Detection of structural inconsistency in systems of equations with degrees of freedom and its applications
The concept of structural inconsistency of equations is studied with regard to analysis of large-scale engineering systems. The concept of structural inconsistency of systems of equations, where the number of equations equals that of unknowns, is generalized to systems, where the number of unknowns is greater than that of equations (due to degrees of freedom of their solution). Starting from the matroid theory a theorem is proven which relates the consistency of a primary structure to the maximum flow of the associated network. Based on this result two algorithms are presented for efficient detection of inconsistency in the systems of equations. Some examples illustrating applications of the algorithms for analyzing various engineering problems (e.g. line drawings of polyhedrons, dimensioning in engineering drawings or general linked structures) are presented. Analysis of time complexity shows that the presented method is useful both for detecting errors in formulation of large-scale systems of equations and for analyzing some essential properties of various engineering systems.
scientific article; zbMATH DE number 3913574
scientific article