Discrete dynamical systems are widely used in a variety of scientific and engineering applications. Modeling these systems involves performing statistical analysis of the system output to estimate the parameters of a model so it can behave statistically similar to the original system. These models can be used for simulation, performance analysis, fault detection, among other applications. This work presents a new algorithm to model discrete dynamical systems using probabilistic finite state automata (PFSA) by initially finding a special class of PFSA called D-Markov machines (a D-ary Markov process) and then applying machine learning algorithms and graph minimization techniques to obtain compact and precise PFSA models. Modeling examples are provided to discuss the trade-off between accuracy and the number of PFSA states. Results using simulated datasets show that the proposed FPSA construction achieves good sensitivity and precision for anomaly detection.

离散动力系统广泛用于各种科学和工程应用中。对这些系统进行建模涉及对系统输出进行统计分析，以估计模型的参数，从而使其在统计上可以类似于原始系统。这些模型可用于仿真，性能分析，故障检测以及其他应用。这项工作提出了一种通过概率有限状态自动机（PFSA）建模离散动力学系统的新算法，方法是首先找到一类称为D -Markov机器（D-ary Markov过程），然后应用机器学习算法和图形最小化技术来获得紧凑而精确的PFSA模型。提供了建模示例，以讨论精度和PFSA状态数之间的权衡。使用模拟数据集的结果表明，所提出的FPSA构造对于异常检测具有良好的灵敏度和精度。