Time-delay assisted mechanism and adaptive LSTM hybrid train braking model of heavy haul trains

The train braking model (TBM) that describes the dynamic relations of operation speed, mileage, and control force is essential for achieving stable operation and precise stopping of heavy haul trains (HHTs). However, it is difficult to establish the TBM of HHTs due to complex characteristics: (i) the long body and air braking process of the HHTs may lead to unexpected time-delays of control force; and (ii) there are significant unmodeled dynamics caused by rough tracks and external poor environment. Traditional TBM does not take into account the unmodeled dynamics and time-delays caused by air transmission during braking. To address these issues, this study proposes a data mechanism hybrid modeling strategy, which incorporates a braking time-delay assisted mechanism model and an adaptive long and short-term memory (LSTM) model. A new Bayesian optimization based time-delay estimation method is first proposed to determine unknown time-delays of each carriage and the estimated time-delays are incorporated to generate the multi-point-mass kinetic mechanism model. Moreover, the error of the mechanism-driven model is adaptively compensated by a sliding window LSTM model to conduct the unmodeled dynamics. The effectiveness of the proposed method is demonstrated using the field data.