Feasibility evaluation of Copula theory for substation equipment with multiple nonlinear-related seismic response indexes

Seismic vulnerability evaluations of substation equipment under multiple correlated failure modes are urgently needed. The Copula method, an efficient tool for considering the correlation between variables, holds significant potential application value. However, due to the evident nonlinear correlation between structural and functional responses of substation equipment, the effectiveness of the Copula method is adversely affected. Therefore, this study takes four seismic intensity levels, investigates the distribution and correlation characteristics of seismic responses of typical substation equipment at different levels, and demonstrates the feasibility of the Copula method. The results indicate that the nonlinear correlation features of equipment responses have a significant impact on the choice of Copula functions. The widely used Gaussian Copula exhibits evident limitations, while the Archimedean family Copula is more suitable for substation equipment assessment. Traditional methods that do not consider multiple failure modes or neglect correlation between different modes yield significantly lower seismic vulnerability compared to the Copula-based method that considers correlations. Additionally, compared to traditional non-correlation assessment methods, the Copula method demonstrates better stability, with assessment results less affected by variations in the selection of sample ground motions. Therefore, the Copula method is suitable for assessing the seismic vulnerability of substation equipment and merits widespread application.