AN EFFICIENT ADJOINT VARIABLE METHOD FOR SENSITIVITY ANALYSIS OF SEISMIC RESPONSE POWER SPECTRAL DENSITY

Sensitivity analysis of structural response power spectra under seismic excitation serves as a fundamental basis for research on seismic design optimization of structures. In existing studies, one category of methods directly computes the sensitivity of the power spectral density matrix. However, because in engineering practice only the sensitivities of responses at a few locations with respect to different parameters are typically of interest, these methods must first compute the full global matrix and then extract the target components, which results in considerable redundant computation. Another category of methods can directly compute the sensitivity of power spectral components, thus avoiding global redundant calculation across all frequencies. However, they still require extensive time-history integration at every discrete frequency point within the frequency band of interest. Moreover, both categories of methods predominantly adopt direct differentiation strategies, which exhibit low efficiency when addressing multi-parameter sensitivity problems. To address these issues, this study directly targets the sensitivity of response power spectral components under seismic excitation, thereby circumventing the redundant computations inherent in full-matrix methods, and combines the pseudo-excitation method with the adjoint variable method to derive an expression for the pseudo-response sensitivity. On this basis, the Dirichlet integral formula is introduced to reconstruct the double integration domain; by exchanging the order of integration, the coupled time-frequency terms are decoupled, and a considerably more efficient adjoint variable method is derived. Finally, numerical examples are designed using a planar frame and a truss structure as test objects, under both uniformly modulated and non-uniformly modulated seismic excitations, to compare the accuracy and efficiency of the proposed method with those of existing methods. The numerical results demonstrate that the computational accuracy of the proposed method for the sensitivity of displacement response power spectra is basically consistent with that of existing methods, while it exhibits a significant advantage in terms of computational efficiency.