Hierarchical multi-agent predictive maintenance scheduling for trains using price-based approach

While the progress of predictive maintenance has been rising in various application fields and several feasibility studies and prototypes have been developed, the operational implementation of predictive maintenance requires a more flexible and adaptive scheduling of the predicted maintenance interventions. Contrary to the traditional preventive maintenance tasks that are typically known long in advance, predictive maintenance may require very short-term schedule changes which are also affecting the operation. Railway rolling stock has some special requirements in terms of time table adherence and vehicle scheduling and routing that make the operational implementation of predictive maintenance particularly challenging. In this paper, we propose a hierarchical multi-agent framework for the predictive maintenance scheduling of passenger railway wagons. Besides fulfilling the requirement of scheduling the maintenance of a wagon before it fails (and potentially causes delays), also the passenger demand must be satisfied and the trains must be accordingly assigned to different routes following the time table. We propose a hierarchical distributed learning algorithm using dual decomposition and mechanism design approach. The proposed framework enables to preserve local preferences and particularities and to avoid high computational cost. In the proposed method, first, we decompose the centralized problem using the dual decomposition method, and handle the passenger demand fulfillment constraints by Lagrange multiplier ("shadow price"). Furthermore, the wagons with the private information on the system health need to perform the maintenance before their failure time (with a predicted remaining useful lifetime (RUL) and the corresponding uncertainty). To achieve this aim, we propose a mechanism design approach to align the wagons' objective function to the aim of the central system using an incentive signal. The incentive signal creates a noncooperative game among the wagons. We prove that the Nash Equilibrium (NE) of this game is the optimal solution of the predictive maintenance scheduling. The effectiveness of the proposed method is demonstrated on a case study of a small railway network.