Analytical sensitivity and Hessian matrix analysis of PSD functions for random seismic responses

This paper describes three analytical methods to calculate sensitivity and Hessian matrix of structural Power Spectral Density (PSD) functions for random seismic responses. The methods are derived based on Complete Quadratic Combination method (CQC), Square Root of the Sum of Squares method (SRSS) and Pseudo-Excitation Method (PEM) by direct differentiation. A planar frame and a building are demonstrated. The results indicate the first and second derivatives of PSD functions, achieved by CQC-based method, PEM-based method, are exactly same. The first and second derivatives achieved by SRSS-based method are almost the same as that obtained by other two methods. PEM-based method is the most efficient method. SRSS-based method is much more efficient than CQC-based method.

► CQC-based method is developed to calculate sensitivity and Hessian matrix of PSD functions. ► SRSS-based method is developed to calculate sensitivity and Hessian matrix of PSD functions. ► PEM-based method is developed to calculate sensitivity and Hessian matrix of PSD functions. ► Efficiency: PEM-based method > SRSS-based method > CQC-based method. ► PEM-based method is recommended to calculate sensitivity and Hessian matrix of PSD functions.