Simulation of a Gaussian stationary process with a stable correlation function with a given reliability and accuracy

In this paper, the representation of random processes in the form of random series with uncorrelated members obtained in the work by Yu. V. Kozachenko, I.V. Rozora, E.V. Turchina (2007) [1]. Similar constructions were studied in the book by Yu. V. Kozachenko and others. [2] in the general case. However, there are additional difficulties in construction of models of specific process, such as, for example, selection of the appropriate basis in L_2(R). In this paper, models are constructed that approximate the Gaussian process with a stable correlation function $\rho_{\alpha} (h) = E X_{\alpha}(t + h) X_{\alpha}(t) = B^2 \exp{-d|h|^{\alpha}}, \alpha > 0, d > 0$ with parameter $\alpha = 2$, which is a centered stationary process with a given reliability and accuracy in the space L_p ([0,T]). And also the rates of convergence of the models are found, the corresponding theorems are formulated. Methods of representation and main properties of the process with a stable correlation function $\rho_2(h) = B^2 \exp{-d|h|^2}, d > 0$ are considered. As a basis in the space L_2(T) Hermitian functions are used.

An improvement on the estimation of pseudoresponse spectral velocity using RVT method

The basic assumption in the prediction of peak ground acceleration (PGA), peak ground velocity (PGV), and pseudoresponse spectral values by the random vibration theory (RVT) method is that the ground motion process is a bandlimited Gaussian random process (BGRP). However, for the estimation of pseudoresponse spectral values, the process is the output of a single-degree-of-freedom (SDOF) system subjected to the input of a BGRP. The output process is a narrow-band random process because a SDOF system acts as a narrow-bandpass filter. The property of a narrow-band process is significantly different from that of a bandlimited process. There is an obvious difference in the estimations of the pseudoresponse spectral values based on bandlimited or narrow-band process, especially in the lower frequency part. In this study, we propose an empirical method to improve the estimation of the pseudoresponse spectral values by the RVT based on the consideration of properties of a narrow-band Gaussian stationary process. Comparisons of our results with those of previous research studies and the time domain simulation (TDS) shows that our empirical approach improves the estimation of pseudoresponse spectral values in the long period range.

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.