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.

The probabilistic damage tolerance analysis of aeroengine rotor disks is essential for determining if the disk is safe. To calculate the probability of failure, the numerical integration method is efficient if the integral formula of the probability density function is known. However, obtaining an accurate integral formula for aeroengine disks is generally complicated due to their complex failure mechanism. This article proposes a multivariable numerical integral method for calculating the probability of failure. Three random variables (initial defect length a, life scatter factor S, and stress scatter factor B) are considered. A compressor disk model is evaluated. The convergence, efficiency, and accuracy of the proposed method are compared with the Monte Carlo simulation and importance sampling method. The results show that the integral-based method is 100 times more efficient under the same convergence and accuracy conditions.

In the risk assessment of turbine rotor disks, the probability of failure of a certain disk type (after N flight cycles) is a vital criterion for estimating whether the disk is safe to use. Monte Carlo simulation (MCS) is often used to calculate the failure probability but is costly because it requires a large sample size. The numerical integration (NI) algorithm has been proven more efficient than MCS in conditions entailing three random variables. However, the previous studies on the NI method have not dealt with the influence of random variable dimension on calculation efficiency. Hence, this study aims to summarize the influence of variable dimensions on the time cost of a fastintegration algorithm. The time cost increases exponentially with the number of variables in the NI method. This conclusion provides a reference for the selection of probability algorithms involving multiple variables. The findings are expected to be of interest to the practice of efficient security design that considers multivariable conditions.

Probabilistic failure risk analysis of aeroengine life-limited parts is of great significance for flight safety. Current probabilistic failure risk analysis uses equal amplitude load calculations for conservative estimation, avoiding inclusion of the interference effect analyzing random loads due to its massive computational complexity and leading to reduced analysis accuracy. Here, an efficient algorithm is established to solve this computational problem, and an analytical framework is established to consider the interference effect of variable amplitude load. The corresponding probabilistic failure risk analysis is performed for the centrifugal compressor disk. The results show that considering the interference effect of random variable amplitude loads causes a significant decrease in the risk of failure, and the efficient algorithm has advantages over the Monte Carlo sampling method in accuracy and efficiency when considering load interference. This work provides a reference for exploring the probabilistic damage tolerance method under complex loads and supports the optimal design of life-limited parts.

Probabilistic damage tolerance assessment is an essential method to evaluate the safety of aeroengine rotors. The stress intensity factors (SIFs) are the core parameters. The weight function method can calculate SIF efficiently. The available weight functions for corner cracks are suitable for cracks with universal stresses. However, when cracks are under bivariant stress distributions, the lack of the weight function database makes the damage tolerance assessment impractical. Therefore, this paper derives the point weight functions for corner cracks, which are suited for cracks in real-world components with two-directional stress distributions. The response surface method is used to build the surrogate model of the point weight functions. By integrating the weight functions with the stress distributions, SIFs can be calculated with high accuracy. In sum, 81% of the differences between the point weight function method and finite element results are less than 10%.