Circular arc rules of complex plane plot for model parameters determination of viscoelastic material

Yin, Yilin; Yang, Zhenghong; Mei-lun, Shi

doi:10.1007/s11043-020-09465-x

Cited by 3 publications

(3 citation statements)

References 31 publications

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“…In view of the convergence properties (30), (31) the computation of the parameter g * N approximation the parameter g * of the optimal FMM requires the next steps:…”

Section: Identification Algorithmmentioning

confidence: 99%

“…Different identification methods for the recovery of the parameters of the non-integralorder models, including the FMM, from both static [16,[25][26][27][28] and dynamic [12,[29][30][31] experiments data have been proposed so far. It is known that different identification methods in association with different experiment plans result in different identification data yield models, which may differ [32].…”

Section: Introductionmentioning

confidence: 99%

“…For the selected identification index, the model identified is usually dependent, sometimes even very strongly, on the experiment data. This is the case with FMM identification methods known in the literature [12,16,[25][26][27][28][29][30][31]. This paper deals with the problem of the FMM identification using measurement data from the stress relaxation test.…”

Section: Introductionmentioning

confidence: 99%

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Sampling Points-Independent Identification of the Fractional Maxwell Model of Viscoelastic Materials Based on Stress Relaxation Experiment Data

Stankiewicz

2024

Materials

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Considerable development has been observed in the area of applying fractional-order rheological models to describe the viscoelastic properties of miscellaneous materials in the last few decades together with the increasingly stronger adoption of fractional calculus. The fractional Maxwell model is the best-known non-integer-order rheological model. A weighted least-square approximation problem of the relaxation modulus by the fractional Maxwell model is considered when only the time measurements of the relaxation modulus corrupted by additive noises are accessible for identification. This study was dedicated to the determination of the model, optimal in the sense of the integral square weighted model quality index, which does not depend on the particular sampling points applied in the stress relaxation experiment. It is proved that even when the real description of the material relaxation modulus is entirely unknown, the optimal fractional Maxwell model parameters can be recovered from the relaxation modulus measurements recorded for sampling time points selected randomly according to respective randomization. The identified model is a strongly consistent estimate of the desired optimal model. The exponential convergence rate is demonstrated both by the stochastic convergence analysis and by the numerical studies. A simple scheme for the optimal model identification is given. Numerical studies are presented for the materials described by the short relaxation times of the unimodal Gauss-like relaxation spectrum and the long relaxation times of the Baumgaertel, Schausberger and Winter spectrum. These studies have shown that the appropriate randomization introduced in the selection of sampling points guarantees that the sequence of the optimal fractional Maxwell model parameters asymptotically converge to parameters independent of these sampling points. The robustness of the identified model to the measurement disturbances was demonstrated by analytical analysis and numerical studies.

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“…In view of the convergence properties (30), (31) the computation of the parameter g * N approximation the parameter g * of the optimal FMM requires the next steps:…”

Section: Identification Algorithmmentioning

confidence: 99%