用于强震记录仿真地动位移的高精度累积数值积分方法研究

Study on High-Precision Accumulate Numerical Integration Method for Simulation of Ground Displacement from Strong Motion Records

针对传统梯形积分方法的低精度缺陷,提出了一套高精度累积数值积分方法。首先对被积数据进行分段三次Hermite插值,之后采用积分区间四等分的Newton-Cotes积分公式进行积分。误差分析表明,本方法精度远高于梯形积分方法精度。在对构建信号进行方法验证的前提下,采用2013年4月20日雅安芦山地震和2008年5月12日汶川地震的真实强震动加速度记录对本方法进行测试,测试结果表明,本方法适用于将强震动加速度记录积分为位移记录。

Aiming at the low precision defect of traditional trapezoidal integral method, a set of high precision accumulate numerical integration method is proposed in this paper. Firstly, piecewise cubic Hermite interpolation is processed to the target data. Then the data were integrated by Newton-Cotes integral formula with integrating range divided into four equal parts. Error analysis shows that the precision of this method is much higher than that of trapezoidal integral. Through the premise of structured signal verification, the method is verified by strong motion records of Yaan lushan earthquake on Apr. 20, 2013. The results demonstrate that this method is applicable to integrate the strong motion acceleration records into displacement records.