A semi-analytic method to estimate the response spectrum of the synthetic acceleration records with evolutionary spectrum

In this paper, we introduce a semi-analytic procedure for deriving the response spectrum of the synthetic acceleration records generated using the Double-Frequency Model (DFM). DFM is a filtered white noise method for fully non-stationarity synthetic acceleration records. The proposed semi-analytic procedure is based on the theory of the first passage problem, which precludes time and computationally extensive methods such as Monte Carlo simulations. Assuming a slowly-varying envelope and evolutionary transfer functions, the procedure of estimating the elastic response of a structure is implemented in both time and frequency domains. Comparing the results of our model with previous models and approximations, we concluded that for a set of 10000 realizations of the DFM model, the semi-analytic model produces an error of less than 10% for 92% of the realizations. The accuracy of estimations is higher in the short-period compared to the long-period ranges of the response spectrum. Comparing the accuracy of approximations used to arrive at peak factors, results show that Michaelov approximation executed in the frequency domain yields the best results compared to Poisson or Vanmarcke procedures.