共查询到19条相似文献,搜索用时 187 毫秒
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陈胜军 《数学的实践与认识》2005,35(1):126-130
在综合考虑系统功能函数变量不同属性的基础上 ,建立了单一失效模式下复杂系统模糊随机可靠性的广义模型 ,并讨论了广义模型与各个单一模型之间的关系 ,为产品在复杂状态下的可靠性求解提供了统一的数学模型 .分析讨论表明 :所建立的模糊随机可靠性广义模型更具有一般性 . 相似文献
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单源模糊数的模糊随机有限元方程的解法 总被引:4,自引:0,他引:4
在工程实际情况下,有时候可以利用单源模糊数的运算法则,来减少模糊随机有限元方程的计算量.通过推导证明,其计算量仅相当于求解普通的随机有限元方程.为了更好地适应现代工程设计的需要,还提出用模糊随机有限元方程计算结果求结构模糊失效概率的近似方法. 相似文献
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工程实践中存在着各种不确定性因素,影响着工程结构的安全运行。结构可靠性分析以失效概率的形式考虑了不确定性的影响,可为结构的安全设计提供指导。然而,失效概率的评估往往涉及昂贵功能函数的调用,导致难以负担的计算成本。为解决该问题,基于Kriging模型的可靠性分析法在近年来受到了广泛的关注。该方法以训练良好的Kriging模型近似真实功能函数,从而在失效概率的计算中达到减少功能函数评价次数的目的。本文在主动学习Kriging模型的框架下,提出了基于两阶段局部抽样策略的结构可靠性分析法,以提高失效概率的估计精度和计算效率。在该方法中,Kriging模型的训练样本以两阶段局部抽样的方式从候选样本池中被逐渐添加。第一阶段以输入变量的均值点为抽样中心,利用概率密度函数确定抽样区域。当所估计失效概率满足基于置信区间的阶段划分阈值时,则开始第二阶段的局部抽样。第二阶段则以最可能失效点为抽样中心,以目标可靠度和功能函数的非线性度确定抽样区域。应用案例表明:所提方法能平衡有效抽样区域的全局探索和局部搜索,实现高精度失效概率估计的同时提高计算效率。 相似文献
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本文基于模糊结构元方法建立并讨论了一类含有直觉模糊弹性约束的广义模糊变量线性 规划问题。首先,简单介绍了结构元方法并对结构元加权排序中权函数表征决策者风险态度进行了深入分析。然后,通过选取风险中立型决策态度来定义序关系并拓展Verdegay模糊线性规划方法,将新型模糊变量线性规划问题转化为两个含一般模糊弹性约束的模糊变量线性规划模型,给出了此类规划最优直觉模糊解的求法。最后,通过数值算例进一步说明该方法的有效性。 相似文献
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由于风险投资的高不确定性和风险性,使得人们难以准确预测风险投资项目的收益和状态概率,而只能得到其大致的区间范围。鉴于这种情况,本文将投资项目收益和状态概率描述为模糊变量,利用模糊变量的均值和方差建立了模糊风险投资决策模型,并给出利用模糊模拟方法计算的实例。 相似文献
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基于模糊可能性理论,建立2-型模糊环境下的能源分配优化模型,其中各种类型能源的成本用2-型模糊变量刻画.用均值简约方法简约2-型模糊成本,建立广义期望值意义下的模糊能源分配优化模型.当成本用相互独立的三角2-型模糊变量刻画时,所建立的模糊能源分配优化模型可以转化为等价的参数线性规划.最后提供一个数值例子表明建模思想. 相似文献
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The safety analysis of systems with nonlinear performance function and small probability of failure is a challenge in the field of reliability analysis. In this study, an efficient approach is presented for approximating small failure probabilities. To meet this aim, by introducing Probability Density Function (PDF) control variates, the original failure probability integral was reformulated based on the Control Variates Technique (CVT). Accordingly, using the adaptive cooperation of the subset simulation (SubSim) and the CVT, a new formulation was offered for the approximation of small failure probabilities. The proposed formulation involves a probability term (resulting from a fast-moving SubSim) and an adaptive weighting term that refines the obtained probability. Several numerical and engineering problems, involving nonlinear performance functions and system-level reliability problems, are solved by the proposed approach and common reliability methods. Results showed that the proposed simulation approach is not only more efficient, but is also robust than common reliability methods. It also presents a good potential for application in engineering reliability problems. 相似文献
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Ghatee and Hashemi [M. Ghatee, S.M. Hashemi, Ranking function-based solutions of fully fuzzified minimal cost flow problem, Inform. Sci. 177 (2007) 4271–4294] transformed the fuzzy linear programming formulation of fully fuzzy minimal cost flow (FFMCF) problems into crisp linear programming formulation and used it to find the fuzzy optimal solution of balanced FFMCF problems. In this paper, it is pointed out that the method for transforming the fuzzy linear programming formulation into crisp linear programming formulation, used by Ghatee and Hashemi, is not appropriate and a new method is proposed to find the fuzzy optimal solution of multi-objective FFMCF problems. The proposed method can also be used to find the fuzzy optimal solution of single-objective FFMCF problems. To show the application of proposed method in real life problems an existing real life FFMCF problem is solved. 相似文献
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In structural reliability analysis, computation of reliability index or probability of failure is the main purpose. The Hasofer–Lind and Rackwitz–Fiessler (HL-RF) method is a widely used method in the category of first-order reliability methods (FORM). However, this method cannot be trusted for highly nonlinear limit state functions. Two proposed methods of this paper replace the original real valued constraint of FORM with a non-negative constraint, in all steps and during the whole procedure. First, the non-negative constraint is directly used to construct a non-negative Lagrange function and a search direction vector. Then, the first- and second-order Taylor approximation of the non-negative constraint are employed to compute step sizes of the first and second proposed methods, respectively. Contribution of the non-negative constraint and the effective approach of determining step sizes have led to the efficient computation of reliability index in nonlinear problems. The robustness and efficiency of two proposed methods are shown in various mathematical and structural examples of the literature. 相似文献
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Two basic problems in reliability-based structural optimization 总被引:5,自引:0,他引:5
Optimization of structures with respect to performance, weight or cost is a well-known application of mathematical optimization theory. However optimization of structures with respect to weight or cost under probabilistic reliability constraints or optimization with respect to reliability under cost/weight constraints has been subject of only very few studies. The difficulty in using probabilistic constraints or reliability targets lies in the fact that modern reliability methods themselves are formulated as a problem of optimization. In this paper two special formulations based on the so-called first-order reliability method (FORM) are presented. It is demonstrated that both problems can be solved by a one-level optimization problem, at least for problems in which structural failure is characterized by a single failure criterion. Three examples demonstrate the algorithm indicating that the proposed formulations are comparable in numerical effort with an approach based on semi-infinite programming but are definitely superior to a two-level formulation. 相似文献
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In the literature, several methods are proposed for solving transportation problems in fuzzy environment but in all the proposed methods the parameters are represented by normal fuzzy numbers. [S.H. Chen, Operations on fuzzy numbers with function principal, Tamkang Journal of Management Sciences 6 (1985) 13–25] pointed out that in many cases it is not to possible to restrict the membership function to the normal form and proposed the concept of generalized fuzzy numbers. There are several papers in the literature in which generalized fuzzy numbers are used for solving real life problems but to the best of our knowledge, till now no one has used generalized fuzzy numbers for solving the transportation problems. In this paper, a new method is proposed for solving fuzzy transportation problems by assuming that a decision maker is uncertain about the precise values of the transportation cost, availability and demand of the product. In the proposed method transportation cost, availability and demand of the product are represented by generalized trapezoidal fuzzy numbers. To illustrate the proposed method a numerical example is solved and the obtained results are compared with the results of existing methods. Since the proposed method is a direct extension of classical method so the proposed method is very easy to understand and to apply on real life transportation problems for the decision makers. 相似文献
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Stackelberg solutions for fuzzy random two-level linear programming through probability maximization with possibility 总被引:1,自引:0,他引:1
This paper considers Stackelberg solutions for decision making problems in hierarchical organizations under fuzzy random environments. Taking into account vagueness of judgments of decision makers, fuzzy goals are introduced into the formulated fuzzy random two-level linear programming problems. On the basis of the possibility and necessity measures that each objective function fulfills the corresponding fuzzy goal, together with the introduction of probability maximization criterion in stochastic programming, we propose new two-level fuzzy random decision making models which maximize the probabilities that the degrees of possibility and necessity are greater than or equal to certain values. Through the proposed models, it is shown that the original two-level linear programming problems with fuzzy random variables can be transformed into deterministic two-level linear fractional programming problems. For the transformed problems, extended concepts of Stackelberg solutions are defined and computational methods are also presented. A numerical example is provided to illustrate the proposed methods. 相似文献
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针对矿山大型排土场所出现的滑坡等工程环境灾害的预测与防治问题,着重探讨排土场边坡失稳破坏预测问题.文中采用Fuzzy数学中的Fuzzy概率测度理论建立理论预测分析模型,并对大型排土场边坡失稳破坏的Fuzzy概率测度进行具体的预测分析,所获结果与已有的经典分析方法所获理论结果一致.针对矿山大型排土场所出现的滑坡等工程环境灾害防治问题,提出了具体的防治技术措施. 相似文献