STUDYING THE FOCAL VALUE OF ORDINARY DIFFERENTIAL EQUATIONS BY NORMAL FORM THEORY

ＳＴＵＤＹＩＮＧＴＨＥＦＯＣＡＬＶＡＬＵＥＯＦＯＲＤＩＮＡＲＹＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＳＢＹＮＯＲＭＡＬＦＯＲＭＴＨＥＯＲＹＺｈａｎｇＱｉｃｈａｎｇ（张琪昌）（ＴｉａｎｊｉｎＵｎｉｖｅｒｓｉｔｙ．Ｔｉａｎｊｉｎ３０００７２．Ｐ．Ｒ．Ｃ...     

Unsupervised neural network model optimized with evolutionary computations for solving variants of nonlinear MHD Jeffery-Hamel problem

A heuristic technique is developed for a nonlinear magnetohydrodynamics(MHD) Jeffery-Hamel problem with the help of the feed-forward artificial neural network(ANN) optimized with the genetic algorithm(GA) and the sequential quadratic programming(SQP) method. The two-dimensional(2D) MHD Jeffery-Hamel problem is transformed into a higher order boundary value problem(BVP) of ordinary differential equations(ODEs). The mathematical model of the transformed BVP is formulated with the ANN in an unsupervised manner. The training of the weights of the ANN is carried out with the evolutionary calculation based on the GA hybridized with the SQP method for the rapid local convergence. The proposed scheme is evaluated on the variants of the Jeffery-Hamel flow by varying the Reynold number, the Hartmann number, and the angles of the walls. A large number of simulations are performed with an extensive analysis to validate the accuracy, convergence, and effectiveness of the scheme. The comparison of the standard numerical solution and the analytic solution establishes the correctness of the proposed designed methodologies.     

用神经网络和优化方法进行结构参数识别

本文分别采用优化方法和神经网络方法,对工程中经常碰到的结构参数识别问题进行了研究,论文对一个二层试验框架和香港青马大桥马湾塔的实测资料进行了分析,结果表明,两种方法对于解决实际 工程结构的参数识别问题都是可行的,精度可以满足工程要求,并对这两种方法作了对比,指出了各自的优缺点和值得进一步研究的问题。     

On the boundary value problems for ordinary differential equations with turning points

In this paper,we consider the boundary value problems of the formsy″-f(x,ε)y′ g(x,ε)=0 (-a≤x≤b,0≤ε《1 )y(-a)=a,y(b)=βwhere f(x,0)has several and multiple zeros on the interval[-a,b].The conditions forexhibiting boundary and interior layers are given,and the corresponding asymptoticexpansions of solutions are constructed.     

The estimation of solution of the boundary value problem of the systems for quasi-linear ordinary differential equations

This paper deals.with the singular perturbation of the boundary value problem of the systems for quasi-linear ordinary differential equations where x,f, y, h, A, B and C all belong to Rm, and g is an n×n matrix function. Under suitable conditions we prove the existence of the solutions by diagonalization and the fixed point theorem and also estimate the remainder.     

Multivariate padé approximation for solving partial differential equations (PDE)

In this paper, numerical solution of partial differential equations (PDEs) is considered by multivariate padé approximations. We applied these method to two examples. First, PDE has been converted to power series by two‐dimensional differential transformation, Then the numerical solution of equation was put into multivariate padé series form. Thus, we obtained numerical solution of PDE. Copyright © 2010 John Wiley & Sons, Ltd.     

时变环境与损伤耦合下桥梁结构频率及阻尼比的统计分析

对时变环境与损伤耦合下我国某斜拉桥的结构频率及阻尼比进行统计分析,以提高结构损伤识别的精度.首先,利用该桥的长期监测数据,采用环境激励技术结合特征系统实现算法识别该桥梁结构的频率及阻尼比;其次,利用人工神经网络算法建立该桥梁结构的环境温度与结构频率及阻尼比的关系模型;然后,通过统计分析,建立完好状态下该桥梁结构模态参数误差因子的概率分布模型;最后,通过分析不同时段与完好结构状态下该桥梁结构模态参数误差因子的相交概率比识别结构损伤,并利用该桥的实测结果验证所提算法的有效性.     

部分输入未知时求解动力复合反演问题的补偿算法

将作者提出的全量补偿算法[8] 推广为一类适用于一般多自由度系统的时域补偿识别算法。该方法是基于最小二乘原则的一类迭代计算方法 ,对于结构上的部分作用力已知的情况 ,可用来同时识别结构的参数并反演输入。文中应用不同类型的结构分析实例说明了此方法适用于实际工程动力检测的可能性。     

A UNIFORMLY DIFFERENCE SCHEME OF SINGULAR PERTURBATION PROBLEM FOR A SEMILINEAR ORDINARY DIFFERENTIAL EQUATION WITH MIXED BOUNDARY VALUE CONDITION

ＡＵＮＩＦＯＲＭＬＹＤＩＦＦＥＲＥＮＣＥＳＣＨＥＭＥＯＦＳＩＮＧＵＬＡＲＰＥＲＴＵＲＢＡＴＩＯＮＰＲＯＢＬＥＭＦＯＲＡＳＥＭＩＬＩＮＥＡＲＯＲＤＩＮＡＲＹＤＩＦＦＥＲＥＮＴＩＡＬＥＱＵＡＴＩＯＮＷＩＴＨＭＩＸＥＤＢＯＵＮＤＡＲＹＶＡＬＵＥＣＯＮＤＩＴ...     

ASYMPTOTIC STABILITIES OF STOCHASTIC FUNCTIONAL DIFFERENTIAL EQUATIONS

Asymptotic characteristic of solution of the stochastic functional differential equation was discussed and sufficient condition was established by multiple Lyapunov functions for locating the limit set of the solution. Moreover, from them many effective criteria on stochastic asymptotic stability, which enable us to construct the Lyapunov functions much more easily in application, were obtained. The results show that the well-known classical theorem on stochastic asymptotic stability is a special case of our more general results. In the end, application in stochastic Hopfield neural networks is given to verify our results.     

SELF-ADAPTIVE STRATEGY FOR ONE-DIMENSIONAL FINITE ELEMENT METHOD BASED ON ELEMENT ENERGY PROJECTION METHOD

Based on the newly-developed element energy projection (EEP) method for computation of super-convergent results in one-dimensional finite element method (FEM), the task of self-adaptive FEM analysis was converted into the task of adaptive piecewise polynomial interpolation. As a result, a satisfactory FEM mesh can be obtained, and further FEM analysis on this mesh would immediately produce an FEM solution which usually satisfies the user specified error tolerance. Even though the error tolerance was not completely satisfied, one or two steps of further local refinements would be sufficient. This strategy was found to be very simple, rapid, cheap and efficient. Taking the elliptical ordinary differential equation of second order as the model problem, the fundamental idea, implementation strategy and detailed algorithm are described. Representative numerical examples are given to show the effectiveness and reliability of the proposed approach.     

部分输入未知条件下结构参数识别法研究

深入研究了输入信息测试不完备条件下的结构参数识别问题,从理论上论证了部分输入未知时动力复合反演问题补偿算法的实质,指出了全量补偿算法在严格意义上的适用条件,提出了更为简便的二阶段识别法,使部分输入未知条件下结构参数识别的理论进一步完善,并可为工程应用提供指导。数值算例验证了理论上的正确性。     

Self-adaptive one-dimensional nonlinear finite element method based on element energy projection method

The element energy projection （EEP） method for computation of super- convergent resulting in a one-dimensional finite element method （FEM） is successfully used to self-adaptive FEM analysis of various linear problems, based on which this paper presents a substantial extension of the whole set of technology to nonlinear problems. The main idea behind the technology transfer from linear analysis to nonlinear analysis is to use Newton＇s method to linearize nonlinear problems into a series of linear problems so that the EEP formulation and the corresponding adaptive strategy can be directly used without the need for specific super-convergence formulation for nonlinear FEM. As a re- sult, a unified and general self-adaptive algorithm for nonlinear FEM analysis is formed. The proposed algorithm is found to be able to produce satisfactory finite element results with accuracy satisfying the user-preset error tolerances by maximum norm anywhere on the mesh. Taking the nonlinear ordinary differential equation （ODE） of second-order as the model problem, this paper describes the related fundamental idea, the imple- mentation strategy, and the computational algorithm. Representative numerical exam- ples are given to show the efficiency, stability, versatility, and reliability of the proposed approach.     

A semi-analysis method of differential equations with variable coefficients under complicated boundary conditions

IntroductionInthemostcases,asfarasthesolutiontothedifferentialequationwithvariablecoefficientsisconcerned ,therehasbeennoanysatisfactoryanswer.Forthisreason ,thescholarsbothathomeandabroadhavedonesomeresearchjustasindicatedinRefs.[1 ] ,[2 ]and [3 ] ,etc.Theauthorsinthispaperhaveusedthefiniteelementmodelandthemetricfunctiontheoryincombinationwithadjustableparametermodelwithvariablecoefficientstosimplifythesolutiontothedifferentialequationwithvariablecoefficientsintothefeaturevalueaswellasthefea…     

Ordinary differential equations (ODEs) on inertial manifolds for reaction-diffusion systems in a singularly perturbed domain with several thin channels

Dynamics of solutions to a reaction-diffusion system in a domain of specific shape is investigated under the homogeneous Neumann boundary conditions. It is assumed that the domain hasN large regionsD _i ,i=1,...,N, and thin channelsQ _i,j () connectingD _i andD _j , which approach a line segment as 0 in some sense. In such a domain the firstN eigenvalues of – with the Neumann boundary conditions tend to zero as 0, while the (N + 1)-th eigenvalue is bounded away from zero. By virtue of this gap of the eigenvalues, an inertial manifold which is invariant and attracts every solution exponentially can be constructed under a certain condition. Moreover, the ODE describing the dynamics on the inertial manifold can be given in quite an explicit form through the analysis of the limit of the manifold as 0.     

组合神经网络在结构损伤检测中的应用

子结构的动态响应变化与整体结构相比,对结构内部损伤反应更为敏感。组合神经网络可以克服单个神经网络功能的单一局限性,实现更加全面综合的仿真识别功能。本文首先运用双协调自由界面模态综合法对结构进行模态分析,获取各子结构及整体结构的模态信息。然后,通过组合BP神经网络将损伤子结构与整体结构的模态频率变化率组合起来进行结构损伤检测。该方法在改善网络训练性能的同时,提高了检测结果的准确性和可靠性。文章最后通过数值算例验证了该方法的可行性和有效性。     

基于控制响应的时变系统模态参数辨识的改进子空间方法

提出了一种基于系统控制信号激发的响应数据来辨识时变系统模态参数的改进子空间方法。该方法以系统控制响应信号建立系统的状态空间输出方程并构造了一个广义Hankel矩阵,通过对该矩阵做奇异值分解(SVD),用广义能观阵的估计代替输出矩阵,然后利用奇异值矩阵的正交性,有效地降低了噪声敏感性和计算量,从而容易地辨识出等效状态下的系统矩阵,最后采用转换矩阵辨识出时变系统的模态参数。通过理论分析、仿真和实验,讨论了不同信噪比对辨识结果的影响,验证了该方法的有效性。     

基于附加虚拟质量的结构损伤识别方法

针对大型土木结构的模态信息往往对局部损伤灵敏度较低的特点,提出通过在各个子结构上附加虚拟质量的方法提高局部灵敏度,实现整体结构的准确损伤识别。该方法无需在结构上布置真实质量,它首先利用虚拟变形法（VDM）可进行结构快速重分析的思想,由实测结构的激励和加速度响应,构造结构附加虚拟质量后虚拟结构的频率响应;然后结合灵敏度分析和附加质量与频率关系,确定所需附加质量和对应具有较高灵敏度的频率;最后分别在每个子结构上附加虚拟质量,联合所有虚拟结构和对应的频率即可准确快速地识别出整体结构各个子结构的损伤。本文通过两层平面框架有限元模型验证了附加质量损伤识别方法的有效性。     

Solving shock wave with discontinuity by enhanced differential transform method (EDTM)

An enhanced differential transform method (EDTM), which introduces the Padé technique into the standard differential transform method (DTM), is proposed. The enhanced method is applied to the analytic treatment of the shock wave. It accelerates the convergence of the series solution and provides an exact power series solution.     

Two-dimensional equations for thin-films of ionic conductors

A theoretical model is developed for predicting both conduction and diffusion in thin-film ionic conductors or cables. With the linearized Poisson-Nernst-Planck (PNP) theory, the two-dimensional (2D) equations for thin ionic conductor films are obtained from the three-dimensional (3D) equations by power series expansions in the film thickness coordinate, retaining the lower-order equations. The thin-film equations for ionic conductors are combined with similar equations for one thin dielectric film to derive the 2D equations of thin sandwich films composed of a dielectric layer and two ionic conductor layers. A sandwich film in the literature, as an ionic cable, is analyzed as an example of the equations obtained in this paper. The numerical results show the effect of diffusion in addition to the conduction treated in the literature. The obtained theoretical model including both conduction and diffusion phenomena can be used to investigate the performance of ionic-conductor devices with any frequency.