Determination of optimal accelerometer locations using modal sensitivity for identifying a structure

A new algorithm is proposed to determine optimal accelerometer locations (OAL) when a structure is identified by frequency domain system identification (SI) method. As a result, a guideline is presented for selecting OAL which can reflect modal response of a structure properly. The guideline is to provide a minimum number of necessary accelerometers with the variation in the number of measurable target modes. To determine OAL for SI applications effectively, the modal sensitivity effective independence distribution vector (MS-EIDV) is developed with the likelihood function of measurements. By maximizing the likelihood of the occurrence of the measurements relative to the predictions, Fisher Information Matrix (FIM) is derived as a function of mode shape sensitivity. This paper also proposes a statistical approach in determining the structural parameters with a presumed parameter error which reflects the epistemic paradox between the determination of OAL and the application of a SI scheme. Numerical simulations have been carried out to examine the proposed OAL algorithm. A two-span multi-girder bridge and a two-span truss bridge were used for the simulation studies. To overcome a rank deficiency frequently occurred in inverting a FIM, the singular value decomposition scheme has been applied.