https://www.mdu.se/

Decentralized power systems are commonly used in high-speed trains. However, many parameters in decentralized power systems are uncertain and inevitably have errors. We present a reasoning method based on the interval numbers for decentralized power systems in high-speed trains. Uncertain parameters and their unavoidable errors are quantitatively described by interval numbers. We also define generalized linear equations with interval numbers (LAIs), which can be used to describe the movement of the train. Furthermore, it is proven that the zero sets of LAIs are convex. Therefore, the inside of the fault-tolerance area can be formed by their vertexes and edges and represented by linear inequalities. Consequently, we can judge whether the system is working properly by verifying that the current system state is in the fault-tolerance area. Finally, a fault-tolerance area is obtained, which can be determined by linear equations with an interval number, and we test the correctness of the fault-tolerance area through large-scale random test cases.