Efficient Online Monitoring and Formula Synthesis with Past STL

In online monitoring, it is crucial to detect a deviation from normal behavior as soon as it occurs. During online monitoring, the system traces are checked against monitoring rules in real-time to detect such deviations. In general, the rules are defined as boundary conditions by the experts of the monitored system. In this work, we study the problem of synthesizing online monitoring rules in the form of temporal logic formulas in an automated way. We describe the monitoring rules as past time signal temporal logic (ptSTL) formulas and propose an algorithm to synthesize such formulas from a given set of labeled system traces. The algorithm searches the formula space for a predefined number of operators in an efficient way and produce the best formula representing a monitoring rule. In addition, we improve online STL monitoring algorithm to efficiently compute a quantitative valuation for piecewise-constant signals from ptSTL formulas, thus, reduce the overhead of the the real-time computation.

I. Introduction

In this day and age, various services such as e-government, e-mail, e-shopping and e-news that serve directly to the users are provided via web-based technologies. In addition, cyber-physical systems are in use everywhere in a very wide range of technologies such as autonomous vehicles, smart grid, smart buildings, smart agriculture systems, medical devices etc. Reliability and accessibility for these types of services are critical [1]. Those properties are enhanced via deployment of monitoring systems that are used to detect unusual events in time to avoid system and security failures. In monitoring, metrics produced by the systems are evaluated according to certain criteria known as monitoring rules. Experts define such rules and the cost of the mistakes done in this step can be very high. In this work, the system monitoring rules are expressed in a formal language, and the rule maximizing the success of the monitoring system is automatically generated.