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.
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The data that support the findings of this study are openly available in Soft Computing.
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Funding
This work was funded by the National Natural Science Foundation of China (Grant Nos. 12061072 and 62162059) and the Xinjiang Key Laboratory of Applied Mathematics (Grant No. XJDX1401).
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All authors contributed to the research concept and paper design. The topic selection of the thesis, the analysis of the research results, the selection of references and the revision of the article were completed by LY and YS. The first draft of the thesis was completed by LY. Final manuscript read and approved by all authors.
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Yao, L., Sheng, Y. Moments estimation for multi-factor uncertain differential equations based on residuals. Soft Comput 27, 11193–11203 (2023). https://doi.org/10.1007/s00500-023-08317-3
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DOI: https://doi.org/10.1007/s00500-023-08317-3