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Modeling Hierarchical System with Operads
arXiv - CS - Symbolic Computation Pub Date : 2020-09-15 , DOI: arxiv-2009.09848
Spencer Breiner (NIST), Blake Pollard (NIST), Eswaran Subrahmanian (CMU), Olivier Marie-Rose (Prometheus Computing)

This paper applies operads and functorial semantics to address the problem of failure diagnosis in complex systems. We start with a concrete example, developing a hierarchical interaction model for the Length Scale Interferometer, a high-precision measurement system operated by the US National Institute of Standards and Technology. The model is expressed in terms of combinatorial/diagrammatic structures called port-graphs, and we explain how to extract an operad LSI from a collection of these diagrams. Next we show how functors to the operad of probabilities organize and constrain the relative probabilities of component failure in the system. Finally, we show how to extend the analysis from general component failure to specific failure modes.

中文翻译:

使用操作数建模分层系统

本文应用操作数和函数语义来解决复杂系统中的故障诊断问题。我们从一个具体的例子开始,为美国国家标准与技术研究所运营的高精度测量系统——长度尺度干涉仪开发了一个分层交互模型。该模型用称为端口图的组合/图解结构表示,我们解释了如何从这些图的集合中提取操作数 LSI。接下来,我们将展示概率操作数的函子如何组织和约束系统中组件故障的相对概率。最后,我们展示了如何将分析从一般组件故障扩展到特定故障模式。
更新日期:2020-09-22
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