Curve fitting problem: torque–velocity relationship with polynomials and Boltzmann sigmoid functions

• Autorzy: Milanov P. , Koroleova G. , Mavrevski R. , Pencheva N.

Identyfikatory

DOI

10.5277/ABB-01048-2017-03

• Języki publikacji: EN

Abstrakty

EN

The aim of this study was to investigate the curve fitting and model selection problem of the torque–velocity relationship of elbow flexors and extensors in untrained females. The second goal was to determine the optimal models in different function classes and the best, among the optimal ones. Lastly, test the best models to predict the torque were tested. Methods: Using the polynomials (second – fourth degree) and Boltzmann sigmoid functions, and a different presentation of data points (averages, a point cloud, etc.), we determined the optimal models by both error criteria: minimum residual sum of squares and minimum of the maximal absolute residue. To assess the best models, we applied Akaike and Bayesian information criteria, Hausdorff distance and the minimum of the smallest maximal absolute residue and the predictive torque–velocity relationships of the best models with torque values, calculated beyond the experimental velocity interval. Results: The application of different error and model selection criteria showed that the best models in the majority of cases were polynomials of fourth degree, with some exceptions from second and third degree. The criteria values for the optimal Boltzmann sigmoids were very close to those of the best polynomial models. However, the predicted torque–velocity relationships had physiological behavior only in Boltzmann’s sigmoid functions, and their parameters had a clear interpretation. Conclusion: The results obtained suggest that the Boltzmann sigmoid functions are suitable for modeling and predicting of the torque–velocity relationship of elbow flexors and extensors in untrained females, as compared to polynomials, and their curves are physiologically relevant.

Słowa kluczowe

EN

torque–velocity relationship; elbow flexors; extensors; Boltzmann sigmoid; polynomials; fitting function; model selection criteria

PL

prędkość; staw łokciowy; wielomiany; funkcja Boltzmanna

• Wydawca: Oficyna Wydawnicza Politechniki Wrocławskiej
• Czasopismo: Acta of Bioengineering and Biomechanics
• Rocznik: 2018
• Tom: Vol. 20, no. 1
• Strony: 169--184
• Opis fizyczny: Bibliogr. 27 poz., tab., wykr.

Twórcy

autor

Milanov P.

• South-West University “Neofit Rilski”, Department of Informatics, Faculty of Mathematics and Natural Sciences, University Center for Advanced Bioinformatics Research, Blagoevgrad, Bulgaria
• Bulgarian Academy of Sciences, Institute of Mathematics and Informatics, Sofia, Bulgaria

autor

Koroleova G.

• South-West University “Neofit Rilski”, Department of Informatics, Faculty of Mathematics and Natural Sciences, University Center for Advanced Bioinformatics Research, Blagoevgrad, Bulgaria.

autor

Mavrevski R.

• South-West University “Neofit Rilski”, Department of Electrical Engineering, Electronics and Automatics

autor

Pencheva N.

• South-West University “Neofit Rilski”, Department of Anatomy and Physiology, Faculty of Public Health, Health Care and Sport, University Center for Functional Research in Sports and Kinesitherapy, Blagoevgrad, Bulgaria

Bibliografia

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Uwagi

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

This work is partially supported by the project of the Bulgarian National Science Fund, entitled: “Bioinformatics research: protein folding, docking and prediction of biological activity”, code NSF I02/16, 12.12.14.