Probabilistic analyses of structural dynamic response with modified Kriging-based moving extremum framework

Mechanical system is usually composed of multiple complex structures, which endure the combine action of multi-physical fields (e.g., flow field, thermal field, structural field, and so forth) during operation. Structural response, for instance, deformation, stress, strain, fatigue life, etc., have dynamic and time-varying attributes, their values play an important role in safeguarding function properly, and affects the safety of entire system. Probabilistic analyses (including reliability evaluation and sensitivity analysis) can effectively identify potential risk and improve the reliability level. The traditional way is to use Monte Carlo (MC) simulation to achieve probabilistic analyses of complex structures. However, the MC simulation needs to perform a large amount of calculations to complete the specified task analysis, the computational burden is too heavy for the reliability evaluation and sensitivity analysis of structural dynamic response. To efficiently perform probabilistic analyses of structural dynamic response, we therefore developed a surrogate model method, namely modified Kriging-based moving extremum framework (MKMEF, short for), absorbing extremum thought, moving least squares (MLS) technique, Kriging model and collaborative evolution genetic algorithm (CEGA). For this proposed MKMEF, the extremum thought is used to transform dynamic output response into extremum values within a time domain, and the MLS method is applied to obtain efficient samples to derive Kriging model. Besides, the CEGA is employed to replace gradient descent method to resolve maximum likelihood equation (MLE) and find the optimal hyperparameters of Kriging model. Furthermore, an aeroengine high-pressure turbine blisk is treated as a case study, the probabilistic analyses of radial running deformation is executed to validate the effectiveness of the proposed method by considering the fluid-thermal-solid interaction. The analytical results show that the reliability degree of turbine blisk is 99.78%, when the allowable value of radial running deformation is 2.5071 × 10⁻³ m (determined by 3 sigma levels), and the highest impact on the turbine blisk radial running deformation is gas temperature, followed by inlet velocity, rational speed, material density and outlet pressure. The comparison of methods including direct simulation, response surface method-based extremum thought (ERSM) and traditional Kriging model, shows that the developed MKMEF holds high-efficiency and high-accuracy for the probabilistic analyses of turbine blisk radial running deformation. The presented efforts provide a useful insight for assessing probabilistic analyses of structural dynamic response and enrich mechanical reliability theory.