Time-balanced MSE for machinery imbalanced degradation trend prediction

Accurate degradation trend prediction (DTP) is crucial for optimizing equipment operation and maintenance. With the rapid development of artificial intelligence, many data-driven methods have been applied to machinery degradation trend prediction. In practice, most machineries are in the early stages of degradation, with only a few reaching the final stages, leading to a temporal imbalanced data distribution. Current research on imbalanced distributions mainly focuses on classification tasks. However, DTP involves multiple time-dependent continuous targets, making classification-based methods unsuitable. To address this issue, the degradation trend prediction task is reformulated as a multi-task problem and a novel time-balanced Mean Square Error (TBMSE) loss function is proposed. In each prediction task, the Gaussian Mixture Model (GMM) is used to fit the training label distribution. Additionally, the cumulative information noise for each prediction task is modeled using GMM, and an end-to-end network structure is designed to learn the GMM parameters. Experiments are conducted on the IMS bearing dataset and the turboprop engine dataset, demonstrating that the TBMSE loss effectively mitigates the issue of temporal imbalanced distribution in degradation trend prediction.