Ghent University, Department of Electromechanical, Systems and Metal Engineering, Research laboratory on Dynamical Systems and Control, Tech Lane Science Park 125, 9052 Ghent, Belgium.
Technical University of Cluj Napoca, Department of Automatic Control, Memorandumului street 28, Cluj, Romania.
Philos Trans A Math Phys Eng Sci. 2020 May 29;378(2172):20190284. doi: 10.1098/rsta.2019.0284. Epub 2020 May 11.
The paper proposes a mathematical framework for the use of fractional-order impedance models to capture fluid mechanics properties in frequency-domain experimental datasets. An overview of non-Newtonian (NN) fluid classification is given as to motivate the use of fractional-order models as natural solutions to capture fluid dynamics. Four classes of fluids are tested: oil, sugar, detergent and liquid soap. Three nonlinear identification methods are used to fit the model: nonlinear least squares, genetic algorithms and particle swarm optimization. The model identification results obtained from experimental datasets suggest the proposed model is useful to characterize various degree of viscoelasticity in NN fluids. The advantage of the proposed model is that it is compact, while capturing the fluid properties and can be identified in real-time for further use in prediction or control applications. This article is part of the theme issue 'Advanced materials modelling via fractional calculus: challenges and perspectives'.
本文提出了一种利用分数阶阻抗模型在频域实验数据中捕捉流体力 学特性的数学框架。概述了非牛顿（NN）流体的分类，以说明分数阶模型作为捕捉流 体动力学的自然解的使用。测试了四类流体：油、糖、清洁剂和液体肥皂。使用三种非线性识别方法来拟合模型：非线性最小二乘法、遗传算法和粒子群优化。从实验数据集获得的模型识别结果表明，所提出的模型可用于表征 NN 流体中不同程度的粘弹性。所提出模型的优点是紧凑，同时捕捉流体力 学特性，并可实时识别，以便进一步用于预测或控制应用。本文是主题为“通 过分数阶微积分进行高级材料建模：挑战和展望”的一部分。
