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Reliability analysis for the fractional-order circuit system subject to the uncertain random fractional-order model with Caputo type
Journal of Advanced Research ( IF 11.4 ) Pub Date : 2021-04-27 , DOI: 10.1016/j.jare.2021.04.008
Ting Jin 1 , Shangce Gao 2 , Hongxuan Xia 3 , Hui Ding 4
Affiliation  

Introduction

According to the competing failure theorem, the fractional-order Resistor Capacitance (RC) circuit system suffers not only from internal degradation but also from external shocks. However, due to the general differences of each failure type in the data availability and cognitive uncertainty, a better model is needed to describe the degradation process within the system. Also, a new reliability analysis method is needed for the circuit system under internal degradation and external shocks.

Objectives

To demonstrate this problem, this paper proposes a novel class of Caputo-type uncertain random fractional-order model that focuses on the reliability analysis of a fractional-order RC circuit system.

Methods

First, an uncertain Liu process is used to describe the internal degradation of soft faults and a stochastic process is used to describe the external random shocks of hard faults. Secondly, taking into account the correlation and competition among the fault types, an extreme shock model and a cumulative shock model are constructed, and chance theory is introduced to further explore the fault mechanisms, from which the corresponding reliability indices are derived. Finally, the predictor–corrector method is applied and numerical examples are given.

Results

This paper presents a reliability analysis of a fractional-order RC circuit system with internal failure obeying an uncertain process and external failure obeying a stochastic process, and gives the calculation of the reliability indexes for different cases and the corresponding numerical simulations.

Conclusion

A new competing failure model for a fractional-order RC circuit system is presented and analyzed for reliability, which is proved to be of practical importance by numerical simulations.



中文翻译:

Caputo型不确定随机分数阶模型下分数阶电路系统的可靠性分析

介绍

根据竞争失效定理,分数阶电阻电容 (RC) 电路系统不仅会受到内部退化的影响,还会受到外部冲击的影响。然而,由于每种故障类型在数据可用性和认知不确定性方面的普遍差异,需要更好的模型来描述系统内的退化过程。此外,对于内部退化和外部冲击下的电路系统,需要一种新的可靠性分析方法。

目标

为了证明这个问题,本文提出了一类新的 Caputo 型不确定随机分数阶模型,该模型侧重于分数阶 RC 电路系统的可靠性分析。

方法

首先,用不确定的刘过程描述软断层的内部退化,用随机过程描述硬断层的外部随机冲击。其次,考虑到故障类型之间的相关性和竞争性,构建了极端冲击模型和累积冲击模型,并引入机会理论进一步探索了故障机理,从中推导出了相应的可靠性指标。最后,应用了预测-校正方法并给出了数值例子。

结果

对内部失效服从不确定过程、外部失效服从随机过程的分数阶RC电路系统进行可靠性分析,给出了不同情况下可靠性指标的计算和相应的数值模拟。

结论

提出了一种新的分数阶 RC 电路系统的竞争失效模型,并对其可靠性进行了分析,并通过数值模拟证明了该模型具有实际重要性。

更新日期:2021-04-27
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