Experimental Determination of Mechanical Properties Is, In General, NP-Hard -- Unless We Measure Everything

Authors

Yan Wang, Georgia Institute of TechnologyFollow
Oscar Galindo, The University of Texas at El PasoFollow
Michael Baca, The University of Texas at El PasoFollow
Jake Lasley, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow

Publication Date

10-2018

Comments

Technical Report: UTEP-CS-18-72

Abstract

When forces are applied to different parts of a construction, they cause displacements. In practice, displacements are usually reasonably small. In this case, we can safely ignore quadratic and higher order terms in the corresponding dependence and assume that the forces linear depend on displacements. The coefficients of this linear dependence determine the mechanical properties of the construction and thus, need to be experimentally determined. In the ideal case, when we measure the forces and displacements at all possible locations, it is easy to find the corresponding coefficients: it is sufficient to solve the corresponding system of linear equations. In practice, however, we only measure displacements and forces at some locations. We show that in this case, the problem of determining the corresponding coefficients becomes, in general, NP-hard.