This review helps the researchers in civil and mechanical engineering, especially those who are focused on reliability and structural analysis or dealing with product assurance problems. Moreover, imperative considerations on the management of samples in the Monte Carlo simulation for SRA purposes and the treatment of the SRA problem as pattern recognition or classification task are provided. In this regard, the focus of the current manuscript is on the different models’ structures and diverse applications of each ML method in different aspects of SRA. Aiming towards a fast and accurate SRA, the ML techniques adopted for the approximation of the limit state function with Monte Carlo simulation (MCS), first/second-order reliability methods (FORM/SORM) or MCS with importance sampling well as the methods for efficiently computing the probabilities of rare events in complex structural systems. More specifically, the application of artificial neural networks (ANN), support vector machines (SVM), Bayesian methods and Kriging estimation with active learning perspective in SRA are explained, and a state-of-the-art review of the prominent literature in these fields is presented. The review includes the most common types of ML methods used in SRA. This paper presents a review of the development and use of ML models in SRA. Machine learning-based (ML) techniques have been introduced to the SRA problems to deal with this huge computational cost and increase accuracy. However, an accurate SRA in most cases deals with complex and costly numerical problems. Structural Reliability analysis (SRA) is one of the prominent fields in civil and mechanical engineering. The efforts of this paper validate the feasibility and validity of GRENN in the reliability analysis of blisk LCF life and give the influence degrees of various random parameters on blisk LCF life, which are promising to provide useful insights for the probabilistic optimization of turbine blisk LCF life. Poisson’s ratio and elastic modulus of materials have little effect. Material density, rotor speed, the fatigue ductility coefficient, the fatigue strength coefficient and the fatigue ductility index are also significant parameters for LCF life. In light of the sensitivity analysis, the fatigue ductility index and temperature are the key factors of determining blisk LCF life because their effect probabilities reach 41% and 26%, respectively. Moreover, high efficiency and high precision of the developed GRENN become more obvious with the increasing number of simulations. This is improved by 15.18% in computational efficiency and 1.39% in accuracy, respectively. In comparison with ERSM, the computing time and precision of the proposed GRENN under 10,000 simulations is 1.311 s and 99.95%. The analytical results reveal that the reliability degree was 0.99848 and the fatigue life is 9419 cycles for blisk LCF life when the allowable value is 6000 cycles so that the blisk has some life margin relative to 4500 cycles in the deterministic analysis. Next, the reliability and sensitivity analyses of blisk LCF life were performed utilizing the GRENN method under a thermal-structural interaction by regarding the randomness of gas temperature, rotation speed, material parameters, LCF performance parameters and the minimum fatigue life point of the objective of study. The method and procedure for reliability and sensitivity analysis based on the GRENN model were discussed. The mathematical model of the developed GRENN method was first established in respect of the LCF life model and the ERSM model. To study the influence of thermal-structural coupling on the reliability of blisk LCF life, the generalized regression extreme neural network (GRENN) method was proposed by integrating the basic thoughts of generalized regression neural network (GRNN) and the extreme response surface method (ERSM). Turbine blisk low cycle fatigue (LCF) is affected by various factors such as heat load, structural load, operation parameters and material parameters it seriously influences the reliability and performance of the blisk and aeroengine.
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