灰色组合模型及其应用

本建立了GM(1．1)与线性回归模型的组合模型，改进了单一模型的局限性，并用此模型预测了郑州市粮食总产量，得到了较为满意的结果。     

敏感性问题“随机变量和”回答模型

孔圣元，孟生旺．敏感性问题“随机变量和”回答模型．数理统计与管理，１９９８，１７（２），３５～３９．本文依据概率论中“随机变量和”的分布理论，对敏感性问题的调查，提出了一个新模型，即“随机变量和”回答模型，实现了敏感性问题的问卷调查。本文给出了模型的最优估计量及其方差的计算公式，讨论了模型参数的合理选择，同时还得出了一个有趣的结果：“随机化回答模型”包含在“随机变量和”回答模型之中。     

开发区居民分布模型研究

本文从规划区土地利用状况出发，建立了居民分布的引力模型和概率模型，在规划区就业人口分成就业区就业人口和居住区服务就业人口的基础上，研究了运用模型分布这两种就业人口的方法，并建立分布全部居民的模型，最后给出了模型应用实例．     

软件可靠性M-O模型和逆线性模型的参数估计

Musa-Okumoto模型和逆线性模型是研究软件可靠性的重要模型，给出了在分组数据下，M－O模型和逆线性模型中参数的最大似然估计及其存在的充分性条件，指出了[4]中的错误，并且给出了一个实例。     

具有测量误差的非线性模型的Bayes估计

测量中大量的函数模型都是非线性回归模型．当回归变量含有一定的测量误差时，我们得到非线性测量误差模型．本讨论了这种模型中未知参数具有正态先验分布时的参数Bayes估计方法，并对这种估计进行了影响分析，证明了删除模型与均值漂移模型中参数的Bayes估计相同，利用Cook统计量给出了删除模型下参数的Bayes估计的影响度量．     

项目投资组合的风险度及其最优决策

本文针对项目组合投资问题引入了风险度概念，并建立其风险度模型．在无零风险度项目的情况下，给出了该模型的最优项目组合投资策略并证明该策略为马氏有效．在有零风险度项目的情况下，讨论了该模型的有效前沿的结构、性质和有效性，同时还论证了该模型的有效前沿与威廉·夏普提出的资本资产定价模型的有效前沿相一致的线性关系．最后作为本模型的应用，构造了”保证还本”模型，给出了其最优项目投资组合的策略．     

股票价格波动的塑性性质及模型探讨

首先基于股票价格和成交量，根据股票的量价规律，分析了股价波动的塑性性质；然后使用计量经济学方法建立描述股价波动的塑性模型，包括股价塑性基本模型、基本模型的一阶自回归模型、幂指数模型及幂指数模型的一阶自回归模型，基于12支样本股对这些模型进行参数估计和检验；最后对4种形式的股价塑性模型进行了总结。由4种模型均能够通过经济学检验和统计学检验可知股价波动具有塑性性质，且幂指数模型描述股价塑性较为科学、合理。     

基于模糊数变换的DEA模型与应用

在数据包络分析(DEA)的C^2R模型的基础上，建立FC^2R模型。但现有的FC^2R模型，要求模糊输入输出指标值之间满足一定的严格条件，这在实际应用中有一定的局限性。为此本文在FC^2R模型的基础上，提出了一种基于模糊数变换的DEA模型(α-FC^2R模型)，拓展了传统DEA的应用范围，并将其应用于综合评价，取得了很好效果。     

考虑时间效应的机器负荷分配模型

机器人高低负荷分配问题是动态规划的应用之一，但该问题的动态规划模型一般都没有考虑资金，产值的时间价值效应，本在机器负荷分配的原动态规划模型基础之上，加入了时间因索，建立了考虑时间效应的机器高低负荷分配的动态规划模型，从而扩大了原模型的适应范围。     

腐败的三方动态博弈模型及其治理对策

本建立了腐败问题的三方动态博弈模型，并求出博弈模型的均衡解模型，根据均衡解，提出了治理腐败问题的对策。     

导弹贮存可靠性评估

本文针对导弹上不同部件在长期贮存中、所受影响不同及可修性不同等特点 ,将弹上部件分为五类 .在此基础上、研究给出了该类导弹的贮存可靠性物理模型和相应的数学模型 ,可称作配套系统模型 ,并通过一个简单实例介绍了具体计算方法     

Maintainability of a Grade Structure as a Transportation Problem

A new approach to the maintainability of a grade structure in a deterministic environment, using promotion control, is sought. Our main objective is to show how this manpower planning issue can be viewed in the context of transportation problems. By the same token, a condition for the maintainability of a structure will be proved to be sufficient.     

Reliability Measures of Semi-Markov Systems with General State Space

The aim of this paper is to present a systematic modeling of reliability and related measures: availability, maintainability, failure rate, rate of occurrence of failures, mean times, etc., known in the literature under the term dependability. This model includes the continuous and discrete time semi-Markov processes with general state space. This is one of the most general models in reliability theory since it includes as particular cases the Markov and renewal processes.     

Optimal component selection based on cohesion & coupling for component based software system under build-or-buy scheme

Component based software system approach is concerned with the system development by integrating components. The component based software construction primarily focuses on the view that software systems can be built up in modular fashion. The modular design is a logical collection of several independent developed components that are assembled with well defined software architecture. These components can be developed in-house or can be obtained commercially from outside market making build versus buy decision an important consideration in development process. Cohesion and coupling (C&C) plays a major role in determining the system quality in terms of reliability, maintainability and availability. Cohesion is defined as the internal interaction of components within the module. On the other hand, coupling is the external interaction of the module with other modules i.e. interaction of components amongst the modules of the software system. High cohesion and low coupling is one of the important criteria for good software design. Intra-modular coupling density (ICD) is a measure that describes the relationship between cohesion and coupling of modules in a modular software system and its value lies between zero and one. This paper deals with the selection of right mix of components for a modular software system using build-or-buy strategy. In this paper, fuzzy bi-criteria optimization model is formulated for component selection under build-or-buy scheme. The model simultaneously maximizes intra-modular coupling density (ICD) and functionality within the limitation of budget, reliability and delivery time. The model is further extended by incorporating the issue of compatibility amongst the components of the modules. A case study is devised to explain the formulated model.     

Advanced general-purpose computational mechanics system for large-scale analysis and design

We have been developing an advanced general-purpose computational mechanics system, named ADVENTURE, which is designed to be able to analyze a model of arbitrary shape with a 10–100 million degrees of freedom (DOFs) mesh, and additionally to enable parametric and nonparametric shape optimization. Domain-decomposition-based parallel algorithms are implemented in pre-processes (domain decomposition), main processes (system matrix assembling and solutions) and post-process (visualization), respectively. The hierarchical domain decomposition method with a pre-conditioned iterative solver (HDDM) is adopted in the main processes as one of the major solution techniques. Module-based architecture of the system with standardized I/O format and libraries are also developed and employed to attain flexibility, portability, extensibility and maintainability of the whole system. This paper describes some key technologies employed in the system, and shows some latest results including elastic stress analysis of a precise three-dimensional (3D) model of a nuclear reactor vessel with a 60 million DOF mesh on Hitachi SR2201 $\text{(1024}\text{PEs}\text{)}$, and nonparametric shape optimization of a support structure for an express way with a one million DOF mesh on a PC cluster $\text{(10}\text{PEs}\text{)}$.     

A low-order active fault-tolerant state space self-tuner for the unknown sampled-data nonlinear singular system using OKID and modified ARMAX model-based system identification

In this paper, we present two control schemes for the unknown sampled-data nonlinear singular system. One is an observer-based digital redesign tracker with the state-feedback gain and the feed-forward gain based on off-line observer/Kalman filter identification (OKID) method. The presented control scheme is able to make the unknown sampled-data nonlinear singular system to well track the desired reference signal. The other is an active fault tolerance state-space self-tuner using the OKID method and modified autoregressive moving average with exogenous inputs (ARMAX) model-based system identification for unknown sampled-data nonlinear singular system with input faults. First, one can apply the off-line OKID method to determine the appropriate (low-) order of the unknown system order and good initial parameters of the modified ARMAX model to improve the convergent speed of recursive extended-least-squares (RELS) method. Then, based on modified ARMAX-based system identification, a corresponding adaptive digital control scheme is presented for the unknown sampled-data nonlinear singular system with immeasurable system state. Moreover, in order to overcome the interference of input fault, one can use a fault-tolerant control scheme for unknown sampled-data nonlinear singular system by modifying the conventional self-tuner control (STC). The presented method can effectively cope with partially abrupt and/or gradual system input faults. Finally, some illustrative examples including a real circuit system are given to demonstrate the effectiveness of the presented design methodologies.     

Lur''''e系统稳定与同步的脉冲控制

提出了Lur’e系统的脉冲控制系统，利用关于脉冲系统稳定的几个定理，得到了具变化的脉冲区间的Lur'e系统镇定的充分条件；并且给出了Lur'e系统的适当参数与脉冲控制律，使得两个Lur'e系统脉冲同步。最后，给出数值例子说明本结论的有效性。     

噪声实验室供气系统的可靠性分析

文章研究了噪声实验室供气系统的可靠性问题,根据供气系统的工程设计框图绘制了可靠性框图．进而得到了供气系统的可靠性表达式．根据可靠性的评估方法,结合模拟试验的数据得到了供气系统可靠性评估的定量结果．通过时评估结果的分析,给出了改进噪声实验室供气系统的工程设计从而提高其可靠性的方法．     

Small-Amplitude free vibrations of straight beams subjected to large displacements and rotation

In this study, a systematic approach to study small-amplitude vibrations of large deflected straight beams is presented. The differential equation system of small-amplitude free vibrations about the deflected configuration is presented considering the effects of axial extension, shear deformation, and rotatory inertia. It is shown that in the absence of axial, and shear forces, the differential equation system of small-amplitude vibrations of the deflected beam becomes identical to that of an initially curved beam. To solve the differential equation system of the large deflection problem, Variational Iterational Method is used. Free vibration analysis around the deflected configuration is performed by using Differential Quadrature Method. Several numerical examples are solved to show the versatility of the presented approach.     

Approximate solutions of linear Volterra integral equation systems with variable coefficients

In this paper, a new approximate method has been presented to solve the linear Volterra integral equation systems (VIEs). This method transforms the integral system into the matrix equation with the help of Taylor series. By merging these results, a new system which corresponds to a system of linear algebraic equations is obtained. The solution of this system yields the Taylor coefficients of the solution function. Also, this method gives the analytic solution when the exact solutions are polynomials. So as to show this capability and robustness, some systems of VIEs are solved by the presented method in order to obtain their approximate solutions.