Methodology for Optimum Sensor Locations for Parameter Identification in Dynamic Systems

Abstract

This paper provides a methodology for optimally locating sensors in a dynamic system so that data acquired from those locations will yield the best identification of the parameters to be identified. It addresses the following questions: (1) Given m sensors, where should they be placed in a spatially distributed dynamic system so that data from those locations will yield best estimates of the parameters that need to be identified?; and (2) given that we have already installed p sensors in a dynamic system, where should the next s be located? The methodology is rigorously founded on the Fisher information matrix and is applicable to both linear and nonlinear systems. A rapid algorithm is provided for use in large multi‐degree‐of‐freedom systems. After developing the general methodology, the paper goes on to develop the method in detail for a linear N‐degree‐of‐freedom, classically damped, system. Numerical examples are provided and it is verified that the optimal placement of sensors, as dictated by the methodology that is developed, could provide significantly improved estimates of the parameters to be identified.