Model transformation tools assist system designers by reducing the labor-intensive task of creating and updating models of various aspects of systems, ensuring that modeling assumptions remain consistent across every model of a system, and identifying constraints on system design imposed by these modeling assumptions. We have proposed a model transformation approach based on abstract interpretation, a static program analysis technique. Abstract interpretation allows us to define transformations that are provably correct and specific. This work develops the foundations of this approach to model transformation. We define model transformation in terms of abstract interpretation and prove the soundness of our approach. Furthermore, we develop formalisms useful for encoding model properties. This work provides a methodology for relating models of different aspects of a system and for applying modeling techniques from one system domain, such as smart power grids, to other domains, such as water distribution networks.
Complex system design often proceeds in an iterative fashion, starting from a high-level model and adding detail as the design matures. This process can be assisted by metamodeling techniques that automate some model manipulations and check for or eliminate modeling mistakes. Our work focuses on metamodeling reliability models: we describe generalization and refinement operations for these models. Generalization relaxes constraints that may be infeasible or costly to evaluate; refinement adds further detail to produce a model that more closely describes the desired system. We define these operations in terms of operations on system constraints. To illustrate the proposed method, we relate these constraints to a common Markov chainbased reliability modeling formalism.1 In short, the transition probability matrices for consecutive-k-of-n systems are not upper triangular; for more detail, see [1, pp. 344-345].
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