基于单变量降维模型和坐标旋转的可靠度混合分析方法

发布时间：2018-09-12 05:01

【摘要】：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。
[Abstract]:The classical first-order reliability method has the applicability problem to the problem of implicit function and strongly nonlinear function, although the quadratic reliability method can deal with the problem of strong nonlinear function to some extent. However, the theoretical basis and calculation process are quite complex, which is not conducive to practical. In order to overcome the above problems, it is an effective way to combine the process of determining the checking point with the method of response surface. For this reason, this paper first introduces a universal first-order reliability method, in which the Nataf transformation of correlated non-normal random variables is considered, and the unilateral difference method is introduced to solve the problem of implicit function finding partial derivative. According to the gradient value, the coordinate rotation vector is introduced, and the univariate function reduced dimension approximate model is introduced to the rotated function. Thirdly, the function value, gradient value and additional point function value of the checking point are combined. Determine the quadratic polynomial approximation of each component function, and obtain the approximate global function. Then, the importance sampling method is used to calculate the failure probability of the approximate functional function. The accuracy and efficiency of the method are verified by numerical examples and engineering examples respectively. The results show that the proposed method has the characteristics of high accuracy and high efficiency, and it is widely applicable to both explicit and implicit function functions.
【作者单位】：重庆大学山地城镇建设与新技术教育部重点实验室;重庆大学土木工程学院;美国加州大学欧文分校;
【基金】：国家自然科学基金(51678092,51478064,50908243)
【分类号】：TB114.3

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