An innovative metamodel-based importance sampling coupled with semi-surrogate model method for efficiently estimating the fatigue life reliability and its application to the aeroengine turbine components

Fatigue life reliability analysis constitutes a critical component in ensuring structural integrity throughout service lifetimes. Distinct from stress-strength reliability assessment, fatigue life reliability analysis necessitates coupled structural and fatigue life evaluations within its limit state function. This inherently involves integrating implicit finite element analysis for structural response prediction with explicit phenomenological mathematical model for fatigue life estimation. A critical challenge in fatigue life reliability analysis lies in selectively constructing adaptive surrogate models for the implicit finite element component within existing reliability frameworks. Compared to the existing semi-surrogate model combined Monte Carlo simulation method, the method proposed in this paper will enhance the analysis efficiency of fatigue life reliability from the following two aspects. First, an efficient error propagation analysis method is constructed by first order reliability analysis method, which facilitates the rapid transfer of errors associated with the structural analysis surrogate model to the limit state function. Secondly, a mathematical correlation between the reliability index and the probability classification function is established. Building on this foundation, we derive an approximately analytical relationship between the probability classification function of the limit state function and the structural analysis surrogate model. This relationship allows for the efficient construction of the importance sampling density function by adaptively building a surrogate of the structural analysis model only. Then, the fatigue life reliability can be accurately and efficiently analyzed from reducing the size of candidate sampling pool involved in updating the surrogate model of the structural analysis model and rapid analysis of error transformation from the surrogate model of the structural analysis model to the final limit state function. The results of fatigue life reliabilities in the turbine shaft structure and turbine disk structure illustrate that under the same accuracy the proposed method can save at least 76% computational time compared to the existing semi-surrogate model combined with Monte Carlo simulation method, which verifies the efficiency and accuracy of the proposed method.