Use of transform pairs to represent and simulate nonstationary non-Gaussian process with applications

•Emphasize a new concept to represent nonstationary non-Gaussian process using transform pairs.•Use the iterative power and amplitude correction (IPAC) algorithm with different transform pairs.•Propose a modified version of the IPAC algorithm for nonstationary non-Gaussian process (NNP)•Compare the performance of the IPAC algorithm and spectral representation method to simulate NNP.•Apply the IPAC algorithm to estimate structural reliability for a catalogue of seismic events. We extend the use of the iterative power and amplitude correction (IPAC) algorithm to simulate nonstationary non-Gaussian processes by considering five transform pairs, including the redundant and non-redundant transform pairs that could provide time–frequency or time-scale decomposition. We compare the performance of the IPAC algorithm to that of the spectral representation method (SRM) in terms of matching the prescribed power spectral density function (PSDF) and the marginal probability distribution function. We also extend and examine the IPAC algorithm to simulate concatenated nonstationary non-Gaussian processes. It is emphasized that the IPAC algorithm can be used with a power or energy distribution defined in a transform domain corresponding to a selected transform pair and without directly relying on the definition of the evolutionary process. Unlike SRM, the use of the IPAC algorithm to simulate the nonstationary non-Gaussian process does not require evaluating the underlying Gaussian PSDF. This is especially advantageous for cases when one is interested in estimating the reliability or performance of a structural system during its design life that is subjected to a number of nonstationary non-Gaussian excitations, each defined by a different PSDF.