A Stochastic Approach in Estimating the Pseudo-Relative Spectral Velocity

In the prediction of ground motion from seismological model by random vibration theory, the basic assumption as that the ground motion process is a bandlimited Gaussian white noise (BGWN). For pseudo-response spectral values, the estimation is based on the response of a single-degree-of-freedom (SDOF) system due to the input of BGWN. The function of an SDOF is a narrowband filter. Therefore, the response of an SDOF is a narrowband process that no longer satisfies the assumption of bandlimited random process. The property of a narrowband process is significantly different from that of a bandlimited process and should be incorporated into the estimation of pseudo-spectral values. A stochastic methodology is proposed to estimate the spectral values on the basis of narrowband Gaussian stationary process. A key feature of the method is the use of envelope crossings in lieu of press crossings of the ground motion amplitude level. This substitution makes the estimation of spectral values more accurate. Comparing our results with those of previous research studies, we will illustrate that our proposed approach is in a good agreement with that of the simulation of time domain.