Multiple Markov chains-based layered random fault injection method for the air braking system

The air braking system is one of the key systems to ensure the safe operation of high-speed trains, and it's also one of the most frequent sources of fault. In order to achieve the requirements of low risk, low cost and short cycle in the research, fault injection is often carried out in the form of simulation. Due to the random occurrence of faults in the system, random fault injection can simulate the scenario of fault occurrence more realistically than deterministic fault injection. However, the challenges are the lack of raw fault data for the air braking systems and the process of building the fault distribution function is too cumbersome. This paper proposes a layered random fault injection method based on multiple Markov chains (MCs). First, a multi-layer structure fault model base is established for the system, and layered fault injection is performed. On this basis, the fault type and fault degree Markov chains are constructed, the state transition matrix is constructed, and the steady-state probability distribution is solved by using the steady-state property of the Markov chain to obtain the fault probability distribution. Then, a low-complexity Alias Sampling algorithm is used for discrete random sampling, and the normal model is transformed into a corresponding