Mass-weighting methods for sensor placement using sensor set expansion techniques

Placement of sensors is one of the most important tasks performed during pretest planning. The purpose of this work was to develop and investigate the use of an iterative Guyan expansion for mass weighting of target modes for sensor placement analogous to the common iterative Guyan reduction technique. The goal was to determine the appropriate mass-weighting approach to use in conjunction with effective independence sensor set expansion. In either sensor set expansion, or reduction, mass weighting requires a reduction of the FEM mass matrix to the current sensor set size Test-Analysis-Model (TAM). A general theory is presented for target mode mass weighting that can accommodate any type of reduction technique. The theory predicts that sensor set expansion using static mass weighting will result in sensor configurations that produce poor static TAMs. In contrast, sensor set expansion using modal mass weighting exactly reproduces the correct mass distribution during the expansion process. The results of a numerical example corroborate the theory. The modal mass sensor set expansion process produced significantly more accurate static TAMs than the static mass expansion. The modal expansion process was not quite as accurate as the iterative static reduction approach, but modal expansion was over 1600 times faster.