Multi-objective Lagrangian inverse function stratified Monte Carlo method for quantifying instability risks in compressor aerodynamic systems

This study addresses the safety analysis requirements of aero-engine aerodynamic systems under complex uncertainty conditions by developing a multi-objective optimization algorithm utilizing the stratified Monte Carlo method. Traditional Monte Carlo methods suffer from high computational costs and slow convergence when handling high-dimensional nonlinear systems. To address these limitations, this paper proposes a Multi-Objective Lagrangian Inverse Function Stratified Monte Carlo (SLI-MOMC) method, which incorporates dual-stage processing: the pre-processing stage employs Lagrange multipliers to optimize stratified sample allocation and reduce variance errors, the post-processing technique integrating inverse function matching is introduced to enhance the accuracy of sample distribution, ensuring the minimization of both the mean and distribution errors. Applied to the safety assessment of aero-engine aerodynamic systems, the proposed method reveals the safety response mechanisms of these systems under external input factors, such as total pressure distortion. The results demonstrate the method exhibits desirable performance in sampling efficiency, comprehensive sample quality, and the functional realization of the compressor system’s stability margin analysis. Compared to the single-objective approach, the present method reduces the dispersion by 1–2 orders of magnitude and mean value error by 0.5–1 order. This approach provides reliable support for analyzing complex nonlinear physical relationships and failure probability within aero-engines.