On fatigue cycle distribution in non-stationary switching loadings with Markov chain structure

The non-stationary loadings experienced by structural members can be often modelled as a sequence of stationary load states, with different mean and variance levels, where load switches are controlled by an underlying random process (regime process). The structural integrity of structures and mechanical components under such complex loadings requires the assessment of the statistical distribution of rainflow cycles counted within single load states, as well as of transition cycles caused by load state switches. Under the assumption of a constant mean for the switching loading, the authors showed in a previous paper that a linear combination of single loading spectra would provide a fairly good estimation of the overall loading spectrum of the switching loading. However, when mean value differences among load states are large, additional fatigue cycles caused by load state transitions would be present, besides cycles counted within load states. This work presents a comprehensive approach to assess the overall loading spectrum in switching loadings with variable mean value, when modelling the underlying regime process as a stationary Markov chain. For large relative mean value differences compared to load state variances, transition cycles are found by rainflow counting the regime process. The rainflow matrix for transition cycles is then estimated from the transition probability matrix of regime process by a method available in the literature. The distribution of the ranges of transition cycles is finally estimated from the statistical distribution of the largest peak and the lowest valley within load states. An illustrative example is finally discussed to show the accuracy of the proposed method.