Application of Markov Processes Theory for Computational Prediction of Turbine Blade Reliability

The article presents the theoretical basics of the application of the theory of Markov processes to the computational approach of prediction of the reliability of mechanical objects. The considered theoretical principles are applied to determine the reliability of the turbine blade, the failure of which is determined due to high-cycle fatigue. Computational three-dimensional modeling based on finite element method is used to determine the initial data in the reliability assessment – indicators of the deformed state of the blade. The reliability of the blade is studied by solving the kinetic damage equation in a linear setting. The assumption was used that process of damage accumulation is quasi-Markovian process, which made it possible to reduce the problem of finding probabilistic fatigue characteristics to solving the Fokker-Planck-Kolmogorov equation. To obtain an analytical solution, the method of characteristic functions and the assumption of the normal law of the loading process were used. Calculations and plots were made using the Python programming language.