Fault Detection of Discrete-Time Stochastic Systems Subject to Temporal Logic Correctness Requirements

Abstract

This paper studies the fault detection of discrete-time stochastic systems with linear-time temporal logic (LTL) as correctness requirement-A fault is a violation of LTL specification. The temporal logic allows system correctness properties to be specified compactly and in a user-friendly manner (being close to natural-languages), and supports automatic translation into other formal models such as automata. We introduce the notion of input-output stochastic hybrid automaton (I/O-SHA) and show that the refinement of a continuous physical system (modeled as stochastic difference equations) against a certain class of LTL correctness requirement can be modeled as an I/O-SHA. The refinement preserves the behaviors of the physical system and also captures requirement-violation as a reachability property. Probability distribution over the discrete locations of hybrid system is estimated recursively by computing the distributions for continuous variables for each discrete location. This is then used to compute the likelihood of fault, a statistic that we employ for the purpose of fault detection. The performance of the detection scheme is measured in terms of false alarm (FA) and missed detection (MD) rates, and the condition for the existence of a detector to achieve any desired rates of FA and MD is captured in form of Stochastic-Diagnosability, a notion that we introduce in this paper for stochastic hybrid systems. The proposed method of fault detection is illustrated by a practical example.Note to Practitioners-Many cyberphysical systems, such as building automation systems, automotive vehicles and smart power grids, can be modeled as stochastic systems with mixed continuous and discrete dynamics subject to disturbance and noise, whose behaviors are monitored and controlled by networked (digital) control systems. This paper investigates fault detection in the form of temporal logic specification violation in model-based approach, by transforming it into a state estimation problem for stochastic system models. We provide an algorithm for online fault detection and introduce the notion of Stochastic-Diagnosability for the existence of a detector with any desired accuracy of detection as measured by false alarms and missed detections. The work is illustrated by a room heating system example.

A Uniform Framework for Diagnosis of Discrete-Event Systems with Unreliable Sensors using Linear Temporal Logic

“…We note that using linear temporal logic in diagnosability analysis of DES has been investigated in the literature. For example, in [17], [23], the authors investigated how to detect faults described by the violations of LTL formulae. In [7], [15], [33], [47], the verification of standard diagnosability (with reliable sensors) was solved using LTL model checking techniques.…”

Model‐based validation of diagnostic software with application in automotive systems

“…The functionality of the diagnostic software (i.e. a diagnoser) can be illustrated by Figure 2, where L denotes the set of all possible system behaviours while K is the set of nominal behaviours, denoted as no-fault specification [31]. The diagnoser reports 'Fail' whenever the system executes a behaviour in L − K while reports 'Pass' for K. Note that here K represents the set of behaviour that is considered as 'no-fault' by the diagnoser, while the set of true 'no-fault' system behaviour (denoted as L) may be different from K, which needs to be validated in the validation process.…”

“…The functionality of the diagnostic software (i.e. a diagnoser) can be illustrated by Figure 2, where L denotes the set of all possible system behaviours while K is the set of nominal behaviours, denoted as no‐fault specification [31]. The diagnoser reports ‘Fail’ whenever the system executes a behaviour in L − K while reports ‘Pass’ for K .…”

“…Specifically, LTL formula will be used for model-checking. In the following, we present a brief description of LTL; a more thorough introduction of LTL and modelchecking can be found in [31,[36][37][38].…”