ESTAN – A toolbox for global sensitivity based estimability analysis

Recently in process engineering field, there is an increasing demand for high fidelity, large and multi-scale mathematical models. In most cases, these models involve several unknown parameters whose identifiability from experimental measurements is often not guaranteed. It is therefore necessary to carry out an estimability analysis to determine which parameters can be reliably estimated. This task is however laborious and is still neglected in most studies. Most importantly, its wide adoption is hampered by the lack of standardized tools or methodologies. To address these issues, a new estimability toolbox, ESTAN, was developed to make the estimability analysis accessible to a broader community of specialist and non-specialist users. ESTAN can handle different types of mathematical models including dynamic and non-dynamic models. It uses a Quasi-Monte Carlo method to sample the unknown model parameters within their range of variation. Then, depending on whether the studied model is computationally cheap or expensive, global sensitivity indices are calculated using either the Sobol method or the Fourier Amplitude Sensitivity Test. The sensitivities are exploited within an orthogonalization algorithm to rank the parameters from the most to the least estimable followed by the identification of the subset of the most estimable parameters based on a preset estimability threshold. Finally, more reliable parameter estimates are obtained for the subset of the most estimable parameters. To validate the toolbox and demonstrate its capabilities, ability analysis of three models is performed using the developed toolbox. They are given by a non-dynamic, a dynamic, and a computationally expensive model. The results for the case studies are found to be very promising, showing how the presented toolbox simplifies the investigation of the estimability analysis, and significantly improves the model's precision.