基于链式贝叶斯网络的结构可靠性分析

将贝叶斯网络与传统可靠性方法结合,建立结构系统的可靠性贝叶斯网络模型,通过改进的分支限界法确定结构主要失效模式,并将贝叶斯网络链式化来提升计算效率。根据可靠性方法计算条件概率表;使用概率网络估算法来考虑主要失效模式之间的相关性,计算系统可靠性;当有新信息出现时,利用贝叶斯网络推理,对结构系统可靠性进行评估。以一桁架结构为研究对象,计算结构系统的可靠性,并在新信息出现的情况下对系统可靠性进行了更新。     

Comparative study of honeycomb optimization using Kriging and radial basis function

Structural optimization for crashworthiness criteria is of particular significance especially at early stage of design. The comparative study of Kriging and radial basis function network (RBFN) was performed in order to improve the crashworthiness effects of honeycomb. Improving the crashworthiness characteristic of honeycomb was achieved using LS-OPT® and domain reduction strategy. This optimization is performed on the basis of validated numerical simulation to establish the approximated model to illustrate the relationship between the responses and design variables. The results showed that Kriging meta-model is excelled in accuracy, robustness and efficiency compared to radial basis function (RBF) and crashworthiness characteristic of honeycomb is improved by 4%.     

Artificial neural network modeling of fixed bed biosorption using radial basis approach

In modern day scenario, biosorption is a cost effective separation technology for the removal of various pollutants from wastewater and waste streams from various process industries. The difficulties associated in rigorous mathematical modeling of a fixed bed bio-adsorbing systems due to the complexities of the process often makes the development of pure black-box artificial neural network (ANN) models particularly useful in this field. In this work, radial basis function network has been employed as ANN to model the breakthrough curves in fixed bed biosorption. The prediction has been compared to the experimental breakthrough curves of Cadmium, Lanthanum and a dye available in the literature. Results show that this network gives fairly accurate representation of the actual breakthrough curves. The results obtained from ANN modeling approach shows the better agreement between experimental and predicted breakthrough curves as the error for all these situations are within 6%.     

基于更新径向基函数网络模型的广义Pareto分布函数拟合

广义Pareto分布函数GPD(Generalized Pareto Distribution)是一种针对随机参数尾部进行渐进插值的方法,能够对高可靠性问题进行评估。但这种方法要求样本空间较大,计算成本较高,尽管可以通过径向基函数网络RBFNN(Radial Basis Function Neural Network)辅助抽样的方法削减计算成本,但对于非线性程度较高的问题,RBFNN精度问题使得辅助抽样方法失效。针对这类问题,根据GPD的特点,提出了高效的更新RBFNN训练样本的方法,改善了RBFNN在功能函数分布尾部的精度,将RBFNN辅助抽样方法推广应用到非线性程度较高的问题,准确地得到了所有需要的尾部样本,基于该尾部样本集的GPD拟合结果与基于直接计算所有样本的GPD拟合结果完全一致。     

梯度RBF神经网络在MEMS陀螺仪随机漂移建模中的应用

为了提高使用精度，研究了某型号MEMS陀螺仪的随机漂移模型。采用游程检验法分析了该陀螺仪随机漂移数据的平稳性，并根据该漂移为均值非平稳、方差平稳的随机过程的结论，采用梯度径向基（RBF）神经网络对漂移数据进行了建模。实验结果表明：相比经典RBF网络模型而言，这种方法建立的模型能更好地描则EMs陀螺仪的漂移特；相对于季节时间序列模型而言，其补偿效果提高了大约15％。     

Numerical solution of Navier–Stokes equations using multiquadric radial basis function networks

A numerical method based on radial basis function networks (RBFNs) for solving steady incompressible viscous flow problems (including Boussinesq materials) is presented in this paper. The method uses a ‘universal approximator’ based on neural network methodology to represent the solutions. The method is easy to implement and does not require any kind of ‘finite element‐type’ discretization of the domain and its boundary. Instead, two sets of random points distributed throughout the domain and on the boundary are required. The first set defines the centres of the RBFNs and the second defines the collocation points. The two sets of points can be different; however, experience shows that if the two sets are the same better results are obtained. In this work the two sets are identical and hence commonly referred to as the set of centres. Planar Poiseuille, driven cavity and natural convection flows are simulated to verify the method. The numerical solutions obtained using only relatively low densities of centres are in good agreement with analytical and benchmark solutions available in the literature. With uniformly distributed centres, the method achieves Reynolds number Re = 100 000 for the Poiseuille flow (assuming that laminar flow can be maintained) using the density of , Re = 400 for the driven cavity flow with a density of and Rayleigh number Ra = 1 000 000 for the natural convection flow with a density of . Copyright © 2001 John Wiley & Sons, Ltd.     

基于径向基函数的频响函数模型修正

针对使用频响函数进行有限元模型修正存在的时间成本和精度问题,结合模态参与变异系数法和模态动能法分别优化激励点和测点,使获得的模态信息更完整;然后,引入径向基函数(RBF)模型减少原有限元模型计算次数,并根据均方根误差准则对所构建代理模型的参数(spread)进行优选,提高模型预测精度;最后,选用一个36自由度的二维桁架模型进行可行性验证,对比有限元法、Kriging模型及二阶响应面模型的修正精度和迭代时间,结果表明,本文方法具有较好的优势。     

结构模糊区间可靠性分析方法

在结构模糊可靠性分析模型的基础上,充分考虑了状态变量分布密度函数的相关参数的不确定性。这些参数的取值范围可以被确定在相应的区间内,并将这些区间引入到结构模糊可靠性的分析中,基于区间数学理论,提出了一种可以预测结构模糊可靠度所在范围的求解方法,并讨论了当状态变量服从正态分布时,结构的模糊区间可靠性的分析过程。算例表明该方法比传统的模糊可靠性方法能提供更多的关于结构安全程度的有用信息,也更具有工程实用价值。     

A numerical method for KdV equation using collocation and radial basis functions

Recently, there has been an increasing interest in the study of initial boundary value problems for Korteweg–de Vries (KdV) equations. In this paper, we propose a numerical scheme to solve the third-order nonlinear KdV equation using collocation points and approximating the solution using multiquadric (MQ) radial basis function (RBF). The scheme works in a similar fashion as finite-difference methods. Numerical examples are given to confirm the good accuracy of the presented scheme.     

基于逆复合二次径向基函数的对称复合材料层合板自由振动分析

利用逆复合二次径向基函数无网格配点法对Reddy的高阶剪切变形理论进行离散,预测了对称复合材料层合板的自由振动特性.将不同材料参数、几何尺寸和边界条件的层合板固有频率计算结果与相关文献中的结果进行对比,结果表明:逆复合二次径向基函数在对称复合材料层合板自由振动分析方面具有收敛性好及精度高等一系列优点.     

Multilayer perceptron neural network activated by adaptive Gaussian radial basis function and its application to predict lid-driven cavity flow

Acta Mechanica Sinica - To improve the performance of multilayer perceptron (MLP) neural networks activated by conventional activation functions, this paper presents a new MLP activated by...     

Numerical study of radial basis function interpolation for data transfer across discontinuous mesh interfaces

Allowing discontinuous or non‐matching mesh spacing across zonal interfaces within a computational domain offers many advantages, particularly in terms of easing the mesh generation process, reduction of required mesh densities, and relative motion between mesh zones. This paper presents a numerical study of a universal method for interpolating solution data across such interfaces. The method utilises radial basis functions (RBFs) for n‐dimensional volume interpolation, and treats the available solution data points simply as arbitrary clouds of points, eliminating all connectivity requirements and making it applicable to a wide range of computational problems. Properties of the developed meshless interface interpolation are investigated using analytic functions, and three issues are considered: the achievable order of spatial accuracy of the RBF interpolation alone and comparison with a variable order polynomial; the effect of a combined RBF and polynomial interpolation; and the ability of the method to recover frequency content. RBF interpolation alone is shown to achieve fourth‐order to sixth‐order spatial accuracy in one and two dimensions, and in three dimensions, using a small number of data points, third‐order and above is achievable even for a 3 : 1 discontinuous cell spacing ratio, that is a 27 : 1 volume ratio, across the interface. Hence, it is inefficient to include polynomial terms, since improving on the RBF spatial accuracy results in a significant increase in the system size and deterioration in conditioning. It is also shown that only five points per wavelength are required to capture both frequency and amplitude content of periodic solutions to less than 0.01% error.Copyright © 2013 John Wiley & Sons, Ltd.     

结构可靠度模拟的方向重要抽样法

方向抽样法是结构可靠度Monte—Carlo模拟的方法之一。同其他的抽样方法一样，为提高抽样效率，需进行重要抽样。本文提出一种新的方向重要抽样法，该方法通过构造以验算点为球心的椭球，将以验算点为抽样中心的方向矢量变换为以原坐标系原点为中心的方向矢量，进而建立重要方向抽样的失效概率估计公式。在这种方法中，所构造的椭球半轴的长度为待定参数。分析表明，对于实际结构中的非闭合型极限状态方程，理论上应使与极限状态曲面正交的半轴的长度大于由一次二阶矩方法计算的可靠指标，本文建议取可靠指标值的1．1—1．2倍，其余半轴的长度可通过优化确定，本文采用了边模拟边优化的方法。算例分析表明，本文方法可以大大提高模拟的效率和精度，在随机变量数目较多时效果更为明显。     

一种分析区间参数结构可靠性的减基快速计算方法

将减基法与蒙特卡洛模拟结合,提出了一种快速计算区间不确定结构可靠性的方法。该方法分为离线和在线计算两个阶段,离线阶段利用减基法建立减基空间,进而形成减缩模型;而在线阶段则将减缩模型融入蒙特卡洛方法,进而快速求解区间失效概率及相应的区间参数失效域。该方法在减基空间而非有限元空间中分析区间结构的可靠性,减少了求解时间,提高了计算效率,通过算例验证了该方法的可行性和有效性。     

Computing non‐Newtonian fluid flow with radial basis function networks

This paper is concerned with the application of radial basis function networks (RBFNs) for solving non‐Newtonian fluid flow problems. Indirect RBFNs, which are based on an integration process, are employed to represent the solution variables; the governing differential equations are discretized by means of point collocation. To enhance numerical stability, stress‐splitting techniques are utilized. The proposed method is verified through the computation of the rectilinear and non‐rectilinear flows in a straight duct and the axisymmetric flow in an undulating tube using Newtonian, power‐law, Criminale–Ericksen–Filbey (CEF) and Oldroyd‐B models. The obtained results are in good agreement with the analytic and benchmark solutions. Copyright © 2005 John Wiley & Sons, Ltd.     

Integrated radial basis functions‐based differential quadrature method and its performance

In this paper, indirect radial basis function networks (IRBFN) proposed by Nam and Tranh (Neural Networks 2001; 14 (2):185–199; Appl. Math. Modelling 2003; 27 :197–220) are incorporated into the differential quadrature (DQ) approximation of derivatives. For simplicity, this new variant of RBF‐DQ approach is named as iRBF‐DQ method. The proposed approach is validated by its application to solve the one‐dimensional Burger's equation, and simulate natural convection in a concentric annulus by solving Navier–Stokes equations. It was found that as compared to the benchmark data, the iRBF‐DQ approach can provide more accurate results than the original RBF‐DQ method. Copyright © 2006 John Wiley & Sons, Ltd.     

Thin plate spline radial basis functions for vibration analysis of clamped laminated composite plates

A meshless method based on thin plate spline radial basis functions and higher-order shear deformation theory are presented to analyze the free vibration of clamped laminated composite plates. The singularity of thin plate spline radial basis functions is eliminated by adding infinitesimal to the zero distance. Convergence characteristics of the present thin plate spline radial basis functions for the vibration analysis of the clamped laminated plates are investigated. The frequencies computed by the present method agree well with the available published results.     

基于径向基函数的机翼二维气动代理模型设计

采用多学科设计优化方法进行机翼气动/结构优化时,结构学科的优化需要气动学科提供机翼压力分布的代理模型。本文引入了等参单元形函数的几何变换思想,利用径向基函数,解决了复杂形状机翼的二维气动代理模型的构造问题,进行了某巡航导弹弹翼考虑结构变形的气动力代理模型的构建。算例结果表明,本文所用代理模型构造方法简单易行,预测结果的精度很好。     

A generalised finite difference scheme based on compact integrated radial basis function for flow in heterogeneous soils

In the present paper, we develop a generalised finite difference approach based on compact integrated radial basis function (CIRBF) stencils for solving highly nonlinear Richards equation governing fluid movement in heterogeneous soils. The proposed CIRBF scheme enjoys a high level of accuracy and a fast convergence rate with grid refinement owing to the combination of the integrated RBF approximation and compact approximation where the spatial derivatives are discretised in terms of the information of neighbouring nodes in a stencil. The CIRBF method is first verified through the solution of ordinary differential equations, 2–D Poisson equations and a Taylor‐Green vortex. Numerical comparisons show that the CIRBF method outperforms some other methods in the literature. The CIRBF method in conjunction with a rational function transformation method and an adaptive time‐stepping scheme is then applied to simulate 1–D and 2–D soil infiltrations effectively. The proposed solutions are more accurate and converge faster than those of the finite different method used with a second‐order central difference scheme. Additionally, the present scheme also takes less time to achieve target accuracy in comparison with the 1D‐IRBF and higher order compact schemes.     

基于改进径向基神经网络的MEMS惯导系统误差抑制方法

由微机电惯性导航系统和全球定位系统构成的组合导航系统在卫导信号失锁的情况下,纯惯导定位误差将迅速发散。为了抑制惯导系统误差发散,提出了改进的径向基神经网络与自适应卡尔曼滤波算法,并提出了新的网络训练模型,采用自适应量子粒子群算法改进径向基神经网络的结构设计与参数。在卫导信号可用时用组合导航数据训练神经网络,当卫导信号失锁时,由改进的径向基神经网络预测自适应卡尔曼滤波的量测,使滤波器继续为系统提供速度与位置修正值。实验结果表明,转弯行驶状态下,卫星失锁15 s时,相比较原算法,水平定位精度提高了62%,有效抑制了惯导误差。