关键词: 桥梁, 灰色GM(1, 1)模型, 马尔科夫链模型, 预测, 转移概率矩阵

Abstract: In order to obtain a high-precision and high-efficiency method to predict the bridge operating conditions, this paper presents a Gray-Markov GM(1,1)prediction model based on gray theoretical model and modified with Markov chain. This method was applied to test the data of a total of 159 bridges in a certain area of Hebei Province. The results show that based on the bridge data from 2007 to 2016, the average relative error of the Gray-Markov model is -0.11%, and the average relative error of the gray theoretical model is -0.34%, which is obviously improved, and the Gray-Markov model offers more stable data. Using the gray theory model optimized by Markov chain to predict the number of first-class bridges from 2017 to 2019,we can see that the number of the first-class bridges is 49, 39 and 34 respectively. Thus we can see that the Gray-Markov model can provide a more accurate prediction on the basis of known periodic- DOI:10.3969/j.issn.1000-1565.2019.01.003灰色-马尔科夫模型在桥梁运营状况预测中的应用刘历波¹,裴彧²,裴同松³(1.河北工程大学 土木工程学院,河北 邯郸 056038;2.河北交通职业技术学院 土木工程系,河北 石家庄 050035;3.河北交通职业技术学院 电气与信息工程系,河北 石家庄 050035)摘 要:为了找到一种能够精确有效地预测桥梁运营状况的方法,提出一种基于灰色GM(1,1)理论模型并用马尔科夫链修正的灰色-马尔科夫预测模型.结合河北省某地区的159座桥梁数据对该方法进行应用检验,结果表明:灰色-马尔科夫模型预测数据的平均相对误差为-0.11%,相比灰色GM(1,1)理论模型预测数据的平均相对误差-0.34%,在精度上有了明显的提高,而且灰色-马尔科夫模型预测出的数据更加稳定.利用马尔科夫链优化过的灰色GM(1,1)理论模型预测出2017年至2019年该地区一类桥的数量分别为49座、39座以及34座.由此可知灰色-马尔科夫模型在已知的桥梁定期检查数据基础上可以提供较为精确的预测,相较于灰色GM(1,1)预测模型,该方法具有更高的精度和稳定性.关键词:桥梁;灰色GM(1,1)模型;马尔科夫链模型;预测;转移概率矩阵中图分类号:U446 文献标志码:A 文章编号:1000-1565(2019)01-0011-07Application of Gray-Markov model in prediction of bridge operation conditionLIU Libo¹,PEI Yu²,PEI Tongsong³(1.College of Civil Engineering,Hebei University of Engineering,Handan 056038,China; 2.Department of Civil Engineering,Hebei Jiaotong Vocational and Technical College,Shijiazhuang 050035,China;3.Department of Electrical and Information Engineering,Hebei Jiaotong Vocational and Technical College,Shijiazhuang 050035,China)Abstract:In order to obtain a high-precision and high-efficiency method to predict the bridge operating conditions, this paper presents a Gray-Markov GM(1,1)prediction model based on gray theoretical model and modified with Markov chain. This method was applied to test the data of a total of 159 bridges in a certain area of Hebei Province. The results show that based on the bridge data from 2007 to 2016, the average relative error of the Gray-Markov model is -0.11%, and the average relative error of the gray theoretical model is -0.34%, which is obviously improved, and the Gray-Markov model offers more stable data. Using the gray theory model optimized by Markov chain to predict the number of first-class bridges from 2017 to 2019,we can see that the number of the first-class bridges is 49, 39 and 34 respectively. Thus we can see that the Gray-Markov model can provide a more accurate prediction on the basis of known periodic- 收稿日期:2018-01-29 基金项目:河北省高校百名优秀人才计划项目(BR206) 第一作者:刘历波(1979—),男,河北唐山人,河北工程大学副教授,主要从事道路桥梁与集成管理研究.E-mail:liulibo@hebeu.edu.cn 通信作者:裴彧(1993—),男,河北石家庄人,河北交通职业技术学院助教,主要从事道路桥梁研究.E-mail:421380827@qq.com第1期刘历波等:灰色-马尔科夫模型在桥梁运营状况预测中的应用inspection data. Compared with the single gray prediction model, the Gray-Markov model shaws higher accuracy and stability.

Key words: bridge, gray model GM(1,1), Markov chain model, prediction, transfer probability matrix