In hydropower engineering, monitoring the instability of rock slopes is a crucial undertaking. Current early warning models of rock slopes lack consideration of the overall stability and cannot reflect the stability differences of different structure forms. Addressing these issues, we have successfully developed an integrative early warning indicator for the overall stability of rock slopes, utilizing the copula function and the safety stability rate. Initially, we introduce the safety stability rate to quantify the impact of rock structure on stability. Subsequently, the ISSR-MDF model, which integrates the safety stability rate with the marginal distribution function, is proposed. On this basis, we established the early warning indicator using the copula function. The results show that the indicator can reflect the structural characteristics of rock slopes and the trend of changes in multi-point residuals. The early warning model can provide valuable references for the stability assessment of slopes in hydropower engineering.

中文翻译：

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数据驱动的岩质边坡整体稳定性预警指标：以水电工程为例

在水电工程中，岩质边坡的失稳监测是一项至关重要的工作。目前的岩质边坡预警模型缺乏对整体稳定性的考虑，无法反映不同结构形式的稳定性差异。针对这些问题，我们利用copula函数和安全稳定率，成功开发了岩质边坡整体稳定性综合预警指标。首先，我们引入安全稳定率来量化岩石结构对稳定性的影响。随后，提出了将安全稳定率与边际分布函数相结合的ISSR-MDF模型。在此基础上，我们利用Copula函数建立了预警指标。结果表明，该指标能够反映岩质边坡的结构特征和多点残差的变化趋势。该预警模型可为水电工程边坡稳定性评价提供有价值的参考。