[1]赖文杰,齐昌广,郑金辉,等.含分数阶的灰色模型及其在地基沉降预测中的应用[J].水文地质工程地质,2019,46(3):124.[doi:10.16030/j.cnki.issn.1000-3665.2019.03.17]
 LAI Wenjie,QI Changguang,ZHENG Jinhui,et al.Gray model with fractional order and its application to settlement prediction[J].Hydrogeology & Engineering Geology,2019,46(3):124.[doi:10.16030/j.cnki.issn.1000-3665.2019.03.17]
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含分数阶的灰色模型及其在地基沉降预测中的应用()
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《水文地质工程地质》[ISSN:1000-3665/CN:11-2202/P]

卷:
46卷
期数:
2019年3期
页码:
124
栏目:
工程地质
出版日期:
2019-05-15

文章信息/Info

Title:
Gray model with fractional order and its application to settlement prediction
文章编号:
1000-3665(2019)03-0124-05
作者:
赖文杰1齐昌广1郑金辉1王新泉2左殿军3 4
1.宁波大学建筑工程与环境学院,浙江 宁波315211;2. 浙江大学城市学院土木工程系,浙江 杭州310015;3. 交通运输部天津水运工程科学研究院岩土工程研究中心,天津300456; 4. 河海大学土木与交通学院,江苏 南京210098
Author(s):
LAI Wenjie1QI Changguang1ZHENG Jinhui1WANG Xinquan2ZUO Dianjun34
1.Faculty of Architectural, Civil Engineering and Environment, Ningbo University, Ningbo, Zhejiang315211, China; 2.Department of Civil Engineering, Zhejiang University City College, Hangzhou, Zhejiang310015, China; 3.Geotechnical Research Center, Tianjin Research Institute for Water Transport Engineering, Ministry of transport, Tianjin300456, China; 4.College of Civil and Transportation Engineering, Hohai University, Nanjing, Jiangsu210098, China
关键词:
高速公路灰色模型沉降预测分数阶
Keywords:
expressway gray model settlement prediction fractional order
分类号:
TU433
DOI:
文献标志码:
A
摘要:
基于灰色理论建立的传统沉降预测模型均为整数阶,存在不连续、与实测数据差异较大的缺陷。鉴于此,本文以灰色模型为研究对象,通过改变模型中的整数阶微分为分数阶微分来改进灰色模型的预测效果。本模型与传统模型的最大区别在于增加了分数阶阶次的识别,首先结合灰色理论得到无输入的常微分方程;接着对其引入输入项,并将常微分方程做变换得到含分数阶的微分方程;最后将该模型与实测数据进行对比,且与传统灰色理论沉降预测模型进行误差计算,发现本文建立的沉降预测模型可以较好地预测地基沉降。
Abstract:
The traditional settlement prediction models based on the gray theory are all of integer orders, and there are defects that are discontinuous and have large differences from the measured data. In this paper, an improved gray model, which uses fractional derivatives to replace the integer ones, is suggested. The biggest difference between this model and the traditional model is the increased recognition of fractional orders. First, combined with the gray theory, the ordinary differential equation with no input is obtained. Then, an input term is introduced to the equation, and the ordinary differential equation is transformed to obtain a differential equation with a fractional order. Finally, the model is compared with the measured data, and the error is calculated with the traditional gray theory settlement prediction model. The results show that the settlement prediction model established in this paper can provide better prediction for the foundation settlement.

参考文献/References:

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备注/Memo

备注/Memo:
收稿日期: :2018-09-14;修订日期: 2019-01-10
基金项目: 浙江省自然科学基金项目资助(LY18E080010);国家自然科学基金项目资助(51508282);宁波市自然科学基金项目资助(2017A610317)
第一作者: 赖文杰(1994-),男,硕士研究生,主要从事地基处理和透明土模型试验研究。E-mail:1404037602@qq.com
通讯作者: 齐昌广(1986-),男,博士,副教授,主要从事基础工程、地基处理、透明土和岩土物理模拟试验等教学与研究工作。E-mail:qichangguang@163.com
更新日期/Last Update: 2019-05-15