地震响应的凸集分析*

本文提出了一种用于表示地震动不确定性的椭球傅立叶界限凸集模型．从数学上严格推出了这种模型对单自由度系统的最坏响应．并给出了模型参数的几种选取方法．通过合理地选取模型界限参数,将椭球傅立叶界限凸集模型与模拟的地震波结果进行比较,证实了基于标准地震波的抗震设计的危险性．     

基于熵的不确定性敏感性分析

为确定影响维修保障信息分析结果不确定性的关键输入参数,提出一种基于熵的不确定性敏感性分析方法.首先分析了模型输出结果的不确定性的表现形式、度量方法、产生机制;其次基于条件熵思想给出分析不确定性的敏感性参数以及敏感性分析方法;然后,简单介绍了盲数理论在计算不确定性数据中的应用;最后,结合平均维修时间模型进行了案例研究,说明了基于熵的不确定性敏感性分析方法的可用性,并证明了不确定性敏感性分析与求导不能等同的结论.     

在消费者偏好不确定下双寡头定位定价博弈

本文通过建立在企业对消费者偏好信息不确定情形下,双寡头企业动态定位、定价博弈模型,研究企业的定位策略、定价策略以及产品差异化问题。证明了该动态博弈存在唯一的子博弈精炼均衡。均衡结果表明,偏好不确定性是一种差异化力量,与消费者偏好信息确定情形相比,企业的不确定性能够提高均衡价格、增加均衡利润。最后,分析了偏好不确定性对社会最优定位和社会最优差异化的影响。     

一种面向可靠性的改进不确定性重要度分析方法

作为识别和评估系统薄弱环节的有效工具之一的重要度理论,一直都被广泛应用于系统可靠性和安全性工程。而作为其主要环节的不确定性重要度分析更是扮演着不可或缺的角色。因此,为有效表征多态系统的可靠性,本文给出了一种变换数据处理方式的改进不确定性重要度分析方法。该模型是以两个累积分布函数之间的空间几何距离为基础,通过改变随机输入变量的不确定性范围和对应分布情况,模拟和描述输入对系统输出变量的相对影响趋势,并以两个累积分布函数之间的定积分面积表示。最后利用系统故障树对其进行不确定性重要度分析。结果表明,空间几何距离是一种用来表示输入变化对输出分布变化的相对影响的不确定性重要度度量的有效工具。     

集对分析法在联合火力打击陆军弹药消耗预测方案评估优选中的应用研究

联合火力打击陆军弹药消耗预测是一个复杂的问题,影响弹药消耗的因素很多,许多因素难以在预测过程中定量地计算,具有较强的不确定性.集对分析是一种新的不确定性分析方法,其联系度概念具有鲜明的辩证性、完整性,使其成为处理不确定性问题的有效方法.因此,引入集对分析理论,建立分析模型,针对联合火力打击陆军弹药消耗多种预测方案进行评估优选.结果表明,方法简便、通用,计算结果较为客观和稳定,可为联合火力打击陆军弹药消耗预测方案评估优选提供新的有效途径.     

因素空间中的背景分布与模糊背景关系

背景关系在因素空间的因果分析理论中是一个重要的概念,由它决定了因素之间的因果联系.但是在现实生活中,背景关系往往带有不确定性,由之而产生的推理也具有不确定性.为了适应人工智能对处理不确定性信息的根本需要,本文将针对随机性和模糊性的特点而提出因素空间的背景分布和模糊背景关系.背景分布是因素相空间中的概率分布,基于背景分布,可以得到各个因素的边缘相分布和因素之间的条件相分布,对于事物因果分析提供了一种概率推理的方法.模糊背景关系的引入更对事物的因果分析提供了一种模糊推理的方法.     

可靠性参数不确定性重要度研究

在系统可靠性分析中,参数不确定性是个突出的问题。本文从工程实际应用出发,提出了一种实用的不确定性重要度度量,从而为控制系统可靠性参数不确定性提供了有效途径。本文最后还给出一个算例演示了该重要度的计算。     

基于集对分析的多种不确定偏好形式大群体决策方法

针对具有多种不确定偏好形式的多方案大群体决策问题,提出一种基于集对分析的群决策方法。将区间数、三角模糊数以及语言值三种形式的不确定偏好转换为联系数,保留了不确定偏好信息中的确定性与不确定性。提出一种区间聚类算法,在决策成员权重未知的情况下对成员进行赋权。利用加权综合联系数对大群体偏好进行集结,根据方案的集对势大小给出方案的排序。该方法避免了确定权重时的主观性,同时考虑决策信息的确定性与不确定性,提高了决策结果的可信度。通过实例分析验证了方法的有效性和实用性。     

覆盖粗糙集的不确定性度量研究进展

覆盖粗糙集作为经典粗糙集一种较为流行的扩充模型,其现有不确定性度量方法主要包括覆盖粒度、粗糙度、粗糙熵、模糊度和模糊熵等。本文从纯粗糙集、信息论和模糊性三个视角对覆盖粗糙集的不确定性度量方法进行了分类梳理,通过结合覆盖粒度对覆盖粗糙度、覆盖精确度和覆盖粗糙熵进行了修正定义;设计了基于最小描述交的隶属函数,结合隶属函数对覆盖模糊度和覆盖模糊熵重新定义,给出了相关推论,分析了相关性质,为后续研究覆盖粗糙集不确定性的相关问题提供了新思路。     

区间数特性集对分析及在多指标决策中的应用

针对区间数多指标决策过程中区间数运算的不确定性问题,对区间数特性进行集对分析,利用区间数的确定性与不确定性,数量特性与空间位置特性以及这两对特性的相互关系,定义一种新的区间数加法运算和两区间数大小关系判别准则.实例应用表明方法在区间数多指标决策中简明实用.     

Systems framework for fuzzy sets in civil engineering

Civil engineering projects and designs are commonly developed in a systems framework that includes different types of uncertainty. In general, uncertainty can be of the ambiguity or vagueness type. The theory of probability and statistics has been extensively used in civil engineering to deal with the ambiguity type of uncertainty. The theory of fuzzy sets and systems have been used in civil engineering to model the vagueness type of uncertainty in many civil engineering applications. In this paper, the role of fuzzy sets in civil engineering systems is described using several example applications, e.g., quality assessment of wildlife habitat, construction engineering and management, structural reliability, and damage assessment of existing structures.     

基于区间的土体参数敏感性分析方法研究

将一种新的工程结构不确定性分析方法——区间分析方法溶入工程参数的敏感性分析之中,获得了一种新的工程参数敏感性分析方法,进一步拓宽了区间分析方法理论的应用领域．给出了土体参数敏感性因子矩阵求解的区间分析过程,依据区间分析给出了参数区间和决策目标区间的确定方法．基于MARC软件进行了二次开发,实现了Duncan-Chang非线性弹性模型以及与Fortran程序的相互调用功能．通过工程算例验证了该方法的合理可行性,并与文献的结果进行了对比．     

An additive stochastic model of mortality rates: An application to longevity risk in reserve evaluation

The paper proposes an additive continuous-time stochastic mortality model which revises that (B&H model) of Ballotta and Haberman (2006). The structure of the B&H model implies that the future hazard rate is proportional to the stochastic component, thus inducing two questionable features. First, in the B&H model, the uncertainty of the future hazard rate will be enlarged as the base hazard rate increases. However, an increase in the base hazard rate may not cause a dramatic increase suggested by the exponential component of B&H (2006). Second, in the B&H model, the uncertainty of the future hazard rate will be larger in the group which is older and will be greatly augmented by the interaction of age and time. But the uncertainty of the future hazard rate may not increase with an increase in age. The problems can be resolved by our additive structure which is the sum of a deterministic estimator and a stochastic component. Since using the additive structure will contribute to the fact that the stochastic component is independent of age and the base hazard rate, in our model the uncertainty of the future hazard rate will not be affected by an increase in age or in the base hazard rate. We further demonstrate an application of our model by calculating reserves of longevity risks for pure endowments and various common annuity products in the UK. We also compare our results with those of the B&H model.     

Reversed hazard function of uncertain lifetime

Reversed hazard function is widely applied in reliability analysis. This paper considers the human uncertainty in a system, and employs uncertain variable to model the lifetime of a component. Concepts of mean residual life and residual entropy are proposed to describe a failed system, and their relationships with the reversed hazard function are discussed. In addition, this paper provides some applications of reversed hazard function to the mean past lifetime and past entropy.     

Differences in bidding strategies

Methodological understanding is increased and the appreciation of discernible competitive bidding strategies widened by investigating the problems of two construction companies, one being a kitchen equipment manufacturer and the other a civil engineering contractor. Detailed strategies are estimated for the former but not for the latter, due primarily to the greater uncertainty in cost estimates for civil engineering contracts producing larger variability in outcomes.     

基于贝叶斯网络的工程项目进度完工概率分析

针对传统计划评审技术(Program Evaluation and Review Technique,PERT)在计算完工概率时假设条件的局限性(假设条件与工程实际存在偏差,导致完工概率偏大),提出了基于贝叶斯网络的施工进度完工概率分析方法.首先,分析了贝叶斯网络与进度计划网络之间的相似性,将两者结合起来构建了贝叶斯进度网络;在此基础上,综合考虑贝叶斯网络在节点取值及概率计算方面的优越性,并结合工程项目的不确定性及复杂性特点,建立了基于贝叶斯网络的施工进度完工概率分析模型.最后,将该模型应用于具体工程进行实例分析,验证了模型的可行性与有效性.研究结果表明:基于贝叶斯网络的进度完工概率模型充分考虑了工程施工中的风险因素,其结果能更客观地反映工程实际,可为工程项目决策者提供可靠的依据.     

一类离散系统基于偏差分离的输出反馈控制

针对一类不确定离散系统,提出一种基于偏差分离的输出反馈双控制策略,首先设计动态输出反馈控制器镇定其标称系统(即不确定性为零的情形);然后通过构造降维观测器,在线获取不确定性信息,并采用线性的补偿器实时补偿系统的不确定性.该控制策略采用线性控制,在工程中可以方便地实现,具有好的工程意义.理论分析证明了闭环指数渐近稳定的充分条件.仿真结果表明该双控制策略的有效性.     

An enhanced two-quantile Wilks methodology for engineering uncertainty analysis

Complex computational engineering uncertainty analyses have become more prevalent. When input parameters of such engineering models are uncertain, the output metric's uncertainty distribution is of an unknown parametric form. Since Wilks' method, named after the seminal paper by SS Wilks in 1941 entitled “Determination of sample sizes for setting tolerance limits”, is a nonparametric statistical procedure, it has received renewed interest, in particular in nuclear and chemical safety engineering. Unfortunately, the prevailing Wilks' method applied relies on arbitrary specification of order statistics' ranks with undue influence on the sample size recommendations that follow. Herein, a novel modification of Wilks' method involving two quantiles is proposed resolving that arbitrary rank selection. Together with a confidence level to be exceeded, these quantiles uniquely determine the parameters of an order statistics' beta distribution which drive the selection of symmetric tolerance limits. The modified procedure is demonstrated in two illustrative engineering uncertainty analysis examples drawn from the nuclear and chemical engineering domains.     

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??The mean residual life (MRL) function plays a very important role in the area of reliability engineering, survival analysis, and many other fields. In this paper, we introduce and study a new stochastic order which gives stochastic comparison for mean residual life of strictly increasing concave function of two random variables. We show that this new stochastic order lies between the hazard rate and mean residual life orders. The preservation properties under mixtures are presented here. Finally, we give some applications of this new order in reliability theory.