On the investigation of utility functions on optimal sensor locations

Structural Health Monitoring uses data collected from sensors placed on structures to determine their operating condition and whether maintenance is required. Often, optimal sensor placement strategies are used to find the optimal locations for the identification of their modal properties, structural parameters and/or abnormal behaviours under the influence of model and measurement uncertainty. An approach that has been frequently used to solve the problem of sensor placement is the Bayesian experimental design. This approach chooses the locations using the data measured by the sensors to reduce the prior uncertainty of the parameters that are being inferred. The Bayesian experimental design minimizes the uncertainty of the parameters to be inferred through the use of metrics called utility functions. Most of these metrics are based on functions of the posterior distribution. In this paper, the use of three utility functions (Bayesian D-posterior precision, Bayesian A-posterior precision, and Expected Information Gain) is investigated for the problem of sensor placement. The case study chosen consists of a beam with translational and rotational springs connected to the ground subject to an impulsive load. The goal of the analysis is to select the most informative position of a sensor in order to update the distribution of two uncertain physical parameters of the beam based on natural frequencies extracted using the Eigensystem Realization Algorithm. It is shown that for the case investigated, the three utility functions yield the same optimal sensor location.