Data-Driven Combination-Interval Prediction for Landslide Displacement Based on Copula and VMD-WOA-KELM Method

Abstract

To tackle the difficulties of the point prediction in quantifying the reliability of landslide displacement prediction, a data-driven combination-interval prediction method (CIPM) based on copula and variational-mode-decomposition associated with kernel-based-extreme-learning-machine optimized by the whale optimization algorithm (VMD-WOA-KELM) is proposed in this paper. Firstly, the displacement is decomposed by VMD to three IMF components and a residual component of different fluctuation characteristics. The key impact factors of each IMF component are selected according to Copula model, and the corresponding WOA-KELM is established to conduct point prediction. Subsequently, the parametric method (PM) and non-parametric method (NPM) are used to estimate the prediction error probability density distribution (PDF) of each component, whose prediction interval (PI) under the 95% confidence level is also obtained. By means of the differential evolution algorithm (DE), a weighted combination model based on the PIs is built to construct the combination-interval (CI). Finally, the CIs of each component are added to generate the total PI. A comparative case study shows that the CIPM performs better in constructing landslide displacement PI with high performance.

References

[1] Cao Y, Yin K L, Alexander D E . Using an Extreme Learning Machine to Predict the Displacement of Step-Like Landslides in Relation to Controlling Factors. Landslides, 2016, 13(4): 725-736.

[2] Corominas J, Moya J, Ledesma A . Prediction of Ground Displacements and Velocities from Groundwater Level Changes at the Vallcebre Landslide (Eastern Pyrenees, Spain). Landslides, 2005, 2(2): 83-96.

[3] Deng D M, Liang Y, Wang L Q . Displacement Prediction Method Based on Ensemble Empirical Mode Decomposition and Support Vector Machine Regression—A Case of Landslides in Three Gorges Reservoir Area. Rock and Soil Mechanics, 2017, 38(12): 3660-3669 (in Chinese with English Abstract)

[4] Dragomiretskiy K, Zosso D. Variational Mode Decomposition. IEEE Transactions on Signal Processing, 2014, 62(3): 531-544.

[5] Du J, Yin K L, Lacasse S. Displacement Prediction in Colluvial Landslides, Three Gorges Reservoir, China. Landslides, 2013, 10(2): 203-218.

[6] Gao Q Y Study on Combination of Risk Probability Rainfall Threshold of Flash Flood in Small Watershed Based on Copula formed by adding a bunch of IMF PIs. Function, 2019 Zhengzhou Zhengzhou University 54-60 (in Chinese with English Abstract)

[7] Herrera G, Fernández-Merodo J A, Mulas J . A Landslide Forecasting Model Using Ground Based SAR Data: The Portalet Case Study. Engineering Geology, 2009, 105(3/4): 220-230.

[8] Huang F M, Huang J S, Jiang S H . Landslide Displacement Prediction Based on Multivariate Chaotic Model and Extreme Learning Machine. Engineering Geology, 2017, 218 173-186.

[9] Huang G B. Learning Capability and Storage Capacity of Two-Hidden-Layer Feedforward Networks. IEEE Transactions on Neural Networks, 2003, 14(2): 274-281.

[10] Huang G B, Chen L, Siew C K. Universal Approximation Using Incremental Constructive Feedforward Networks with Random Hidden Nodes. IEEE Transactions on Neural Networks, 2006, 17(4): 879-892.

[11] Huang G B, Zhu Q Y, Siew C K. Extreme Learning Machine: Theory and Applications. Neurocomputing, 2006, 70(1/2/3): 489-501.

[12] Huang G B, Zhou H M, Ding X J . Extreme Learning Machine for Regression and Multiclass Classification. IEEE Transactions on Systems, Man, and Cybernetics Part B, Cybernetics: A Publication of the IEEE Systems, Man, and Cybernetics Society, 2012, 42(2): 513-529.

[13] Intrieri E, Gigli G, Casagli N . Brief Communication “Landslide Early Warning System: Toolbox and General Concepts”. Natural Hazards and Earth System Sciences, 2013, 13(1): 85-90.

[14] Khosravi A, Nahavandi S, Creighton D. A Prediction Interval-Based Approach to Determine Optimal Structures of Neural Network Metamodels. Expert Systems with Applications, 2010, 37(3): 2377-2387.

[15] Khosravi A, Nahavandi S, Creighton D . Comprehensive Review of Neural Network-Based Prediction Intervals and New Advances. IEEE Transactions on Neural Networks, 2011, 22(9): 1341-1356.

[16] Li C D, Criss R E, Fu Z Y . Evolution Characteristics and Displacement Forecasting Model of Landslides with Stair-Step Sliding Surface along the Xiangxi River, Three Gorges Reservoir Region, China. Engineering Geology, 2021, 283 105961.

[17] Li D Y, Yin K L, Leo C. Analysis of Baishuihe Landslide Influenced by the Effects of Reservoir Water and Rainfall. Environmental Earth Sciences, 2010, 60(4): 677-687.

[18] Li L Q, Wang M Y, Zhao H Q . Baishuihe Landslide Displacement Prediction Based on CEEMDAN-BA-SVR-Adaboost Model. Journal of Yangtze River Scientific Research Institute, 2021, 38(6): 52-59+66 (in Chinese with English Abstract)

[19] Li L W, Wu Y P, Miao F S . Displacement Prediction of Landslides Based on Variational Mode Decomposition and GWO-MIC-SVR Model. Chinese Journal of Rock Mechanics and Engineering, 2018, 37(6): 1395-1406 (in Chinese with English Abstract)

[20] Li L W, Wu Y P, Miao F S . Displacement Interval Prediction Method for Step-Like Landslides Considering Deformation State Dynamic Switching. Chinese Journal of Rock Mechanics and Engineering, 2019, 38(11): 2272-2287 (in Chinese with English Abstract)

[21] Li X Z, Kong J M, Wang Z Y. Landslide Displacement Prediction Based on Combining Method with Optimal Weight. Natural Hazards, 2012, 61(2): 635-646.

[22] Lian C, Zeng Z G, Yao W . Extreme Learning Machine for the Displacement Prediction of Landslide under Rainfall and Reservoir Level. Stochastic Environmental Research and Risk Assessment, 2014, 28(8): 1957-1972.

[23] Liao K, Wu Y P, Li L W . Displacement Prediction Model of Landslide Based on Time Series and GWO-ELM. Journal of Central South University (Science and Technology), 2019, 50(3): 619-626 (in Chinese with English Abstract)

[24] Lin D C, An F P, Guo Z L . Prediction of Landslide Displacement by Multi-Modal Support Vector Machine Model. Rock and Soil Mechanics, 2011, 32(S1): 451-458 (in Chinese with English Abstract)

[25] Lins I D, Droguett E L, das Chagas Moura M . Computing Confidence and Prediction Intervals of Industrial Equipment Degradation by Bootstrapped Support Vector Regression. Reliability Engineering & System Safety, 2015, 137 120-128.

[26] Liu Y, Yin K L, Chen L X . A Community-Based Disaster Risk Reduction System in Wanzhou, China. International Journal of Disaster Risk Reduction, 2016, 19 379-389.

[27] Ma J W, Tang H M, Liu X . Establishment of a Deformation Forecasting Model for a Step-Like Landslide Based on Decision Tree C5.0 and Two-Step Cluster Algorithms: a Case Study in the Three Gorges Reservoir Area, China. Landslides, 2017, 14(3): 1275-1281.

[28] Ma J W, Tang H M, Liu X . Probabilistic Forecasting of Landslide Displacement Accounting for Epistemic Uncertainty: a Case Study in the Three Gorges Reservoir Area, China. Landslides, 2018, 15(6): 1145-1153.

[29] Miao F S, Wu Y P, Xie Y H . Prediction of Landslide Displacement with Step-Like Behavior Based on Multialgorithm Optimization and a Support Vector Regression Model. Landslides, 2018, 15(3): 475-488.

[30] Miao S J, Hao X, Guo X L . Displacement and Landslide Forecast Based on an Improved Version of Saito’s Method Together with the Verhulst-Grey Model. Arabian Journal of Geosciences, 2017, 10(3): 53.

[31] Mirjalili S, Mirjalili S M, Lewis A. Grey Wolf Optimizer. Advances in Engineering Software, 2014, 69(3): 46-61.

[32] Phoon K K, Kulhawy F H. Characterization of Geotechnical Variability. Canadian Geotechnical Journal, 1999, 36(4): 612-624.

[33] Phoon K K, Kulhawy F H. Evaluation of Geotechnical Property Variability. Canadian Geotechnical Journal, 1999, 36(4): 625-639.

[34] Posada D, Buckley T R. Model Selection and Model Averaging in Phylogenetics: Advantages of Akaike Information Criterion and Bayesian Approaches over Likelihood Ratio Tests. Systematic Biology, 2004, 53(5): 793-808.

[35] Reboredo J C. How Do Crude Oil Prices Co-Move? A Copula Approach. Energy Economics, 2011, 33(5): 948-955.

[36] Saito M. Forecasting the Time of Occurrence of a Slope Failure. Proceedings of the 6th International Mechanics and Foundation Engineering, 1965 Oxford Pergamon Press 537-541

[37] Sebbar A, Heddam S, Djemili L. Kernel Extreme Learning Machines (KELM): A New Approach for Modeling Monthly Evaporation (EP) from Dams Reservoirs. Physical Geography, 2020, 42(4): 351-373.

[38] Shrestha D L, Solomatine D P. Machine Learning Approaches for Estimation of Prediction Interval for the Model Output. Neural Networks, 2006, 19(2): 225-235.

[39] Shrivastava N A, Lohia K, Panigrahi B K. A Multiobjective Framework for Wind Speed Prediction Interval Forecasts. Renewable Energy, 2016, 87 903-910.

[40] Shrivastava N A, Panigrahi B K. Point and Prediction Interval Estimation for Electricity Markets with Machine Learning Techniques and Wavelet Transforms. Neurocomputing, 2013, 118 301-310.

[41] Sklar A. Random Variables, Distribution Functions, and Copulas—A Personal Look Backward and Forward. Institute of Mathematical Statistics Lecture Notes: Monograph Series, 1996, 28 1-14

[42] Tang J Correlation Analysis and Modeling of Power Network Planning Index Based on Copula Function, 2018 Kunming Kunming University of Science and Technology (in Chinese with English Abstract)

[43] Wan C, Xu Z, Wang Y L . A Hybrid Approach for Probabilistic Forecasting of Electricity Price. IEEE Transactions on Smart Grid, 2014, 5(1): 463-470.

[44] Wang L The Method of Optimum Combined Power Load Forecasting Based on Differential Evolution Optimization Weight, 2018 Tianjin Tianjin University (in Chinese with English Abstract)

[45] Wang X L, Xie H Y, Wang J J . Prediction of Dam Deformation Based on Bootstrap and ICS-MKELM Algorithms. Journal of Hydroelectric Engineering, 2020, 39(3): 106-120 (in Chinese with English Abstract)

[46] Wang Y K, Tang H M, Wen T . A Hybrid Intelligent Approach for Constructing Landslide Displacement Prediction Intervals. Applied Soft Computing, 2019, 81 105506.

[47] Wu X L, Zhan F B, Zhang K X . Application of a Two-Step Cluster Analysis and the Apriori Algorithm to Classify the Deformation States of Two Typical Colluvial Landslides in the Three Gorges, China. Environmental Earth Sciences, 2016, 75(2): 146-161.

[48] Xiang Q L Study for Dam Deformation Monitoring Data Based On Time Series Anylysis, 2012 Yanglin Northwest A&F University (in Chinese with English Abstract)

[49] Xu S L, Niu R Q. Displacement Prediction of Baijiabao Landslide Based on Empirical Mode Decomposition and Long Short-Term Memory Neural Network in Three Gorges Area, China. Computers & Geosciences, 2018, 111 87-96.

[50] Yang M, Yang C L, Dong J C. Ultra-Short Term Probabilistic Intervals Forecasting of Wind Power Based on Optimization Model of Forecasting Error Distribution. Acta Energiae Solaris Sinica, 2019, 40(10): 2067-2978 (in Chinese with English Abstract)

[51] Yang X Y, Zhang Y F, Ye T Z . Prediction of Combination Probability Interval of Wind Power Based on Naive Bayes. High Voltage Engineering, 2020, 46(3): 1099-1108 (in Chinese with English Abstract)

[52] Yao W M, Li C D, Zuo Q J . Spatiotemporal Deformation Characteristics and Triggering Factors of Baijiabao Landslide in Three Gorges Reservoir Region, China. Geomorphology, 2019, 343 34-47.

[53] Yao W, Zeng Z G, Lian C . Training Enhanced Reservoir Computing Predictor for Landslide Displacement. Engineering Geology, 2015, 188 101-109.

[54] Yin K L, Yan T Z. Landslide Prediction and Related Models. China Journal of Rock Mechanics and Engineering, 1996, 1 1-8 (in Chinese with English Abstract)

[55] Yin Y P, Wang H D, Gao Y L . Real-Time Monitoring and Early Warning of Landslides at Relocated Wushan Town, the Three Gorges Reservoir, China. Landslides, 2010, 7(3): 339-349.

[56] Zhang K, Zhang K, Bao R . Intelligent Prediction of Landslide Displacements Based on Optimized Empirical Mode Decomposition and K-Mean Clustering. Rock and Soil Mechanics, 2021, 42(1): 211-223 (in Chinese with English Abstract)

[57] Zhou C, Yin K L, Cao Y . Application of Time Series Analysis and PSO-SVM Model in Predicting the Bazimen Landslide in the Three Gorges Reservoir, China. Engineering Geology, 2016, 204 108-120.

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