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.     

滑坡位移的多模态支持向量机模型预测

将支持向量机（support vector machine,SVM）方法与信号分析中的经验模态分解（empirical mode decomposition, EMD）方法相匹配,提出了一种通过多模态支持向量机函数回归分析建模预测滑坡位移的理论方法。以边坡位移历史观测数据为基础,应用EMD方法获得滑坡形成过程中位移演化的几个特征时间模态,构成了多模态信息统计学习样本,确定了边坡位移演化的自适应多尺度变化信息。对应于每个经验模态的位移变化信息,引入了多模态SVM建模方法,然后合成不同经验模态下边坡位移的计算结果,得到滑坡位移的预测值。以卧龙寺新滑坡和新滩滑坡的监测数据为基础的理论预测结果表明,与采用遗传算法的神经网络方法的预测结果相比,支持向量机经验模态方法具有更强的预测能力,理论预测结果与实际监测值具有很好的一致性     

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.     

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.     

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。     

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.     

Probabilistic forecasting of landslide displacement accounting for epistemic uncertainty: a case study in the Three Gorges Reservoir area,China

Accurate and reliable displacement forecasting plays a key role in landslide early warning. However, due to the epistemic uncertainties associated with landslide systems, errors are unavoidable and sometimes significant in traditional methods of deterministic point forecasting. Transforming traditional point forecasting into probabilistic forecasting is essential for quantifying the associated uncertainties and improving the reliability of landslide displacement forecasting. This paper proposes a hybrid approach based on bootstrap, extreme learning machine (ELM), and artificial neural network (ANN) methods to quantify the associated uncertainties via probabilistic forecasting. The hybrid approach consists of two steps. First, a bootstrap-based ELM is applied to estimate the true regression mean of landslide displacement and the corresponding variance of model uncertainties. Second, an ANN is used to estimate the variance of noise. Reliable prediction intervals (PIs) can be computed by combining the true regression mean, variance of model uncertainty, and variance of noise. The performance of the proposed hybrid approach was validated using monitoring data from the Shuping landslide, Three Gorges Reservoir area, China. The obtained results suggest that the Bootstrap-ELM-ANN approach can be used to perform probabilistic forecasting in the medium term and long term and to quantify the uncertainties associated with landslide displacement forecasting for colluvial landslides with step-like deformation in the Three Gorges Reservoir area.     

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.      

WA联合ELM与OS-ELM的滑坡位移预测模型

滑坡累积位移监测曲线往往呈现出复杂的非线性增长特性,对此建立了不少相关的预测模型,而以往的预测模型存在着许多不足。本文基于小波函数（Wavelet Analysis,WA）,ELM与OS-ELM,提出一种名为WA联合ELM、OS-ELM的预测方法。首先,该方法基于小波函数,将滑坡累积位移分解成受内部地质条件影响的趋势项和受外部影响因子影响的周期项;然后,基于ELM与OS-ELM分别对趋势项和周期项进行预测;最后将趋势项和周期项的预测值叠加得到累积位移的预测值。结果表明,小波函数得到的趋势项展现出良好的趋势性,而周期项也展现出良好的周期性;以Sigmoid方程为核函数,隐含层神经元个数为33的ELM模型能准确高效对趋势项进行预测,而以RBF方程为核函数,隐含层神经元个数为100的OS-ELM模型能准确高效对周期项进行预测;累积位移预测数据的RMSE分别为0.1423和0.1315,预测结果相对较好,能够在滑坡位移预测领域发挥一定的作用。     

A graph deep learning method for landslide displacement prediction based on global navigation satellite system positioning

The accurate prediction of displacement is crucial for landslide deformation monitoring and early warning. This study focuses on a landslide in Wenzhou Belt Highway and proposes a novel multivariate landslide displacement prediction method that relies on graph deep learning and Global Navigation Satellite System (GNSS) positioning. First model the graph structure of the monitoring system based on the engineering positions of the GNSS monitoring points and build the adjacent matrix of graph nodes. Then construct the historical and predicted time series feature matrixes using the processed temporal data including GNSS displacement, rainfall, groundwater table and soil moisture content and the graph structure. Last introduce the state-of-the-art graph deep learning GTS (Graph for Time Series) model to improve the accuracy and reliability of landslide displacement prediction which utilizes the temporal-spatial dependency of the monitoring system. This approach outperforms previous studies that only learned temporal features from a single monitoring point and maximally weighs the prediction performance and the priori graph of the monitoring system. The proposed method performs better than SVM, XGBoost, LSTM and DCRNN models in terms of RMSE (1.35 mm), MAE (1.14 mm) and MAPE (0.25) evaluation metrics, which is provided to be effective in future landslide failure early warning.     

基于优化经验模态分解和聚类分析的滑坡位移智能预测研究

针对三峡库区"阶跃式"滑坡的变形特征,提出了一种新的滑坡位移预测方法。以白水河滑坡ZG118和XD-01监测点位移数据为例,采用基于软筛分停止准则的经验模态分解(SSSC-EMD)将累计位移-时间曲线和影响因子时间序列自适应地分解为多个固有模态函数(IMF),并采用K均值(K-Means)聚类法对其进行聚类累加,得到有物理含义的位移分量(趋势性位移、周期性位移以及随机性位移)和影响因子分量(高频影响因子和低频影响因子)。使用最小二乘法对趋势性位移进行拟合预测;采用果蝇优化-最小二乘支持向量机(FOA-LSSVM)模型对周期性位移和随机性位移进行预测。将各位移分量预测值进行叠加处理,实现滑坡累计位移的预测。研究结果表明,所提出的(SSSC-EMD)-K-Means-(FOA-LSSVM)模型能够预测"阶跃式"滑坡的位移变化规律,且预测精度高于传统的支持向量机回归(SVR)、最小二乘支持向量机(LSSVM)模型;并通过改变训练集长度,进行单因素分析,发现其与预测精度之间呈正相关关系。     

考虑监测离群值朱家店滑坡位移预测研究

滑坡位移预测预报是滑坡防灾减灾的重要组成部分,提高滑坡位移预测的准确性与精确度是该项研究的重点与难点。本文在滑坡位移预测中考虑了监测样本的离群值,通过忽略、指定与修正离群值3种方式,研究滑坡位移预测样本离群值的最优处理方式。以三峡库区朱家店滑坡为例,基于ARIMA(p,d,q)模型,分别对累积位移与位移速率时间序列开展了预测研究。研究结果表明:修正离群值的预测结果介于忽略和指定离群值两者之间,更适用于存在监测离群值的滑坡位移预测;对于ARIMA模型,更适合采用位移速率进行预测预报;使用位移速率时间序列ARIMA(1,0,1)并修正离群值的预测结果为:2016年和2017年6月份滑坡前缘GP3"阶跃"位移分别为79. 0 mm和70. 2 mm,截止2017年8月,GP3累积位移将达1647. 7 mm。     

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。     

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。     

Landslide displacement prediction based on combining method with optimal weight

Predicting the deformation and evolution tendency of landslides is essential to landslide disaster prevention and mitigation. At present, most of the proposed models for landslide displacement prediction belong to single models. It is difficult to accurately describe the deformation and evolution law only by a single model for the complexity of landslides and limitation of the models. In this paper, we presented an application of linear combination model with optimal weight in landslide displacement prediction. We took Huanlongxicun and Saleshan landslides in Gansu province of China as examples, firstly to build GM(1,1) and Verhulst models for displacement prediction of the two landslides; then build two linear combination models of the two landslides, on the basis of the combining theory with optimal weight and the prediction results of the GM(1,1) and Verhulst models. The results show that the prediction accuracies of the combining models are much higher than those of the single models for both Huanglongxicun landslide and Saleshan landslide. Therefore, the combining model with optimal weight is an effective and feasible method to further improve accuracy for landslide displacement prediction.     

阶跃型位移特征滑坡时间预测预报研究

滑坡时间预测预报目前主要以滑坡最终破坏的时间为目标函数,但对于变形特征为阶跃型的滑坡却难以准确地预测其破坏时间。为此,提出以位移作为此类滑坡时间预报的目标函数。将滑坡位移分解为蠕变位移和波动位移,采用二次移动平均法分别提取,然后采用多项式拟合和灰色GM(1,1)模型分别对蠕变位移和波动位移进行预测,最后将两部分预测位移相加得到滑坡预测的总位移。以典型阶跃型位移特征滑坡——三峡库区八字门滑坡为例,运用其位移监测数据进行验证,并对多模型预测结果进行对比分析,结果表明,该位移预测模型预测精度良好,能较好地预测阶跃型位移特征滑坡位移。     

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.

     

极限学习机模型在季冻区深基坑地表沉降预测中的应用

针对传统数据驱动模型存在收敛速度慢、过度拟合等问题,提出了基于极限学习机算法的基坑地表沉降预测方法。结合季冻区地铁车站基坑的特点,提取基坑开挖时间、开挖深度、围护桩顶位移、围护桩内力、支撑轴力及地表温度等特征信息,建立极限学习机回归预测模型,选用实例数据进行算例分析,并将其与传统回归预测模型进行对比,实验结果表明,极限学习机模型收敛速度快,泛化能力强,其预测精度优于传统预测模型,且在学习速度方面优势明显,对深基坑安全监控有一定的实用价值。     

Landslide Susceptibility Assessment Using Bagging Ensemble Based Alternating Decision Trees,Logistic Regression and J48 Decision Trees Methods: A Comparative Study

In this study, we have evaluated and compared prediction capability of Bagging Ensemble Based Alternating Decision Trees (BADT), Logistic Regression (LR), and J48 Decision Trees (J48DT) for landslide susceptibility mapping at part of the Uttarakhand State (India). The BADT method has been proposed in the present study which is a novel hybrid machine learning ensemble approach of bagging ensemble and alternating decision trees. The J48DT is a relative new machine learning technique which has been applied only in few landslide studies, and the LR is known as a popular landslide susceptibility model. For the model studies, a spatial database of 930 historical landslide events and 15 landslide affecting factors have been collected and analyzed. This database has been used to build and validate the landslide models namely BADT, LR and J48DT Predictive capability of these models has been validated and compared using statistical analyzing methods and Receiver Operating Characteristic (ROC) curve. Results show that these three landslide models (BADT, LR and J48DT) performed well with the training dataset. However, using the validation dataset the BADT model has the highest prediction capability, followed by the LR model, and the J48DT model, respectively. This indicates that the BADT is a promising method which can be used for landslide susceptibility assessment also for other landslide prone areas.     

基于时间序列与混合核函数SA-SVR的滑坡位移预测模型研究

本文针对阶跃型滑坡变形定量预测困难,提出一种基于时间序列分解与混合核函数SA-SVR的滑坡位移预测模型.首先基于时间序列分解原理,反复使用指数平滑法将滑坡累积位移分解为趋势项位移和周期项位移,使分解后的趋势项位移较平滑且能保证周期项位移的预测精度.同时针对多项式预测容易过拟合造成预测值偏离真实值的问题,采用K-flod...