Fractional-order Quadratic Time-varying Parameters Discrete Grey Model FQDGM (1, 1) and Its Application
Several objects in scientific research and engineering applications present fractional-order time-varying characteristics. When developing mathematical models of considering fractional-order time-varying, the dynamic analysis results are often inconsistent with the actual statistical data due to ina...
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| Veröffentlicht in: | IAENG international journal of applied mathematics 2021-12, Vol.51 (4), p.1-6 |
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| creator | Yang, Xiaogao Ding, Deqiong Luo, Youxin |
| description | Several objects in scientific research and engineering applications present fractional-order time-varying characteristics. When developing mathematical models of considering fractional-order time-varying, the dynamic analysis results are often inconsistent with the actual statistical data due to inaccurate description of the analysis model. To solve this problem, the present paper proposes a discrete grey model of fractional-order quadratic time-varying parameters based on grey fractional-order characteristics and integral theory. By taking the minimum mean relative error and the minimum mean square error as the objective function, two optimization models, namely FQDGM-I and FQDGM-II, are constructed to perform parameter estimation. A comparative analysis based on examples shows that the background value reconstructed using the proposed model is more accurate. The fitting accuracy is greatly improved compared to those obtained using previous models. These results verify the effectiveness and practicability of the proposed fractional-order quadratic time-varying parameter discrete grey model. |
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When developing mathematical models of considering fractional-order time-varying, the dynamic analysis results are often inconsistent with the actual statistical data due to inaccurate description of the analysis model. To solve this problem, the present paper proposes a discrete grey model of fractional-order quadratic time-varying parameters based on grey fractional-order characteristics and integral theory. By taking the minimum mean relative error and the minimum mean square error as the objective function, two optimization models, namely FQDGM-I and FQDGM-II, are constructed to perform parameter estimation. A comparative analysis based on examples shows that the background value reconstructed using the proposed model is more accurate. The fitting accuracy is greatly improved compared to those obtained using previous models. These results verify the effectiveness and practicability of the proposed fractional-order quadratic time-varying parameter discrete grey model.</description><identifier>ISSN: 1992-9978</identifier><identifier>EISSN: 1992-9986</identifier><language>eng</language><publisher>Hong Kong: International Association of Engineers</publisher><subject>Accuracy ; Mathematical models ; Mean square errors ; Optimization ; Parameter estimation</subject><ispartof>IAENG international journal of applied mathematics, 2021-12, Vol.51 (4), p.1-6</ispartof><rights>2021. This work is published under https://creativecommons.org/licenses/by-nc-nd/4.0/ (the“License”). 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| ispartof | IAENG international journal of applied mathematics, 2021-12, Vol.51 (4), p.1-6 |
| issn | 1992-9978 1992-9986 |
| language | eng |
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| source | EZB-FREE-00999 freely available EZB journals |
| subjects | Accuracy Mathematical models Mean square errors Optimization Parameter estimation |
| title | Fractional-order Quadratic Time-varying Parameters Discrete Grey Model FQDGM (1, 1) and Its Application |
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