Turbofan Engine Remaining Useful Life Prediction with Reliable Prediction Intervals via LSTM-Based Quantile Regression and Conformal Calibration.

To overcome the inability of point estimates to adequately characterize uncertainty and the unstable coverage of prediction intervals in turbofan engine remaining useful life (RUL) prediction, this study proposes an LSTM-based quantile regression framework (LSTM-QR). The framework generates a point prediction together with upper and lower predictive bounds in a single forward pass, thereby directly constructing a prediction interval with a nominal coverage of 80%. During training, a weighted pinball loss and an overestimation penalty are introduced to improve the robustness of quantile estimation. During inference, Conformalized Quantile Regression (CQR) is further applied for post hoc interval calibration. Experiments on the NASA C-MAPSS dataset show that the proposed method maintains stable point-prediction performance while substantially improving interval reliability after calibration. Under the same operating condition, PICP increases from 0.590 ± 0.035 to 0.800 ± 0.026 for FD001 → FD001 and from 0.722 ± 0.050 to 0.793 ± 0.032 for FD002 → FD002, corresponding to gains of 21.0 and 7.1 percentage points, respectively, with calibrated RMSE values of 16.235 ± 1.297 and 18.323 ± 0.411. Under cross-condition transfer, where the raw intervals exhibit clear under-coverage, CQR further raises PICP from 0.696 ± 0.046 to 0.806 ± 0.032 for FD001 → FD002 and from 0.593 ± 0.071 to 0.803 ± 0.021 for FD002 → FD001, corresponding to gains of 11.0 and 21.0 percentage points, respectively, while preserving RMSE at 21.758 ± 1.208 and 17.562 ± 0.062. These results indicate that the proposed method provides more reliable and interpretable prediction intervals under varying operating conditions, thereby offering effective support for predictive maintenance decision-making.