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Sensor network scheduling for identification of spatially distributed processes

Uciński D.

International Journal of Applied Mathematics and Computer Science

2012

Vol. 22, no. 1

25-40

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.

Optymalizacja pobudzeń dla celów identyfikacji parametrów modeli zmiennych stanu

Kalicka R., Pietrenko-Dąbrowska A., Lipiński S.

Pomiary Automatyka Kontrola

2008

R. 54, nr 3

114-117

W pracy omówiono zagadnienie optymalizacji pobudzeń dla celów identyfikacji parametrów modeli kompartmentowych systemów farmakokinetycznych opisanych w kategoriach zmiennych stanu. Przedstawiono pobudzenia optymalne zaprojektowane według kryterium A-optymalności. Zaprojektowane pobudzenia optymalne, w obrębie klasy pobudzeń o ograniczonej energii, zapewniają maksymalną osiągalną dokładność estymat parametrów. W farmakokinetyce nałożenie ograniczenia na energię pobudzenia konieczne jest w przypadku leków, których szybkie podawanie powoduje występowanie skutków ubocznych.

Optimal input design for parameter estimation of compartmental state-space models of pharmacokinetic systems is presented in the paper. The results presented were obtained for two-compartmental model of procainamide pharmacokinetics. In the paper A-optimality criterion was utilised. A-optimal inputs presented, in the equienergy class of optimal inputs, ensure the best achievable accuracy of parameter estimates. The optimisation procedure delivered optimal inputs of non-positive values presented in Fig. 2. In order to ensure the applicability of the optimal inputs in drug delivery the additional constraint, lower bound was imposed on the optimal inputs. The applicable optimal inputs presented in Fig. 3 were used for parameter estimation. In the Tab. 2 the parameter estimates as well as their accuracies are presented.