ABSTRACT
Natural and artificially made porous materials are encountered and used in numerous fields of engineering, medicine, and physics. One of the challenges is to be able to reliably characterise the pore structure of these materials, as it has a great influence on their physical properties. Characterising porous materials using acoustical methods has become a common procedure in many laboratories, in part because the methods are non-destructive and can be performed on relatively cheap instruments. The characterisation is commonly carried out using deterministic inversion methods, where a cost functional of model residuals is minimised, typically with a least squares (LS) approach. These approaches can provide reliable parameter estimates when the number of parameters is small, but with an increasing number of parameters the LS parameter estimates and, in particular, error estimates often become unreliable.
In this thesis, we study the characterisation of porous materials in the Bayesian framework for inverse problems, where uncertainties can be treated and quantified naturally. We first examine air-saturated porous materials whose frame can be modelled as rigid, which has been often the assumption in inverse characterization methods. Next, we focus on water-saturated materials and the more general case where the frame is elastic. A key contribution of this thesis is to develop inversion methods with which we can reliably characterise these poroviscoelastic materials. Each proposed method is tested with real measurements, carried out either in an impedance tube using audible frequencies or in a water tank with ultrasound. To compute the Bayesian parameter estimates and assess the uncertainties related to them, we employ Markov chain Monte Carlo algorithms. The results of this thesis indicate that the Bayesian approach for porous material characterisation can provide robust estimates for the parameters and their uncertainties.
The doctoral dissertation of MSc Matti Niskanen, entitled Bayesian inversion methods for acoustical characterisation of poroviscoelastic media will be examined at the Faculty of Science and Forestry. The opponent in the public examination will be Professor Nuutti Hyvönen, Aalto University, ja Maître de Conférences Jean-Daniel Chazot, Université de Technologie de Compiègene, France, and the custos will be Docent Timo Lähivaara, University of Eastern Finland.
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