PROBABILISTIC REPRESENTATION AND TRANSMISSION OF NONSTATIONARY PROCESSES IN MULTI-DEGREE-OF-FREEDOM SYSTEMS

A relatively simple and straightforward procedure is presented for rep resenting nonstationary random process data in a compact probabilistic format which can be used as excitation input in multi-degree-of-freed om analytical random vibration studies. The method involves two main s tages of compaction. The first stage is based on the spectral decompos ition of the covariance matrix by the orthogonal Karhunen-Loeve expans ion. The dominant eigenvectors are subsequently least-squares fitted w ith orthogonal polynomials to yield an analytical approximation. This compact analytical representation of the random process is then used t o derive an exact closed-form solution for the nonstationary response of general linear multi-degree-of-freedom dynamic systems. The approac h is illustrated by the use of an ensemble of free-field acceleration records from the 1994 Northridge earthquake to analytically determine the covariance kernels of the response of a two-degree-of-freedom syst em resembling a commonly encountered problem in the structural control field. Spectral plots of the extreme values of the mts response of re presentative multi-degree-of-freedom systems under the action of the s ubject earthquake are also presented. It is shown that the proposed ra ndom data-processing method is not only a useful data-archiving and ea rthquake feature-extraction tool, but also provides a probabilistic me asure of the average statistical characteristics of earthquake ground motion corresponding to a spatially distributed region. Such a represe ntation could be a valuable tool in risk management studies to quantif y the average seismic risk over a spatially extended area.