This article deals with the problem of discovering a Petri net (PN) model of a discrete-event system, starting from the observation of long-event sequences. Precisely, given an interpreted PN (IPN) system modeling the relations between input and output events of the system (i.e., the reactive/observable behavior), the internal state evolutions of the system (i.e., the unobservable behavior) are first discovered and then modeled. The proposed unobservable discovery takes advantage of the novel concept of interpreted sequences, which better characterize the system and model the behavior by considering both observable markings (outputs) and transition firings (inputs). The unobservable modeling is approached as a net synthesis problem. It relies on an optimization-based procedure that identifies the complementary structure; in particular, places only are added to the original model. Note to Practitioners —Black-box identification procedures process an input–output sequence recorded for a long period of time during the functioning of a closed-loop controlled system, and then return a model of the system. However, even if these models simulate well the recorded sequence, they are not very accurate. Indeed, they simulate also other sequences that, in general, are not admitted by the real system. The method proposed here aims to make more accurate these models by discovering the unobservable behavior of a controlled system, related to evolutions of the internal state (and variables) of the system without changing the capability of simulating the observed behavior.

中文翻译：

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一种基于优化的方法，通过解释性 Petri 网发现离散事件系统的不可观测行为


本文讨论从长事件序列的观察出发，发现离散事件系统的 Petri 网 (PN) 模型的问题。准确地说，给定一个解释性 PN (IPN) 系统，对系统的输入和输出事件之间的关系（即反应/可观察行为）进行建模，首先发现系统的内部状态演化（即不可观察行为），然后建模。所提出的不可观察发现利用了解释序列的新概念，它通过考虑可观察标记（输出）和转换激发（输入）来更好地表征系统并建模行为。不可观察的建模被视为一个网络综合问题。它依赖于基于优化的程序来识别互补结构；特别是，仅将地点添加到原始模型中。从业者须知——黑匣子识别程序处理闭环控制系统运行过程中长时间记录的输入输出序列，然后返回系统模型。然而，即使这些模型很好地模拟了记录的序列，它们也不是很准确。事实上，它们还模拟了一般情况下真实系统不承认的其他序列。这里提出的方法旨在通过发现受控系统的不可观察行为来使这些模型更加准确，这些行为与系统内部状态（和变量）的演化相关，而不改变模拟观察行为的能力。