Recently, integrated machine learning (ML) metaheuristic algorithms, such as the artificial bee colony (ABC) algorithm, genetic algorithm (GA), gray wolf optimization (GWO) algorithm, particle swarm optimization (PSO) algorithm, and water cycle algorithm (WCA), have become predominant approaches for landslide displacement prediction. However, these algorithms suffer from poor reproducibility across replicate cases. In this study, a hybrid approach integrating k-fold cross validation (CV), metaheuristic support vector regression (SVR), and the nonparametric Friedman test is proposed to enhance reproducibility. The five previously mentioned metaheuristics were compared in terms of accuracy, computational time, robustness, and convergence. The results obtained for the Shuping and Baishuihe landslides demonstrate that the hybrid approach can be utilized to determine the optimum hyperparameters and present statistical significance, thus enhancing accuracy and reliability in ML-based prediction. Significant differences were observed among the five metaheuristics. Based on the Friedman test, which was performed on the root mean square error (RMSE), Kling-Gupta efficiency (KGE), and computational time, PSO is recommended for hyperparameter tuning for SVR-based displacement prediction due to its ability to maintain a balance between precision, computational time, and robustness. The nonparametric Friedman test is promising for presenting statistical significance, thus enhancing reproducibility.

Predicting landslide displacement is challenging, but accurate predictions can prevent casualties and economic losses. Many factors can affect the deformation of a landslide, including the geological conditions, rainfall and reservoir water level. Time series analysis was used to decompose the cumulative displacement of landslide into a trend component and a periodic component. Then the least-squares support vector machine (LSSVM) model and genetic algorithm (GA) were used to predict landslide displacement, and we selected a representative landslide with episodic movement deformation as a case study. The trend component displacement, which is associated with the geological conditions, was predicted using a polynomial function, and the periodic component displacement which is associated with external environmental factors, was predicted using the GA-LSSVM model. Furthermore, based on a comparison of the results of the GA-LSSVM model and those of other models, the GA-LSSVM model was superior to other models in predicting landslide displacement, with the smallest root mean square error (RMSE) of 62.4146 mm, mean absolute error (MAE) of 53.0048 mm and mean absolute percentage error (MAPE) of 1.492 % at monitoring station ZG85, while these three values are 87.7215 mm, 74.0601 mm and 1.703 % at ZG86 and 49.0485 mm, 48.5392 mm and 3.131 % at ZG87. The results of the case study suggest that the model can provide good consistency between measured displacement and predicted displacement, and periodic displacement exhibited good agreement with trends in the major influencing factors.

As vital comments on landslide early warning systems, accurate and reliable displacement prediction is essential and of significant importance for landslide mitigation. However, obtaining the desired prediction accuracy remains highly difficult and challenging due to the complex nonlinear characteristics of landslide monitoring data. Based on the principle of “decomposition and ensemble”, a three-step decomposition-ensemble learning model integrating ensemble empirical mode decomposition (EEMD) and a recurrent neural network (RNN) was proposed for landslide displacement prediction. EEMD and kurtosis criteria were first applied for data decomposition and construction of trend and periodic components. Second, a polynomial regression model and RNN with maximal information coefficient (MIC)-based input variable selection were implemented for individual prediction of trend and periodic components independently. Finally, the predictions of trend and periodic components were aggregated into a final ensemble prediction. The experimental results from the Muyubao landslide demonstrate that the proposed EEMD-RNN decomposition-ensemble learning model is capable of increasing prediction accuracy and outperforms the traditional decomposition-ensemble learning models (including EEMD-support vector machine, and EEMD-extreme learning machine). Moreover, compared with standard RNN, the gated recurrent unit (GRU)-and long short-term memory (LSTM)-based models perform better in predicting accuracy. The EEMD-RNN decomposition-ensemble learning model is promising for landslide displacement prediction.

With the widespread application of machine learning methods, the continuous improvement of forecast accuracy has become an important task, which is especially crucial for landslide displacement predictions. This study aimed to propose a novel prediction model to improve accuracy in landslide prediction, based on the combination of multiple new algorithms. The proposed new method includes three parts: data preparation, multi-swarm intelligence (MSI) optimization, and displacement prediction. In the data preparation, the complete ensemble empirical mode decomposition (CEEMD) is adopted to separate the trend and periodic displacements from the observed cumulative landslide displacement. The frequency component and residual component of reconstructed inducing factors that related to landslide movements are also extracted by the CEEMD and t-test, and then picked out with edit distance on real sequence (EDR) as input variables for the support vector regression (SVR) model. MSI optimization algorithms are used to optimize the SVR model in the MSI optimization; thus, six predictions models can be obtained that can be used in the displacement prediction part. Finally, the trend and periodic displacements are predicted by six optimized SVR models, respectively. The trend displacement and periodic displacement with the highest prediction accuracy are added and regarded as the final prediction result. The case study of the Shiliushubao landslide shows that the prediction results match the observed data well with an improvement in the aspect of average relative error, which indicates that the proposed model can predict landslide displacements with high precision, even when the displacements are characterized by stepped curves that under the influence of multiple time-varying factors.