Electromagnetic Modelling for the Estimation of Wood Parameters

Abstract: Spiral grain in trees causes trouble to the wood industry, since boards sawn from trees with large grain angle have severe problems with form stability. Measurements of the grain angle under bark enable the optimisation of the refining process. The main objective of this thesis is to study the potential in estimating the grain angle by using microwaves. To do this, electromagnetic modelling and sensitivity analysis are combined.The dielectric properties of wood are different along and perpendicular to the wood fibres. This anisotropy is central for the estimation of the grain angle by means of microwaves. To estimate the grain angle, measurements are used together with electromagnetic modelling for the scattering from plane surfaces and cylinders. Measurement set-ups are proposed to determine the material parameters, such as the grain angle, for plane boards and cylindrical logs. For cylindrical logs both near-field and far-field measurements are investigated. In general, methods for determining material parameters exhibit large errors in the presence of noise. In this case, acceptable levels of these errors are achieved throug using few material parameters in the model: the grain angle and two dielectric parameters, characterising the electrical properties parallel and perpendicular to the fibres.From the case with plane boards, it is concluded that it is possible to make use of the anisotropy of wood to estimate the grain angle from the reflected electromagnetic field. This property forms then the basis of the proposed methods for the estimation of the grain angle in cylindrical logs. For the proposed methods, a priori knowledge of the moisture content or temperature of the wood is not needed. Furthermore, since the anisotropy persist also for frozen wood, the method is valid for temperatures below zero degrees Celsius.For the case with cylindrical logs, sensitivity analysis is applied to the near-field as well as the far-field methods, to analyse the parameter dependence with respect to the measurement model and the errors introduced by noise. In this sensitivity analysis, the Cram\'{e}r-Rao bound is used, giving the best possible variance for estimating the parameters. The levels of the error bounds are high, indicating a problematic estimation problem. However, the feasibility of accurate estimation will be improved through higher signal-to-noise ratios, repeated measurements, and better antenna gain. The sensitivity analysis is also useful as an analytical tool to understand the difficulties and remedies related to the method used for determining material parameters, as well as a practical aid in the design of a measurement set-up.According to the thesis, grain angle estimation is possible with microwaves. The proposed methods are fast and suitable for further development for in-field use in the forest or in saw mills.