Sensor network scheduling for identification of spatially distributed processes

Abstract

The work treats the problem of fault detection for processes described by partial differential equations as that of maximizing the power of a parametric hypothesis test which checks whether or not system parameters have nominal values. A simple node activation strategy is discussed for the design of a sensor network deployed in a spatial domain that is supposed to be used while detecting changes in the underlying parameters which govern the process evolution. The setting considered relates to a situation where from among a finite set of potential sensor locations only a subset of them can be selected because of the cost constraints. As a suitable performance measure, the Ds-optimality criterion defined on the Fisher information matrix for the estimated parameters is applied. The problem is then formulated as the determination of the density of gauged sites so as to maximize the adopted design criterion, subject to inequality constraints incorporating a maximum allowable sensor density in a given spatial domain. The search for the optimal solution is performed using a simplicial decomposition algorithm. The use of the proposed approach is illustrated by a numerical example involving sensor selection for a two-dimensional diffusion process.

A branch-and-bound algorithm for the exact optimal experimental design problem

“…In particular, the box-constrained problem is a special case of experimental design problems with linear constraints studied in [9,10,27] and theory and solution techniques developed in these references apply here. Similarly, although there are related results in [13,33,34,35], the equivalence theorem for this specific version of the problem (see Theorem 3.1 below) is novel and will be useful in future studies, potentially for different applications.…”

An efficient goal‐based reduced order model approach for targeted adaptive observations

“…There is a need to optimally place observations that will maximally improve the accuracy of numerical solutions at forecast times typical for the considered models. The resulting observation network could be adapted for a wide range of forecasting goals, and it could be adapted either by allocating existing observations differently or by adding observations from programmable platforms to the existing network . Expensive field‐deployed resources can thus be utilised more effectively by selecting an optimal observational network.…”

Robust sensor scheduling via iterative design for parameter estimation of distributed systems

“…Sensor location problem for DPSs has already attained a lot of attention [6]-[10, for reviews, see] and various effective approaches have been proposed concentrating mainly on the stationary (or motionless) sensor placement [8], [11]- [14]. A very attractive alternative is the application of moving [15]- [23] or scanning [24]- [30] observations, because they offers possibility to significantly increase the degree of optimality for solutions.…”