Based on error analysis of dimensionality reduction method in structural system reliability, the problem of inaccurate correlation coefficient between one element and multi-elements in dimensionality reduction method was studied. First, the states of structural elements were mapped to standard normal space, thereby establishing the element failure model based on state vector. Based on structural reliability and the basic principle of probability theory, the change rule of state vector was analyzed when multi-elements were joint failure. Then, the change rule that multi-elements are joint failure was described by equivalent state vector. The correlation analysis between one element and multi-elements was converted into the computing problem of included angle cosine between equivalent state vector of one element and equivalent state vector of multi-elements; On account of the difference between reliability index and correlation coefficient between one element and multi-elements, the calculation method of correlation coefficient between one element and multi-elements was discussed in three different cases. Finally, the precision and rationality of this method was discussed when compared with Monte Carlo Method. It is proved that the method is rational and it is better than multiple correlation theory; this method is applicable to reliability analysis of structural system, and a better result can be obtained by this method.%在结构系统可靠度降维算法误差分析的基础上,针对降维计算中涉及的一个单元与多个单元间相关系数计算不准确问题展开研究.首先,将结构单元状态映射至标准正态空间,建立了状态矢量描述的单元失效模型.基于结构可靠性和概率论基本原理,分析了多单元联合失效时状态矢量的变化规律;然后,通过利用等效状态矢量描述多单元联合失效的方式,将一个单元与多单元间相关性分析问题,转化为一个单元状态矢量与多个单元等效状态矢量间夹角余弦的计算问题;根据单元间相关性及单元可靠性指标不同,分3种情况讨论了基于状态矢量计算一个与多个单元间相关系数的方法;最后,通过与蒙特卡洛模拟对比分析,讨论了该方法的精度及合理性.证明该方法合理有效,优于复相关原理,适用于结构系统可靠性分析,并能获得较理想的计算结果.
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