Optimal Sampling Placement in a Gaussian Random Field Based on Value of Information

Abstract

In the context of sampling, monitoring, and sensing in infrastructures, there is an interest in algorithms to produce an observation plan that is cost effective, while maximizing the benefits of the new observations. This paper proposes a method to obtain an optimal sampling plan in terms of the number and placement of additional sampling points based on value of information (VoI). VoI can be computed easily through updating a Gaussian random field, i.e., kriging, which is a probabilistic interpolation method. Particle swarm optimization is introduced to optimize a set of sites for new observations with respect to VoI. In the paper, after presenting the basic concept and formulation, we describe applying the method to the placement of additional borings as a liquefaction countermeasure for an embankment along a river. The optimal sampling placement may be obtained at a feasible computational cost even when the number of additional sampling points is greater than 1. The optimal number of sampling points is also evaluated based on VoI.