Exploring Distance Metrics for Early RUL Estimation: a Liquid Neural Network Approach

Selecting the initial remaining-life threshold is a hidden hyper-parameter that is rarely studied. Accurate Remaining Useful Life (RUL) prediction is essential for efficient predictive maintenance of turbofan engines. A crucial yet under-explored preprocessing step is the assignment of the initial RUL value, the cycle at which labels begin to decrement. This paper systematically investigates and compares several distance metrics—Cosine, Manhattan, Euclidean, and Chebyshev—on the accuracy of early-stage RUL predictions. The study aims to fill this knowledge gap and establish the first baseline comparative framework for aiding in selecting a threshold value. By isolating the effect of it is shown that the choice of metric can shift testing error by up to 15% RMSE and 30% S-score. Predictions are generated by a lightweight, biologically inspired Liquid Neural Network (LNN), a type of Recurrent Neural Network that can adapt in real time to changing input conditions. The results demonstrate that label engineering can have a significant impact on model performance. RMSE, MAE, S-score, and R<sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">2</sup> are reported to establish a baseline for this preprocessing step.