A multiobjective evolutionary optimization method based critical rainfall thresholds for debris flows initiation

At present, most researches on the critical rainfall threshold of debris flow initiation use a linear model obtained through regression. With relatively weak fault tolerance, this method not only ignores nonlinear effects but also is susceptible to singular noise samples, which makes it difficult to characterize the true quantization relationship of the rainfall threshold. Besides, the early warning threshold determined by statistical parameters is susceptible to negative samples (samples where no debris flow has occurred), which leads to uncertainty in the reliability of the early warning results by the regression curve. To overcome the above limitations, this study develops a data-driven multiobjective evolutionary optimization method that combines an artificial neural network (ANN) and a multiobjective evolutionary optimization implemented by particle swarm optimization (PSO). Firstly, the Pareto optimality method is used to represent the nonlinear and conflicting critical thresholds for the rainfall intensityIand the rainfall durationD.An ANN is used to construct a dual-target (dual-task) predictive surrogate model, and then a PSO-based multiobjective evolutionary optimization algorithm is applied to train the ANN and stochastically search the trained ANN for obtaining the Pareto front of theI-Dsurrogate prediction model, which is intended to overcome the limitations of the existing linear regression-based threshold methods. Finally, a double early warning curve model that can effectively control the false alarm rate and negative alarm rate of hazard warnings are proposed based on the decision space and target space maps. This study provides theoretical guidance for the early warning and forecasting of debris flows and has strong applicability.