区间模型非概率可靠性指标的仿射算法

NON-PROBABILISTIC RELIABILITY INDEX AND AFFINE ARITHMETIC

针对标准区间运算易引发误差爆炸,导致计算结果丧失实用价值的缺陷,文中将不确定性变量的仿射型及仿射运算引入区间模型非概率可靠性指标的计算中。利用仿射型表示变量的不确定性,由仿射运算计算出结构的响应区间(功能函数的上下界),并由响应区间与其许用区间获得非概率可靠性指标。仿射运算的规则具有优化意义,不会引发误差爆炸。以仿射运算求取区间模型非概率可靠性指标,其计算精度远高于区间运算。

For the first time, affine forms of bounded uncertain quantifies and affine arithmetic are introduced into modeling and calculating the non-probability reliability index. A method for reciprocal transformation between interval variables and affine forms is developed. Synchronously, how a more accurate non-probability reliability index can be found by using affine arithmetic is expatiated thoroughly. The affine arithmetic for getting the non-probability reliability index is small in computational complexity and simple in analytic process, and can be implemented by craft. An example validates its rationality and accuracy.