Shape expressions (SEs) is a novel specification language that was recently introduced to express behavioral patterns over real-valued signals observed during the execution of cyber-physical systems. An SE is a regular expression composed of arbitrary parameterized shapes, such as lines, exponential curves, and sinusoids as atomic symbols with symbolic constraints on the shape parameters. SEs enable a natural and intuitive specification of complex temporal patterns over possibly noisy data. In this article, we propose a novel method for mining a broad and interesting fragment of SEs from time-series data using a combination of techniques from linear regression, unsupervised clustering, and learning finite automata from positive examples. The learned SE for a given dataset provides an explainable and intuitive model of the observed system behavior. We demonstrate the applicability of our approach on two case studies from different application domains and experimentally evaluate the implemented specification mining procedure.

中文翻译：

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从正例中挖掘形状表达式


形状表达式（SE）是一种新颖的规范语言，最近被引入，用于表达在网络物理系统执行期间观察到的实值信号的行为模式。 SE 是由任意参数化形状组成的正则表达式，例如直线、指数曲线和正弦曲线作为原子符号，对形状参数具有符号约束。 SE 能够对可能有噪声的数据进行复杂时间模式的自然且直观的规范。在本文中，我们提出了一种新颖的方法，结合使用线性回归、无监督聚类和从正例中学习有限自动机等技术，从时间序列数据中挖掘广泛且有趣的 SE 片段。给定数据集学习到的 SE 提供了观察到的系统行为的可解释且直观的模型。我们在来自不同应用领域的两个案例研究中证明了我们的方法的适用性，并通过实验评估了所实施的规范挖掘过程。