Efficient Numerical Integration Algorithm of Probabilistic Risk Assessment for Aero-Engine Rotors Considering In-Service Inspection Uncertainties

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 (<i>N</i> = 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.