The Log-Rayleigh Distribution for Local Maxima of spectrally Represented Log-normal Processes

We address a novel probability distribution, namely the log-Rayleigh distribution, suited to model the maximum occurring loads in a log-normal process. Log-normal processes in engineering applications can be used to model for example wave or wind loads acting on structures. Usually, to assess probabilistic events, e.g. the probability of failure of structures under log-normal load processes, the generation of time-histories is necessary. With the given probability distribution, the maximum load events can directly be sampled, eliminating this step. Also, since a closed form of the PDF is given, the integrals involved in reliability analysis can directly be evaluated. We show that the proposed log-Rayleigh distribution can accurately model the distribution of local maxima in each log-normal process when compared to samples obtained from a Monte Carlo approach. Furthermore, we conduct a parameter study to evaluate the influence of the parameters in the log-Rayleigh distribution. Details on the generation of a log-normal process and a benchmark of this process are also included. Finally, a mechanical model related to a static structural reliability analysis is evaluated to show suitable utilities of the newly formed log-Rayleigh distribution.