基于MARS与AIC的泥石流冲出距离数据驱动预测方法

A data-driven prediction method of debris flow runout distance based on MARS and AIC

融合多元自适应回归样条(multivariate adaptive regression splines,MARS)模型与赤池信息量准则(Akaike information criterion,AIC),提出准确预测泥石流最大冲出距离的数据驱动法。首先,基于不同输入参数(如泥石流体积、泥石流流域高差等)建立最大冲出距离的MARS预测模型。然后,根据AIC选择最合适的MARS模型及相应的模型参数。最后,采用汶川震区泥石流数据验证了所提方法的有效性,并对比了所提方法与现有经验模型的预测效果。计算结果表明:1)对于汶川震区泥石流,基于不同输入参数预测的泥石流最大冲出距离存在显著差异,基于泥石流体积VD、流域地形高差H和流域面积A构建的最大冲出距离MARS模型的预测效果最好;2)通过与现有经验统计模型对比可知,所提方法能准确预测研究区特大规模泥石流的最大冲出距离,而经验统计方法难以给出准确估计;3)所提泥石流冲出距离数据驱动预测方法的准确性整体优于经验回归模型,能根据勘察数据自适应地选择最合适的MARS模型及相应的模型参数,无需预先假定模型参数与预测模型函数形式,其后向剪枝过程可以避免模型复杂化造成的过拟合,能够给出最合适的冲出距离预测模型的显性表达式;4)如果收集到更多的泥石流勘察数据,可以进一步训练模型选择最合适的MARS模型,从而提高预测精度。

Combining the multivariate adaptive regression splines(MARS)and Akaike information criterion(AIC),this paper proposes a data-driven method to accurately predict the maximum runout distance of debris flow.Firstly,MARS prediction models of maximum runout distance are developed based on different input parameters(e.g.,debris flow volume,debris flow catchment relief,etc.).Then,the most appropriate MARS model and the corresponding input parameters are selected according to AIC.Finally,the effectiveness of the proposed approaches is verified by using debris flow data in Wenchuan earthquake area,and the prediction effect of the proposed method is compared with the existing empirical models.The calculation results show that:1)for debris flow in Wenchuan earthquake area,there are significant differences in the maximum runout distance of debris flow predicted by different input parameters.The MARS model based on debris flow volume VD,watershed elevation difference H and watershed area A has the best prediction effect.2)Compared with the existing empirical statistical models,the proposed method can accurately predict the maximum runout distance of extremely large-scale debris flow in the study area,but the empirical statistical models have lower prediction accuracy.3)The prediction accuracy of the data-driven method proposed in this paper is generally better than that of the empirical regression models,and it can adaptively select the most suitable MARS model and corresponding model parameters according to the survey data,without assumption of the model function form and input parameters.The backward pruning procedure of the MARS model can avoid over-fitting caused by model complexity,and provide the explicit expression of the most appropriate prediction model of the runout distance.4)If more site investigation data of debris flows are collected,the models can be further trained to select the most appropriate MARS model to improve the prediction accuracy.