Optimal embedded sensor placement for spatial variability assessment of stationary random fields

Structural reliability assessment is largely influenced by the spatial variability of material properties or defaults; however, there are still various challenges for their characterization and modeling. Structural Health Monitoring (SHM) could provide useful information in space and time for spatial variability characterization of material properties and mechanical solicitations; nevertheless, this challenge is arduous because of the large number of potential sensor positions of local disruptions/failures. This paper proposes a methodology to optimize the spatial distribution of embedded sensors used for spatial variability assessment of stationary random fields. The optimization criterion relies on the width of the confidence interval of statistics for the characteristics to identify. For sake of simplicity, the paper illustrates the method for one-dimensional problems. The proposed method is applied firstly to a numerical example were several hypothetical structural configurations that could be found in practice are studied. It is finally applied to two case studies (a reinforced concrete beam and a steel wharf) where water content and loss of steel thickness are respectively measured. The results show that the stationary property is useful to deduce the minimum quantity of sensors and their position for a given quality requirement. They also allow us to propose a criterion for defining if regular or non-regular spacing of sensors along the inspection zone is more appropriate depending on the component length and autocorrelation structure of the random field.