An Efficient Methodology for Multivariate Return Period‐Based Target Spectrum Construction Using Copula Function

ABSTRACT In performance‐based earthquake engineering, selecting hazard consistent ground motions is critical for seismic demand assessment. Traditional ground motion selection based on a single conditional intensity measure (IM) cannot capture the joint hazard of vector‐valued IMs. Although the concept of a multivariate return period (MRP) target spectrum addresses this limitation, its practical application has been restricted by high computational costs especially for high‐dimensional IM vectors or long return periods. This paper presents a computationally efficient framework for constructing MRP‐based target spectra through two key innovations. First, the direct integration of the high‐dimensional Gaussian mixture distribution (GMD) is replaced with a fitted Gaussian Copula‐based evaluation. Second, A pre‐screening strategy based on Fréchet bounds is introduced to filter more than 94% of irrelevant Monte Carlo samples, substantially improving computational efficiency across different MRP definitions. The hazard consistency of the resulting Kendall‐based MRP target spectrum is evaluated at both scalar and vector levels. A case study of an eight‐story reinforced concrete frame designed according to Chinese codes demonstrates the applicability of the method to both intensity‐ and risk‐based assessments. The calculated engineering demand hazard curve results confirm that the multi‐period MRP target spectrum eliminates potential biases associated with a single conditioning period at low annual exceedance probability. It leads to more stable assessments for both drift‐ and acceleration‐sensitive engineering demand parameters. This research offers an efficient and robust solution for MRP‐based hazard‐consistent ground motion selection in practice.