Correlation of Thermal Mathematical Models to test data using Jacobian matrix formulation
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A good thermal model-to-test correlation is crucial in space projects in order to validate thermal mathematical models and reduce their uncertainty for other scenarios predictions. The correlation consists mainly in adjusting the model parameters so that they fit the experimental data within certain margins previously defined. This task is often performed manually, and the process requires engineering knowledge and experience to reach a successful result. However, the results obtained this way are not the optimum, and with the aid of a mathematical tool, the correlation process could be improved, considering in this case the correlation process as the minimization of the error of the model predictions with regard to test data. Following this approach, a simple method is presented for thermal balance tests correlations, that is, for steady-state cases. The method is based on using Jacobian matrix formulation and Moore-Penrose pseudo-inversion. The formulation allows the correlation of a model with several load cases, as it is usually the case in space projects, where at least a hot thermal balance and a cold thermal balance are tested. As an example of the method, it has been applied to thermal mathematical model of the Optics Unit of the instrument PHI of the ESA Solar Orbiter mission, expected to be launched in February 2019.