Two distinct and parallel research communities have been working along the lines of the model-based diagnosis approach: the fault detection and isolation (FDI) community and the diagnostic (DX) community that have evolved in the fields of automatic control and artificial intelligence, respectively. This paper clarifies and links the concepts and assumptions that underlie the FDI analytical redundancy approach and the DX consistency-based logical approach. A formal framework is proposed in order to compare the two approaches and the theoretical proof of their equivalence together with the necessary and sufficient conditions is provided.

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Diagnosis is the process of identifying or determining the nature and root cause of a failure, problem, or disease from the symptoms resulting from selected measurements, checks or tests. The different facets of this problem and the wide spectrum of classes of systems make it interesting to several communities and require bridging several theories. Diagnosis is actually a functional fragment in fault management architectures and it must smoothly interact with other functions. This paper presents diagnosis as it is understood in the Control and Artificial Intelligence fields, and exemplifies how different theories of these fields can be synergistically integrated to provide better diagnostic solutions and to achieve improved fault management in different environments 1 .

Identifiability is the property that a mathematical model must satisfy to guarantee an unambiguous mapping between its parameters and the output trajectories. It is of prime importance when parameters must be estimated from experimental data representing inputoutput behavior and clearly when parameter estimation is used for fault detection and identification. Definitions of identifiability and methods for checking this property for linear and nonlinear systems are now well established and, interestingly, some scarce works ([8, 16]) have provided identifiability definitions and numerical tests in a bounded-error context. This paper resumes and better formalizes the two complementary definitions of set-membership identifiability and µ-set-membership identifiability of [16] and presents a method applicable to nonlinear systems for checking them. This method is based on differential algebra and makes use of relations linking the observations, the inputs and the unknown parameters of the system. Using these results, a method for fault detection and identification is proposed. The relations mentioned above are used to estimate the uncertain parameters of the model. By building the parameter estimation scheme on the analysis of identifiability, the solution set is guaranteed to reduce to one connected set, avoiding this way the pessimism of classical set-membership estimation methods. Fault detection and identification are performed at once by checking the estimated values against the parameter nominal ranges. The method is illustrated with an example describing the capacity of a macrophage mannose receptor to endocytose a specific soluble macromolecule. This work is a extended version of a conference paper with the same title, that appeared in the proceedings of the 8th IFAC Symposium SAFEPROCESS, August 29-31, 2012.

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