Abstract:To solve the problem that the traditional landslide displacement point prediction model cannot effectively describe the reliability of the prediction result,a landslide displacement interval prediction model based on different Bootstrap methods and KELM-BPNN model was proposed by introducing the method of interval prediction. In this model,firstly,the original dataset consisting of the monitoring information from various external trigger factors and landslide surface displacement was randomly sampled with an equal probability for B times and then,B dummy datasets were obtained based on different Bootstrap processes. B KELM models were trained to estimate the variance of the system error respectively and consequently,a BPNN model was trained to regress the variance of the random error. Finally,the variances of the system error and the random error,both obtained from the same Bootstrap process,were combined to construct the landslide displacement prediction intervals with different confidence levels. Through comparisons,an optimal displacement interval prediction model fitting in the deformation characteristics of actual landslides was proposed. Baishuihe Landslide,a typical colluvial landslide with step-like behaviour in the area of Three Gorges Reservoir,was taken as an example. The monitoring data of ZG93 and ZG118 from July 2004 to December 2013 were analysed. The results show that, compared with the traditional point prediction model,the developed model not only provides a relatively accurate point prediction result but also constructs a clear and reliable displacement prediction interval to cover the landslide displacement curve completely. In addition,the dynamic variation of the prediction interval width can be used to better quantify and explain the uncertain impact of the dynamic change of external triggering factors on the landslide evolution,which offers a new idea or option for the forecasting and the early warning of landslides.
[1] 黄润秋. 20世纪以来中国的大型滑坡及其发生机制[J]. 岩石力学与工程学报,2007,26(3):433–454.(HUANG Runqiu. Large-scale landslides and their sliding mechanisms in China since the 20th century[J]. Chinese Journal of Rock Mechanics and Engineering,2007,26(3):433–454.(in Chinese))
[2] 许 强,黄润秋,李秀珍. 滑坡时间预测预报研究进展[J]. 地球科学进展,2004,19(3):478–483.(XU Qiang,HUANG Runqiu,LI Xiuzhen. Research progress in time forecast and prediction of landslides[J]. Advance in Earth Sciences,2004,19(3):478–483.(in Chinese))
[3] 许 强,汤明高,徐开祥,等. 滑坡时空演化规律及预警预报研究[J]. 岩石力学与工程学报,2008,27(6):1 104–1 112.(XU Qiang,TANG Minggao,XU Kaixiang,et al. Research on space-time evolution laws and early warning-prediction of landslides[J]. Chinese Journal of Rock Mechanics and Engineering,2008,27(6):1 104–1 112.(in Chinese))
[4] MIAO F,WU Y,XIE Y,et al. Prediction of landslide displacement with step-like behavior based on multialgorithm optimization and a support vector regression model[J]. Landslides,2018,15(3):475–488.
[5] 林大超,安凤平,郭章林,等. 滑坡位移的多模态支持向量机模型预测[J]. 岩土力学,2011,32(增1):451–458.(LIN Dachao,AN Fengping,GUO Zhanglin,et al. Prediction of landslide displacements through multimode support vector machine model[J]. Rock and Soil Mechanics,2011,32(Supp.1):451–458.(in Chinese))
[6] LIAN C,ZENG Z,YAO W,et al. Displacement prediction model of landslide based on a modified ensemble empirical mode decomposition and extreme learning machine[J]. Natural Hazards,2013,66(2):759–771.
[7] HUANG F,YIN K,ZHANG G,et al. Landslide displacement prediction using discrete wavelet transform and extreme learning machine based on chaos theory[J]. Environmental Earth Sciences,2016,75(20):1 376.
[8] 李麟玮,吴益平,苗发盛,等. 基于变分模态分解与GWO- MIC-SVR模型的滑坡位移预测研究[J]. 岩石力学与工程学报,2018,37(6):1 395–1 406.(LI Linwei,WU Yiping,MIAO Fasheng,et al. Displacement prediction of landslides based on variational mode decomposition and GWO-MIC-SVR model[J]. Chinese Journal of Rock Mechanics and Engineering,2018,37(6):1 395–1 406.(in Chinese))
[9] 吴益平,滕伟福,李亚伟. 灰色–神经网络模型在滑坡变形预测中的应用[J]. 岩石力学与工程学报,2007,26(3):632–636.(WU Yiping,TENG Weifu,LI Yawei. Application of grey-neural network model to landslide deformation prediction[J]. Chinese Journal of Rock Mechanics and Engineering,2007,26(3):632–636.(in Chinese))
[10] 杜 娟,殷坤龙,柴 波. 基于诱发因素响应分析的滑坡位移预测模型研究[J]. 岩石力学与工程学报,2009,28(9):1 783–1 789.(DU Juan,YIN Kunlong,CHAI Bo. Study of displacement prediction model of landslide based on response analysis of inducing factors[J]. Chinese Journal of Rock Mechanics and Engineering,2009,28(9):1 783–1 789.(in Chinese))
[11] ZHOU C,YIN K,CAO Y,et al. Application of time series analysis and PSO-SVM model in predicting the Bazimen Landslide in the Three Gorges Reservoir,China[J]. Engineering Geology,2016,204:108–120.
[12] 杨背背,殷坤龙,杜 娟. 基于时间序列与长短时记忆网络的滑坡位移动态预测模型[J]. 岩石力学与工程学报,2018,37(10):2 334– 2 343.(YANG Beibei,YIN Kunlong,DU Juan. A model for predicting landslide displacement based on time series and long and short term memory neural network[J]. 2018,37(10):2 334–2 343.(in Chinese))
[13] 亓孝武,李可军,于小晏,等. 基于核极限学习机和Bootstrap方法的变压器顶层油温区间预测[J]. 中国电机工程学报,2017,37(19):5 821–5 828.(QI Xiaowu,LI Kejun,YU Xiaoyan,et al. Transformer top oil temperature interval prediction based on kernel extreme learning machine and bootstrap method[J]. Proceedings of the CSEE,2017,2017,37(19):5 821–5 828.(in Chinese))
[14] HUANG G. An insight into extreme learning machines:random neurons,random features and kernels[J]. Cognitive Computation,2014,6(3):376–390.
[15] KHOSRAVI A,NAHAVANDI S,CREIGHTON D,et al. Comprehen-sive review of neural network-based prediction intervals and new advances[J]. IEEE Transactions on Neural Networks,2011,22(9): 1 341–1 356.
[16] KHOSRAVI A,NAHAVANDI S,CREIGHTON D,et al. Lower upper bound estimation method for construction of neural network–based prediction intervals[J]. IEEE Transactions on Neural Networks,2011,22(3):337–346.
[17] WAN C,XU Z,WANG Y,et al. A hybrid approach for probabilistic forecasting of electricity price[J]. IEEE Transactions on Smart Grid,2014,5(1):463–470.
[18] WAN C,XU Z,PINSON P,et al. Probabilistic forecasting of wind power generation using extreme learning machine[J]. IEEE Transactions on Power Systems,2014,29(3):1 033–1 044.
[19] RODRIGUES A B,SILVA M D G D. Confidence intervals estimation for reliability data of power distribution equipments using bootstrap[J]. IEEE Transactions on Power Systems,2013,28(3):3 283–3 291.
[20] ZIO E. A study of the bootstrap method for estimating the accuracy of artificial neural networks in predicting nuclear transient processes[J]. IEEE Transactions on Nuclear Science,2006,53(3):1 460–1 478.
[21] MA J,TANG H,LIU X,et al. Probabilistic forecasting of landslide displacement accounting for epistemic uncertainty:a case study in the Three Gorges Reservoir area,China[J]. Landslides,2018,15(6):1 145–1 153.
[22] 晏鄂川,刘广润. 试论滑坡基本地质模型[J]. 工程地质学报,2004,12(1):21–24.(YAN Echuan,LIU Guangrun. Discussion on the essential geological model for landslide[J]. Journal of Engineering Geology,2004,12(1):21–24.(in Chinese))
[23] 姚 为,廉 城,程 立. 滑坡位移的动态概率预测模型[J]. 水文地质工程地质,2015,42(5):134–139.(YAO Wei,LIAN Cheng,CHENG Li. A dynamic probabilistic model for landslide displacement prediction[J]. Hydrogeology and Engineering Geology,2015,42(5):134–139.(in Chinese))
[24] ZHOU C,YIN K,CAO Y,et al. Displacement prediction of step-like landslide by applying a novel kernel extreme learning machine method[J]. Landslides,2018,15(11):2 211–2 225.
[25] LIAN C,ZENG Z,YAO W,et al. Landslide displacement prediction with uncertainty based on neural networks with random hidden weights[J]. IEEE Transactions on Neural Networks and Learning Systems,2016,27(12):2 683–2 695.
[26] EFRON B. Bootstrap methods:another look at the jackknife[J]. Annals of Statistics,1979,7(1):1–26.
[27] LI D,TANG X,PHOON K. Bootstrap method for characterizing the effect of uncertainty in shear strength parameters on slope reliability[J]. Reliability Engineering and System Safety,2015,140:99–106.
[28] 龙志和,欧变玲. Bootstrap方法在经济计量领域的应用[J]. 工业技术经济,2008,27(7):132–135.(LONG Zhihe,OU Bianling. Bootstrap method in econometric applications[J]. Industrial Technology and Economy,2008,27(7):132–135.(in Chinese))
[29] 李麟玮,吴益平,苗发盛. 基于灰狼支持向量机的非等时距滑坡位移预测[J]. 浙江大学学报:工学版,2018,52(10):1 998–2 006. (LI Linwei,WU Yiping,MIAO Fasheng. Prediction of non-equidistant landslide displacement time series based on grey wolf support vector machine[J]. Journal of Zhejiang University:Engineering Science,2018,52(10):1 998–2 006.(in Chinese))
[30] HECHT-NIELSEN R. Theory of the back propagation neural network[C]// Proceeding of the International Joint Conference on Neural Networks. New York:[s. n.],1989:593–605.
[31] 易庆林,曾怀恩,黄海峰. 利用BP神经网络进行水库滑坡变形预测[J]. 水文地质工程地质,2013,40(1):124–128.(YI Qinglin,ZENG Huaien,HUANG Haifeng. Reservoir landslide deformation forecast using BP neural network[J]. Hydrogeology and Engineering Geology,2013,40(1):124–128.(in Chinese))
[32] 卢书强,易庆林,易 武,等. 库水下降作用下滑坡动态变形机制分析——以三峡库区白水河滑坡为例[J]. 工程地质学报,2014,22(5):869–875.(LU Shuqiang,YI Qinglin,YI Wu,et al. Study on dynamic deformation mechanism of landslide in drawdown of reservoir water level—take Baishuihe Landslide in Three Gorges Reservoir area for example[J]. Journal of Engineering Geology,2014,22(5):869–875.(in Chinese))
[33] 许 强,汤明高,黄润秋. 大型滑坡监测预警与应急处置[M]. 北京:科学出版社,2015:46–48.(XU Qiang,TANG Minggao,HUANG Runqiu. Monitoring,early warning and emergency disposal of large- scale landslides[M]. Beijing:Science Press,2015:46–48.(in Chinese))
[34] 张 俊,殷坤龙,王佳佳,等. 基于时间序列与PSO-SVR耦合模型的白水河滑坡位移预测研究[J]. 岩石力学与工程学报,2015,34(2):382–391.(ZHANG Jun,YIN Kunlong,WANG Jiajia,et al. Displacement prediction of Baishuihe Landslide based on time series and PSO-SVR model[J]. Chinese Journal of Rock Mechanics and Engineering,2015,34(2):382–391.(in Chinese))
[35] DAVIDSON R,FLACHAIRE E. The wild bootstrap,tamed at last[J]. Journal of Econometrics,2008,146(1):162–169