Simulation of non-Gaussian stochastic processes with prescribed rainflow cycle count using short-time Fourier transform

Random phenomena described by non-Gaussian processes are ubiquitous in many scientific fields. Properly understanding their characteristics is crucial in safety analysis, where the random occurrence of extreme values is often critical. In practice, the information available for fully characterizing a stochastic process is often limited by experimental constraints. Thus, prediction based on simulations comes as a valid alternative. Motivated by applications in structural fatigue assessment, this research presents a simulation method for non-Gaussian stochastic processes that is able to jointly reproduce a prescribed power spectral density and a rainflow cycle count. The main idea is to model non-Gaussian behavior by a frequency-dependent non-linearity in the short-time Fourier transform. As such, the power spectral density is directly imposed, while the non-linear model is optimized to match the rainflow cycle count. It is shown that the model is flexible enough to be interpolated between different operating points, so as to allow the simulation of stochastic processes at non-measured operating conditions. The full methodology is illustrated for assessing the fatigue assessment of a hydroelectric turbine runner.