Rainnow Cycles for Switching Processes with Markov Structure

The concept of rainnow cycles is often used in fatigue of materials for analysing load processes, which in most realistic cases should be modelled stochastically. Methods are developed for computation of the rainnow matrix for random loads that are changing properties over time due to changes of the system dynamics. For a random vehicle load the change of properties could reeect diierent driving conditions. Mathematically, the random load is modelled by a switching process with Markov regime, i.e. the random load changes properties according to a hidden (not observed) Markov chain. An algorithm is developed for a switching process where each part of the load is modelled by a Markov chain. As only the local extremes are of importance for rainnow analysis, another approach is to model the sequence of turning points by a Markov chain. The main result of this paper is an algorithm for computation of the rainnow matrix for a switching process where each part is described by a Markov chain of turning points. The algorithms are illustrated by several numerical examples, including analysis of measurements of a truck load.