Two-stage scheme for identification of parallel Scott-Blair fractional model of viscoelastic biological materials

• Autorzy: Stankiewicz A.
• Języki publikacji: EN

Abstrakty

EN

Fractional calculus considers derivatives and integrals of an arbitrary order. This article focuses on fractional parallel Scott-Blair model of viscoelastic biological materials, which is a generalization of classic Kelvin-Voight model to non-integer order derivatives suggested in the previous paper. The parallel Scott-Blair model admit the closed form of analytical solution in terms of two power functions multiplied by Debye type weight function. To build a parallel Scott-Blair model when only discrete-time measurements of the relaxation modulus are accessible for identification is a basic concern. Based on asymptotic models a two-stage approach is proposed for fitting the measurement data, which means that in the first stage the data are fitted by solving two dependent, but simple, linear least-squares problems in two separate time intervals. Next, at the second stage of the identification procedure the exact parallel Scott-Blair model optimal in the least-squares sense is computed. The log-transformed relaxation modulus data is used in the first stage of identification scheme, while the original relaxation modulus data is applied for the second stage identification. A complete identification procedure is presented. The usability of the method to find the parallel Scott-Blair fractional model of real biological material is demonstrated. The parameters of the parallel Scott-Blair model of a sample of sugar beet root, which very closely approximate the experimental relaxation modulus data, are given.

Słowa kluczowe

EN

fractional calculus; viscoelasticity; relaxation modulus; parallel Scott-Blair fractional model; model identification

• Wydawca: Polish Academy of Sciences, Branch in Lublin
• Czasopismo: ECONTECHMOD : An International Quarterly Journal on Economics of Technology and Modelling Processes
• Rocznik: 2018
• Tom: Vol. 7, No 1
• Strony: 87--96
• Opis fizyczny: Bibliogr. 22 poz., rys., wz.

Twórcy

autor

Stankiewicz A.

• Department of Technology Fundamentals, University of Life Sciences in Lublin, Poland

Bibliografia

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Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).