Diagnosis in Infinite-State Probabilistic Systems

In a recent work, we introduced four variants of diagnosability (FA, IA, FF, IF) in (finite) probabilistic systems (pLTS) depending whether one considers (1) finite or infinite runs and (2) faulty or all runs. We studied their relationship and established that the corresponding decision problems are PSPACE-complete. A key ingredient of the decision procedures was a characterisation of diagnosability by the fact that a random run almost surely lies in an open set whose specification only depends on the qualitative behaviour of the pLTS. Here we investigate similar issues for infinite pLTS. We first show that this characterisation still holds for FF-diagnosability but with a G-delta set instead of an open set and also for IF- and IA-diagnosability when pLTS are finitely branching. We also prove that surprisingly FA-diagnosability cannot be characterised in this way even in the finitely branching case. Then we apply our characterisations for a partially observable probabilistic extension of visibly pushdown automata (POpVPA), yielding EXPSPACE procedures for solving diagnosability problems. In addition, we establish some computational lower bounds and show that slight extensions of POpVPA lead to undecidability

Distinguishing Hidden Markov Chains

Hidden Markov Chains (HMCs) are commonly used mathematical models of probabilistic systems. They are employed in various fields such as speech recognition, signal processing, and biological sequence analysis. We consider the problem of distinguishing two given HMCs based on an observation sequence that one of the HMCs generates. More precisely, given two HMCs and an observation sequence, a distinguishing algorithm is expected to identify the HMC that generates the observation sequence. Two HMCs are called distinguishable if for every $\varepsilon > 0$ there is a distinguishing algorithm whose error probability is less than $\varepsilon$. We show that one can decide in polynomial time whether two HMCs are distinguishable. Further, we present and analyze two distinguishing algorithms for distinguishable HMCs. The first algorithm makes a decision after processing a fixed number of observations, and it exhibits two-sided error. The second algorithm processes an unbounded number of observations, but the algorithm has only one-sided error. The error probability, for both algorithms, decays exponentially with the number of processed observations. We also provide an algorithm for distinguishing multiple HMCs. Finally, we discuss an application in stochastic runtime verification.Comment: This is the full version of a LICS'16 pape

Stochastic event counter for discrete-event systems under unreliable observations

This paper addresses the issues of counting the occurrence of special events in the framework of partiallyobserved discrete-event dynamical systems (DEDS). First, we develop a noble recursive procedure that updates active counter information state sequentially with available observations. In general, the cardinality of active counter information state is unbounded, which makes the exact recursion infeasible computationally. To overcome this difficulty, we develop an approximated recursive procedure that regulates and bounds the size of active counter information state. Using the approximated active counting information state, we give an approximated minimum mean square error (MMSE) counter. The developed algorithms are then applied to count special routing events in a material flow system

Selective Monitoring

We study selective monitors for labelled Markov chains. Monitors observe the outputs that are generated by a Markov chain during its run, with the goal of identifying runs as correct or faulty. A monitor is selective if it skips observations in order to reduce monitoring overhead. We are interested in monitors that minimize the expected number of observations. We establish an undecidability result for selectively monitoring general Markov chains. On the other hand, we show for non-hidden Markov chains (where any output identifies the state the Markov chain is in) that simple optimal monitors exist and can be computed efficiently, based on DFA language equivalence. These monitors do not depend on the precise transition probabilities in the Markov chain. We report on experiments where we compute these monitors for several open-source Java projects

Discrete and hybrid methods for the diagnosis of distributed systems

Many important activities of modern society rely on the proper functioning of complex systems such as electricity networks, telecommunication networks, manufacturing plants and aircrafts. The supervision of such systems must include strong diagnosis capability to be able to effectively detect the occurrence of faults and ensure appropriate corrective measures can be taken in order to recover from the faults or prevent total failure. This thesis addresses issues in the diagnosis of large complex systems. Such systems are usually distributed in nature, i.e. they consist of many interconnected components each having their own local behaviour. These components interact together to produce an emergent global behaviour that is complex. As those systems increase in complexity and size, their diagnosis becomes increasingly challenging. In the first part of this thesis, a method is proposed for diagnosis on distributed systems that avoids a monolithic global computation. The method, based on converting the graph of the system into a junction tree, takes into account the topology of the system in choosing how to merge local diagnoses on the components while still obtaining a globally consistent result. The method is shown to work well for systems with tree or near-tree structures. This method is further extended to handle systems with high clustering by selectively ignoring some connections that would still allow an accurate diagnosis to be obtained. A hybrid system approach is explored in the second part of the thesis, where continuous dynamics information on the system is also retained to help better isolate or identify faults. A hybrid system framework is presented that models both continuous dynamics and discrete evolution in dynamical systems, based on detecting changes in the fundamental governing dynamics of the system rather than on residual estimation. This makes it possible to handle systems that might not be well characterised and where parameter drift is present. The discrete aspect of the hybrid system model is used to derive diagnosability conditions using indicator functions for the detection and isolation of multiple, arbitrary sequential or simultaneous events in hybrid dynamical networks. Issues with diagnosis in the presence of uncertainty in measurements due sensor or actuator noise are addressed. Faults may generate symptoms that are in the same order of magnitude as the latter. The use of statistical techniques,within a hybrid system framework, is proposed to detect these elusive fault symptoms and translate this information into probabilities for the actual operational mode and possibility of transition between modes which makes it possible to apply probabilistic analysis on the system to handle the underlying uncertainty present

Optimal Sensor Selection for Health Monitoring Systems

Sensor data are the basis for performance and health assessment of most complex systems. Careful selection and implementation of sensors is critical to enable high fidelity system health assessment. A model-based procedure that systematically selects an optimal sensor suite for overall health assessment of a designated host system is described. This procedure, termed the Systematic Sensor Selection Strategy (S4), was developed at NASA John H. Glenn Research Center in order to enhance design phase planning and preparations for in-space propulsion health management systems (HMS). Information and capabilities required to utilize the S4 approach in support of design phase development of robust health diagnostics are outlined. A merit metric that quantifies diagnostic performance and overall risk reduction potential of individual sensor suites is introduced. The conceptual foundation for this merit metric is presented and the algorithmic organization of the S4 optimization process is described. Representative results from S4 analyses of a boost stage rocket engine previously under development as part of NASA's Next Generation Launch Technology (NGLT) program are presented

An Efficient Model-based Diagnosis Engine for Hybrid Systems Using Structural Model Decomposition

Complex hybrid systems are present in a large range of engineering applications, like mechanical systems, electrical circuits, or embedded computation systems. The behavior of these systems is made up of continuous and discrete event dynamics that increase the difficulties for accurate and timely online fault diagnosis. The Hybrid Diagnosis Engine (HyDE) offers flexibility to the diagnosis application designer to choose the modeling paradigm and the reasoning algorithms. The HyDE architecture supports the use of multiple modeling paradigms at the component and system level. However, HyDE faces some problems regarding performance in terms of complexity and time. Our focus in this paper is on developing efficient model-based methodologies for online fault diagnosis in complex hybrid systems. To do this, we propose a diagnosis framework where structural model decomposition is integrated within the HyDE diagnosis framework to reduce the computational complexity associated with the fault diagnosis of hybrid systems. As a case study, we apply our approach to a diagnostic testbed, the Advanced Diagnostics and Prognostics Testbed (ADAPT), using real data