Estimation of Evolutionary Spectra of Monitored Seismic Ground Motions by Transformation of Correlation Functions

Abstract

Spatially varying seismic ground motions recorded by distributed structural health monitoring systems (SHMS) can be used to improve the performances of civil engineering structures, necessitating estimation of the evolutionary power spectral density as an indispensable procedure for utilizing records of SHMS. This paper proposes a method for the estimation of evolutionary power spectral density of a nonstationary process by transforming the correlation functions of its sample time histories. First, the background of the theory of evolutionary power spectral density is reviewed in detail. Relationship between the EPSD and the correlation function of a reference stationary process is then established. Formulas are derived for estimating this correlation function directly from nonstationary sample time histories so that the EPSD can be obtained. The implementation procedure of the proposed method is also detailed. Finally, a numerical example is presented, which validates the proposed method, demonstrates its application for SHMS, and displays its capabilities by comparison with the traditional method.