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

Step-Like Displacement Prediction of Landslide Based on Time Series Decomposition and Multivariate Chaotic Model

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.

The GPS monitoring cumulative displacement on reservoir landslides in the Three Gorges Reservoir area shows steplike characteristics and is a probable chaotic time series under the influences of the seasonal rainfall and reservoir water level fluctuation.Traditionally,the uni-variable chaotic model is commonly used to predict the landslide displacement;and all existing multivariable models select the input variables empirically without theoretical exploration of the nonlinear dynamic evolution process of landslide displacement and its inducing factors.A new combined model based on double exponential smoothing（DES）,multivariable chaotic model,extreme learning machine（ELM）is proposed in this study.First,the chaos characteristicof landslide displacement is identified by the combined DES and multivariable chaotic ELM.Second,the DES method is used to predict the cumulative displacement.The predictive results are the trend displacement,and the periodic displacement is obtained by reducing the trend displacement from the cumulative displacement.Third,the multivariate phase space reconstruction method of chaotic theory is used to explore the dynamic relationship between the periodic displacement and its inducing factors,and the ELM model is established to predict the periodic displacement.Finally,the total forecast cumulative displacement is obtained by adding the predictive trend and periodic displacement.The GPS monitoring cumulative displacement on the Baishuihe landslide is used as case study.In addition,the proposed model is compared with the combined DES and multivariable chaotic particle swarm optimized support vector machine model,the combined DES and uni-variable chaotic ELM model.The results show that the prediction accuracy of the proposed model is higher than that of other models.The proposed model explores the nonlinear characteristic of landslide displacement and its dynamic relationship with inducing factors.The model also reflects the physical meaning of the nonlinear evolution of the landslide displacement.