马尔科夫链优化Richards曲线的沉降预测模型
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摘要
针对建筑物沉降具有非线性及随机性的特点,建立了基于马尔科夫链修正的Richards曲线预测模型,以提高模型的预测精度。首先利用Matlab平台的fminsearch函数,以拟合值与实测值误差平方和最小为原则,然后求得Richards模型的最优参数解,最后利用马尔科夫思想修正拟合残差,进行沉降预测。以安阳市某高层建筑实际数据为研究对象,通过实例比较分析模型的预测精度。结果表明利用fminsearch进行Richards参数估计是有效的,经马尔科夫链优化后的Richards模型预测值平均绝对百分误差及均方根误差都比单模型预测小,预测精度有了一定的提高,能更好地反映数据序列随时间发展变化的总体趋势,适合于建筑物沉降预测。
Aiming at the nonlinear and random characteristics of building settlement,a Richards curve prediction model based on Markov chain correction was established to improve the prediction accuracy of the model. First,the fminsearch function of Matlab platform was used to obtain the optimal parameter solution of Richards model,based on the principle of minimizing the sum of squared error between the fitted value and the measured value.Then,the residual error was corrected by Markov's method,finally the combination model was used to predict the settlement. The prediction accuracy of the model was compared and analyzed by examples. The results show that it was effective to estimate the Richards parameters by using fminsearch. The average absolute percentage error and the root mean square error of the Richards model optimized by Markov chain were smaller than the single model prediction,and the prediction accuracy was improved.The combined model prediction results can be better reflect the overall trends of data series development and changes over time as well as the inherent laws between the various states of the system,and it is suitable for building settlement prediction.
Aiming at the nonlinear and random characteristics of building settlement,a Richards curve prediction model based on Markov chain correction was established to improve the prediction accuracy of the model. First,the fminsearch function of Matlab platform was used to obtain the optimal parameter solution of Richards model,based on the principle of minimizing the sum of squared error between the fitted value and the measured value.Then,the residual error was corrected by Markov's method,finally the combination model was used to predict the settlement. The prediction accuracy of the model was compared and analyzed by examples. The results show that it was effective to estimate the Richards parameters by using fminsearch. The average absolute percentage error and the root mean square error of the Richards model optimized by Markov chain were smaller than the single model prediction,and the prediction accuracy was improved.The combined model prediction results can be better reflect the overall trends of data series development and changes over time as well as the inherent laws between the various states of the system,and it is suitable for building settlement prediction.
引文
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[2]KOYA P R,GOSHU A T.Generalized Mathematical Model for Biological Growths[J].Open Journal of Modelling and Simulation,2013,1(4):42-53.
[3]龙四春,彭强,黄两宜,等.一种加权Logistic-Richards组合模型的地表沉降预测方法[J].大地测量与地球动力学,2015,35(5):821-824.
[4]任云志,周飞,陆鹏宇.基于Richards-BP模型的地表沉降特征预测模型研究[J].交通科技,2015(1):89-92.
[5]胡晓阳,王连俊,张光宗.Logistic及Verhulst预测模型在路基沉降预测中的拟合研究[J].铁道标准设计,2013(9):1-4.
[6]刘光秀,曹海莹,李玉根.灰色-Gompertz组合模型在软土路基沉降预测中的应用[J].中国科技论文,2016,11(13):1488-1491.
[7]刘淑官,黄声享,徐北海,等.基于无偏灰色马尔科夫链的基坑沉降预测研究[J].测绘地理信息,2015,40(4):10-13.
[8]邹进贵,肖扬宣,张士勇.马尔科夫链改进的ARIMABP神经网络模型研究[J].测绘地理信息,2016,41(4):32-36.
[9]杨世安.优化的灰色马尔科夫模型在建筑物沉降预测中的应用[D].南昌:东华理工大学,2014:21-35.
[10]王军龙.围岩变形预测的Richards模型及变形发展趋势分析[J].公路工程,2014,39(3):145-148.
[11]程毛林.Richards模型参数估计及其模型应用[J].数学的实践与认识,2010,40(12):139-143.
[12]乔钰,徐文科.Richards增长曲线的参数估计[J].哈尔滨师范大学自然科学学报,2015,31(5):23-26.
[13]燕振刚,胡贺年,李广.基于粒子群优化算法的Richards模型参数估计和算法有效性[J].计算机应用,2014,34(10):2827-2830.
[14]王江荣.Richards生长曲线模型在大坝变形监测数据处理中的应用[J].矿山测量,2015(5):59-61,64.
[15]王钧.基于变步长果蝇优化算法的Richards模型参数估计[J].计算机工程与设计,2017,38(9):2402-2406.
[16]张庆伟,肖建清.GM(1,1)与Verhulst模型在地基沉降预测中的适用性比较[J].沈阳工业大学学报,2014,36(6):716-720.