Optimal experiment design is the definition of the conditions under which an experiment is to be conducted in order to maximize the accuracy with which the results are obtained. This paper summarizes a number of methods by which the parameters of the mathematical model of the system are estimated and describes the application of the Fisher information matrix. Examples are given for thermal property estimation in which the estimation is affected both by measurement noise, which is present during any experiment, but also by uncertainties in the parameters of the model used to describe the system.

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Accurate modeling of thermal systems depends upon the determination of the material properties and the surface heat transfer coefficients. These parameters are frequently estimated from temperatures measured within the system or on the surface or from measured surface heat fluxes. Because of sensor errors or lack of sensitivity, the measurements may lead to erroneous estimates of the parameters. These errors can be ameliorated if the sensors are placed at points of maximum sensitivity. This paper describes two methods to optimize sensor locations: one to account for signal error, the other to consider interacting parameters. The methods are based upon variants of the normalized Fisher information matrix and are shown to be equivalent in some cases, but to predict differing sensor locations under other conditions, usually transient.

Communicated by G. S. DulikravichComputational methods for the solution of boundary inverse heat conduction problems are widely used at present in experimental investigations of thermal processes between the solids and the environment. To solve three-dimensional ill-posed boundary inverse problems, an iterative regularization method is suggested in this study. The method is based on gradient methods of the first kind, and on the principle of the residual. The accuracy of the solution of inverse problems obtained by the suggested algorithms is discussed. The application of the considered method is demonstrated as the reconstruction of spatial-time heat flux distribution over the thermal protection of the spacecraft equipment.