Redundant Information Rejection in Sensor Localisation Using System Gramians

Abstract

Sensors placement is important in vibration testing. The method of effective independence, recently extended to account for triaxial sensors, is widely used for this purpose in case a finite element model of the structure is available. In this paper a criteria is added to reject redundant information that usually arises in symmetric structures or finite element models with high candidate sensor density. A sensor placement strategy is proposed in which, initially, the method of effective independence is used to select the best sensors from a candidate set by maximising the Fisher information matrix determinant. Next, the gramians of a balanced realisation is used to compare the information between systems consisting of only previously added sensors to the final set with systems of the previous and candidate sensors. Sensors with redundant information will have negligible effect on the gramian and can be rejected. The method is fast, as gramians of systems with only one or two outputs are evaluated. It is sub-optimal in the sense that all possible sensor placement combinations are not evaluated for optimality. A test case, consisting of a rectangular plate, is presented, but the method has been used on a large scale industrial model with good results.