Genetic algorithm based optimal sensor placement for L₁-regularized damage detection

Abstract

Sparse recovery theory has been applied to damage detection by utilizing the sparsity feature of structural damage. The theory requires that the columns of the sensing matrix suffice certain independence criteria. In l1-regularized damage detection, the sensitivity matrix serves as the sensing matrix and is directly related to sensor locations. An optimal sensor placement technique is proposed such that the resulting sensitivity matrix is of the maximum independence in the columns or is of the least mutual coherence. Given a total number of sensors, the selection of sensor locations is a combinatorial problem. A genetic algorithm is thus used to solve this optimization problem, in which the mutual coherence of the sensitivity matrix is minimized. The obtained optimal sensor locations and associated sensitivity matrix are used in l1-regularized damage detection. An experimental cantilever beam and a three-storey frame are utilized to verify the effectiveness and reliability of the proposed sensor placement technique. Results show that using the modal data based on the optimal sensor placement can identify damage location and severity more accurately than using the ones based on uniformly selected sensor locations.