Mining Road Traffic Rules with Signal Temporal Logic and Grammar-Based Genetic Programming

Abstract

Traffic systems, where human and autonomous drivers interact, are a very relevant instance of complex systems and produce behaviors that can be regarded as trajectories over time. Their monitoring can be achieved by means of carefully stated properties describing the expected behavior. Such properties can be expressed using Signal Temporal Logic (STL), a specification language for expressing temporal properties in a formal and human-readable way. However, manually authoring these properties is a hard task, since it requires mastering the language and knowing the system to be monitored. Moreover, in practical cases, the expected behavior is not known, but it has instead to be inferred from a set of trajectories obtained by observing the system. Often, those trajectories come devoid of human-assigned labels that can be used as an indication of compliance with expected behavior. As an alternative to manual authoring, automatic mining of STL specifications from unlabeled trajectories would enable the monitoring of autonomous agents without sacrificing human-readability. In this work, we propose a grammar-based evolutionary computation approach for mining the structure and the parameters of an STL specification from a set of unlabeled trajectories. We experimentally assess our approach on a real-world road traffic dataset consisting of thousands of vehicle trajectories. We show that our approach is effective at mining STL specifications that model the system at hand and are interpretable for humans. To the best of our knowledge, this is the first such study on a set of unlabeled real-world road traffic data. Being able to mine interpretable specifications from this kind of data may improve traffic safety, because mined specifications may be helpful for monitoring traffic and planning safety promotion strategies.

One-Shot Learning of Ensembles of Temporal Logic Formulas for Anomaly Detection in Cyber-Physical Systems

“…In line 12, a single child individual is generated by the selectAndReproduceWithEnfDiv procedure, using tournament selection with enforced-diversity. In the solutions update step (lines [15][16][17][18][19][20][21][22][23][24][25], the variables of the individuals that satisfies the isSolution condition are considered and added to the set of solved variables V solved ; all individuals that contain at least one of these variables are extracted from the population and added to the solutions ensemble S. If necessary, the population is refilled with newly generated individuals (lines 26-28). The stop condition (line 5) counts the number of distinct variables in V solved and, stops the iterative algorithm if V solved ≥ n target .…”

“…Unlike our proposal, template-free approaches usually require training data with both normal and anomalous examples annotated as such [21,2,6]. Template-free STL mining with normal data only was proposed in [24], that also exploited evolutionary computation (as [21] did): differently than this work, the cited papers do not produce ensembles of STL formulas, and are hence less suitable for CPSs where more properties should be monitored at once for an effective anomaly detection.…”

Toward Formalization and Monitoring of Microscopic Traffic Parameters Using Temporal Logic

“…Since STL provides powerful expressive capabilities, its use in transportation is gaining traction. Many studies are using STL to describe various traffic systems as well as safe vehicle behavior ( 21 , 22 , 23 , 29 – 31 ). This reflects such systems becoming more integrated by combing both cyber and physical aspects and therefore producing continuous signals that can be expressed using formal languages such as STL.…”

Data-Driven Model Discrimination of Switched Nonlinear Systems With Temporal Logic Inference

“…For example, LTL task specifications were inferred/learned from demonstrations of a task using Bayesian inference approach to address the problem of acceptability of task execution, as presented in [54]. Moreover, in [55], both formal grammar and temporal logic have been used for mining the structure and the parameters of a signal temporal logic specification from a set of unlabeled trajectories while in [56]- [58], formal grammar and temporal logic have been used for automated recognition of complex human activities and the task of run time verification. Nonetheless, the works mentioned above do not consider the learning and inference of the unknown system dynamics and task specifications simultaneously, which we find to be synergistic for the purpose of model discrimination.…”