Extreme value analysis of bimodal Gaussian processes

Extreme value analysis of a stochastic process features in many engineering problems. The widely used Poisson approximation can be excessively conservative if a process has narrowband traits, as upcrossings tend to manifest in clumps. Over the years, various authors have developed techniques for predicting the extremes of narrowband Gaussian processes. A bimodal process, comprising two narrowband components, is often encountered in practice, but related studies are scarce. This paper outlines a semi-analytical approach for extending any given narrowband method to bimodal processes. The method is simple to use, and its solution always specializes to the respective narrowband result if either component becomes infinitesimal. Numerical simulations are conducted for verification. The proposed bimodal approach is found to be in good agreement with simulation results, provided that the individual component extremes have been accurately evaluated using a suitable technique.