Monitoring of industrial processes is a critical capability in industry and in government to ensure reliability of production cycles, quick emergency response, and national security. Process monitoring allows users to gauge the progress of an organization in an industrial process or predict the degradation or aging of machine parts in processes taking place at a remote location. Similar to many data science applications, we usually only have access to limited raw data, such as satellite imagery, short video clips, event logs, and signatures captured by a small set of sensors. To combat data scarcity, we leverage the knowledge of Subject Matter Experts (SMEs) who are familiar with the actions of interest. SMEs provide expert knowledge of the essential activities required for task completion and the resources necessary to carry out each of these activities. Various process mining techniques have been developed for this type of analysis; typically such approaches combine theoretical process models built based on domain expert insights with ad-hoc integration of available pieces of raw data. Here, we introduce a novel mathematically sound method that integrates theoretical process models (as proposed by SMEs) with interrelated minimal Hidden Markov Models (HMM), built via nonnegative tensor factorization. Our method consolidates: (a) theoretical process models, (b) HMMs, (c) coupled nonnegative matrix-tensor factorizations, and (d) custom model selection. To demonstrate our methodology and its abilities, we apply it on simple synthetic and real world process models.

翻译：工业过程的监控是保障生产周期可靠性、快速应急响应及国家安全的关键能力。过程监控使用户能够评估组织在工业流程中的进展，或预测远程地点设备部件的退化与老化。与众多数据科学应用类似，我们通常仅能获取有限的原始数据，如卫星影像、短视频片段、事件日志及少量传感器采集的特征信号。为应对数据稀缺性，我们借助熟悉目标行为的领域专家（SMEs）知识。领域专家提供完成任务所需的基本活动及每项活动所需资源的专业知识。针对此类分析，已有多种过程挖掘技术被开发；典型方法将基于领域专家洞察构建的理论过程模型与现有原始数据碎片进行临时性集成。本文提出一种创新的数学严谨方法，通过非负张量分解构建与理论过程模型（由领域专家提出）相互关联的最小隐马尔可夫模型（HMM）。该方法整合了：（a）理论过程模型，（b）隐马尔可夫模型，（c）耦合非负矩阵-张量分解，及（d）自定义模型选择。为验证该方法及其能力，我们将其应用于简单合成过程模型及真实世界过程模型。