Accurate delineation of debris-flow-endangered areas (e.g., the maximum runout distance) is a necessary prerequisite for the debris-flow risk assessment and countermeasures design. Recently, machine-learning models have been proved to be an effective tool in predicting debris-flow parameters. However, existing machine-learning models are generally developed based on a very limited number of observation data, which may result in the predictive model overfitting or underfitting. How to develop a robust model for accurate forecasting of debris-flow-endangered areas still remains a difficult task. This paper proposes a hybrid method for predicting debris-flow hazard zone by integrating machine-learning algorithms and an empirical regression model. The proposed method takes the calculated maximum runout distance obtained from the empirical model as supplementary inputs to increase the amount of training data to construct hybrid machine-learning models. Three commonly used machine-learning models (i.e., multivariate adaptive regression splines (MARS), random forest (RF), and support vector machine (SVM)) are developed based on the training datasets of a specific debris basin. Then, these three machine-learning models are combined with an empirical relationship developed using the same training datasets to generate corresponding hybrid models. Finally, the performance metrics (i.e., coefficient of determination (R²), root-mean-square error (RMSE), and mean absolute error (MAE)) of the proposed hybrid models are comprehensively investigated and compared with the single predictive model (i.e., MARS, RF, SVM, and the empirical model) under fivefold cross-validation. The proposed method is illustrated using 134 channelized debris-flow events in Sichuan province, China. Results show that compared with the three individual machine-learning models, hybridization of machine-learning algorithms and the empirical model results in R², RMSE, and MAE improved by 70.5, 32.9, and 41.1, respectively. In contrast to the empirical model, the R², RMSE, and MAE value of the proposed hybrid models are improved by 29.6, 22.3, and 32.5, respectively. The proposed hybrid models generally perform better than the single machine-learning and the empirical model, providing a promising tool for accurate forecasting of a debris-flow-endangered area.

This paper proposes a probabilistic hazard assessment model for debris flows considering the uncertainties of multiple influencing factors based on copula approaches. Fifty‐nine rainfall‐induced debris flows occurred between 2001 and 2009 in Taiwan are taken as an illustrative example to validate the proposed approaches. A copula‐based probabilistic model is developed to model the joint probability distribution of debris‐flow volume V and its influencing factors (e.g., rainfall intensity, RI and landslide area, A_L). The developed model is then used to make probabilistic prediction of debris‐flow volume for a specific hazard level, and compared with the empirical approaches. The proposed probabilistic model is also used to develop the exceedance probability charts of quantities for a specific debris‐flow basin. Results show that the developed V–RI–A_L probabilistic model can provide reasonable estimates of debris‐flow volume in Taiwan for a specific probability level of 0.94, and show better predictive performance than the empirical relationships by using an independent debris‐flow dataset in Taiwan for validation. The developed multivariate joint probabilistic model can also provide the exceedance probability of debris flows through considering the uncertainties of debris flow and its influencing factors, providing a preliminary reference for hazard assessment of the debris flows.

Probabilistic reservoir slope stability analysis usually suffers from computational inefficiency of complicated implicit performance functions. To address this problem, numerous machine learning (ML) algorithms have been successfully applied to calculate the index of factor of safety (FS) to facilitate slope reliability analysis. However, current ML surrogate models generally select an optimal algorithm with good performance while discarding all the others. Meanwhile, ML models mainly provide a point-value deterministic evaluation of failure probability and ignores the predictive uncertainties associated with the models. How to ensemble the strengths of different ML algorithms to improve the estimation accuracy of slope failure probability and rationally quantify the predictive uncertainties still remains an open issue. This paper proposes ML ensembled probabilistic methods for time-dependent reliability analysis of reservoir slopes under rapid water level drawdown using Bayesian model averaging (BMA). A practical slope in the Three Gorges Reservoir Area is selected to illustrate the proposed approach. Firstly, two machine-learning models, namely support vector machine (SVM) and back propagation-based neural network (BPNN), are used to evaluate the safety factor of reservoir slopes. Then, the deterministic evaluations of FS are ensembled together by the weighting of each member using BMA to make probabilistic evaluation of time-dependent failure probability. Finally, the predictive performance of individual ML models and the ensemble BMA model are systematically investigated. Results show that the ensemble surrogate model has better predictive performance on slope failure probability than individual ML model. Ensemble models can not only combine the strengths of different models to improve the prediction accuracy of time-dependent failure probability of reservoir slope, but also provide probabilistic forecasts to reasonably quantify the predictive uncertainty

Relief well designs mainly focus on conventional parameters such as well diameter and well spacing by engineering experience, lacking rigorous analysis. The impact of wellhead elevation remains unclear. This paper proposes a multi-objective optimization method for determining the design parameters (i.e., the wellhead elevation and number of wells) of relief wells. MODFLOW is used to develop a three-dimensional transient seepage numerical model of the levee. The design parameters of relief wells are optimized by balancing the safety factor and the economic cost by non-dominated sorting genetic algorithm-II (NSGA-II). To remove computational burden within NSGA-II, random forest (RF) is used to establish an intelligent surrogate model for evaluating the hydraulic characteristics of levees. The final optimal design parameters are determined by entropy weight and the Technique for Order Preference by Similarity to Ideal Solution (TOPSIS). Finally, the proposed approaches are illustrated using the Wuhan Yangtze River Levee, China. Results show that compared with the empirical approach, the optimal design parameters obtained by the proposed approaches can not only meet the safety threshold for the levee, but also reduce the costs by 15%. The importance of wellhead elevation on the hydraulic gradient is about six times that of the number of wells.