Robust Online Monitoring of Signal Temporal Logic

TL;DR

This paper introduces a new efficient method for real-time monitoring of Signal Temporal Logic (STL) in cyberphysical systems, enabling online assessment of system behavior during simulations, with demonstrated benefits in automotive and educational applications.

Contribution

It formalizes a semantics for robust online STL monitoring of partial traces and proposes an efficient algorithm, filling a gap in existing offline-focused methods.

Findings

Significant computational savings in large-scale simulations

Successful application in automotive and MOOC CPS scenarios

Overheads of online monitoring are outweighed by efficiency gains

Abstract

Signal Temporal Logic (STL) is a formalism used to rigorously specify requirements of cyberphysical systems (CPS), i.e., systems mixing digital or discrete components in interaction with a continuous environment or analog com- ponents. STL is naturally equipped with a quantitative semantics which can be used for various purposes: from assessing the robustness of a specification to guiding searches over the input and parameter space with the goal of falsifying the given property over system behaviors. Algorithms have been proposed and implemented for offline computation of such quantitative semantics, but only few methods exist for an online setting, where one would want to monitor the satisfaction of a formula during simulation. In this paper, we formalize a semantics for robust online monitoring of partial traces, i.e., traces for which there might not be enough data to decide the Boolean satisfaction (and to compute its quantitative counterpart). We propose an efficient algorithm to compute it and demonstrate its usage on two large scale real-world case studies coming from the automotive domain and from CPS education in a Massively Open Online Course (MOOC) setting. We show that savings in computationally expensive simulations far outweigh any overheads incurred by an online approach.