Development of a stochastic effective independence (SEFI) method for optimal sensor placement under uncertainty

Finding optimal sensor placement for data acquisition is an essential initial stage in the development of many engineered systems. For this purpose, the effective independence (EFI) method was developed and has been widely used. In this method, sensor locations are selected to maximize the linear independency of the target mode shape matrix. However, the EFI method lacks consideration of the uncertainty that is present in real applications. To overcome this limitation, in this study, a new stochastic EFI method is derived. The resultant equation is composed of the conventional deterministic term and an additional random term. Using the derived equation, optimal sensor locations are found. The results of stochastic EFI give the best linear independency of the mode shape matrix in the mean sense. In this paper, stochastic EFI is also extended to the energy-based EFI method. In the energy-based EFI method, the mass or stiffness matrix is weighted to have the kinetic or strain energy form of the EFI method. By decomposing the weighted matrix, the same form is obtained as in the EFI method; thus, its stochastic version follows naturally, as in the stochastic EFI method. Further, the stochastic sensor placement method is also derived for a different optimization criterion called the A-optimality criterion, which uses a matrix trace for its measure. Finally, the proposed method is validated using a truss bridge case. Its results are compared with the Monte Carlo simulation based method, which is another approach used to handle the system uncertainty. The case study indicates that the suggested method shows higher linear independency than the EFI method and the energy-based EFI method; it is also better with different optimality conditions.