应力-强度干涉的直方图模型及可靠度计算的发生函数法

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Based on UGF approach and histograms of stress and strength, a method for approximately calculating the component reliability was proposed when the probability density functions of stress and strength can not be determined exactly. For finite experimental data about stress acted on a component and its strength, the histograms of stress and strength were obtained through statistical analysis. The conventional UGF was extended and an interval-valued UGF（IVUGF） was proposed to characterize the interval-valued discrete random variables. The stress and strength characterized by histograms were expressed by using IVUGF,and then a histogram-based stress-strength interference model was proposed. A combination operator of IVUGF was applied to component＇s limit state function（LSF） and the IVUGF of the LSF was obtained. The weighting coefficient of probability mass was defined. The component reliability was obtained by calculating the weighted sum of all probability mass within the safety margin determined by LSF. Three typical examples were presented and it is showed that the proposed method can achieve satisfactory accuracy of reliability calculation and possesses practical value in engineering.为解决应力与强度的精确概率分布密度函数未知时的结构可靠性分析问题，提出了一种基于通用发生函数和直方图的可靠度近似计算方法。对于应力与强度的有限个实验数据，经过统计分析后绘出其直方图。对传统的通用发生函数法进行扩展，提出了一种区间值型的发生函数。用扩展后的发生函数对应力与强度的统计直方图进行数学表征，进而提出了一种基于直方图的应力-强度干涉模型。用区间值型发生函数法对结构的极限状态函数进行组合运算，获得极限状态函数的区间值型发生函数表示。定义了极限状态函数的概率质量加权系数，通过安全域内所有概率质量的加权累加获得结构的可靠度。给出了三个典型的可靠度计算实例。实例表明，所提出的方法具有较高的可靠度计算精度，是一种有效的可靠性分析新方法。