Using an extreme learning machine to predict the displacement of step-like landslides in relation to controlling factors

In the evolution of landslides, besides the geological conditions, displacement depends on the variation of the controlling factors. Due to the periodic fluctuation of the reservoir water level and the precipitation, the shape of cumulative displacement-time curves of the colluvial landslides in the Three Gorges Reservoir follows a step function. The Baijiabao landslide in the Three Gorges region was selected as a case study. By analysing the response relationship between the landslide deformation, the rainfall, the reservoir water level and the groundwater level, an extreme learning machine was proposed in order to establish the landslide displacement prediction model in relation to controlling factors. The result demonstrated that the curves of the predicted and measured values were very similar, with a correlation coefficient of 0.984. They showed a distinctive step-like deformation characteristic, which underlined the role of the influencing factors in the displacement of the landslide. In relation to controlling factors, the proposed extreme learning machine (ELM) model showed a great ability to predict the Baijiabao landslide and is thus an effective displacement prediction method for colluvial landslides with step-like deformation in the Three Gorges Reservoir region.     

基于H-P滤波法、ARIMA和VAR模型的库区滑坡位移综合预测

受库水位涨落及降雨等影响,库区滑坡位移表现出明显的周期性。基于位移时间序列分析,将滑坡监测位移分解为趋势项与周期项之和。趋势项反映滑坡变形的长期趋势,其主要受滑坡本身地质结构等因素影响。周期项反映滑坡变形的波动性,其主要受外部因素影响。以三峡库区巫山塔坪滑坡为例,考虑长江水位与降雨量影响,采用H-P滤波法从滑坡位移中分解出趋势项及周期项,利用差分自回归滑动平均模型（ARIMA）对趋势项进行平稳处理并计算趋势项预测值,利用向量自回归模型（VAR）计算周期项预测值。趋势项预测值与周期项预测值之和为滑坡位移预测值。与实际监测值及多种方法分析比较,表明综合预测所得结果能较好反映滑坡变形的趋势性和波动性,位移预测效果较好。     

Displacement prediction of step-like landslide by applying a novel kernel extreme learning machine method

Landslide displacement prediction is an essential component for developing landslide early warning systems. In the Three Gorges Reservoir area (TGRA), landslides experience step-like deformations (i.e., periods of stability interrupted by abrupt accelerations) generally from April to September due to the influence of precipitation and reservoir scheduled level variations. With respect to many traditional machine learning techniques, two issues exist relative to displacement prediction, namely the random fluctuation of prediction results and inaccurate prediction when step-like deformations take place. In this study, a novel and original prediction method was proposed by combining the wavelet transform (WT) and particle swarm optimization-kernel extreme learning machine (PSO-KELM) methods, and by considering the landslide causal factors. A typical landslide with a step-like behavior, the Baishuihe landslide in TGRA, was taken as a case study. The cumulated total displacement was decomposed into trend displacement, periodic displacement (controlled by internal geological conditions and external triggering factors respectively), and noise. The displacement items were predicted separately by multi-factor PSO-KELM considering various causal factors, and the total displacement was obtained by summing them up. An accurate prediction was achieved by the proposed method, including the step-like deformation period. The performance of the proposed method was compared with that of the multi-factor extreme learning machine (ELM), support vector regression (SVR), backward propagation neural network (BPNN), and single-factor PSO-KELM. Results show that the PSO-KELM outperforms the other models, and the prediction accuracy can be improved by considering causal factors.     

基于时间序列分解和多变量混沌模型的滑坡阶跃式位移预测

三峡库区某些库岸滑坡在强降雨、库水位涨落等诱发因素影响下,其位移时间序列表现出阶跃式变化特征且可能存在混沌特性.但目前常用于滑坡位移预测的混沌模型,均建立在单变量混沌理论的基础之上.且已有的考虑了诱发因素的常规多变量模型,大都采用经验性的方法来选取输入变量;常规多变量模型对滑坡位移序列的非线性特征,及其与诱发因素间的动态响应关系缺乏数学理论上的深入分析.因此,提出一种基于指数平滑法、多变量混沌模型和极限学习机（extreme learing machine,ELM）的滑坡位移组合预测模型.指数平滑多变量混沌ELM模型首先对滑坡累积位移序列的混沌特性进行识别;然后用指数平滑法对累积位移进行预测,得到趋势项位移,并用累积位移减去趋势项位移得到剩余的波动项位移;之后对波动项位移及降雨量、库水位变化量这3个因子进行多变量相空间重构,并用ELM模型对多变量重构后的波动项位移进行预测;最后将预测得到的趋势项和波动项位移值相加,得到最终的累积位移预测值.以三峡库区白水河滑坡ZG93监测点的累积位移作为实例进行分析,并将模型与指数平滑多变量混沌粒子群-支持向量机（PSO-SVM）模型、指数平滑单变量混沌ELM模型作对比.结果表明滑坡位移序列存在混沌特性,模型能有效预测滑坡位移,其预测效果优于对比模型.且本文模型从混沌理论的角度将波动项位移与降雨量、库水位变化量的动态响应关系进行综合分析,更能反映滑坡位移系统演化的物理本质.      

基于多算法参数优化与SVR模型的白水河滑坡位移预测

滑坡预测对于减轻地质灾害的危害十分重要,但对科学研究却很有挑战性。基于变形特征和位移监测数据,建立了三峡库区白水河滑坡的时间序列加法模型。在模型中,累计位移分为3个部分:趋势、周期和随机项,解释了由内部因素（地质环境,重力等）、外部因素（降雨,水库水位等）、随机因素（不确定性）共同作用的影响。在对位移数据进行统计分析后,提出了一个3次多项式模型对趋势项进行学习,并利用多算法寻优的支持向量回归机（SVR）模型对周期项进行训练与预测。结果表明,在预测精度上,基于时间序列与遗传算法-支持向量回归机（GA-SVR）耦合的位移预测模型要明显优于网格寻优（GS）以及粒子群算法（PSO）优化的支持向量回归机模型。因此,GA-SVR模型在滑坡位移预测方面可以得到较好的应用。在“阶跃型”滑坡位移预测中,GA-SVR将具有广阔的应用前景。     

Prediction of landslide displacement with step-like behavior based on multialgorithm optimization and a support vector regression model

Landslide prediction is important for mitigating geohazards but is very challenging. In landslide evolution, displacement depends on the local geological conditions and variations in the controlling factors. Such factors have led to the “step-like” deformation of landslides in the Three Gorges Reservoir area of China. Based on displacement monitoring data and the deformation characteristics of the Baishuihe Landslide, an additive time series model was established for landslide displacement prediction. In the model, cumulative displacement was divided into three parts: trend, periodic, and random terms. These terms reflect internal factors (geological environmental, gravity, etc.), external factors (rainfall, reservoir water level, etc.), and random factors (uncertainties). After statistically analyzing the displacement data, a cubic polynomial model was proposed to predict the trend term of displacement. Then, multiple algorithms were used to determine the optimal support vector regression (SVR) model and train and predict the periodic term. The results showed that the landslide displacement values predicted based on data time series and the genetic algorithm (GA-SVR) model are better than those based on grid search (GS-SVR) and particle swarm optimization (PSO-SVR) models. Finally, the random term was accurately predicted by GA-SVR. Therefore, the coupled model based on temporal data series and GA-SVR can be used to predict landslide displacement. Additionally, the GA-SVR model has broad application potential in the prediction of landslide displacement with “step-like” behavior.     

Comparison on landslide nonlinear displacement analysis and prediction with computational intelligence approaches

Landslide displacement is widely obtained to discover landslide behaviors for purpose of event forecasting. This article aims to present a comparative study on landslide nonlinear displacement analysis and prediction using computational intelligence techniques. Three state-of-art techniques, the support vector machine (SVM), the relevance vector machine (RVM), and the Gaussian process (GP), are comparatively presented briefly for modeling landslide displacement series. The three techniques are discussed comparatively for both fitting and predicting the landslide displacement series. Two landslides, the Baishuihe colluvial landslide in China Three Georges and the Super-Sauze mudslide in the French Alps, are illustrated. The results prove that the computational intelligence approaches are feasible and capable of fitting and predicting landslide nonlinear displacement. The Gaussian process, on the whole, performs better than the support vector machine, relevance vector machine, and simple artificial neural network (ANN) with optimized parameter values in predictive analysis of the landslide displacement.     

Displacement prediction model of landslide based on a modified ensemble empirical mode decomposition and extreme learning machine

In this paper, an M–EEMD–ELM model (modified ensemble empirical mode decomposition (EEMD)-based extreme learning machine (ELM) ensemble learning paradigm) is proposed for landslide displacement prediction. The nonlinear original surface displacement deformation monitoring time series of landslide is first decomposed into a limited number of intrinsic mode functions (IMFs) and one residual series using EEMD technique for a deep insight into the data structure. Then, these sub-series except the high frequency are forecasted, respectively, by establishing appropriate ELM models. At last, the prediction results of the modeled IMFs and residual series are summed to formulate an ensemble forecast for the original landslide displacement series. A case study of Baishuihe landslide in the Three Gorges reservoir area of China is presented to illustrate the capability and merit of our model. Empirical results reveal that the prediction using M–EEMD–ELM model is consistently better than basic artificial neural networks (ANNs) and unmodified EEMD–ELM in terms of the same measurements.     

Numerical subarea of sensitive zone of monitoring variable of landslides to fluctuation of water level of Three Gorges Reservoir — a case of Xietan Landslide

In the period of impounding and running of the Three Gorges Reservoir, the sensitive degrees of change of groundwater table and displacement to the fluctuation of water level are different in different parts of landslides induced by the fluctuation of water level (as the case of Xietan Landslide). According to the relationship between different sensitive degrees of monitoring variables (underground water level and displacement) and quantity of monitoring information, the sensitive zones of groundwater table and displacement to the fluctuation of reservoir water level are divided into different degrees by the approach of fuzzy pattern recognition. The result of numerical subarea of sensitive zone of groundwater table and displacement indicates that the middle and front part of the landslide are the main places with groundwater table affected by the fluctuation of water level of reservoir; the variation of horizontal displacement of surficial part of the middle and front part of the landslide is more sensitive to water impounding and sudden fall of water level; and with the increase of elevation and depth of the landslide, the horizontal displacement changes less and less; the change of vertical displacement of surficial parts of the landslide is most sensitive to the fluctuation of water level of Three Gorges Reservoir; and with the increase of depth, the change of vertical displacement become smaller and smaller. By the means of the numerical subarea regulation of Xietan Landslide, the suggestions to the point layout for monitoring the groundwater table and displacement in the landside of Three Gorges Reservoir are put forward.     

联合多种数据驱动建模方法的滑坡位移预测研究

边坡位移是滑坡演化的宏观体现,分析并预测滑坡位移发展态势对于防灾减灾具有重要意义。由于滑坡位移曲线具有明显的非线性特征,单一模型往往难以刻画其非线性与复杂性。为发展一种普遍适用于滑坡位移的预测方法,提出了一种联合多种数据驱动模型的新方法。该方法根据时间序列分析理论,将滑坡位移序列分解为趋势项和周期项,趋势项采用并联型灰色神经网络处理,周期项则采用人工蜂群算法（ABC）优化后的极限学习机模型（ELM）处理,从而充分应用各种模型的优点。以三峡库区白水河和八字门滑坡为例,对位移数据进行分析处理后,灰色神经网络模型预测其趋势性位移,改进后的极限学习机模型对周期性位移进行训练及预测。结果表明:在预测精度上,优化后的极限学习机模型准确度高于极限学习机模型及小波神经网络等方法,提出的灰色神经网络与ABC-ELM的组合模型可作为实际工程的一个参考。     

三峡工程库区巴东县赵树岭滑坡稳定性与防治对策研究

赵树岭滑坡是三峡工程库区的重要滑坡，其稳定性直接关系到巴东新县城沿江大道的安全，并对新县城土地利用意义重大。在阐述赵树岭滑坡基本特征的基础上，运用水岩耦合三维有限元数值方法模拟了滑坡稳定性，预测了三峡水库蓄水后滑坡稳定性发展趋势和渗流特征。研究表明，水库蓄水及水位波动是影响滑坡稳定性的主要因素，三峡水库蓄水后，滑坡将发生局部失稳，必须加以治理，提出了滑坡防治的原则与对策。     

基于时间序列与人工蜂群支持向量机的滑坡位移预测研究

总结以往滑坡预测方法存在的诸多不足,针对滑坡监测位移-时间曲线特点,本文提出了一种基于时间序列的人工蜂群算法（ABC）与支持向量回归机（SVR）相结合的滑坡位移预测方法。以三峡库区白水河滑坡为例,通过对滑坡位移、降雨、库水位等因素的分析,研究影响滑坡位移变化的因素。用时间序列加法模型和移动平均法将滑坡位移分解为趋势项和周期项。以多项式最小二乘法拟合滑坡位移趋势项,用人工蜂群支持向量机模型对滑坡位移周期项进行训练和预测。通过灰色系统关联分析法计算多项因子与滑坡位移周期项之间的关联性。最终的滑坡总位移预测值为周期项预测值与趋势项预测值之和。与BP神经网络、PSO-SVR模型方法相比,该方法在滑坡位移预测中有更高的精度,在防灾减灾工作中有较好的推广应用前景。     

Real-time monitoring and early warning of landslides at relocated Wushan Town,the Three Gorges Reservoir,China

A special monitoring and warning system has been established and improved in the Three Gorges Reservoir area since 1999. It is necessary to develop a real-time monitoring system on landslides because there are dense populations centered in the reservoir area and geo-hazards may be triggered by a 30-m water level fluctuation between 145 and 175 m in elevation during reservoir operation; the regular monitoring could not be suitable to the early warning on landslides. Since 2003, the authors have carried out a real-time monitoring and early warning project on landslides at the relocated Wushan town in the Three Gorges Reservoir area. The monitoring station includes Global Positioning System with high-accuracy double frequency to monitor ground displacement, time domain reflection technology, and immobile borehole, inclinometer to monitor deep displacement, piezometer to monitor pore water pressure, and precipitation and reservoir water level monitoring. Compared with traditional methods, the real-time monitoring is continuous and traceable in the acquisition process, and the cycle of data acquisition is very short, usually within hours, minutes, or even shorter. Based on the landslide monitoring experience at the Three Gorges Reservoir area, the early warning criteria on landslide are established in which the critical situation is classified into four levels: blue, yellow, orange, and red, respectively, expressed by no, slight, moderate, and high risk situation. Comprehensive judgment from multimonitoring data of Yuhuangge landslide in this area since 2004 suggested that the new Wushan town will be at the blue early warning level, although some monitoring data of individual displacement at deep borehole showed that the displacement was increased by 5 mm in 5 months with an average velocity of 1.0 mm/month, and the data of BOTDR also showed an obvious dislocation along a stairway on the landslide.     

Effects of soil heterogeneity on susceptibility of shallow landslides

Uncertainties in parameters of landslide susceptibility models often hinder them from providing accurate spatial and temporal predictions of landslide occurrences. Substantial contribution to the uncertainties in landslide assessment originates from spatially variable geotechnical and hydrological parameters. These input parameters may often vary significantly through space, even within the same geological deposit, and there is a need to quantify the effects of the uncertainties in these parameters. This study addresses this issue with a new three-dimensional probabilistic landslide susceptibility model. The spatial variability of the model parameters is modeled with the random field approach and coupled with the Monte Carlo method to propagate uncertainties from the model parameters to landslide predictions (i.e., factor of safety). The resulting uncertainties in landslide predictions allow the effects of spatial variability in the input parameters to be quantified. The performance of the proposed model in capturing the effect of spatial variability and predicting landslide occurrence has been compared with a conventional physical-based landslide susceptibility model that does not account for three-dimensional effects on slope stability. The results indicate that the proposed model has better performance in landslide prediction with higher accuracy and precision than the conventional model. The novelty of this study is illustrating the effects of the soil heterogeneity on the susceptibility of shallow landslides, which was made possible by the development of a three-dimensional slope stability model that was coupled with random field model and the Monte Carlo method.

     

Prediction of landslide displacement with an ensemble-based extreme learning machine and copula models

Research on the dynamics of landslide displacement forms the basis for landslide hazard prevention. This paper proposes a novel data-driven approach to monitor and predict the landslide displacement. In the first part, autoregressive moving average time series models are constructed to analyze the autocorrelation of landslide triggering factors. A linear ensemble-based extreme learning machine using the least absolute shrinkage and selection operator is applied in predicting the displacement of landslides. Five benchmarking data-driven models, the support vector machine, neural network, random forest, k-nearest neighbor, and the classical extreme learning machine, are considered as baseline models for validating the ensemble-based extreme learning machines. Numerical experiments demonstrated that the proposed prediction model produces the smallest prediction errors among all the algorithms tested. In the second part, parametric copula models are fitted on the predicted displacement, to investigate the relationship between the triggering factors and landslide displacement values. The Gumbel-Hougaard copula model performs best, which indicates strong upper tail correlation between the triggering factors and displacement values. Thresholds for the triggering factors can be obtained by monitoring the landslide moving patterns with large displacement values. The effectiveness and utility of the proposed data-driven approach have been confirmed with the landslide case study in the region of the Three Gorges Reservoir.     

基于非平稳时间序列分析的滑坡变形预测

滑坡的位移监测资料通常可用来预测滑坡的变形发展趋势,位移的发展反映了滑坡的变形过程.为了预测在现有条件持续情况下的滑坡变形趋势,将滑坡位移监测数据视为非平稳时间序列,应用时间序列分析方法,建立了滑坡变形趋势的预测模型.以三峡库区秭归县白水河滑坡为例,通过对变形预警区监测点位移实测时间序列的分析,取监测点ZG93和XD-04为代表,建立了时间序列预测模型,从第17个月开始向前做6步预测,分析预测曲线与实测曲线之间的关系,并计算预测误差,结果显示除个别数据点之外,预测误差均在±9%以内,曲线吻合较好,说明所建模型效果良好,从而为判断白水河滑坡未来的变形发展趋势提供了可靠的理论依据.     

三峡库区大坪滑坡变形对前缘塌岸的响应分析

随着三峡水库的长期运行,受库水位涨落和波浪作用影响,三峡水库土质岸坡的塌岸问题愈发严重,塌岸不仅造成了水土流失,甚至会诱发滑坡复活。大坪滑坡是三峡库区前缘塌岸发育最为明显的滑坡之一,以三峡库区大坪滑坡为例,结合大坪滑坡的地表宏观变形、地表GPS位移等数据,分析滑坡变形特征以及塌岸对滑坡变形的影响,在此基础上通过ABAQUS生死单元功能实现前缘塌岸对滑坡稳定性影响的数值模拟,进一步探索滑坡变形对前缘塌岸的响应关系。结果表明:大坪滑坡的变形主要受库水位涨落影响,前缘塌岸较发育,塌岸一侧GPS监测点地表位移变化较明显,显然塌岸对大坪滑坡地表变形影响较大;ABAQUS的有限元计算结果表明,塌岸对滑坡的变形影响十分明显,影响大小主要与塌岸方量相关;塌岸导致的滑坡变形主要集中在滑坡前部,并向后部逐渐扩展;ABAQUS中的生死单元法可以很好地实现塌岸对滑坡稳定性影响的模拟。     

Interval prediction of landslide displacement with dual-output least squares support vector machine and particle swarm optimization algorithms

For landslide displacement, interval predictions are generally more realistic and reliable compared with traditional point predictions. This paper presents a new interval prediction method for landslide displacement integrating dual-output least squares support vector machine (DO-LSSVM) and particle swarm optimization (PSO) algorithms. In this new method, the PSO algorithm is employed to optimize coefficients of the least squares support vector machine (LSSVM) model for obtaining point prediction results, and the interval prediction of the landslide displacement is made based on the dual-outputs obtained from the DO-LSSVM model. To assess the rationality of the predictions, three performance evaluation indicators, including the prediction interval coverage probability (PICP), normalized mean prediction interval width (NMPIW), and coverage width-based criterion (CWC), are established. Case studies of the Tanjiahe landslide and the Baishuihe landslide in the Three Gorges Reservoir region are then used to demonstrate the effectiveness of the proposed method in predicting the landslide displacement interval. The case study results demonstrate that this new method has the best overall performance compared with other existing methods, and this new method can provide accurate and reliable results for the medium- to long-term interval prediction of landslide displacement.

     

基于数据挖掘技术的白水河滑坡多场信息关联准则分析

为探究滑坡多场监测数据间的关联准则,采用数据挖掘技术中的两步聚类法与Apriori算法,开展滑坡多场信息关联准则研究。以三峡库区白水河滑坡为例,分析ZG93监测点于2003年6月—2016年12月期间的监测数据,选取影响滑坡变形的主要诱发因子,采用两步聚类法对不同的影响因子进行预聚类和聚类,将数值型变量转化为离散型变量后,应用Apriori算法进行处理,生成满足最小置信度的关联准则,建立白水河滑坡多场耦合作用模式下的影响因子与滑坡位移变形关联准则判据。研究表明,关联准则对于滑坡灾害的变形分析具有重要的意义,数据挖掘技术可较好地应用于三峡库区地质灾害位移预测预报中。