A Direct Least Square Formulation of the KMA Method

Abstract

∗ Senior Engineering Specialist, Structural Dynamics Department, P.O. Box 92957-M4/911, Member AIAA † Director, Structural Dynamics Department, P.O. Box 92957-M4/911, Associate Fellow AIAA ABSTRACT A direct least square (DLS) formulation of the KMA method is presented. The KMA method belongs to a class of procedures that refines dynamic models using test-measured modes and structural connectivity. Viewed as a constrained minimization problem, most of these methods have applied the Lagrange multiplier method (LMM) in their development. It is shown that the DLS and LMM approaches result in linear systems of equations that are algebraically equivalent and therefore, have identical solutions. By virtue of this equivalence, the DLS formulation of the KMA method is shown to be equivalent to its original LMM formulation. The DLS versions of other model refinement methods that preserve structural connectivity are also discussed. In this respect, the DLS approach provides a rigorous framework for unifying these optimal update procedures and indicate how their solutions should compare. Numerical results are presented that illustrates the equivalence between the LMM and DLS formulations and also the conditions under which the various methods yield identical solutions. The results also indicate that because of improved numerical conditioning, the DLS approach yields more accurate computational solutions and generally requires less computer storage than methods which were developed using Lagrange multipliers.