Model Updating of Nonproportionally Damped Structural Systems Using an Adapted Complex Sum-of-Squares Optimization Algorithm

Various model updating approaches relying on solving nonconvex optimization problems have been developed; however, few of them can reach the global optimum. To obtain the global optimum, the real sum-of-squares optimization algorithm (SOSOA) was proposed to minimize the modal dynamic residuals of proportionally damped structural systems by recasting the nonconvex optimization into a convex optimization. However, this algorithm becomes inefficient for model updating of nonproportionally damped systems with complex-valued eigenvalues and eigvenvectors. This study proposes a model updating approach that exploits and adapts a complex SOSOA to minimize the modal dynamic residuals of nonproportionally damped systems. Numerical considerations unique to using the adapted complex SOSOA to update medium- or large-scale structural models are discussed. Finite-element models of three nonproportionally damped structures-including a base-isolated shear building, a frame building implemented with a tuned mass damper, and a frame building implemented with buckling-restrained braces-are updated to demonstrate that the adapted complex SOSOA finds the global optimum while being orders of magnitude more computationally efficient and far less demanding of computer memory than the real SOSOA.