Abstract
ABSTRACTEstimation of physical parameters in dynamical systems driven by linear partial differential equations is an important problem. In this paper, we introduce the least costly experiment design framework for these systems. It enables parameter estimation with an accuracy that is specified by the experimenter prior to the identification experiment, while at the same time minimising the cost of the experiment. We show how to adapt the classical framework for these systems and take into account scaling and stability issues. We also introduce a progressive subdivision algorithm that further generalises the experiment design framework in the sense that it returns the lowest cost by finding the optimal input signal, and optimal sensor and actuator locations. Our methodology is then applied to a relevant problem in heat transfer studies: estimation of conductivity and diffusivity parameters in front-face experiments. We find good correspondence between numerical and theoretical results.
Highlights
Accurate estimation of key physical parameters in a system is an important problem
It enables parameter estimation with an accuracy that is specified by the experimenter prior to the identification experiment, while at the same time minimising the cost of the experiment
We introduce a progressive subdivision algorithm that further generalises the experiment design framework in the sense that it returns the lowest cost by finding the optimal input signal, and optimal sensor and actuator locations
Summary
We mention some examples: a material can be characterised by its conductivity and diffusivity constants in heat transfer studies (Gabano & Poinot, 2009), realistic groundwater contamination simulations require accurate estimates of diffusivity and advection constants (Wagner & Harvey, 1997; Yeh, 1986), permeability and porosity of rock aid in oil extraction from subsurface reservoirs (Mansoori, Van den Hof, Janssen, & Rashtchian, 2014), etc. In this context, we consider in this paper the problem of optimally designing the identification experiment leading to the estimates of these physical parameters. We are interested in those systems that can be described by linear partial differential equations (PDEs) with spatially independent coefficients
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