基于线性递推滤波算法的地震反应谱计算方法

为提高地震反应谱的计算精度和效率，将线性递推滤波算法（linear recursive filtering method, LRFM）引入地震反应谱计算中，基于单自由度动力系统方程推导采用该方法计算反应谱的一般表达式。为验证本文方法的计算精度和效率，采用合成正弦简谐波作为系统输入，分别利用LRFM方法、Duhamel逐步积分法、Newmark-β方法和精确解法（ASM）计算得到反应谱结果，并与ASM方法作对比来验证其误差，结果表明LRFM方法稳定性好、计算效率高。为进一步证明本文方法处理实际数据的效果，选取ESM强震数据库中不同卓越周期和频谱的强震加速度数据，对比分析LRFM方法和ASM方法在不同阻尼条件下的反应谱计算结果。结果表明，LRFM方法的计算结果与ASM方法一致，加速度反应谱的计算结果随着阻尼的增大存在一定误差，但总体计算结果可满足精度要求。本文提出的LRFM方法可快速高效地计算得到反应谱信息，对于快速评估场地的地震强度特征及工程结构的受力情况具有重要意义。

The Seismic Response Spectrum Calculation Method Based on the Linear Recursive Filtering Method

In order to improve the calculation accuracy and efficiency of the seismic response spectrum, we introduce the linear recursive filtering method(LRFM) to calculate the seismic response spectrum. We derive the general expression of the response spectrum, which is based on the single degree of freedom dynamic system equation. To verify the calculation accuracy and efficiency of this method, we use the synthetic sinusoidal simple harmonic wave as the system input to compare the results of response spectrum which are calculated by the LRFM, the Duhamel step-by-step integration method, the Newmark-β method and the analytical solution method (ASM), and verify the error comparing with the ASM. We prove that the calculation method of the LRFM has good stability and high efficiency. In order to further prove the effectiveness of this method in calculating the actual data, we select the acceleration data of strong earthquakes with different prominent periods and spectrum from the ESM strong earthquake database, and the response spectrum of the LRFM and ASM is compared and analyzed under different damping conditions. The results show that the LRFM is consistent with the ASM in calculating the velocity response spectrum. The calculation result of the acceleration response spectrum has some errors with the increase of the damping, but the overall calculation accuracy could meet the requirements. The LRFM proposed in this paper could quickly and efficiently calculate the response spectrum information, so it has great significance for the rapid assessment of seismic intensity characteristics of the site and the stress condition of engineering structure.