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.

Model Updating of Multiple Nominally Identical Car Components

“…The rear subframe FE model was used in pre-test planning to find good sensor locations. A total of 170 candidate sensor locations were selected, from which 20 uniaxial sensor locations were found for the 20 first flexible modes using the expansion effective independence method [30] with an added gramian rejection step for rejection of locations with similar modal information [19]. In addition, six more accelerometer locations were added for visualisation purposes.…”

Calibration, Validation and Uncertainty Quantification of Nominally Identical Car Subframes

“…Thus, the subframes were efficiently isolated from its surrounding and the rigid body modes were kept low, with eigenfrequencies below 5 Hz. Sensor positions were selected by the modified set expansion EfI [8] algorithm with added gramian rejection for nodes containing similar information [9]. The candidate set consisted of 170 possible locations, or 510 degrees-of-freedom.…”

“…The candidate set consisted of 170 possible locations, or 510 degrees-of-freedom. The 10 triaxial accelerometers were placed first, with a rejection threshold of T s = 0.05, see [9]. Two accelerometers were initially positioned at the exhaust hangers seen at the top middle in Figure 2a.…”

“…Previous work using this method has been performed on various industrial components with good results [4][5][6][7]. Pretest planing has been performed with the expansion method of effective independence (EfI) [8] with an added gramian rejection step, described further in [9]. The three components were tested in a vibration-test with an improved frequency strategy [10] for subspace state-space system identification [11].…”