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Abstract Rolling bearings are essential supporting components for most rotating machinery and are commonly placed at great risk of sudden failure. Accurate prediction of the remaining service life of rolling bearings is essential for ensuring reliable operation and establishing an effective maintenance strategy. Focusing on the extreme learning machine (ELM) methodology, an innovative predictive model with error feedback neuron integration is established to eliminate the deficiency in model generalization capability. To further improve the predictive accuracy, an improved bat algorithm (IBA) is introduced into the FELM model, in which the Levy flight and frequency influence factor are embedded into the traditional BA algorithm to enhance the parameter searching ability. Inverse hyperbolic function-based statistical indicators are proposed and verified by comparing with the classical RMS curve of full-life data, whose cosine similarity and correlation coefficient both exceed 0.95. Two sets of accelerated life experiments were selected to validate the effectiveness of the proposed IBA-FELM model. The results show that the integrated model can obtain high prediction accuracy and satisfactorily fit the real-life data. The maximal prediction error can be reduced from 1.57 to 0.0401 for experimental Case 1, and from 0.7375 to 0.1492 for Case 2. Compared with the other machine learning models, such as SVR, CNN, and LSTM networks, the IBA-FELM model also presents stronger optimization ability, higher generalization performance, and operation stability.