A combination weighting method for debris flow risk assessment based on t-distribution and linear programming optimization algorithm

Abstract

Debris flow risk assessment can provide some reference for debris flow prevention and control projects. In risk assessment, researchers often only focus on the impact of objective or subjective indicators. For this purpose, this paper proposed a weight calculation method based on t-distribution and linear programming optimization algorithm (LPOA). Taking 72 mudslides in Beichuan County as an example, this paper used analytic hierarchy process (AHP), entropy weight method (EWM) and variation coefficient method (VCM) to obtain the initial weights. Based on the initial weights, weight intervals with different confidence levels were obtained by t-distribution. Subsequently, the final weights were obtained by LOPA in the 90% confidence interval. Finally, the final weights were used to calculate the risk score for each debris flow, thus delineating the level of risk for each debris flow. The results showed that this paper’s method can avoid overemphasizing the importance of a particular indicator compared to EWM and VCM. In contrast, EWM and VCM ignored the effect of debris flow frequency on debris flow risk. The assessment results showed that the 72 debris flows in Beichuan County were mainly dominated by moderate and light risks. Of these, there were 8 high risk debris flows, 24 medium risk debris flows, and 40 light risk debris flows. The excellent triggering conditions provide favorable conditions for the formation of high-risk debris flows. Slightly and moderate risk debris flows are mainly located on both sides of highways and rivers, still posing a minor threat to Beichuan County. The proposed fusion weighting method effectively avoids the limitations of single weight calculating method. Through comparison and data analysis, the rationality of the proposed method is verified, which can provide some reference for combination weighting method and debris flow risk assessment.