过滤白噪声地震动模型的CQC振型相关系数计算

摘要

当地震动模型为过滤白噪声时,通过频域有理分式积分,求完全二次型组合 (complete quad-ratic combination, CQC) 振型相关系数的闭合表达式将变得困难和不实用.本研究提出将传递函数转化为状态空间方程,通过求解Lyapunov方程得到振型相关系数的方法,且通过用Kanai/Tajimi模型验证了方法的有效性.该方法可推广到常见的过滤白噪声地震动模型,避免了频域有理分式积分闭合解的冗长公式,计算量小,可靠性好,是精确解.%When filtered white noise is used to model ground motion, the computation of complete quadratic combination (CQC) modal correlation coefficients by integration of rational function becomes difficult, and the closed-form formulas become tedious and impractical. We propose a new method to obtain modal correlation coefficients by transforming transfer function model into state space model and then by solving a Lyapunov equation. This method can be extended to the situation where filtered white noise ground motion models are used. Kanai/Tajimi model is used to verify the correctness of the proposed method. It is not only concise,reliable and numerical efficient but also can avoid solving tedious closed-form formulas of integration of rational functions.