From Statistical Model Checking to Run-Time Monitoring Using a Bayesian Network Approach

Abstract

We propose a framework for monitoring and updating, at run-time, the probabilities of temporal properties of stochastic timed automata. Our method is based on Bayesian networks and can be useful in various real-time applications, such as flight control systems and cardiac pacemakers. The framework has been implemented by exploiting the statistical model checking engine of Uppaal-SMC. By run-time monitoring a set of interesting temporal properties of a given stochastic automaton we update their probabilities, modeled through a Bayesian Network. The main advantages of our method are the capacity to discover non-trivial dependencies between properties and to efficiently update probabilities of unobserved properties given real-time observations. We present empirical results on three application scenarios, showing that the query time can keep up with the speed of some realistic real-time applications. We also present experiments demonstrating that the Bayesian Network approach performance-wise enables run-time monitoring while maintaining or even increasing the accuracy of probability estimation compared to statistical model checking.

Conservative Safety Monitors of Stochastic Dynamical Systems

“…In [2], the same authors employ importance sampling to efficiently learn discrete time Markov chain (DTMC) models from data, which they then use to synthesize predictive monitors. In [17], the authors use Bayesian networks to model temporal properties of stochastic timed automata. The Bayesian networks are updated online to improve their performance.…”

“…Other lines of work use system execution data to learn discrete probabilistic models of the system, which are then used to perform predictive runtime monitoring, as there is rich literature for runtime monitoring of discrete automata. These models range from discrete-time Markov chains (DTMCs) [2] to hidden Markov models (HMMs) [4] to Bayesian networks [17]. However, it is difficult to provide guarantees relating the performance of the automata models to the real system, due to the fact that they are fit using finite data.…”

Theoretical Aspects of Computing – ICTAC 2021

“…one per citizen of Denmark [9]. In addition, using the SMC engine may be used to generate synthetic data from stochastic hybrid automata in order to learn Bayesian networks for infering beliefs of key observable and unobservable properties in settings with scares data [8].…”