DSFT下模糊结构元特征函数构建及结构元化的意义

为解决DSFT通过因素投影拟合法得到的特征函数无法表示原始离散故障数据分布特征的缺点,引入模糊结构元理论将特征函数结构元化,形成模糊结构元特征函数来解决该问题。模糊结构元特征函数可通过模糊结构元E表示原始数据的离散分布特征,并在计算过程中将E传递至最终结果。通过处理结果中E来得到分析结果的置信度。模糊结构元特征函数可将DSFT问题转化为较成熟的CSFT进行处理,而不用为实现相同功能针对DSFT研究新的方法。论文给出了模糊结构元特征函数的构建思想、基础理论、具体步骤和方法。并针对已有数据和特征函数构建了相应的模糊结构元特征函数。     

一类具有二阶细焦点的二次系统

本文为文[3]的继续,研究一类特殊的二次系统,推广了文[3]的结论与方法,并得到了二次系统的焦点量与由该二次系统转换得到的Liénard方程的特征函数的一些内在联系。     

对边简支十次对称二维准晶板弯曲问题的辛分析北大核心CSCD

该文讨论了对边简支十次对称二维准晶中厚板弹性问题的辛方法.将十次对称二维准晶弹性理论基本方程转化为Hamilton对偶方程,采用分离变量方法,获得了相应Hamilton算子矩阵的辛特征值及辛特征函数系.证明了Hamilton算子矩阵的辛特征函数系在Cauchy主值意义下的完备性,在此基础上,基于Hamilton系统的辛特征函数展开,给出了十次对称二维准晶板弯曲问题的解析表达式.     

边界条件中带有谱参数的不连续Sturm-Liouville算子的特征函数系的完备性

本文研究了具有转移条件且边界条件含特征参数的Sturm-Liouville算子L的特征函数系的完备性问题.首先,使用微分算子谱分析经典的方法,得到了λ是该边值问题的特征值的充要条件.之后,借助新空间H和新算子T,证明了算子L的特征函数系作为新算子T的特征函数第一个分量形式H的标准正交基.     

一类基于经验特征函数的正则化数值微分方法

利用经验特征函数,我们提出了一种$\ell^1$正则化数值微分方法.区别于传统的数值微分方法,该方法直接输出了目标函数的近似导数.更进一步,我们的方法可以产生关于经验特征函数的稀疏表示.数值结果显示了该方法的有效性.     

特征函数的性质

得到了特征函数、条件特征函数的一致可微性和条件特征函数的反演公式.     

边界条件中带有谱参数的不连续Sturm-Liouville算子北大核心CSCD

本文研究了具有转移条件且边界条件有特征参数的Sturm-Liouville算子T.首先由算子T本身出发研究其特征值问题,得到了λ是该边值问题的特征值的充要条件.借助新空间H和新算子A,通过构造算子A的Green函数,证明了算子T的特征函数扩张成新算子A的特征函数形成H的标准正交基.     

具有内阻尼和边界反馈控制的一类Euler-Bernoulli梁方程的Riesz基性质

考虑一类具有内阻尼和边界反馈控制的一维Euler-Bernoulli梁方程.中导出系统特征值和特征函数的渐近表达式,并且通过Riesz基生成定理的优点,证明该系统是一个Riesz系统,即该系统存在一列广义特征函数构成能量状态空间的一组Riesz基.从而,系统的谱决定增长条件成立,进而证明系统的指数稳定性.     

带转移条件的Strum-Liouville问题特征函数的振动性

研究了一类带转移条件的Sturm-Liouville问题在区间(a,c)∪(c,b)上特征函数的振动性,构建了一个与该问题相关的新的Hilbert空间,证明了具有分离边界条件的这类问题的第n个特征值λn(n=1,2,…)所对应的特征函数在区间(a,c)∪(c,b)上有n-1个或n个零点,除此之外,还有-个特征值λ0所对应的特征函数在区间(a,c)∪(c,b)上没有零点.     

特征值问题协调/非协调有限元后验误差分析

本文研究对称椭圆特征值问题的有限元后验误差估计,包括协调元和非协调元,具有下列特色:(1)对协调/非协调元建立了有限元特征函数uh的误差与相应的边值问题有限元解的误差在局部能量模意义下的恒等关系式,该边值问题的右端为有限元特征值λh与uh的乘积,有限元解恰好为uh.从而边值问题有限元解在能量模意义下的局部后验误差指示子,包括残差型和重构型后验误差指示子,成为有限元特征函数在能量模意义下的局部后验误差指示子.(2)讨论了协调有限元特征函数的基于插值后处理的梯度重构型后验误差估计,对有限元特征函数的导数得到了最大模意义下的渐近准确局部后验误差指示子.     

The parameterization method in optimal control problems and differential–algebraic equations

The paper is devoted to the explanation of the numerical parameterization method (PM) for optimal control (OC) problems with intermediate phase constraint and to its circumstantiation for classical calculus of variation (CV) problems that arise in connection with singular ODEs or DAEs, especially in cases of their essential degeneracy. The PM is based on a finite parameterization of control functions and on derivation of the problem functional with respect to control parameters. The first and the second derivatives are calculated with the help of adjoint vector and matrix impulses. Results of the solution to one phase constrained OC and two degenerate CV problems, connected with singular DAEs nonreducible to the normal form, are presented.     

An Extended Ant Colony Algorithm and Its Convergence Analysis

In this work, we propose a stochastic algorithm for solving combinatorial optimization problems. The procedure is formulated within the Ant Colony Optimization (ACO) framework, and extends the so-called Graph-based Ant System with time-dependent evaporation factor, (GBAS/tdev) studied in Gutjahr (2002). In particular, we consider an ACO search procedure which also takes into account the objective function value. We provide a rigorous theoretical study on the convergence of the proposed algorithm. Further, for a toy example, we compare by simulation the rate of convergence of the proposed algorithm with those from the Random Search (RS) and from the corresponding procedure in Gutjahr (2002).AMS 2000 Subject Classification: 9OC15, 9OC27     

基于集团属性的计数型抽样检验及其研究进展

本文以家蚕微粒子病集团母蛾抽样检验的历史背景为线索,介绍了基于集团属性的计数型抽样检验的概念、OC函数及其算法的研究进展,以及在农业产品质量控制中的应用和意义,同时指出集团抽样检验的应用前景和今后需要解决的问题。     

A new multiobjective simulated annealing algorithm

A new multiobjective simulated annealing algorithm for continuous optimization problems is presented. The algorithm has an adaptive cooling schedule and uses a population of fitness functions to accurately generate the Pareto front. Whenever an improvement with a fitness function is encountered, the trial point is accepted, and the temperature parameters associated with the improving fitness functions are cooled. Beside well known linear fitness functions, special elliptic and ellipsoidal fitness functions, suitable for the generation on non-convex fronts, are presented. The effectiveness of the algorithm is shown through five test problems. The parametric study presented shows that more fitness functions as well as more iteration gives more non-dominated points closer to the actual front. The study also compares the linear and elliptic fitness functions. The success of the algorithm is also demonstrated by comparing the quality metrics obtained to those obtained for a well-known evolutionary multiobjective algorithm.     

Adaptive mesh method for topology optimization of fluid flow

In order to solve the topology optimization problems of fluid flow and obtain higher resolution of the interface with a minimum of additional expense, an automatic local adaptive mesh refinement method is proposed. The optimization problem is solved by a simple but robust optimality criteria (OC) algorithm. A material distribution information based adaptive mesh method is adopted during the optimization process. The optimization procedure is provided and verified with several benchmark examples.     

An approximate subgradient algorithm for unconstrained nonsmooth,nonconvex optimization

In this paper a new algorithm for minimizing locally Lipschitz functions is developed. Descent directions in this algorithm are computed by solving a system of linear inequalities. The convergence of the algorithm is proved for quasidifferentiable semismooth functions. We present the results of numerical experiments with both regular and nonregular objective functions. We also compare the proposed algorithm with two different versions of the subgradient method using the results of numerical experiments. These results demonstrate the superiority of the proposed algorithm over the subgradient method.      

Identification of multiple-input single-output Hammerstein models using Bezier curves and Bernstein polynomials

This paper considers the implementation of Bezier–Bernstein polynomials and the Levenberg–Marquart algorithm for identifying multiple-input single-output (MISO) Hammerstein models consisting of nonlinear static functions followed by a linear dynamical subsystem. The nonlinear static functions are approximated by the means of Bezier curves and Bernstein basis functions. The identification method is based on a hybrid scheme including the inverse de Casteljau algorithm, the least squares method, and the Levenberg–Marquart (LM) algorithm. Furthermore, results based on the proposed scheme are given which demonstrate substantial identification performance.     

进化泛函网络多维函数逼近理论及学习算法

提出了一种用于多维函数逼近的进化策略修正泛函网络基函数系数的新算法,并给出了其算法学习过程.利用进化策略的自适应性来确定基函数前的系数,改进了泛函网络的参数通过解方程组来得到这一传统方法.仿真结果表明,这种新的逼近算法简单可行,能够逼近给定的函数到预先给定的精度,具有较快的收敛速度和良好的逼近性能.     

Incremental allocation of a discrete and convex resource to concave activities

The problem considered is that of the allocation of a given quantity of a discrete resource to activities described by concave return functions. The resource-consumption corresponding to each allocation is described by a convex function of the quantity allocated. An incremental solution algorithm is given, which specializes to the algorithm of Fox if the resource is linear, and to an algorithm of Katoh, Ibaraki and Mine if the return functions are linear.     

General EM algorithm for fitting non-monotone hazard functions from truncated and censored observations

Recently, many researchers focused on modeling non-monotonic hazard functions such as bath-tube and hump shapes. However, most of their estimation methods are focused on complete observations. Since reliability data are typically censored and truncated, a general EM algorithm is proposed, which can fit any of those complex hazard functions. The proposed EM algorithm is analyzed by fitting well-known 4-parameter hazard functions, where its performance is compared by their specific direct methods through extensive Monte Carlo simulations.