Figure 1 – Selection map of the weights k1andk2 . EFFECTIVE INDEPENDENCE METHOD From among the numerous master nodes criteria and optimal sensor placement methods found in literature [7], [8], [9], [10], [11], [12], [13] the well-known effective iterative procedure based on the maximisation of the independence of modal properties is taken into account. The effective independence method (EI) was developed to maximise both the spatial independence and signal strength of a number of targeted mode shapes. It has been implemented for optimal sensor location in modal identification of large structures [1], [11] and is based on the maximisation of the Fisher information matrix determinant Q. Estimating the covariance matrix of the error J to describe a generic configuration with the modal displacements, it results [12]: > @ 1 1 ĭ ĭ J Q T D (3) where D is a constant. The procedure is iterative: the methodology for selecting the best sensor placements is to unselect candidate sensor positions so that the determinant of the Fisher information matrix Qis maximised. Although EI is an iterative technique and is rather computing-time consuming for complex FE models with respect to MoGeSeC, the results obtained with this approach give rise to an effective fairly uniform spacing for the sensor locations along the structure [12]. This objective is similar to the role of the geometrical vector term gW of Equation (3) which allows the addition of physical nodes in a model geometrical area that respects as far as possible the other master nodes. Using just this information creates as main effect that EI can produce experimental setup not well distributed in the space occupied by the structure and a high sensitivity of illconditioning and mode-shapes identification for small error location of sensors. Pursuing independence properties, EI method can select sensor locations with low energy content, with a consequent possible loss of information. In order to overcome this limitation, the weighting of the mode-shape displacement is adopted in MoGeSeC by introducing the modal vector term mW . The aim of the methodology is to minimise the illconditioning and to improve numerical stability of mass and stiffness matrices of the reduced model. Therefore, the selection of added master nodes, based on relevant modal properties, is corrected by means of the geometrical vector term gW in order to obtain an optimal distribution. 284
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