  This paper introduces the $3^{rd}$-order Spectral Representation Method for
simulation of non-stationary and non-Gaussian stochastic processes. The
proposed method extends the classical $2^{nd}$-order Spectral Representation
Method to expand the stochastic process from an evolutionary bispectrum and an
evolutionary power spectrum, thus matching the process completely up to
third-order. A Proper Orthogonal Decomposition (POD) approach is further
proposed to enable an efficient FFT-based implementation that reduces
computational cost significantly. Two examples are presented, including the
simulation of a fully non-stationary seismic ground motion process,
highlighting the accuracy and efficacy of the proposed method.
