Dimensional Consistency Analysis in Complex Algebraic Models

Abstract

Relations in complex algebraic models include numerous variables and parameter that capture the physical dimensions of the objects represented in models (such as "mass", or "volume" of an object). A model developer must ensure the semantic correctness of the model, which includes consistency across physical dimensions and their units of measure in the model relations. Such dimensional consistency analysis is the subject of the research described in this paper. We propose a new methodological framework for this type of analysis which comprises: - a two-level structure for representing knowledge about physical dimensions and units of measure; and - the dimensional analysis algorithm that uses this structured knowledge for the verification of consistency. The proposed methodology allows us to resolve issues related to handling complex non-decomposable units of measure and the situation when instances of the same physical dimension are associated with different physical quantities. We illustrate the proposed methodological framework using mathematical relations from a comprehensive environmental model developed at IIASA