|
Article information
2020 , Volume 25, ¹ 3, p.18-28
Timofeeva A.Y.
Estimation of copolymerization reactivity ratios in the Berkson error regression model
Purpose. The purpose of this paper is to study methods for estimating copolymerization reactivity ratios based on the differential composition equation. Methodology. Most estimation methods reduce the differential composition equation to a linear form. They are based on the least squares method and do not take into account the measurement error in the input variable. Therefore they lead to statistically incorrect results. When analyzing the problem on the basis of the error-in-variables model in the classical case, additional information is required to determine the magnitude of the errors in measuring the concentration of monomers in the mixture and in the copolymer. Inclusion of the measurement error in the input variable into the model as the Berkson error is more consistent with the actual conditions of the experiments. It allows simultaneous estimating both the reactivity ratios and the variances of measurement errors using the maximum likelihood method. Results. The algorithm have been developed for estimating reactivity ratios with no additional information. The empirical study of estimation methods has been carried out using the example of copolymerization of vinyl esters. Findings. It is shown that the method based on symmetric equations gives incorrect results. Estimation results using the proposed algorithm are closest to the estimates obtained by the nonlinear least squares method
[full text] [link to elibrary.ru]
Keywords: copolymerization, monomer reactivity ratio, regression, Berkson error, maximum likelihood method
doi: 10.25743/ICT.2020.25.3.003
Author(s):
Timofeeva Anastasiia Yurievna
PhD.
Position: Associate Professor
Office: Novosibirsk State Technical University
Address: 630073, Russia, Novosibirsk, 20 Prospekt K. Marksa
E-mail: a.timofeeva@corp.nstu.ru
SPIN-code: 8980-1611 References:
1. Deryabina G.I. Sopolimerizatsiya [Copolymerization]. Samara: Samarskiy Univ.; 2013: 48. (In Russ.)
2. Polic L., Duever T.A., Penlidis A. Case studies and literature review on the estimation of copolymerization reactivity ratios. Journal of Polymer Science. Part A: Polymer Chemistry. 1998; 36(7):813–822.
3. Kazemi N., Duever T. A., Penlidis A. A powerful estimation scheme with the error-in-variables-modelfor nonlinear cases: Reactivity ratio estimation examples. Computers & Chemical Engineering. 2013; 48(7):200–208.
4. On the criteria for experimental design in nonlinear error-in-variables models. Advances in StochasticSimulation Methods. Statistics for Industry and Technology. N. Balakrishnan, V.B. Melas, S. Ermakov. (Eds). Boston: Springer; 2000:153–163.
5. Davankov A.B., Zubakova L.B., Gurov A.A. Determination of the monomer reactivity ratios forcopolymerization of 2-methyl-5-vinylpyridine and triethyleneglycoldimethyl acrylate. Polymer Science. 1964; 6(2):237–240. (In Russ.)
6. Yulusov V.V. Zakonomernosti obrazovaniya sopolimerov iz monomerov raznoy aktivnosti v usloviyakhpolimerizatsii s obratimoy peredachey tsepi [Patterns of the formation of copolymers from monomers of various activity under polymerization conditions with reversible chain transfer]. Dis. ... kand. khim. nauk. Moskva: MGU im. M.V. Lomonosova; 2014: 147. (In Russ.)
7. Pozdnyakov A.S. Polifunktsional’nye (so)polimery 1-vinil-1,2,4-triazola i nanokompozity na ikh osnove[Multifunctional (co)polymers of 1-vinyl-1,2,4-triazole and nanocomposites based on them]. Dis. ... kand. khim. nauk. Irkutsk: IrIKh SO RAN; 2011: 175. (In Russ.)
8. Van der Meer R., Linssen H.N., German A.L. Improved methods of estimating monomer reactivityratios in copolymerization by considering experimental errors in both variables. Journal of Polymer Science. Part A: Polymer Chemistry. 1978; 16(11):2915–2930.
9. Kalitkin N.N. Chislennye metody [Numerical methods]. SPb.: BKhV-Peterburg; 2011: 592. (In Russ.)
10. Denisov V.I., Timofeeva A.Y., Khailenko E.A. Estimating parameters of polynomial models witherrors in variables and no additional information. Journal of Applied and Industrial Mathematics. 2016; 10(3):322–332.
11. Ezrielev A.I., Brokhina E.L., Roskin E.S. Analytical method for determination of copolymerizationratios. Polymer Science. Series A. 1969; 11(8):1670–1680. (In Russ.)
12. Timofeev V.S., Faddeenkov A.V., Shchekoldin V.Yu. Ekonometrika [Econometrics]. Moscow: YuRAYT;2016: 328. (In Russ.)
13. Hautus F.L.M., Linssen H.N., German A.L. Dependence of computed copolymer reactivity ratios onthe calculation method. II. Effects of experimental design and error structure. Journal of Polymer Science. Part A: Polymer Chemistry. 1984; 22(12):3661–3671.
14. Kazemi N., Lessard B.H., Mari´c M., Duever T.A., Penlidis A. Reactivity ratio estimation in radical copolymerization: from preliminary estimates to optimal design of experiments. Industrial & Engineering Chemistry Research. 2014; 53(18):7305–7312.
15. Deryabina G.I., Frolov Yu.L., Kalabina A.V. The reaction capacity of vinylidene ethers during copolymerization with vinyl chloride and vinylidene chloride. Polymer Science. Series A. 1971; 13(5): 1162–1169. (In Russ.)
16. Deryabina G.I., Gershengorn G.I. Calculation of copolymerization constants in systems vinyl(vinylidene) chloride-vinylphenyl ether. Polymer Science. Series A. 1969; 11(5):941–945. (In Russ.)
17. Smirnov A.I., Deryabina G.I., Kalabina A.V., Vladimirova T.L. Characteristics of copolymerizationof vinyl ethers with electron-withdrawing monomers. Polymer Science. Series B. 1980; 22(3):173–177. (In Russ.)
Bibliography link:
Timofeeva A.Y. Estimation of copolymerization reactivity ratios in the Berkson error regression model // Computational technologies. 2020. V. 25. ¹ 3. P. 18-28
|
