Numerical integration methods have the characteristics of high efficiency and precision, making them attractive for aero-engine probabilistic risk assessment and design optimization of an inspection plan. One factor that makes the numerical integration method a suitable approach to in-service inspection uncertainties is the explicit derivation of the integration formula and integration domains. This explicit derivation ensures accurate characterization of a multivariable system’s failure risk evolution mechanism. This study develops an efficient numerical integration algorithm for probabilistic risk assessment considering in-service inspection uncertainties. The principle of probability conservation is applied to the transformation of the integration domain from the current flight cycle to the initial (N = 0) computational space. Consequently, the integration formula of failure probability is deduced, and a detailed mathematical demonstration of the proposed method is provided. An actual compressor disk is evaluated using the efficient numerical integration algorithm and the Monte Carlo simulation to validate the accuracy and efficiency of the proposed method. Results show that the time cost of the proposed algorithm is dozens of times lower than that of the Monte Carlo simulation, with a maximum relative error of 5%. Thus, the efficient numerical integration algorithm can be applied to failure analysis in the airworthiness design of commercial aero-engine components.

This paper develops a thermodynamic entropy-based life prediction model to estimate the low-cycle fatigue (LCF) life of the nickel-based superalloy GH4169 at elevated temperature (650 °C). The gauge section of the specimen was chosen as the thermodynamic system for modeling entropy generation within the framework of the Chaboche viscoplasticity constitutive theory. Furthermore, an explicitly numerical integration algorithm was compiled to calculate the cyclic stress–strain responses and thermodynamic entropy generation for establishing the framework for fatigue life assessment. A thermodynamic entropy-based life prediction model is proposed with a damage parameter based on entropy generation considering the influence of loading ratio. Fatigue lives for GH4169 at 650 °C under various loading conditions were estimated utilizing the proposed model, and the results showed good consistency with the experimental results. Finally, compared to the existing classical models, such as Manson–Coffin, Ostergren, Walker strain, and SWT, the thermodynamic entropy-based life prediction model provided significantly better life prediction results.

Aero engine compressor disks are typically life-limited parts and it is necessary to secure them through the implementation of an engineering plan and a manufacturing plan. Specifically, the engineering plan recommends the quantification of the safety of life-limited parts on the basis of probabilistic risk assessment (PRA). However, the direct correlation between plans is limited, and the effect of manufacturing parameters on the safety of life-limited parts remains to be investigated. Shot peening, as a typical method of surface manufacturing, can significantly improve the safety of life-limited parts. Therefore, a modified mathematical surface PRA method considering shot peening parameters is developed in this paper to further bridge the design and manufacturing processes. Additionally, a general database is established using the response surface method to overcome the simulation complexity. On the basis of this method and the general database, an innovative direct and efficient determination of key shot peening parameters through failure risk in the design stage is proposed. The results indicate that failure risk decreased by 3.26%, 11.31%, and 9.71%, respectively, with increasing number, diameter, and velocity of shots, with the effect of diameter being the greatest. In addition, the method improves the efficiency of determining the key parameters by 75.80%, thus satisfying the requirements of abundant and efficient iterations during the design stage.

Probabilistic failure risk analysis is frequently used in the airworthiness area, while efficient stress intensity factor (SIF) solutions are vital in its process. Universal weight function (UWF) is a method that has remarkable computational efficiency and high accuracy in SIF calculation. However, the concrete coefficients in the UWF for different geometries remain unknown, which hinders the subsequent application of the method. This article focuses on general off-center embedded cracks. The response surface method is used to construct the UWF database. The accuracy of the database is confirmed by comparing it with existing literature and the finite element method, although large errors are identified to be inevitable for certain stress. Gaussian process regression is further adopted for better fitting, and the R-square is over 0.96. In addition, the effect of the offset distance on SIFs is discussed for embedded cracks in a given plate. Results show that SIF changes are dependent on the plate boundary in the uniform stress field, while stress predominates the SIF changes in nonuniform stress fields.