The cross-entropy method for reliability assessment of cracked structures subjected to random Markovian loads

The paper investigates the reliability of cracked components subjected to random amplitude loads modeled by discrete-time Markov processes. The proposed approach is able to capture interaction effects between cycles along the random loading sequence, which are of real interest in the damage tolerance design of aircraft structural components. Random fatigue loads are either modeled by discrete-time First-order Markov Chains or hidden Markov chains with continuous state space and their parameters are identified from in-flight data recorded on a fleet of fighter aircrafts. The uncertainties of the initial crack parameters and material properties are not accounted for in this work and some additional simplifying assumptions are made in order to define a tractable problem. The solution strategy for reliability assessment hinges on the cross-entropy method. The application of this method to Markov chains with discrete state space is first presented based on previous works of the literature and the paper then develops its extension to the selected Hidden Markov Model with continuous state space. Several damage tolerance applications are performed to illustrate the relevance and efficiency of the proposed methodology for which the strengths and limitations are finally highlighted.