ESTAN—A toolbox for standardized and effective global sensitivity-based estimability analysis

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The development of accurate and reliable mathematical models is the cornerstone for the modeling and optimization of processes. However, most of the existing models suffer from weak prediction capabilities due to poor data information content and poor parameter estimation methodologies. Several estimability approaches have been developed and increasingly implemented to address some of these issues. However, the wider adoption of these methods is still hampered by the lack of standardized and robust methodologies. In this paper, we present a Matlab Toolbox, called ESTAN, designed and developed to make estimability analysis accessible to non-specialist users. It uses a Quasi-Monte Carlo sequence to sample the main unknown parameters within their variation spaces. Then, depending on whether the studied model is computationally cheap or expensive, sensitivity indices are calculated either using the Sobol method or Fourier Amplitude Sensitivity Test (FAST). The calculated sensitivities are finally used within an orthogonalization algorithm to rank the parameters from the most to less estimable ones and to determine the estimable and non-estimable ones based on an estimability cut-off criterion. Various case studies are used to validate the toolbox and guide the users. The first one deals with the non-dynamic Toth adsorption model, while the second one deals with a dynamic batch cooling crystallization model. The main challenge with these two case studies is to show the importance of estimability analysis in the interpolation/extrapolation of model prediction capabilities. The last case addresses a computationally expensive thermodynamic model. The results for all the case studies are found to be promising, showing how the presented toolbox simplifies the investigation of the estimability analysis.