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提出一种新的基于奇异值分解的地震动合成方法.该方法在合成多点地震动时采用复功率谱矩阵的奇异值分解,将复功率谱矩阵分解为一个埃尔米特矩阵与其共轭转置矩阵的乘积.该埃尔米特矩阵及其共轭转置矩阵分别由低阶的左、右特征值矩阵及奇异值平方根组成的矩阵近似表示,这一过程极大地降低了复功率谱矩阵的分解难度.算例验证表明:奇异值分解法既能避免科列斯基分解法及特征正交分解法中不合理元素的出现,又可通过分解矩阵的降维节省大量的存储空间,在保证精度的前提下提高合成效率.地震动合成实例计算分析表明使用该方法可快速高效地生成大量模拟点处的地震动时程.
A new synthetic method of ground motions based on singular value decomposition is proposed.The singular value decomposition of complex power spectrum matrix is used to decompose the complex power spectrum matrix into an Hermitian matrix and its conjugate Product of transposed matrices The Hermitian matrix and its conjugate transpose matrices are approximated by a matrix composed of low-order left and right eigenvalue matrices and the square root of the singular values, respectively, which greatly reduces the complex power spectrum The computational results show that the singular value decomposition method can not only avoid the occurrence of irrational elements in the Koelitsch decomposition method and the Orthogonal Decomposition method, but also save a large amount of storage space through the dimensionality reduction of the decomposition matrix, The synthetic efficiency is improved with the premise of guaranteed accuracy.Computational analysis of ground motion synthesis examples shows that this method can be used to generate a large number of ground motion time-series at a large number of simulation points quickly and efficiently.