Firstly part of quadratic term of Taylor series is chosen; a low-dimension surface is used to approximate limit state surface; and the modified reliability formula is derived.
首次选取泰勒级数的部分二次项,用一个距原点最近点处拟合的超低维曲面近似极限状态面。
On the other hand, it also derives the covariance propagation formula of non-linear function containing quadratic term in matrix form using the matrix theory etc.
另一方面又利用矩阵理论等推导出含有二次项的非线性函数的协方差传播公式的矩阵形式。
Hessian matrices are used in large-scale optimization problems within Newton-type methods because they are the coefficient of the quadratic term of a local Taylor expansion of a function.