A Two-Dimensional Cloud Model for Early Warning of Tailings Dam Failure Risk Considering Probability and Consequence Coupling

The accurate assessment of tailings dam operational status and timely risk warnings are critical for ensuring their safe operation. To address the limitations of existing models in managing complex environments and multidimensional risk factors, this study proposes an early warning model for tailings dam operational status based on a two-dimensional cloud model. First, a comprehensive early warning system is developed to assess the probability and consequences of dam failure, using risk probability and consequences as two-dimensional coordinates, incorporating the randomness and fuzziness of uncertainty described by cloud theory, and transforming qualitative data into quantitative conclusions. Next, a genetic algorithm optimizes the projection pursuit model to determine weights, and weighted numerical features are utilized to enhance the classification of early warning levels. Furthermore, the two-dimensional cloud model is enhanced by introducing a proximity coefficient to replace the membership function, with the resulting cloud map visualized using a forward cloud generator. Finally, the early warning level of the tailings dam’s operational status is determined based on the clustering of cloud droplets and the proximity coefficient. Empirical application to five tailings dams in Hubei Province confirms the model’s effectiveness and practicality. The results demonstrate that the model effectively addresses the complexity and uncertainty of tailings dam operational status, delivers accurate warnings, and provides robust decision support for emergency response.