| 灰色GM(1,1,k,k2)模型背景值及时间响应函数优化 |
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| 引用本文： | 孔新海,陈佳佳,赵勇.灰色GM(1,1,k,k2)模型背景值及时间响应函数优化[J].运筹与管理,2022,31(7):109-113. |
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| 作者姓名： | 孔新海 陈佳佳 赵勇 |
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| 作者单位： | 广安职业技术学院,四川 广安 638000 |
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| 基金项目： | 四川石油天然气发展研究中心项目(川油气科SKB20-09);四川省教育厅项目(18ZB0259) |
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| 摘 要： | 本文提出了一种新的带有时间幂次项的灰色GM(1,1,k,k2)模型,给出了其灰微分方程和白化微分方程基本形式。基于最小二乘法获得了该模型参数估计值,并推导了该模型时间响应函数。鉴于GM(1,1,k,k2)模型灰微分方程与白化微分方程之间存在跳跃关系,首先对灰微分方程的背景值进行了优化,并推导了优化后的背景值计算公式。为了克服初始值的影响,根据误差平方和最小,进一步优化了GM(1,1,k,k2)模型时间响应函数。最后,该优化后的GM(1,1,k,k2)模型被应用于软土地基沉降预测,获得了较好的模拟预测效果,说明模型是可行的。
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| 关 键 词： | 灰色GM(1 1 k k2)模型 背景值 时间响应函数 预测 |
| 收稿时间： | 2019-06-16 |
Optimization of Background Value and Time Response Function of Grey GM(1,1,k,k2) Model |
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| KONG Xin-hai,CHEN Jia-jia,ZHAO Yong.Optimization of Background Value and Time Response Function of Grey GM(1,1,k,k2) Model[J].Operations Research and Management Science,2022,31(7):109-113. |
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| Authors: | KONG Xin-hai CHEN Jia-jia ZHAO Yong |
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| Affiliation: | Guang’an Vocational and Technical College, Guang’an 638000, China |
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| Abstract: | A new grey GM(1,1,k,k2) model with time power term is proposed in this paper. The basic form of grey differential equation and its corresponding whitening differential equation are given. Based on the least square method, the parameters of the model are estimated and the time response function of the model is deduced. In order to solve the jump relation between the grey differential equation and the whitening differential equation, the background value of the grey differential equation is optimized, and the calculation method of the optimized background value is deduced. In order to overcome the influence of initial value, the time response function is further optimized according to the minimum sum of squares of errors. Finally, the optimized GM(1,1,k,k2) model is applied to predict the settlement of soft soil foundation, and good simulation results are obtained, which shows that the model is feasible. |
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| Keywords: | grey GM(1 1 k k2) model background value time response function prediction |
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