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Modular solution of dynamic multi-phase systems

机译：动态多相系统的模块化解决方案

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摘要

Binary Decision Diagram (BDD)-based solution approaches and Markov chain based approaches are commonly used for the reliability analysis of multi-phase systems. These approaches either assume that every phase is static, and thus can be solved with combinatorial methods, or assume that every phase must be modeled via Markov methods. If every phase is indeed static, then the combinatorial approach is much more efficient than the Markov chain approach. But in a multi-phased system, using currently available techniques, if the failure criteria in even one phase is dynamic, then a Markov approach must be used for every phase. The problem with Markov chain based approaches is that the size of the Markov model can expand exponentially with an increase in the size of the system, and therefore becomes computationally intensive to solve. Two new concepts, phase module and module joint probability, are introduced in this paper to deal with the s-dependency among phases. We also present a new modular solution to nonrepairable dynamic multi-phase systems, which provides a combination of BDD solution techniques for static modules, and Markov chain solution techniques for dynamic modules. Our modular approach divides the multi-phase system into its static and dynamic subsystems, and solves them independently; and then combines the results for the solution of the entire system using the module joint probability method. A hypothetical example multi-phase system is given to demonstrate the modular approach.
机译：基于二进制决策图（BDD）的解决方案方法和基于马尔可夫链的方法通常用于多相系统的可靠性分析。这些方法要么假设每个阶段都是静态的，因此可以使用组合方法求解，要么假设必须通过马尔可夫方法对每个阶段进行建模。如果每个阶段确实都是静态的，那么组合方法比马尔可夫链方法要有效得多。但是，在使用当前可用技术的多阶段系统中，如果即使在一个阶段中的失效准则都是动态的，则必须对每个阶段都使用马尔可夫方法。基于马尔可夫链的方法的问题在于，马尔可夫模型的大小会随着系统大小的增加而呈指数扩展，因此变得计算量很大。本文介绍了两个新概念，即相模和相模联合概率，以处理相之间的s依赖性。我们还为不可修复的动态多相系统提供了一种新的模块化解决方案，该解决方案将静态模块的BDD解决方案技术与动态模块的马尔可夫链解决方案技术结合在一起。我们的模块化方法将多相系统分为其静态和动态子系统，并独立解决它们；然后使用模块联合概率法对整个系统的求解结果进行合并。给出了一个假设的示例多相系统来演示模块化方法。

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