Fault diagnosability utilizing quasi-static and structural modelling

This paper presents a diagnosis model-based method to analyse fault discriminability and assess diagnosability. The technique is based on the state space representation of quasi-static models. Fault diagnosability characterises the faults that can be discriminated using the available sensors in a system. The method can be used to select the minimum set of sensors that guarantee discriminability of an anticipated set of faults. The approach is applied on a two-tanks system benchmark and is compared to a diagnosability analysis method based on structural analysis.     

Simultaneous estimation of thin film thickness and optical properties using two-stage optimization

In this work, we proposed the new method for estimation of the thickness and the optical properties of the thin metal oxide film deposited on a transparent substrate. The developed method uses only transmittance spectra measured. Our method is based on the two stage optimization where the thickness is determined in the outer stage and the optical properties are determined in the inner stage. The differential evolutionary algorithm is used in solving the formulated problem. The proposed method was illustrated in the case study of Titanium dioxide film deposited on a glass substrate. The results indicate that the thickness and the optical properties estimated agree well with the experiment. Moreover, we investigated robustness of the proposed method in the case of transmittance spectra containing noises. The data were modelled by adding random noises ranging between 0 and 30% to the transmittance spectra measured. It is seen that the proposed method has better robustness and performance than the existing method based on pointwise unconstrained minimization approach. In solving the estimation problem, the performance of the proposed method was also compared with the well-known Levenberg?CMarquardt method and single stage differential evolutionary method. The results indicate that the proposed method has better performance than Levenberg?CMarquardt method and single stage differential evolutionary method. Moreover, the proposed method is more robust to random noise than Levenberg?CMarquardt method and single stage differential evolutionary method.     

The Impact of Equal Weighting of Low- and High-Confidence Observations on Robust Linear Regression Computations

Equal weighting of low- and high-confidence observations occurs for Huber, Talwar, and Barya weighting functions when Newton's method is used to solve robust linear regression problems. This leads to easy updates and/or downdates of existing matrix factorizations or easy computation of coefficient matrices in linear systems from previous ones. Thus Newton's method based on these functions has been shown to be computationally cheap. In this paper we show that a combination of Newton's method and an iterative method is a promising approach for solving robust linear regression problems. We show that Newton's method based on the Talwar function is an active set method. Further we show that it is possible to obtain improved estimates of the solution vector by combining a line search method like Newton's method with an active set method.This revised version was published online in October 2005 with corrections to the Cover Date.     

B-Spline collocation method for linear and nonlinear Fredholm and Volterra integro-differential equations

A numerical method based on quintic B-spline has been developed to solve the linear and nonlinear Fredholm and Volterra integro-differential equations up to order 4. The solution and its derivatives are collocated by quintic B-spline and then the integral equation is approximated by the 4-points Gauss–Turán quadrature formula with respect to the weight function Legendre. The error analysis of proposed numerical method is studied theoretically. Numerical results are given to illustrate the efficiency of the proposed method which shows that our method can be applied for large values of N. The results are compared with the results obtained by other methods which show that our method is accurate.     

重尾分布的尾部指数估计及沪深股市实证分析

重尾分布尾部指数α的估计依赖于样本中所用顺序统计量个数k的选取.本文介绍了估计α时选择k的两类不同的方法:Sum-plot方法和Bootstrap方法,并对Hall提出的Bootstrap方法作了改进,称为M-Bootstrap方法.本文利用上述方法对已知分布进行Monte-Carlo模拟,研究它们的可行性,然后对上海和深圳两市股指数据进行了实证分析.计算结果表明,上海和深圳股指收益率具有重尾性.是右偏态的,右尾厚于左尾.通过几种方法计算的结果比较发现Sum-plot方法和M-Bootstrap方法在估计重尾指数上精确性较高一些,而且不受异常值的影响.     

Extended multiscale FEM for design of beams and frames with complex topology

A numerical method for design of beams and frames with complex topology is proposed. The method is based on extended multi-scale finite element method where beam finite elements are used on coarse scale and continuum elements on fine scale. A procedure for calculation of multi-scale base functions, up-scaling and downscaling techniques is proposed by using a modified version of window method that is used in computational homogenization. Coarse scale finite element is embedded into a frame of a material that is representing surrounding structure in a sense of mechanical properties. Results show that this method can capture displacements, shear deformations and local stress-strain gradients with significantly reduced computational time and memory comparing to full scale continuum model. Moreover, this method includes a special hybrid finite elements for precise modelling of structural joints. Hence, the proposed method has a potential application in large scale 2D and 3D structural analysis of non-standard beams and frames where spatial interaction between structural elements is important.     

Resonance and chaos of micro and nano electro mechanical resonators with time delay feedback

The resonance and chaos of micro (nano) electro mechanical resonators with time delay feedback is concerned in the paper. Based on the experimental results, a lumped single degree-of-freedom (1DOF) model is studied and the effects of time delay displacement and velocity feedback on the system are investigated. In order to have a deep insight into the system, the amplitude frequency response curve of the system is firstly obtained using the multiple scales method. The Melnikov function method is then extended to the two time delay systems, and the analytically required condition for chaos was obtained. Finally, the fourth-order Runge–Kutta method, point-mapping method and spectrum diagram are used to simulate the evolution of the dynamic behavior of the time delay control system. Also, the stability of this time delay control system is studied thoroughly. The results show that time delay feedback is a good method for the control system and that reasonable selection of control system parameters can effectively suppress the vibration level for micro/nano-electro-mechanical resonator systems.     

Serial and parallel resource-constrained project scheduling methods revisited: Theory and computation

We consider the so-called parallel and serial scheduling method for the classical resource-constrained project scheduling problem. Theoretical results on the class of schedules generated by each method are provided. Furthermore, an in-depth computational study is undertaken to investigate the relationship of single-pass scheduling and sampling for both methods. It is shown that the performance-ranking of priority rules does not differ for single-pass scheduling and sampling, that sampling improves the performance of single-pass scheduling significantly, and that the parallel method cannot be generally considered as superior.     

滑动数据重心预测方法及其应用研究

本文在研究多因素数据重心法的基础上,进一步提出滑动数据重心预测方法,该方法是对原始样本数据提出了一种新的数据处理方法,大大降低了由于历史数据组中的异常点对预测结果产生的破坏性。通过建立我国钢材消费量与国内生产总值(GDP)的计量动态模型对该方法与多因素数据重心预测法进行对比研究。同时利用时间序列自回归AR(p)对计量动态模型的初级预测结果进行差值校正,并将该方法应用于我国2015年、2020年的钢材消费量预测。对比研究表明该方法使得预测结果更加精确、稳健。     

一种新的迭代收敛阶数的证明与推广

迭代方法是求解非线性方程近似根的重要方法.本文基于隐函数存在定理,提出了一种新的迭代方法收敛性和收敛阶数的证明方法,并分别对牛顿(Newton)和柯西(Cauchy)迭代方法迭代收敛性和收敛阶数进行了证明.最后,利用本文提出的证明方法,证明了基于三次泰勒(Taylor)展式构成的迭代格式是收敛的,收敛阶数至少为4,并提出猜想,基于n次泰勒展式构成的迭代格式是收敛的,收敛阶数至少为(n+1).     

PLK方法与符号运算

阐述将PLK方法与符号运算相结合的途径和有效性.首先简述PLK方法的思路和发展简史:其次,概述运行符号运算时经常遇到的“中间表达式爆炸”困难,为克服这一困难,作者提出一种半逆序算法:通过以符号形式“冻结”中间表达式中冗长的部分,到最后阶段再予“解冻”;并且通过综述作者在一系列非线性波动和非线性振动方面的工作,讨论PLK-符号运算方法的具体应用,其中,Duffing方程的摄动解的计算机延伸表明,用PLK方法导得的渐近级数解的收敛半径为1,从而大大拓广了解的适用范围;分层流体中内孤立波和超弹性杆中孤立波对撞的研究表明,用所提出的方法可以进行手工计算难以进行的复杂运算,借此可得出高阶演化方程和高阶渐近解,正确地解释实验结果;并说明采用半逆序算法后,可在微机上实现繁复的符号运算.最后得出结论:借助于符号运算,可大大增强PLK方法的生命力,至少对保守系统的振动和波动问题的求解,它是一个非常有效的工具.     

高体积分数颗粒增强复合材料有效线性与非线性介电性质的研究

基于两球相互作用的近似解,提出了一种解析方法来预测颗粒增强复合材料的线性有效介电性质,该方法可以应用于颗粒体积分数较高(可达50%)的情况．利用割线方法还研究了该类复合材料的非线性有效性质．结果表明当外加电场较弱时该文提出的方法与Stroud和Hui的方法比较接近,当外场较强时与Yu和Hui的方法一致．     

遗传算法结合神经网络在油气产量预测中的应用

基于遗传算法的全局搜索能力和BP算法的局部精确搜索特性,通过采用遗传算法优化神经网络的方法,将遗传算法和BP算法有机结合,做到优势互补,在提高油气产量预测精度的研究中得到了很好的应用.在对国内某中小型气田油气产量的预测中,以历史产量资料进行检验,其结果表明,提出的预测方法,预测精度明显优于BP算法,证明了这种方法的有效性和可靠性.     

基于云模型的定性运算理论与方法

将定性值像定量值一样参与运算和推导,是定性理论走向真正实际应用必须解决的极为关键的研究问题.相关研究提出的方法在此方面均有一定的局限性.本文提出了一种基于云模型的定性运算理论与方法.首先在云模型基本运算的基础上提出了基于云模型的定性关系演算方法,其次提出了基于云模型的一元一次定性方程的求解方法.理论和方法能比较科学合理地计算出定性值,且具有定性与定量相互融合的特点.为定性演算和推导在系统分析和仿真等领域中进一步应用提供了重要的借鉴方法.     

Skewness and the Beta Distribution

In this paper, alternative methods for estimating the beta distribution are proposed that utilize more information than the standard method based on the best, worst and most likely estimates. In particular, it is shown how information on skewness or the decision-maker's level of confidence can be incorporated into the estimation process. This provides an alternative to the restrictive assumptions that have to be made in the standard method. This is particularly useful when the skewness is expected to be high, or in situations where the degree of uncertainty is high.     

拉开档次法稳定性分析及改进

采用随机模拟仿真的方法分别从增添异常对象和极端样本两个方面对拉开档次法的稳定性进行了分析,给出了相关结论。在此基础上,基于“因子分析”提出了拉开档次法的改进方法,算例部分的分析表明该方法因兼顾了同类数据之间的内部差异,能够削弱“异常值”对原始数据的干扰作用,从而进一步提升了方法的稳定性。最后,指出拉开档次法适用于评价指标数目较少的评价问题,而基于“因子分析”的改进方法则适合于数据数目较多且指标有相关关系的评价问题。     

藤Copula模型与多资产投资组合VaR预测

投资组合风险管理往往涉及多个资产,在传统的二元Copula函数面临"维度诅咒"问题及多元Copula函数刻画多变量联合分布时其精确性和灵活性存在各种局限性的情况下,引入藤Copula刻画多个资产收益的联合分布,基于不同的Pair-Copula类别构建藤Copula,运用蒙特卡罗模拟方法计算多资产投资组合的VaR,通过Kupiec和Christoffersen返回检验方法测试藤Copula模型的VaR预测效果,并与传统方差-协方差风险管理方法做比较。实证分析表明,传统的方差-协方差风险管理方法和基于正态Pair-Copula作为藤Copula构建模块的方法不能通过多资产投资组合的VaR预测返回检验;而基于student-t Copula、Clayton Copula具有尾部分布特征的Copula作为构建模块的藤Copula模型能够有效地用于多资产投资组合VaR预测,从而更好的用于指导实践。     

DEA与DRF法的整合

本文针对利用DEA模型进行有效性评价时碰到问题，提出了用因子分析法（简称DRF法）与DEA法相结合来进行评价，这是对DEA法的一种改进。并在此基础上对医院绩效进行了评价，为财政部门科学制定《医疗单位财政支出效益评价实施办法》提供依据。     

确定递阶层次结构的简便方法

运用层次分析法(AHP)解决决策问题时,第一步就是要确定问题的递阶层次结构.对此,现有文献中给出的数学方法都是基于可达矩阵的,它通常需要借助计算机来完成.在文中充分考虑到AHP递阶层次结构的特点严格的逐层相关性及元素间无互相关性,给出一种非常简单的方法—划列法(DRM),并严格证明了其正确性,然后通过举例给予说明.该方法使递阶层次结构的确定不必再进行可达矩阵等计算,只依靠手工即可完成.     

二阶和四阶椭圆型偏微分方程的镜像基本解方法及应用

将基本解方法推广到二阶和四阶椭圆型偏微分方程的对称问题,在边界上不需要处理奇异积分.通过坐标变换,将一般二阶和四阶椭圆型偏微分方程化为目前研究较为成熟的调和或双调和方程.再根据镜像法构造出适合对称条件的基本解函数,简化了计算,且不影响计算的精度.通过数值计算结果可以看出,利用镜像技术构造出的基本解,前期准备数据少,可保持精度,是一种有效的数值方法.