RELIABILITY ANALYSIS OF INDIVIDUAL-COMPONENT REPAIRABLE SYSTEM BASED ON STOCHASTIC DIFFERENTIAL EQUATION

Lanlan Huangfu ； Hongsheng Su

《電機工程學刊》 28卷1期 (2021/02) Pp. 23-33

https://doi.org/10.6329/CIEE.202102_28(1).0003

摘要

To improve operation maintenance management levels and increase economic profits for repairable devices, such as electric power equipment, large-scale nuclear power facilities and high-speed EMU, preventive maintenance based on reliability analysis has been widely applied in industrial enterprises in recent years. The traditional reliability analysis on the basis of ordinary differential equation (ODE) cannot essentially describe random processes (e.g., definite integral) and uncertain factors in the maintenance process and cannot reflect the influence of random factors on parts and maintenance. In response to such defects, this paper presents a reliability analysis method for individual-component repairable systems on the basis of stochastic differential equation (SDE). First, the method was used to calculate and decompose the existing reliability exponential function using the Taylor expansion equation, and the difference in equation is used to explain the meaning of higher terms, which are ignored in ODE calculation. Second, by using the knowledge on topological space, the repairable Markov process was running on a certain space of Markov process with absorption, and the set reliability threshold was reached. Theories of stochastic integral and SDE were introduced into the dynamic process of the system, and the knowledge on the polar set was used to prove that the dynamic maintenance process of repairable component belongs to the category of Brownian motion. Therefore, the dynamic maintenance process of repairable component can be described by Brownian motion, and the SDE can be established. On the basis of the properties of solutions and martingale analysis theory, the availability function of the individual component is a supermartingale, and the dynamic behavior of the model can be analyzed. Finally, the effectiveness of the proposed method was verified through the application of key components of in fault analysis of high-voltage electrical appliances in high-speed electric multiple unit(EMU).

關鍵字

individual-component repairable system ； SDE ； reliability analysis ； topological space ； polar set ； Brownian motion ； high-speed EMU

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