Optimal sensor placements using modified Fisher information matrix and effective information algorithm

This article presents an optimal sensor placement algorithm for modifying the Fisher information matrix and effective information. The modified Fisher information matrix and effective information are expressed using a dynamic equation constrained by the condensed relationship of the incomplete mode shape matrix. The mode shape matrix row corresponding to the master degree of freedom of the lowest-contribution Fisher information matrix and effective information indices is moved to the slave degree of freedom during each iteration to obtain an updated shape matrix, which is then used in subsequent calculations. The iteration is repeated until the target sensors attain the targeted number of modes. The numerical simulations are then applied to compare the optimal sensor placement results obtained using the number of installed sensors, and the contribution matrices using the Fisher information matrix and effective information approaches are compared based on the proposed parameter matrix. The mode-shape-based optimal sensor placement approach selects the optimal sensor layout at the positions to uniformly allocate the entire degree of freedom. The numerical results reveal that the proposed F-based and effective information–based approaches lead to slightly different results, depending on the number of parameter matrix modes; however, the resulting final optimal sensor placement is included in a group of common candidate sensor locations. However, the resulting final optimal sensor placement is included in a group of common candidate sensor locations.