径向基函数、散乱数据拟合与无网格偏微分方程数值解

介绍了近年来国际上有关散乱数据拟合研究中的径向基函数方法,及其在散乱线性泛函信息插值,无网格偏微分方程数值解中应用的主要内容。     

径向基函数预测网络拓扑确定新方法

预测能力相对薄弱,已经成为制约PHM(Prognostics and Health Management)技术发展和应用的瓶颈.随着传感器和BIT(Built-in Test)设计技术的日益进步,采用序列分析的方法对复杂系统装备进行故障预测已经成为可能.在基于序列分析的预测方法研究中,径向基函数预测网络具有结构简单、学习速度快、具备非线性建模能力等诸多优点.为了改进其预测性能,在深入分析网络拓扑对模型性能及建模时间影响的基础上,综合考察了序列最佳线性自相关长度、建模精度和模型复杂度等多种因素,提出了基于偏自相关函数统计检测的输入层节点数目确定算法和基于BIC(Bayesian Information Criteria)准则的隐层节点数目确定算法,用以构建径向基函数预测网络;并对算法的有效性进行了分析.仿真结果表明,同传统建模算法相比较,由新算法构建的径向基函数预测网络具有最佳的预测性能,且建模时间不足传统算法的3%.     

对流占优扩散方程的楔形基无网格法

传统的微分方程数值解方法求解对流占优扩散方程时,往往产生数值震荡现象,为了消除数值震荡,本文构建了一种新的数值求解方法――无网格方法进行数值求解。该方法采用配点法并引入一种新的楔形基函数构建了楔形基无网格方法,不需要网格划分,是一种真正的无网格方法,可以避免因为网格划分而影响计算效率。通过对新的楔形基函数的理论分析,证明了本文方法解的存在唯一性。最后,分别通过一维和二维的数值算例,表明该算法计算精度高,可以有效消除对流占优引起的数值震荡,是一种计算对流占优扩散方程数值解的高效方法。     

利用径向基函数网络修正机枪有限元模型

在对机枪进行结构设计时,建立有限元模型并在此基础上进行动力学仿真,对了解其结构动态特性如何影响整个武器射击精度十分重要.提出了一种利用径向基函数网络进行机枪有限元模型修正的方法,将模型修正转化为正问题进行研究.根据实测模态数据对所建立的有限元模型进行修正,以径向基函数网络反映机枪结构参数与其动态特性之间的非线性映射关系,利用神经网络的泛化特性求解设计参数的目标值,不需迭代求解,并且避开了反问题面临的非线性优化计算.反演仿真数据代入的有限元模型计算结果与实测结果较为吻合,证明了该方法的有效性.     

Sequential Approximate Optimization using Radial Basis Function network for engineering optimization

This paper presents a Sequential Approximate Optimization (SAO) procedure that uses the Radial Basis Function (RBF) network. If the objective and constraints are not known explicitly but can be evaluated through a computationally intensive numerical simulation, the response surface, which is often called meta-modeling, is an attractive method for finding an approximate global minimum with a small number of function evaluations. An RBF network is used to construct the response surface. The Gaussian function is employed as the basis function in this paper. In order to obtain the response surface with good approximation, the width of this Gaussian function should be adjusted. Therefore, we first examine the width. Through this examination, some sufficient conditions are introduced. Then, a simple method to determine the width of the Gaussian function is proposed. In addition, a new technique called the adaptive scaling technique is also proposed. The sufficient conditions for the width are satisfied by introducing this scaling technique. Second, the SAO algorithm is developed. The optimum of the response surface is taken as a new sampling point for local approximation. In addition, it is necessary to add new sampling points in the sparse region for global approximation. Thus, an important issue for SAO is to determine the sparse region among the sampling points. To achieve this, a new function called the density function is constructed using the RBF network. The global minimum of the density function is taken as the new sampling point. Through the sampling strategy proposed in this paper, the approximate global minimum can be found with a small number of function evaluations. Through numerical examples, the validities of the width and sampling strategy are examined in this paper.     

Job-shop问题基于RBF网络的自学习算法

通过对Job-shop问题分析,在逐步添加约束到有向图模型来获取可行调度方案基础上,提出一种具备自动学习功能智能算法.设计了可互换工序对4种选取函数,并以此作为网络输入构建了基于RBF的神经网络以实现对可互换工序对选取.利用最小均方算法对网络权重进行训练,经过对更新过的样本进行再学习后,网络选取可互换工序对的准确度得以提高,使算法具备自学习能力.数值仿真结果表明所提算法对于大规模Job-shop问题求解存在较好效果,具较好的应用价值.     

时域径向基函数网络诊断方法在往复泵故障诊断中的应用

往复机械是工程中广泛应用的一种机械设备 ,由于其动力学和运动学形态比旋转机械复杂 ,对其进行故障诊断存在较大难度 ,有效提取往复机械运动中非平稳时变信号中的故障特征和将故障特征准确分类是解决往复机械故障诊断问题的两个关键。本文利用时域数字特征分析方法完成故障特征信息提取 ;通过径向基神经网络对特征信息分类识别 ,实现故障的自动诊断。利用以上原理建立的油田往复塞泵故障监测与诊断系统 ,通过在大庆油田的实际应用表明 ,系统能够比较准确的识别往复柱塞泵多种常见故障 ,且具有较高的运算速度。     

基于径向基函数神经网络的轮轨力检测

用测力轮对检测列车轮轨作用力时,由于轮轨作用力与轮辐贴片点处应变是非线性映射关系,同时作用的垂向力和横向力还会产生相互耦合,导致测量电路复杂,测量精度不高.本文在轮对有限元计算基础上,采用径向基函数神经网络拟合轮轨力与贴片点处应变的非线性关系,通过学习消除横向力与垂向力之间相互影响,简化了测量电路,提高了测量精度,达到很好效果.     

基于RBF径向基神经网络的摩擦学模型

建立了润滑油摩擦学特性影响规律的径向基神经网络模型,可以较准确地计算和预测润滑油摩擦系数与负荷及相对滑动速度之间的关系.试验结果表明这种网络具有很好的准确度和预测性,为摩擦学设计和程序化计算和分析提供了一种方便且有效的工具.     

An Adaptive Meshless Method for Magnetic Field Computation

Increasing energy cost and advance in permanent magnet technology have provided the incentives to develop geometrically compact and energy-efficient electromagnetic (EM) actuators. Design of electromagnetic (EM) actuators often involves solving a magnetic field problem. This paper presents an adaptive meshless method (MLM) that inherits many advantages of the finite-element method (FEM) but needs no explicit mesh structure for design of EM actuators. Specifically, the paper offers a technique to estimate the distribution of numerical errors and a scheme that automatically inserts additional nodes to improve computational accuracy and efficiency. It gives several examples. The first three numerical examples, where exact solutions are available, provide a means to validate the adaptive MLM and evaluate its effectiveness against a regular MLM with a uniform node distribution. The other examples, where magnetic forces are computed from Lorenz's law, illustrate the use of adaptive MLM for practical design of an EM actuator. The paper compares the computed forces against published experimental results.     

Recurrent Radial Basis Function Network-Based Fuzzy Neural Network Control for Permanent-Magnet Linear Synchronous Motor Servo Drive

We propose a recurrent radial basis function network-based (RBFN-based) fuzzy neural network (FNN) to control the position of the mover of a field-oriented control permanent-magnet linear synchronous motor (PMLSM) to track periodic reference trajectories. The proposed recurrent RBFN-based FNN combines the merits of self-constructing fuzzy neural network (SCFNN), recurrent neural network (RNN), and RBFN. Moreover, it performs the structureand parameter-learning phases concurrently. The structure learning is based on the partition of input space, and the parameter learning is based on the supervised gradient descent method, using a delta adaptation law. Furthermore, all the control algorithms are implemented in a TMS320C32 DSP-based control computer. The simulated and experimental results due to periodic reference trajectories show that the dynamic behaviors of the proposed recurrent RBFN-based FNN control system are robust with regard to uncertainties     

用瞬态电磁场测试隐形目标的新方法

本文针对引信隐形目标的测试问题,提出了应用瞬态电磁场的广谱性进行时域测试的新方法.论及了基本原理,并对工程实施方案及应用前景也作了探讨.     

基于小波包变换的径向基神经网络在故障诊断中的应用

提出了一种新的旋转机械故障诊断方法。基于小波包变换的频率划分特性，对旋转机械的振动信号进行小波包分解，建立旋转机械六种典型故障特征矢量，准确地提取了故障的特征信息，结合RBF神经网络训练速度快的优点，将RBF神经网络应用于故障特征的选择，最后，利用所确定特征及RBF分类器进行故障诊断。实验结果表明，该方法可实现典型故障的可靠诊断。而且由于利用小波包变换代替了传统的FFT，故本方法对于诊断频率分布范围较广而复杂且信号具有较强时变性的复杂故障有着良好的应用前景。     

Some comments on the use of Radial Basis Functions in the Dual Reciprocity Method

We comment on the use of radial basis functions in the dual reciprocity method (DRM), particularly thin plate splines as used in Agnantiaris et al. (1996). We note that the omission of the linear terms could have biased the numerical results as has occurred in several previous studies. Furthermore, we show that a full understanding of the convergence behavior of the DRM requires one to consider both interpolation and BEM errors, since the latter can offset the effect of improved data approximation. For a model Poisson problem this is demonstrated theoretically and the results confirmed by a numerical experiment.     

The Electromagnetic Basis for Nondestructive Testing of Cylindrical Conductors

Using an idealized model, we deduce the impedance per unit length of long solenoid of many turns that contains a cylindrical sample. The sample with a specified conductivity and magnetic permeability need not be centrally located within the solenoid provided all transverse dimensions are small compared with the free-space wavelength. The derivation is relatively straightforward and it provides a justification for earlier use of the impedance formula. The dual problem , where the solenoid is replaced by a toroidal coil is also considered. It is shown that both excitation methods have merit in nondestructive testing procedures.     

瞬变电磁法在检测钢质埋地管线壁厚上的应用探讨

本文从瞬变电磁法的检测技术原理入手,通过室内和现场试验,总结出采用瞬变电磁法在检测钢质埋地管线壁厚时的一些规律,得出了瞬变电磁法探测管壁金属蚀失量时的操作方法及局限性,对在现场使用该方法进行埋地钢质管线检测具有一定的参考价值。     

A Meshless Cohesive Segments Method for Crack Initiation and Propagation in Composites

A modeling method aimed at eliminating the need of explicit crack representation in bi-dimensional structures is presented for the simulation of the initiation and subsequent propagation within composite materials. This is achieved by combining a meshless method with a physical stress–displacement based criterion known as Cohesive Model. This model consents to apply a penalty-based approach to delamination modeling where a variable penalty factor along the crack segment allows to loosen or tight the two parts according to their relative displacements. Results are showed for classical single mode loading benchmark cases and compared to experimental results taken from the literature.     

Subcritical and Supercritical Water Radial Distribution Function

A theoretical and analytic expression for the first shell, and an analytic empirical expression for the whole radial distribution function (RDF) of water are introduced. All the asymptotic limits and functionalities of the RDF with temperature and density are incorporated in these expressions. An effective Kihara pair potential function is presented for water intermolecular interactions which incorporates the hydrogen bonding by using the chain association theory. The intermolecular pair potential parameters are adjusted to the experimental x-ray diffraction data of water RDF at various temperatures. The predicted first-shell results for water near critical and in supercritical conditions compare satisfactorily with the available neutron diffraction RDF data, with the simulation RDF results, and with the empirical RDF curves. The empirical expression initially proposed for the RDF of the Lennard–Jones fluid is extended to predict the RDF and the isothermal compressibility of water to conditions where experimental or simulated data are not available. Comparison with the Lennard–Jones fluid shows that the height of the first peak of water RDF changes much less at subcritical and supercritical conditions compared to that of the Lennard–Jones fluid which decreases appreciably going from subcritical to supercritical conditions.