基于功率谱的三参量人工地震动合成

常用的地震动功率谱模型及其人工地震动合成方法在功率谱大小量度、引入时域包线造成功率谱的改变、自相关函数随机噪声成分或功率谱随机波动成分的模拟等方面还存在一些不足。细化地震动的功率谱模型，详细论述平方和作为功率谱强度参数的合理性，提出包含随机波动成分的目标功率谱或包含随机噪声成分的目标自相关函数的数学模型及模拟方法，在目标功率谱中引入随机波动成分。给出了利用地震动功率谱数学模型的3个控制物理量（包含随机波动成分的归一化功率谱、平方和、时域包线函数）合成人工地震动的方法，使合成出的人工地震动时程在能量上严格符合平方和，在频域上严格符合归一化目标功率谱，在时域波形上近似符合目标包线函数，并通过算例演示了给出的人工地震动功率谱模型更加符合实际情况。研究表明平方和、归一化功率谱或归一化自相关函数和时域包线函数是地震动功率谱模型的3个重要物理统计量。

Artificial ground motion using three statistics based on power spectrum

There are some shortcomings in the common power spectrum models of ground motion and in the corresponding synthesis of artificial ground motion, such as the irrationality of the measurement of the size of the power spectrum, the conversion to the power spectrum when leading into the time-domain envelope, and the ignorance of fluctuating ingredient in power spectrum or of random noise part in autocorrelation function. This article elaborated the rationality that the sum of squares should be taken as the measurement of the size of power spectrum. The article discussed that the sum of squares had explicit physics significance, and was the total energy parameter of random stationary signal. A more accurate mathematical model was developed in order to simulate the random fluctuating ingredient of target power spectrum, or the stochastic noise part of corresponding target autocorrelation function, and proposed the non-stationary ground motion’s mathematical model, which was based on power spectrum and included three main controlling physical statistics: the normalized power spectrum containing random fluctuating ingredient, the sum of squares and the time-domain envelope function. Using the synthesis method of ground motion developed by the article, the total energy of artificial ground motion accords with the target sum of squares exactly, the frequent characteristics of the artificial ground motion are in accordance with the normalized target power spectrum accurately, and the wave-shape of the artifical ground motion in time-domain accords with the target envelope function approximately. Studies show that the sum of squares, the normalized power spectrum, and the time domain envelope function are three essential physical statistics of ground motion based on power spectrum model.