracy on these signals. We then combine the Crank-Nicolson in 1D with various multiplicative operator splittings to process images. Based on these ideas we obtain some interesting results. However, from the practical standpoint, due to the computational expenses associated with these schemes and the questionable benefits in applying them to perform nonlinear diffusion filtering when using long timesteps, we conclude that AOS schemes are simple and efficient compared to these alternatives.We then examine the potential utility of using multiple timestep methods combined with AOS schemes, as means to expedite the diffusion process. These methods were developed for molecular dynamics applications and are used efficiently in biomolecular simulations. The idea is to split the forces exerted on atoms into different classes according to their behavior in time, and assign longer timesteps to nonlocal, slowly-varying forces such as the Coulomb and van der Waals interactions, whereas the local forces like bond and angle are treated with smaller timesteps. Multiple timestep integrators can be derived from the Trotter factorization, a decomposition that bears a strong resemblance to a Strang splitting. Both formulations decompose the time propagator into trilateral products to construct multiplicative operator splittings which are second order in time, with the possibility of extending the factorization to higher order expansions. While a Strang splitting is a decomposition across spatial dimensions, where each dimension is subsequently treated with a fractional step, the multiple timestep method is a decomposition across scales. Thus, multiple timestep methods are a realization of the multiplicative operator splitting idea. For certain nonlinear diffusion coefficients with favorable properties, we show that a simple multiple timestep method can improve the diffusion process.     

钻井井架力学性能分析

钻井井架作为钻机系统设备中的关键部分,其力学性能直接关系到整套钻机系统的安全生产。文章推导了常用于分析钻井井架力学性能的理论,即线性屈曲、几何非线性和双重非线性理论。提出同时用这三种理论对钻井井架进行综合比较分析,从而合理地预见井架力学性能的方法。以A形钻井井架为例,进行了详细的分析,得到了井架的失稳形式、极限承载、破坏特征及薄弱部位,为钻井井架的设计、优化与评定提供了参考。     

SVM自适应波束成形算法

在天线阵列过载,以及强干扰与期望用户信号夹角过近的情况下,传统的线性阵列信号处理算法,如MMSE(minimum mean-squareerror)、NLMS(Normalized Least Mean Squares)等表现并不理想。SVM(SupportVectorMachine)是机器学习领域的最新成果,有较强的泛化能力,收敛快以及低复杂度等优点。本文提出了在上行波束成形中使用SVM算法,提高空域滤波的分辨率,与其他相关算法相比较,系统性能有了明显的改进。     

Weak Lower Subdifferentiability in Fractional Programming

We consider generalized fractional programming problems for which numerators and denominators appearing in the objective function satisfy certain tangential convexity conditions ensuring its weak lower subdifferentiability. Estimates of the weak lower subdifferential in terms of the generalized subdifferentials of the numerators and denominators are provided and necessary and sufficient Kuhn-Tucker type optimality conditions involving these sets are obtained for problems with quasiconvex constraints.     

船舶操纵非线性系统的鲁棒变结构控制

本文采用伪线性化变换将船舶操纵非线性系统近似地化为线性可控正则型，并对线性化系统设计了一种连续的变结构以提高整个闭环系统的鲁棒性。该方案用于限制水域中船舶的航向航迹纠编控制中，取得了预期的结果。     

基于神经网络非线性系统辨识和控制的研究

本文提出了由静态的前馈网络和稳定的滤波器构成的非线性系统的辨识模型，在神经网络固有的逼近误差存在的情况下，从理论上讨论了神经网络应用于辨识控制过程中系统的稳定性问题，最后研究了在非线性系统的轨迹跟踪过程中增加滑动控制来偿神经网络的逼近误差，从而提高系统跟踪性能。     

弹性直杆热膨胀状态下的非线性振动

以ＫＢＭ法为基础，引进谐波平衡观点来研究弹性直杆热膨胀状态下的非线性振动．通过实例计算表明，弹性直杆热膨胀状态下非线性振动的频率对温度的变化非常敏感．     

高层结构几何非线性分析的QR法

本文利用ＱＲ法分析高层建筑结构几何非线性问题，建立了新的计算格式。该法不仅未知量的数目少，精度高，而且输入简单，计算速度快，可以用微机分析复杂问题。