Quantiles of critical separation distance for nonstationary seismic excitations

Assessment of the separation necessary to prevent seismic pounding between linear structural systems

“…As shown in several analytical studies [5,6,10,11], the DDC rule provides reasonably accurate results regardless of whether T A and T B are close to each other or not. Although Eq.…”

“…where ρ is the well-known cross-correlation coefficient commonly used in the Complete Quadratic Combination (CQC) rule of modal responses of linear MDOF structures, and is given by [7,8]: (3) is sometimes also referred to simply as the CQC rule [9][10][11]. As shown in several analytical studies [5,6,10,11], the DDC rule provides reasonably accurate results regardless of whether T A and T B are close to each other or not.…”

Prediction on widely factorizable signals

“…As a consequence, subtracting the Equation (19) for t n and t n-1 and using (20) in the resulting equation, the recursive expression (13) is obtained.…”

“…The modulated nonstationary process is given by s(t i ) = d(t i )x(t i ), where x(t i ) is a stationary process with zero mean and known second-order statistics, and d(t i ) is the time modulating function. A stochastic earthquake model commonly used for x(t i ) is the Kanai-Tajimi process (see, e.g., [20]). It is well-known that the Kanai-Tajimi earthquake model is covariance equivalent with the subset of the ARMA(2,1) model corresponding to a unit value of the spring-dashpot input ratio [21].…”

A general solution to the continuous-time estimation problem under widely linear processing

“…In general, the so-called exponential modulating function is adopted [38,39]. A common choice for z(t) is the standard Ornstein-Uhlenbeck process with a particular version of the exponential modulating function given by a (t) = e -t [ [33], p. 38].…”