| A series of practical problems in the field of parameter estimation is considered for which practical solutions are achieved. The work is based on simulation studies, mathematical analyses, and engineering judgement.; The first problem considered is that of estimating the state of a cryolite bath in an aluminum reduction cell. A new method of on-line cryolite state estimation using a thermometer pocket is analyzed and optimally designed. Using the thermometer pocket to dynamically control the heat transfer from the bath through a layer of frozen cryolite, the on-line estimation of the cryolite state is shown to be practical. Statistical analysis shows a small standard deviation of 1.2{dollar}spcirc{dollar}C in the liquidus temperature, but a relatively large standard deviation of 9{dollar}spcirc{dollar}C in the bath temperature. Subsequent estimation of the alumina concentration is accomplished via an on-line phase diagram. The potential impact of this new method has yet to be determined and depends of its robustness in the reduction cell environment.; A second problem considered is the on-line estimation of fluid heat capacity. Using a similar thermometer pocket as described above, the dynamic temperature excitation of a flowing fluid is controlled such that the simultaneous estimation of the fluid heat capacity, the fluid flow rate, and the convective heat-transfer coefficients is made practical. Optimal design of the pocket and its on-line operation is performed in order to minimize coupling and random errors in the heat capacity estimate. Monte Carlo analysis of the estimation method shows an expected standard deviation of 0.5% in the fluid heat capacity, 3.4% in the flow rate, 1.2% and 2.3% in the convective heat-transfer coefficients to the wall and to the heating coil respectively. Robustness of the method against model errors and correlated noise is demonstrated. The subsequent estimation of most thermodynamic properties is shown to be feasible as well.; A study of the non-Gaussian characteristics of estimates for the class of non-linear estimation problems with additive zero-mean Gaussian noise is performed as well. A method of generalized exponential reparameterization is developed and is shown to reduce bias and kurtosis for a large class of estimation problems. An Arrhenius kinetics model is used to demonstrate the effectiveness of the method via Monte Carlo analysis. |
