Two-stage remaining useful life prediction method across operating conditions based on small samples and novel health indicators

A novel frequency-domain similarity-based health indicator (LR-HDSC) and a multi-scale convolutional residual gated recurrent unit (GRU) adversarial transfer model (MSCRGAT) are proposed in this paper for remaining useful life (RUL) prediction of rolling bearings under cross-operational conditions. First, a health indicator is constructed by computing the Hellinger Distance of Spectral Correlation (HDSC), applying Linear Rectification (LR) to suppress noise fluctuations. The adversarial transfer model (MSCRGAT) integrates multi-scale convolutional kernels (to capture local degradation patterns), residual GRU modules (to model temporal dependencies and mitigate gradient vanishing issues), and a dual-domain adaptation strategy (combining adversarial training and Maximum Mean Discrepancy (MMD) for domain-invariant feature alignment). This enables domain-invariant feature learning and transfer across different operating conditions. At the same time, Bayesian optimization is used for hyperparameter tuning. To verify the effectiveness, we constructed four cross-condition RUL prediction tasks using two bearing datasets, comparing MSCRGAT with mainstream methods. Experimental results demonstrate that MSCRGAT provides significantly improved prediction accuracy and robustness under varying operational conditions, notably enhancing the determination coefficient (R²). Despite occasional prediction fluctuations during rapid degradation stages, the proposed method offers an effective and reliable solution for practical equipment RUL prediction.