A novel transfer gear life prediction method by the cross-condition health indicator and nested hierarchical binary-valued network

•1 The cross-condition gear HIs are generated by the designed QFMDCAE and MK-MMD.•2 A Gumbel function is applied to improve the memory capacity of LSTM.•3 A nested hierarchical mechanism is developed for using the sequence information.•4 NHBN model is proposed based on Gumbel function and nested hierarchical mechanism. As one of the crucial techniques in prognostics and health management, the long-term remaining useful life (RUL) prediction of gears is essential for maintenance decisions in engineering applications. However, most previous RUL prediction approaches may have unacceptable prediction performance due to insufficient prior life-cycle data and variable operating conditions. In this paper, a novel transfer life prediction method is proposed for gear RUL estimation under different working conditions. First, a health indicator (HI) transfer construction framework, QFMDCAET, is developed for generating cross-condition HIs under various working conditions based on a quadratic function-based multi-scale deep convolutional auto-encoder network and multi-kernel maximum mean discrepancy. With the acquired gear HIs, the nested hierarchical binary-valued network (NHBN) is designed to estimate the gear RUL. In NHBN, a Gumbel function is applied to improve the memory ability of NHBN. Moreover, a nested hierarchical mechanism is also used to fully utilize the sequence information of the cell state in NHBN. The experimental results illustrate the effectiveness of the proposed NHBN in gear RUL prediction, especially for long-term RUL prediction. Lastly, the comparison results indicate that the proposed NHBN-based RUL prediction method is superior to other conventional and advanced RUL prediction methods.