Complex systems are naturally hybrid: their dynamic behavior is both continuous and discrete. For these systems, maintenance and repair are an increasing part of the total cost of final product. Efficient diagnosis and prognosis techniques have to be adopted to detect, isolate and anticipate faults. This paper presents an original integrated theoretical framework for diagnosis and prognosis of hybrid systems. The formalism used for hybrid diagnosis is enriched in order to be able to follow the evolution of an aging law for each fault of the system. The paper presents a methodology for interleaving diagnosis and prognosis in a hybrid framework.

Counterfactual reasoning arises in broad array of fields, from statistics to economics to law. Not surprisingly, there has been a great deal of work on giving semantics to counterfactuals. Perhaps the best-known approach is due to Lewis [1973] and Stalnaker [1968], and involves possible worlds. The idea is that a counterfactual of the form "ifAwere the case thenB would be the case", typically written A B, is true at a worldwifB is true at all the worlds closest tow whereAis true. Of course, making this precise requires having some notion of "closeness" among worlds. More recently, Pearl [2000] proposed the use of causal models based on structural equations for reasoning about causality. In causal models, we can examine the effect of interventions, and answer questions of the form "if random variable X were set to x, what would the value of random variable Y be". This suggests that causal models can also provide semantics for (at least some) counterfactuals. The relationship between the semantics of counterfactuals in causal models and in counterfactual structures (i.e., possible-worlds structures where the semantics of counterfactuals is given in terms of A preliminary version of this paper appears in the Proceedings of the Twelfth International Conference on Principles of Knowledge Representation and Reasoning (KR 2010), 2010.

We analyze the foundations of cyclic causal models for discrete variables, and compare structural equation models (SEMs) to an alternative semantics as the equilibrium (stationary) distribution of a Markov chain. We show under general conditions, discrete cyclic SEMs cannot have independent noise; even in the simplest case, cyclic structural equation models imply constraints on the noise. We give a formalization of an alternative Markov chain equilibrium semantics which requires not only the causal graph, but also a sample order. We show how the resulting equilibrium is a function of the sample ordering, both theoretically and empirically.

Diagnosis, i.e., the identification of root causes for failing or unexpected system behavior, is an important task in practice. Within the last three decades, many different AI-based solutions for solving the diagnosis problem have been presented and have been gaining in attraction. This leaves us with the question of which algorithm to prefer in a certain situation. In this paper we contribute to answering this question. In particular, we compare two classes of diagnosis algorithms. One class exploits conflicts in their search, i.e., sets of system components whose correct behavior contradicts given observations. The other class ignores conflicts and derives diagnoses from observations and the underlying model directly. In our study we use different reasoning engines ranging from an optimized Horn-clause theorem prover to general SAT and constraint solvers. Thus we also address the question whether publicly available general reasoning engines can be used for an efficient diagnosis.

Counting the models of a propositional formula is a key issue for a number of AI problems, but few propositional languages offer the possibility to count models efficiently. In order to fill the gap, we introduce the language EADT of (extended) affine decision trees. An extended affine decision tree simply is a tree with affine decision nodes and some specific decomposable conjunction or disjunction nodes. Unlike standard decision trees, the decision nodes of an EADT formula are not labeled by variables but by affine clauses. We study EADT, and several subsets of it along the lines of the knowledge compilation map. We also describe a CNF-to-EADT compiler and present some experimental results. Those results show that the EADT compilation-based approach is competitive with (and in some cases is able to outperform) the model counter Cachet and the d-DNNF compilation-based approach to model counting.

Fault diagnosis of web services composition at run time is appealing in creating a consolidated distributed application. For this purpose, we propose a hybrid model-based diagnosis method which exploits service process description or historical execution information to enhance service composition model, and localize faults by comparing the exceptional execution and the correct execution with the maximum likelihood. Experiments are conducted to evaluate the effectiveness of our method in web service composition fault diagnosis.

Intermittent fault localization approaches account for the fact that faulty components may fail intermittently by considering a parameter (known as goodness) that quantifies the probability that faulty components may still exhibit correct behavior. Current, state-of-the-art approaches (1) assume that this goodness probability is context independent and (2) do not provide means for integrating past diagnosis experience in the diagnostic mechanism. In this paper, we present a novel approach, coined Non-linear Feedback-based Goodness Estimate (NFGE), that uses kernel density estimations (KDE) to address such limitations. We evaluated the approach with both synthetic and real data, yielding lower estimation errors, thus increasing the diagnosis performance.

This paper presents a structured power and energy-flow-based qualitative modelling approach that is applicable to a variety of system types including electrical and fluid flow. The modelling is split into two parts. Power flow is a global phenomenon and is therefore naturally represented and analysed by a network comprised of the relevant structural elements from the components of a system. The power flow analysis is a platform for higher-level behaviour prediction of energy related aspects using local component behaviour models to capture a state-based representation with a global time. The primary application is Failure Modes and Effects Analysis (FMEA) and a form of exaggeration reasoning is used, combined with an order of magnitude representation to derive the worst case failure modes. The novel aspects of the work are an order of magnitude(OM) qualitative network analyser to represent any power domain and topology, including multiple power sources, a feature that was not required for earlier specialised electrical versions of the approach. Secondly, the representation of generalised energy related behaviour as state-based local models is presented as a modelling strategy that can be more vivid and intuitive for a range of topologically complex applications than qualitative equation-based representations. The two-level modelling strategy allows the broad system behaviour coverage of qualitative simulation to be exploited for the FMEA task, while limiting the difficulties of qualitative ambiguity explanation that can arise from abstracted numerical models. We have used the method to support an automated FMEA system with examples of an aircraft fuel system and domestic a heating system discussed in this paper.

Within diagnostic reasoning there have been a number of proposed definitions of a diagnosis, and thus of the most likely diagnosis, including most probable posterior hypothesis, most probable interpretation, most probable covering hypothesis, etc. Most of these approaches assume that the most likely diagnosis must be computed, and that a definition of what should be computed can be made a priori, independent of what the diagnosis is used for. We argue that the diagnostic problem, as currently posed, is incomplete: it does not consider how the diagnosis is to be used, or the utility associated with the treatment of the abnormalities. In this paper we analyze several well-known definitions of diagnosis, showing that the different definitions of the most likely diagnosis have different qualitative meanings, even given the same input data. We argue that the most appropriate definition of (optimal) diagnosis needs to take into account the utility of outcomes and what the diagnosis is used for.

Scientists often use directed acyclic graphs (days) to model the qualitative structure of causal theories, allowing the parameters to be estimated from observational data. Two causal models are equivalent if there is no experiment which could distinguish one from the other. A canonical representation for causal models is presented which yields an efficient graphical criterion for deciding equivalence, and provides a theoretical basis for extracting causal structures from empirical data. This representation is then extended to the more general case of an embedded causal model, that is, a dag in which only a subset of the variables are observable. The canonical representation presented here yields an efficient algorithm for determining when two embedded causal models reflect the same dependency information. This algorithm leads to a model theoretic definition of causation in terms of statistical dependencies.