Estimating time-varying parameters in uncertain differential equations

• Published in: Applied mathematics and computation Vol. 425; p. 127084
• Main Authors: Zhang, Guidong, Sheng, Yuhong
• Format: Journal Article
• Language: English
• Published: Elsevier Inc 15.07.2022
• Subjects: Least squares estimation; Regression analysis; Time-varying parameters; Uncertainty theory; Regression analysis; Time-varying parameters; Least squares estimation; Uncertainty theory
• ISSN: 0096-3003
• DOI: 10.1016/j.amc.2022.127084

•A set of estimates of the time-varying parameters was obtained based on rewritten least squares estimates.•The idea of regression fitting was proposed to obtain time-varying parameter functions by fitting estimates of the time-varying parameters.•An uncertain differential equation model for human blood alcohol metabolism was derived, as well as an uncertain differential equation model for the spread of COVID-19. Research on the estimation of unknown parameters in uncertain differential equations has been a concerned subject for scholars in recent years. For this reason, some scholars have proposed many methods to estimate the unknown parameters. However, these unknown parameters are constants. This paper considers estimation methods for time-varying parameters, the least squares estimation method is rewritten. Firstly, estimates of a set of time-varying parameters are obtained. Secondly, the fit function for this set of estimates, which is obtained by means of a regression fit is considered to be a time-varying parameter. Meanwhile, the criteria is given to determine whether the fit function is reasonable. Finally, two numerical examples of uncertain differential equations are presented to verify the feasibility of the above method.