Optimal spatial sampling scheme for parameter estimation of nonlinear distributed parameter systems

In this paper a methodology for the estimation of parameters of distributed parameter systems based on optimal spatial measurements is discussed. The concept of the covariance matrix for sampling design is exploited and D-optimality criteria concerning relevant metrics are linked with the computation of optimal measurement locations. These are obtained at the points where sensitivity functions reach their extrema values and coincide with the locations where system eigenmodes obtained by proper orthogonal decomposition (POD) are maximised or minimised as has been shown in a recent work (Alaña & Theodoropoulos, 2011). A tubular reactor with recycle is used as illustrative example to demonstrate the sampling methodology, including cases where the system behaviour is unstable exhibiting sustained oscillations. The estimates with the highest deviation from the nominal parameter values are the ones with the lowest (absolute) sensitivity coefficients. Using a POD-based reduced model can significantly reduce computational costs and in addition improve the estimation procedure by using measurements at the locations where the POD modes extrema occur. The results are strongly influenced by experimental noise, and filtering techniques are needed to mitigate the related uncertainties.

► We exploit the concept of the covariance matrix for efficient sampling design. ► We link the computation of the covariance matrix with D-optimality criteria. ► We use POD-based reduced models to efficiently compute optimal measurement locations. ► We illustrate our technique for stable and unstable distributed parameter dynamics.