基于单变量降维模型和坐标旋转的可靠度混合分析方法

经典的一次可靠度方法对于隐式功能函数和强非线性功能函数的可靠度问题存在适用性问题，尽管二次可靠度方法可以一定程度上处理强非线性功能函数的问题，但理论基础和计算过程均颇为复杂，不利于实用。为克服上述问题，将一次可靠度确定验算点的过程与响应面法的思路相结合是一种行之有效的思路。为此，文中首先引入具有普适性的一次可靠度法，其中考虑了相关非正态随机变量的Nataf变换，并引入单边差分法针对性地解决了隐式功能函数求偏导数的问题|其次，根据梯度值引入坐标旋转向量，并对旋转后的功能函数引入单变量函数降维近似模型|再次，结合验算点的函数值、梯度值以及附加点的函数值，确定各分量函数的二次多项式近似，从而获得近似的整体功能函数|然后，采用重要性抽样法计算近似功能函数的失效概率|最后，分别通过数值算例和工程算例对建立方法的精度和效率进行了验证。结果表明建议方法具有高精度、高效率的特点，且无论对于显式和隐式功能函数均具有广泛适用性。

Hybrid reliability method based on the univariate dimension-reduction method and rotational transformation of variables

Classical first-order reliability method (FORM) is inappropriate for reliability analysis with implicit or strong nonlinear performance function, and the second-order reliability method (SORM) is more accurate, but involving complex theory and implementation. To exploit the merits of both FORM and response surface method (RSM), the most probable point (MPP) in FORM and RSM are effectively combined. In this work, the general FORM with Nataf transform and difference method is introduced firstly| secondly, the univariate dimension-reduction approximation model is introduced into rotationally transformed performance function| thirdly, each component function is further approximated by the quadratic polynomial function based on the function value and its gradient of MPP and the function value of the additional point, so that the approximated entire performance function can be obtained| furthermore, importance sampling method is applied to calculating the probability of failure for the approximated performance function| finally, the accuracy and efficiency of the proposed hybrid method are verified based on numerical and engineering cases, and the results show that the proposed method has the characteristics such as good precision, high performance and wide application to both implicit and explicit performance functions.