Dimension-reduction Representation of Stochastic Ground Motion and Engineering Applications

This Open Access book delves into the random orthogonal function-based dimension-reduction simulation method for stochastic ground motion processes (fields), and verifies the effectiveness and engineering applicability through numerical case studies. By incorporating the constraint form of random orthogonal function for standard orthogonal random variables’ set in the original spectral (decomposition) representation of non-stationary stochastic processes (fields), the stochastic ground motion can be accurately represented using only a few elementary random variables. This approach effectively overcomes the challenges encountered by the conventional Monte Carlo methods in the nonlinear analysis of stochastic dynamic systems. In terms of research subjects, the dimension-reduction method facilitates the simulations of various stochastic seismic actions, including univariate (1D-1V) and multivariate (1D-nV) processes, as well as continuous spatio-temporal random fields (mD-1V). Theoretically, the dimension-reduction method enables a unified expression of stochastic processes (fields) across frequency and time domain analysis. The dimension-reduction representation of stochastic ground motion is a full probability model, and it can be naturally integrated with probability density evolution theory, enabling refined random seismic response analysis and reliability evaluation of complex engineering structures. This book is intended for graduate students, researchers, and practicing engineers interested in stochastic ground motion simulation and seismic resistance of engineering structures.