Drift reliability-based optimization method of frames subjected to stochastic earthquake ground motion

The paper describes an inter-story drift reliability-based optimization method of frames subjected to stochastic earthquake loads. First, the formulas for eigenvalue and eigenvector, drift PSD functions, drift spectral moments, drift reliabilities, their first and second derivatives are derived based on random vibration theory. The computational procedure of drift reliabilities, their first and second derivatives are given in detail. Second, optimal problem of drift reliability-based optimization design is formulated in a dimensionless way. Optimal mathematic model is converted into unconstrained mathematic model using penalty function method. Gradient and Hessian matrix of penalty function are derived using drift reliabilities and structural mass, their first and second derivatives. Third, solution step of optimal problem is constructed using conjugate gradient method. Finally, optimization designs of two planar frames are demonstrated. Sensitivity analysis of optimum design indicates the drift reliability-based optimization method can obtain local optimum design.