Moments estimation for multi-factor uncertain differential equations based on residuals

Abstract

Parameter estimation is always the focus of constructing differential equations to simulate dynamic systems. In order to estimate unknown parameters in multi-factor uncertain differential equations, the definition of residuals is presented and important properties of residuals are demonstrated. Based on the property that the residuals obey the linear uncertainty distribution, moment estimation of the unknown parameters in the multi-factor uncertain differential equation is performed and the reasonableness of the parameter estimation results is verified. Some examples with real data are given to demonstrate the feasibility of the method.