Imprecise P-Box Sensitivity Analysis of an Aero-Engine Combustor Performance Simulation Model Considering Correlated Variables

Abstract

Uncertainties are widely present in the design and simulation of aero-engine combustion systems. Common non-probabilistic convex models are only capable of processing independent or correlated uncertainty variables, while conventional precise probabilistic sensitivity analysis based on ideal conditions also fails due to the presence of uncertainties. Given the above-described problem, an imprecise p-box sensitivity analysis method is proposed in this study in accordance with a multi-dimensional parallelepiped model, comprising independent and correlated variables in a unified framework to effectively address complex hybrid uncertainty problems where the two variables co-exist. The concepts of the correlation angle and correlation coefficient of any two parameters are defined. A multi-dimensional parallelepiped model is built as the uncertainty domain based on the marginal intervals and correlation characteristics of all parameters. The correlated variables in the initial parameter space are converted into independent variables in the affine space by introducing an affine coordinate system. Significant and minor variables are filtered out through imprecise sensitivity analysis using pinching methods based on p-box characterization. The feasibility and accuracy of the method are verified based on the analysis of the numerical example and the outlet temperature distribution factor. As indicated by the results, the coupling between the variables can be significantly characterized using a multi-dimensional parallelepiped model, and a notable difference exists in the sensitivity ranking compared with considering only the independence of the variables, in which input parameters (e.g., inlet and outlet pressure, density, and reference flow rate) are highly sensitive to changes in the outlet temperature distribution factor. Furthermore, the structural parameters of the flame cylinder exert a secondary effect.

Keywords

• multi-dimensional parallelepiped model
• parameter correlation
• affine transformation
• hybrid uncertainties
• probability box
• imprecise sensitivity analysis