Landslides DOI 10.1007/s10346-013-0443-z Received: 11 February 2013 Accepted: 8 October 2013 © Springer-Verlag Berlin Heidelberg 2013 Zaobao Liu I Jianfu Shao I Weiya Xu I Hongjie Chen I Chong Shi Comparison on landslide nonlinear displacement analysis and prediction with computational intelligence approaches Abstract 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. Keywords Landslide . Displacement prediction . Nonlinear . Computational intelligence . Relevance vector machine . Gaussian process Introduction Landslide displacement is the typical signature of its underlying complex evolution process. Landslide displacement analysis (LDA) is a critical issue of an early warning system and can contribute to prevent suffering property damage and loss of human lives. It provides a potential physically based approach for landslide prediction. Landslide behavior is generally monitored by various instruments, such as extensometers, inclinometers, and clinometers. The most reliable parameter obtained by these instruments is the landslide displacement. Hence, LDA is widely used in landslide forecasting, especially in the short-term forecasting of landslides with creep displacement. Slope or landslide displacement analysis and prediction are valuable and important in predicting slope failures. Based on displacement measurements in the secondary creep range, Saito (1965) proposed an empirical model to predict slope failure time by analysis of the constant strain rate from the relative displacement curve. After that, Saito (1969) extended his theory for impending forecasting by formulating the relationship between the time left before failure and the displacement. Fukuzono (1985) presented a new method for predicting slope failure time using the inverse of surface displacement velocity based on large-scale laboratory experiments. Based on these achievements, slope displacement analysis and prediction have been approached with many other techniques. A predictive model was presented for predicting seismically induced landslide displacements. Seismic slope stability was measured in terms of critical acceleration derived from displacement analysis, which depends on the mechanical soil properties, and pore pressure (Romeo 2000). Landslide displacement was observed by monitoring groundwater composition for the purpose of estimating future landslide occurrence (Sakai 2001). Some regression models were obtained from estimating the coseismal landslide displacement by predicting the Newmark displacement (Newmark 1965) in terms of the critical acceleration ratio, critical acceleration ratio and earthquake magnitude, arias intensity and critical acceleration, and arias intensity and critical acceleration ratio (Jibson 2007 ). The inverse velocity method derived from displacement curves was successfully applied to predict large range slope failures in open pit mines by displacement monitoring and analysis (Rose and Hungr 2007). A typical pattern of landslide displacement was identified for shallow landslides, debris produced by the excavation and gabions, metallic walls, anchored bulkheads distribution, and slope geometry (Bozzano et al. 2011). These works discussed the LDA with various field-monitored factors such as the seismic features, material properties, and pore water presence. Besides the above achievements, slope or landslide displacements are also analyzed and predicted with some time series techniques, including the Verhulst model (Li et al. 1996), exponential smoothing model (Liu et al. 2009a), and grey model (Chen and Wang 1988; Liu et al. 2009b). Comparisons of these models (Yang and Liu 2005; Yi 2007) have been discussed and lead to the fact that these models all have some limitations. Each of the models has a definite form of equation which indicates that the model is mainly valid for landslide displacements with similar features. In fact, each of the former types of models involves an exponential function with varying parameters to be adjusted by observations. These limitations make it necessary to continue the research work on proper predictive models. Recently, some computational intelligence techniques such as the artificial neural network (ANN) (Mayoraza and Vullietb 2002; Chen and Zeng 2012; Lv and Liu 2012; Du et al. 2013), support vector machines (SVMs) (Feng et al. 2004; Dong et al. 2007; Zhu and Hu 2013), and the Gaussian process (GP) (Liu et al. 2012) have been successfully applied for analysis and prediction of landslide displacement and some related subjects (Li et al. 2012; Grelle and Guadagno 2012; Liu et al. 2013; Belle et al. 2013; Lian et al. 2013). These works showed the potential ability of the corresponding methods to analyze the engineering problems such as the landslide displacement prediction. However, there is almost no work made in view of comparing these computational intelligence methods for LDA. Such a comparison could be useful to evaluate the performance and validity domain of each method. The present study aims to give a comparative study on the computational intelligence approaches including the Gaussian process (Rasmussen and Williams 2006), support vector machines (Cortes and Vapnik 1995; Vapnik 1998), and relevance vector machines (RVMs) (Tipping 2000, 2001) for predictive analysis of landslide displacement. The three techniques are typical computational intelligence approaches widely used in Landslides Original Paper