AN AUTOMATIC LOAD STEPPING ALGORITHM WITH ERROR CONTROL

This paper presents an algorithm for controlling the error in non-linear finite element analysis which is caused by the use of finite load steps. In contrast to most recent schemes, the proposed technique is non-iterative and treats the governing load–deflection relations as a system of ordinary differential equations. This permits the governing equations to be integrated adaptively where the step size is controlled by monitoring the local truncation error. The latter is measured by computing the difference between two estimates of the displacement increments for each load step, with the initial estimate being found from the first-order Euler scheme and the improved estimate being found from the second-order modified Euler scheme. If the local truncation error exceeds a specified tolerance, then the load step is abandoned and the integration is repeated with a smaller load step whose size is found by local extrapolation. Local extrapolation is also used to predict the size of the next load step following a successful update. In order to control not only the local load path error, but also the global load path error, the proposed scheme incorporates a correction for the unbalanced forces. Overall, the cost of the automatic error control is modest since it requires only one additional equation solution for each successful load step. Because the solution scheme is non-iterative and founded on successful techniques for integrating systems of ordinary differential equations, it is particularly robust. To illustrate the ability of the scheme to constrain the load path error to lie near a desired tolerance, detailed results are presented for a variety of elastoplastic boundary value problems.     

动态环境下基于自适应步长Informed-RRT*和人工势场法的机器人混合路径规划

为解决移动机器人在动态环境下的路径规划问题,将Informed-RRT*和人工势场法相融合,提出全局与局部规划算法相融合的路径规划方法。首先,针对Informed-RRT*算法采样效率低,以及得到路径不满足机器人运动学约束的问题,采用目标偏置法与自适应步长法,减少冗余搜索与不必要树的生长;同时,引入走廊优化与时间重分配法,优化路径节点,使路径更加平滑。其次,针对人工势场法易陷入局部极小值和目标点附近不可达的问题,采用平滑窗格策略,增设全局路径子目标点,使机器人能够逃离局部极小值,完成规划任务。仿真结果表明,静态环境中自适应步长Informed-RRT*算法相比于Informed-RRT*算法求解时间缩短了71.98%;动态环境中,混合算法相比于人工势场法,搜索时间缩短了15.4%,路径长度缩短了11.1%。     

基于改进萤火虫算法的有限元模型修正

针对标准萤火虫算法后期收敛速度慢、收敛精度低、易陷入局部最优解的问题,提出了参数自适应策略的改进萤火虫算法,建立了基于改进萤火虫算法的有限元模型修正方法。通过隔代随机吸引度因子扩大了算法搜索路径,提升了算法遍历性,避免计算陷入局部最优;通过自适应步长因子使得算法寻优过程中能随迭代次数逐渐减少随机搜索范围,从而提高收敛速度。单、多峰测试函数计算结果表明,改进算法显著提高了收敛速率与收敛精度;简支梁数值算例与某刚构桥实桥有限元模型修正结果表明,简支梁参数最大误差由初始的66.7%降低至修正后的1.08%,刚构桥频率最大误差由14.47%降低至3.25%。所提方法具有良好的更新精度,适用于大型复杂结构的有限元模型修正。     

Solution-adaptive techniques in computational heat transfer and fluid flow

Recent contributions to solution-adaptive grid and solution-adaptive differencing techniques are breifly described in this paper. In solution-adaptive grid techniques, the grid points are dynamically reclustered or refined to improve the resolution in the important regions where the truncation error estimate is high. In solution-adaptive differencing techniques, the order of the differencing scheme in high error estimate region is dynamically increased. Thus both adaptive grid and adaptive differencing techniques represent error-equidistribution procedures. Two strategies for adaptive gridding are described in this paper. In one strategy, termed Global Adaptation, all grid points participate in the grid point redistribution process. In the other strategy, called Local Adaptation, grid refinement is performed only in local regions with high truncation error estimates. Results of various problems are presented which show the improvements obtained with solution-adaptive techniques.     

Adaptive time stepping strategy for solidification processes based on modified local time truncation error

Adaptive time step methods provide a computationally efficient means of simulating transient problems with a high degree of numerical accuracy. However, choosing appropriate time steps to model the transient characteristics of solidification processes is difficult. The Gresho–Lee–Sani predictor–corrector strategy, one of the most commonly applied adaptive time step methods, fails to accurately model the latent heat release associated with phase change due to its exaggerated time steps while the apparent heat capacity method is applied. Accordingly, the current study develops a modified local time truncation error‐based strategy designed to adaptively adjust the size of the time step during the simulated solidification procedure in such a way that the effects of latent heat release are more accurately modeled and the precision of the computational solutions correspondingly improved. The computational accuracy and efficiency of the proposed method are demonstrated via the simulation of several one‐dimensional and two‐dimensional thermal problems characterized by different phase change phenomena and boundary conditions. The feasibility of the proposed method for the modeling of solidification processes is further verified via its applications to the enthalpy method. Copyright © 2009 John Wiley & Sons, Ltd.     

A robust and efficient substepping scheme for the explicit numerical integration of a rate‐dependent crystal plasticity model

This paper describes the development of efficient and robust numerical integration schemes for rate‐dependent crystal plasticity models. A forward Euler integration algorithm is first formulated. An integration algorithm based on the modified Euler method with an adaptive substepping scheme is then proposed, where the substepping is mainly controlled by the local error of the stress predictions within the time step. Both integration algorithms are implemented in a stand‐alone code with the Taylor aggregate assumption and in an explicit finite element code. The robustness, accuracy and efficiency of the substepping scheme are extensively evaluated for large time steps, extremely low strain‐rate sensitivity, high deformation rates and strain‐path changes using the stand‐alone code. The results show that the substepping scheme is robust and in some cases one order of magnitude faster than the forward Euler algorithm. The use of mass scaling to reduce computation time in crystal plasticity finite element simulations for quasi‐static problems is also discussed. Finally, simulation of Taylor bar impact test is carried out to show the applicability and robustness of the proposed integration algorithm for the modelling of dynamic problems with contact. Copyright © 2014 John Wiley & Sons, Ltd.     

基于改进遗传算法的视差拼图缝线搜索方法

为了消除视差图像拼接后的局部不一致、不连续或变形,提出一种视差拼图最优合成拼缝搜索策略.将两浇幅图象重叠区域的归一化差图象作为搜索空间,定义一个与图象高相等维数的向量作为染色体,染色体的基因表示每一行图象中的最优拼接点,采用常用的最小值搜索适应度函数作为视差图像拼缝搜索的适应度函数.针对传统遗传算法在图像整数编码搜索中收敛慢的缺陷,提出了一种基于小区间整数编码,个体互异稳态定标的组合选择策略,按基因适应度自适应重组,自适应、变步长与多点选择性的变异操作等策略的改进遗传算法.实际图像拼缝搜索实验表明:改进后算法比基本遗传算法和传统自适应遗传算法收敛速度加快.     

Finite element/finite volume approaches with adaptive time stepping strategies for transient thermal problems

Transient thermal analysis of engineering materials and structures by space discretization techniques such as the finite element method (FEM) or finite volume method (FVM) lead to a system of parabolic ordinary differential equations in time. These semidiscrete equations are traditionally solved using the generalized trapezoidal family of time integration algorithms which uses a constant single time step. This single time step is normally selected based on the stability and accuracy criteria of the time integration method employed. For long duration transient analysis and/or when severe time step restrictions as in nonlinear problems prohibit the use of taking a larger time step, a single time stepping strategy for the thermal analysis may not be optimal during the entire temporal analysis. As a consequence, an adaptive time stepping strategy which computes the time step based on the local truncation error with a good global error control may be used to obtain optimal time steps for use during the entire analysis. Such an adaptive time stepping approach is described here. Also proposed is an approach for employing combinedFEM/FVM mesh partitionings to achieve numerically improved physical representations. Adaptive time stepping is employed thoughout to practical linear/nonlinear transient engineering problems for studying their effectiveness in finite element and finite volume thermal analysis simulations. Additional support and computing times were furnished by Minnesota Supercomputer Institute at the University of Minnesota.     

Solving numerical difficulties for element-free Galerkin analyses

This study solves the numerical problems associated with the element-free Galerkin method (EFGM) to perform analyses efficiently in shared-memory computers. The truncation error is generally large for the moving least-squares approximation, and this can be overcome by using orthogonal basis functions, 16-byte floats, or the local origin. Then, the analysis accuracy is similar to that obtained with the reproducing kernel particle approximation. Determining the index array of the global stiffness matrix requires a large amount of computer memory. We thus propose a scheme to overcome this problem using slightly more computer time but much less computer memory. A binary search is also proposed to find the support domain nodes for Gaussian points, and this method is much more efficient than the linear search one. A Fortran module is developed to establish parallel solutions in the EFGM, and the programmer does not need to handle the global stiffness directly.     

一种用于自适应有源噪声控制的在线次级通道建模方法

针对前馈式自适应有源降噪系统次级通道在线建模问题,首先分析比较已有的在线次级通道建模方法,给出了各自的优缺点。在此基础上提出了一种基于Fx LMS算法的在线次级通道建模方法,该方法使次级通道建模步长随干扰信号和建模白噪声信号功率自适应更新,降低了初级噪声对建模的不利影响,并利用误差信号相关值和初级噪声能量来更新控制滤波器步长,有效降低了突发随机噪声对系统稳定性的影响。计算机仿真结果表明,该方法显著提高了次级通道模型的精度和系统收敛速度,取得更好的降噪效果。     

Adaptive POD‐based low‐dimensional modeling supported by residual estimates

An adaptive low‐dimensional model is considered to simulate time‐dependent dynamics in nonlinear dissipative systems governed by PDEs. The method combines an inexpensive POD‐based Galerkin system with short runs of a standard numerical solver that provides the snapshots necessary to first construct and then update the POD modes. Switching between the numerical solver and the Galerkin system is decided ‘on the fly’ by monitoring (i) a truncation error estimate and (ii) a residual estimate. The latter estimate is used to control the mode truncation instability and highly improves former adaptive strategies that detected this instability by monitoring consistency with a second instrumental Galerkin system based on a larger number of POD modes. The most computationally expensive run of the numerical solver occurs at the outset, when the whole set of POD modes is calculated. This step is improved by using mode libraries, which may either be generic or result from former applications of the method. The outcome is a flexible, robust, computationally inexpensive procedure that adapts itself to the local dynamics by using the faster Galerkin system for the majority of the time and few, on demand, short runs of a numerical solver. The method is illustrated considering the complex Ginzburg–Landau equation in one and two space dimensions. Copyright © 2015 John Wiley & Sons, Ltd.     

基于自适应引力算法的桥梁监测传感器优化布置

针对桥梁健康监测中传感器布置优化问题,提出了一种基于自适应引力算法的传感器优化布置方法。以模态置信准则为基础,构造满足传感器优化布置的适应度函数;针对引力搜索算法开发能力不足,对衰减因子α进行了自适应改进。搜索初期α较小,粒子以较大步长进行全局搜索,增强了算法的搜索效率;搜索后期α较大,粒子以较小的步长进行局部搜索,提高了算法的搜索能力,避免落入局部极值点。改进后的自适应引力算法通过双重编码的方式,使算法可以解决离散型的传感器布置问题;以马水河大桥为例,验证算法的可行性。结果表明,改进后的算法有很好的寻优能力,能够准确高效的确定传感器优化位置。     

基于自适应伸缩因子的变论域模糊PID振动控制方法

针对传统变论域模糊PID控制算法(VUFP)伸缩因子无法自适应调整的问题,建立了基于自适应伸缩因子的变论域模糊PID振动控制方法,从而进一步提升振动控制效果。在传统VUFP算法的基础上,将系统误差及误差变化率作为输入,伸缩因子参数作为输出,提出了伸缩因子自适应调整函数;从非零性、对偶性、单调性、正规性、协调性入手,通过理论证明了所提自适应调整函数的合理性;基于VUFP算法,利用系统误差及误差变化率实现了自适应调整函数参数的实时自适应调整,从而避免了VUFP算法中伸缩因子缺乏模糊规则导致控制效果降低的问题。3层框架理论模型和实验结构的振动控制结果表明:所提控制方法能实现函数型伸缩因子参数的自适应调整,针对框架结构加速度、速度及位移的控制效果均优于PID和VUFP控制算法,为建筑结构振动控制提供了一种新的控制算法。     

The study of α in GM(1,1) model

Abstract

The purpose of this paper is to analyze a predicted error in using the GM(1, 1) model based on the parameter α. The transfer function for the predicted error with the parameter α in the GM(1, 1) model is presented. The algorithm of solving equations in calculus is used to analyze whether the α is adaptive or not. The criterion of α is applied to describe the adaptive criterion of α. Finally, an example of the cagenet amounts of fish in the Peng‐hu area is used to demonstrate the small prediction error due to the optimal α value. The result shows that the criterion for α is applicable for minimizing the predicted error easily.     

复合材料双面贴补修理拉伸解析分析模型及试验验证

复合材料胶接修理是一种有效并且低成本的修理技术。本文建立了复合材料层合板双面贴补胶接修理解析分析模型。模型中考虑了搭接区阶梯末端截面积变化细节。预测失效时,层合板采用最大应变准则,胶层采用最大剪应变准则和损伤区域理论。定义了残差函数来表征极限载荷解析计算结果与试验值的接近程度。通过试验对解析模型得到的等效刚度与极限载荷进行了验证。解析分析结果与试验数据对比表明:复合材料层合板双面贴补等效刚度随着搭接长度的增加单调增加。解析模型计算的等效刚度与试验结果最大误差不超过15%。当损伤特征长度为4%时,损伤区域理论对应极限载荷残差值最小,仅为4.30%,最大剪应变准则预测极限载荷的残差值为6.41%。解析模型分析表明,双面贴补极限载荷随着搭接长度的增加表现为快速增长、缓慢增长和几乎不增长三个阶段。搭接长度结合结构减重等限制因素应选择15~35mm为宜。     

剪切带内部应变(率)分析及基于能量准则的失稳判据

应用应变梯度塑性理论对局部化剪切带内部(塑性)剪应变(率)规律进行了理论分析。研究了剪切降模量及岩石材料内部长度等参数对剪切带内部应变(率)的影响。推导了剪应力(率)与剪切带相对错距(速度)的本构关系。研究了剪切降模量和岩石材料内部长度对剪切带稳定性的影响。将岩石试件直剪试验试验机简化为钢块,采用能量准则对岩石试件(剪切带)及钢块系统的稳定性进行了理论研究,提出了系统失稳判据。研究表明:岩石材料的剪切降模量越大,岩石材料的内部长度越小,试验机的剪切刚度越小及试验机的等效高度越大剪切带--钢块系统越容易失稳。     

Locally weighted regression models for surrogate-assisted design optimization

We consider engineering design optimization problems where the objective and/or constraint functions are evaluated by means of computationally expensive blackboxes. Our practical optimization strategy consists of solving surrogate optimization problems in the search step of the mesh adaptive direct search algorithm. In this paper, we consider locally weighted regression models to build the necessary surrogates, and present three ideas for appropriate and effective use of locally weighted scatterplot smoothing (LOWESS) models for surrogate optimization. First, a method is proposed to reduce the computational cost of LOWESS models. Second, a local scaling coefficient is introduced to adapt LOWESS models to the density of neighboring points while retaining smoothness. Finally, an appropriate order error metric is used to select the optimal shape coefficient of the LOWESS model. Our surrogate-assisted optimization approach utilizes LOWESS models to both generate and rank promising candidates found in the search and poll steps. The “real” blackbox functions that govern the original optimization problem are then evaluated at these ranked candidates with an opportunistic strategy, reducing CPU time significantly. Computational results are reported for four engineering design problems with up to six variables and six constraints. The results demonstrate the effectiveness of the LOWESS models as well as the order error metric for surrogate optimization.     

A one-step method for direct integration of structural dynamic equations

The choice on an efficient direct integration procedure for linear structural dynamic equations of motion is discussed. It is suggested that as accuracy parameter the truncation error on the exponential terms contained in the modal contributions of the exact solution be assumed. This error does not always coincide with the local truncation error. These considerations were used to design an unconditionally stable one-step method whose accuracy is 0(h⁴). Numerical comparisons with some well-known integration schemes showed the efficiency of the proposed method.     

Crack behavior in a high contact ratio spur gear tooth and its effect on mesh stiffness

The efficiency of high contact ratio (HCR) gearing can be achieved by proper selection of gear geometry for increased load capacity and smoother operation despite of their high sliding velocities. The prediction of variation in mesh stiffness of HCR gearing is critical as the average number of teeth being in contact is high at a given time as compared to conventional low contact ratio (LCR) gearing. In this paper, linear elastic fracture mechanics (LEFM) based finite element method is used to perform the crack propagation path studies of HCR spur gear having tooth root crack for two gear parameters viz. backup ratio and pressure angle. A total potential energy model has been adopted to analytically estimate the mesh stiffness variation. The results depict the mesh stiffness reduction in the presence of the crack. The percentage change in mesh stiffness with increasing crack length is an important parameter in fault diagnosis of geared transmission. Higher the percentage change in mesh stiffness, easier to detect the fault. Two gear parameters viz. back-up ratio and pressure angle has been studied and the effect of crack length on mesh stiffness have been outlined. With the increase of deterioration level gears having lower back-up ratio fault can be detected at an early stage, similarly, chances for early fault detection is more for gears having higher pressure angle.     

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.