Robust and interpretable estimation of engine oil levels in aero-engines via Kolmogorov–Arnold networks

Engine oil level (EOL) is a critical parameter for monitoring lubrication systems, and its accurate estimation is essential for fault diagnosis and prognosis, and engine health management. However, most engines have only a single EOL sensor, lacking hardware redundancy and creating blind spots in the event of sensor failure. This study proposes applying the Kolmogorov–Arnold Network (KAN) to the EOL estimation task. By utilizing its learnable activation functions, symbolic expressions are extracted to construct a Symbolic KAN model that effectively captures nonlinear relationships between EOL and other parameters, while significantly enhancing interpretability. The model was validated on ground test data from a high bypass ratio turbofan engine (Engine A), outperforming baseline models such as Multilayer Perceptrons and Convolutional Neural Networks, achieving an average coefficient of determination (R²) of 0.935, mean absolute error (MAE) of 0.0138, and root mean squared error (RMSE) of 0.0195. Notably, the Symbolic KAN exhibits exceptional inference speed, requiring only 0.0012s to process 10,000 samples, significantly faster than baseline models. Additionally, a structure-preserving affine fine-tuning strategy was proposed to adapt the Symbolic KAN model. This strategy maintains the learned symbolic formulas while compensating for cross-engine distribution shifts by solely adjusting the affine parameters of the activation functions. This strategy facilitated knowledge transfer from Engine A to Engine B, improving the average R² from 0.744 to 0.900, the MAE from 0.0351 to 0.0191, and the RMSE from 0.0428 to 0.0270. The results show high accuracy, robustness, and adaptability, supporting practical application in EOL estimation.