A Compact Probabilistic Representation of the Chi-Chi Earthquake Ground Motion - Reinforced Soil Engineering: Advances in Research and Practice - page 473

Figure 4 Convergence of the eigenvalues of the covariance matrix composed of the
input accelerations.
the higher-frequency energy is being removed from the excitation process, and
this would affect results of response simulations for systems with natural
frequencies in that range. For a complete discussion and error analysis of the
truncation and fitting procedures, see Masri et al. (1998).
4 ANALYTICAL TRANSIENT RESPONSE SOLUTION
Once the excitation process has been condensed into an approximate analytical
form, one can quickly obtain the second-order probabilistic description of the
transient response of linear multidegree-of-freedom systems (Smyth, 1998). For
simple illustration purposes a single-degree-of-freedom system with a natural
frequency of 1 Hz and 5% critical damping is considered for response analysis to
this excitation process. This example could simplistically represent the dominant
modal response of a multistory building. From the closed-form analytical
response solution, the response covariance matrix, shown in Fig. 6, is obtained.
The diagonal of this matrix represents transient mean-square response of