模糊变量与随机变量组合时模糊可靠度计算方法研究

对现有的随机应力、模糊强度可靠度计算方法进行了系统的分析研究,将其分成模糊变量直接转化为随机变量、由模糊强度的隶属函数直接构造模糊失效事件的隶属函数、可能度法和实用计算法四类,根据模糊失效概率的属性又可分成定量计算法和模糊计算法两类;得到了在定量计算方法中,广义密度函数法与面积法等价,当量密度函数法与截集法等价,真正独立的主要方法为广义密度函数法、当量密度函数法和直接转化法三种等结果;对强度模糊隶属函数为线性、正态分布情况推导了有关公式;通过算例给出了各主要方法的计算结果,其值相差较大,因此,哪种方法更合理还必须作进一步研究。     

模糊支撑半径变量贝叶斯网络多态系统故障概率分析

针对现有隶属函数描述系统及部件故障状态的不足,构建了一种含模糊支撑半径变量的隶属函数来描述部件故障状态,提出了一种基于模糊支撑半径变量的贝叶斯网络多态系统故障概率计算方法。在隶属函数的构造中,用变量代替精确值描述隶属函数模糊支撑半径,建立了含模糊支撑半径变量的隶属函数;并将其引入贝叶斯网络,利用桶消元法对多态系统叶节点故障概率进行分析,得到叶节点故障概率变化曲线。将所提出的方法与文献中基于模糊支撑半径为定值的隶属函数贝叶斯网络方法相比较,验证了方法的有效性。最后,将该方法应用到数控机床主轴系统故障分析实例中,对叶节点故障概率进行计算。结果表明,该方法能够有效解决多态系统故障状态隶属函数选择中的主观性问题。     

基于Haar小波和模糊逻辑的纸币图像特征提取方法

针对如何提取纸币图像特征的问题,提出了一种基于离散Haar小波变换和模糊逻辑相结合的纸币特征提取方法。该方法首先使用Haar小波对纸币图像进行分解操作,提取出图像的低频小波系数、高频小波系数。在此基础上引入模糊逻辑方法,把提取的小波系数分别作为语言变量,并构造出相应的隶属度函数,在模糊特征空间中求出每个模糊区域对应的激活强度值,将这些激活强度值进行归一化处理后构成纸币特征向量,使用神经网络分类器对纸币进行识别。此方法在资源约束的嵌入式系统(TI TMS320C6713 DSP)上实现,实验结果表明,离散Haar小波变换和模糊逻辑相结合的特征提取方法可以取得较高的识别率。     

含非闭合隶属函数模糊变量的结构失效概率分布研究

结合工程实际,提出了非闭合隶属函数的截断可能性分布模型,并对模糊强度和模糊应力进行截断处理,给出了结构模糊随机失效概率随截断参数的分布,并给出了结构模糊随机失效概率分布的数值计算方法。所提出的方法不仅可以考虑基本变量的随机模糊性,而且可以考虑安全和失效状态的随机模糊性。关于强度和应力两个基本变量的情况易于推广应用到多个变量的情况,以解决多变量体系中含有非闭合隶属函数模糊变量的安全分析问题。     

人-机-环境系统安全性评价的模糊数学方法

根据安全评价等级系数法的评价指标体系和权重，对人机环境系统安全性评价的模糊数学方法进行研究。研究表明，对于同一个评价对象，采用模糊评价法和等级系数法所得结论并非在所有情况下都完全相同。其主要原因是方法本身存在差别，且等级系数法的最终安全等级取值论域与各层次指标的安全等级取值论域不一致。利用安全等级模糊特征量的概念和方法，指出模糊评价的结果是一个模糊集合ＨμＡ而非安全等级论域中的一个确定点，等级系数法的评价结果Ｄ∈ＨμＡ。模糊评价法中三角函数型隶属函数优于梯形隶属函数。两种方法对比表明，模糊评价法优于等级系数法。     

模糊分布参数的全局灵敏度分析新方法

为合理度量随机输入变量分布参数的模糊性对输出性能统计特征的影响,提出了模糊分布参数的全局灵敏度效应指标,并研究了指标的高效求解方法。首先,分析了不确定性从模糊分布参数至模型输出响应统计特征的传递机理,以输出性能期望响应为例,利用输出均值的无条件隶属函数与给定模糊分布参数取值条件下的隶属函数的平均差异来度量模糊分布参数的影响,建立了模糊分布参数的全局灵敏度效应指标。其次,为减少所提指标的计算成本、提高计算效率,采用了扩展蒙特卡罗模拟法(EMCS)来估算输入变量分布参数与模型输出响应统计特征的函数关系。最后通过对算例的计算,验证该文所提方法的准确性和高效性。     

机械振动状态的模糊描述与分类

本文以美国科学家L.A.Zadeh提出的语言变量和模糊变量的定义为基础,探讨了机械振动状态的模糊描述与分类问题。基于振动烈度给出了ISO 2372和ISO 3945机械振动标准中划分的各型设备关于机械振动状态的模糊分类“故障态”的一致性函数。     

模糊可靠性灵敏度分析的线抽样方法

依据失效域具有模糊性时模糊失效概率的定义,提出了模糊可靠性灵敏度分析方法。推导了线性功能函数、独立正态基本变量和正态型隶属函数情况下,模糊可靠性灵敏度的解析表达式。给出了模糊可靠性灵敏度的Monte Carlo数字模拟方法,该方法结果在模拟次数趋于无穷时,收敛于真值,但效率较低,尤其是针对高维和小失效概率问题。为解决数字模拟法效率低的问题,提出了模糊可靠性灵敏度分析的线抽样方法。通过离散模糊失效概率积分区域,建立了模糊可靠性灵敏度与离散区域随机可靠性灵敏度的关系,进而利用随机可靠性灵敏度分析的线抽样方法求得模糊可靠性灵敏度。该方法的基本原理、计算公式及实现步骤被详细给出,适用于高维问题和小失效概率、精度高及收敛快等优点则由该文的算例进行验证。     

基于SA算法的行星齿轮减速器离散变量优化设计

考虑制造工艺要求,将所有设计变量均视为离散变量,包括一般离散变量和伪离散变量,并就这两种情况下状态产生函数的设计原理进行深入研究,解决了将模拟退火算法用于离散变量函数优化的关键技术问题,介绍了一种基于模拟退火算法的离散变量函数优化的新方法。行星齿轮传动中各齿轮的齿数受传动比条件、同轴条件和装配条件的限制而不能任意取值,齿轮的模数也要受国家标准的制约只能取一些离散值,用以数学规划理论为基础的经典约束优化方法求解效果很差,用基于模拟退火算法的离散变量优化设计方法则可以方便快捷地获得满足各方面要求的最优设计方案。     

任意隶属度函数模糊系统的逼近特性

以四边形隶属函数作为一般的隶属函数，利用StoneWeierstrass定理对任意隶属函数的模糊系统任意逼近紧集上的任意连续实函数进行证明，是对基本模糊系统逼近任意连续非线性函数理论的推广，模糊系统对任意非线性函数的逼近性能，是模糊系统用于系统辩识的理论依据。     

基于模糊因子法的模糊桁架结构动力特性分析

研究了模糊桁架结构动力特性的分析方法,在结构的物理和几何参数同时为模糊变量的情况下,利用模糊因子建立了结构的刚度矩阵和质量矩阵;从结构振动的瑞利商表达式出发,利用区间运算法则推导出结构模糊特征值的表达式。通过算例考察了结构各参数的模糊性对其动力特性模糊性的影响,并获得了一些有意义的结论。该法对模糊结构进行一次动力分析便可求得动力特性,且可充分地反映任一模糊参数对结构模糊动力特性的影响。     

Intuitionistic fuzzy approach for enhancement of low contrast mammogram images

Mammogram image enhancement is very much necessary in diagnosing breast cancer or tumor at an early stage. Nonuniform illumination and low contrast images are commonly encountered in mammogram images. Conventional enhancement algorithms produce either some artifacts or cannot highlight minute details present in the images, particularly when dealing with mammogram images. In this article, we propose a new mammogram image enhancement scheme using Atanassov's intuitionistic fuzzy set (IFS) theory. IFS considers two uncertainties—membership and nonmembership degree apart from membership degree as in fuzzy set theory. As mammogram images are low contrast images and many of the image definitions are vague/unclear, so IFS theory may be suitable for better image enhancement. Initially, the image is transformed to an intuitionistic fuzzy image using a novel intuitionistic fuzzy generator. Hesitation degree is computed and using the hesitation degree, two membership levels are computed to form an interval type 2 fuzzy set. These two membership functions are then combined using Zadeh's fuzzy t-conorm to form a new membership function. Threshold of interval type 2 fuzzy image is obtained using restricted equivalence function. Using the threshold, modified fuzzy hyperbolization is carried out. Real data experiments demonstrate that the proposed algorithm has better performance on contrast and visual quality of the images both quantitatively and qualitatively when compared with different existing methods.     

基于专家控制调整的机器人手臂系统模糊控制器设计

 对一种复杂的控制系统，简单的模糊控制器不能形成很好的控制效果，将专家知识应用到模糊控制器上，构成一种综合集成的智能专家模糊控制器，采用一种直接对隶属度函数参数进行矩阵式个体编码的遗传算法，对模糊控制器中隶属函数进行寻优，大大提高了系统的控制效果，同时由于专家知识的引入改善了系统对环境和机构参数变化的适应性。     

A membership function approach to lot size re-order point inventory problems in fuzzy environments

Inventory models play an important role in logistics and supply chain management for reducing cost and increasing customer satisfaction. This paper develops an approach to derive the fuzzy objective value and decision variables of the fuzzy lot size re-order point inventory problem with parameters being fuzzy numbers and the shortages are backordered with extra cost incurred. Different from the existing studies, the idea is based on Zadeh's extension principle. A pair of mixed integer nonlinear programs (MINLP) parameterised by the possibility level α is formulated to calculate the lower and upper bounds of the minimal total cost per unit time at α, through which the membership function of the minimal total cost per unit time is constructed. At the same time the membership functions of the optimal order quantity and the optimal re-order point are also provided. A numerical example studied by previous studies is solved successfully to demonstrate the validity of the proposed method. Compared with previous studies, the obtained results which precisely and completely conserve the fuzziness of the input information are more informative for finding the best inventory policy since they are expressed by membership functions rather than by crisp ones. Moreover, to provide representative crisp solutions for designing inventory systems, the Yager's ranking index method is adopted to defuzzify the obtained membership functions. The successful extension of inventory models to fuzzy environments permits inventory models to have wider applications in practice.     

基于飞参数据的航空发动机综合性能评估方法

根据航空发动机综合性能分析的需要,建立了某型航空发动机的综合性能评估模型。首先依据发动机工作状态的不同,分别选取了合适的飞参数据作为性能评估指标,然后分别采用层次分析法和模糊隶属函数法计算了各性能评估指标的权重值和归一化值,并在此基础上采用线性加权和法计算了发动机综合性能评估值。实例分析表明,该模型得出的发动机综合性能评估值能够较好地反映发动机综合性能的好坏,对发动机的状态监控及故障诊断有着重要指导意义。     

Robust Design Rule with Definite Purpose Character Based on Fuzzy Probability and Study of its Characteristics

The design target with definite purpose character of product quality was described in a real fuzzy number(named fuzzy target for short in this paper),and its membership functions in common use were given.According to the fuzzy probability theory and the robust design principle,the robust design rule based on fuzzy probability(named fuzzy robust design rule for short)was put forward and its va-lidity and practicability were analyzed and tested with a design example.The theoretical analysis and the design examples make clear that,while the fuzzy robust design rule was used,the fine design effect can be obtained and the fuzzy robust design rule can be very suitable for the choice of the membership function of the fuzzy target;so it has a particular advantage.     

自适应变论域模糊控制器在结构振动控制中的应用

大挠性航天结构具有复杂的动力学特性,建立其精确的数学模型是很困难的,模糊控制不需要精确的数学模型,但是模糊控制的主要缺陷是精度不太高,自适应能力有限,易产生振荡现象。变论域自适应模糊控制是改变模糊控制性能的主要方法之一,针对自适应变论域模糊控制器的稳定性设计这一难题,将输入和输出的隶属度函数分别用论域值表示成解析形式,引进李亚谱诺夫函数,设计了输入和输出的隶属度函数论域值的自适应律,针对大型航天桁架结构振动控制的仿真,结果表明设计的变论域模糊控制器是可行的。     

Multicriteria fuzzy optimization of structural systems

This paper proposes an efficient, systematic and generalized multicriteria fuzzy optimum design method for the structural systems, using the suboptimization concept, introduction of measure membership functions and fuzzy decision‐making techniques. Each objective function is suboptimized first for all discrete sets of common design variables and design parameters. In order to make the relative evaluation of suboptimized data of objective functions rationally and systematically, and involve the fuzziness or tolerance in the decision‐making process and design emphases, the measure membership functions are introduced for all objective functions. The membership functions of the suboptimized objective functions are determined systematically using the corresponding measure membership functions as datum. A hybrid decision‐making process is developed combining the weighted operator method, comparison processes of maximum membership values and backward interpolation processes for the determination of the global optimum solution. The weighted operator method can also involve the relative emphases of each objective function simply. A design example of a practical prestressed concrete bridge system, in which the total expected cost after an earthquake and the aesthetics of the bridge system are the primary objectives, clarifies the applicability to any convex and non‐convex design problems, rationality, systematic design process and efficiency of the proposed design method. Copyright © 1999 John Wiley & Sons, Ltd.     

含模糊参数弹性地基梁及桩的有限元分析

利用模糊有限元方法研究了文克尔地基上的梁和桩在确定性荷载作用下的反应,其中梁和桩身材料的物性参数及地基参数均模拟成模糊变量。在上述模糊变量为小变量的前提下,利用一种基于普通摄动法原理的模糊摄动展开方法求解模糊有限元平衡方程组得到结构反应量的模糊集。导出了用模糊摄动展开方法求解弹性地基上梁和桩的计算公式,并研究了结构中各模糊参变量对结构反应量模糊集的影响。经与数值模拟的结果比较后表明,方法在精度和实用性方面可较好的满足要求。