Fractional-order modeling of a flow rate measurement system utilizing Grünwald–Letnikov based optimization

Modeling the dynamics of the flow rate system is challenged by the nonlinear behavior and the noisy measurement data. Accurate models require a comprehensive understanding of fluid mechanics, as well as knowledge of all instruments in the measurement chain. This study presents a black-box optimization approach to develop a nominal Fractional-Order (FO) model of a laboratory-scale flow system. The model was constructed by repeatedly solving an optimization problem using preprocessed experimental data and averaging the resulting optimal parameters. The nominal FO model was then validated against unseen, unprocessed measurement data to assess its robustness. The parameter sensitivity of the proposed model was analyzed by introducing +10% and +20% perturbations in each parameter individually. Error analysis evidences that root mean squared, mean absolute, and mean absolute percentage errors with the proposed model have reduced to 9.3%,5.1%, and 5.3%, respectively, compared to those integer-order models. Furthermore, residual-based distribution analysis confirms the robustness of the approach, with residuals tightly concentrated around the lowest values. Although the FO model incurs a higher computational cost during optimization, it was significantly reduced using an online optimizer. The proposed model demonstrates superior robustness and accuracy, making it a compelling choice for precise modeling.