Radar-Informed automated back-analysis of rock fall hazards

岩石崩塌对自然山区的基础设施和生计构成重大威胁，对路边和露天矿的工程斜坡也是如此。对于工程师来说，了解这些崩塌事件的可能性和后果在边坡稳定性设计中是至关重要的。目前最先进的落石模拟软件在考虑局部地形和刚体动力学方面非常复杂，然而工程师们缺乏工具来确定适当的参数来选择他们的分析。雷达追踪器已被成功地应用于记录高时间和空间分辨率的落石事件的运动，这为描述岩质斜坡的现场行为提供了一个很好的机会。可以对数值模型参数进行校准，使模拟的落石轨迹与实测轨迹相匹配，然后将校准后的参数应用于附近地质相似的地区。本提案概述了一种自动而稳健地进行校准的方法，从而使工程师能够在他们的现场更准确地模拟落石危险。该方法被制定为一种优化方法，其中损失函数是建模的弹力点与测量的弹力点之间的总和距离。使用高斯过程来估计目标函数的真实形式，从而使落石模拟器的函数调用次数最少。这还允许我们考虑拟合优度的误差，以便为从业者提供最终解决方案的误差界。

Rock falls pose a significant hazard to infrastructure and livelihood in natural mountainous terrain as well as engineered slopes along roadsides and in open-pit mines. It is of utmost importance for engineers to understand the potential for, and consequences of, these rock fall events in slope stability design. Current state-of-the art rock fall simulation software are highly sophisticated in their consideration of local topography and rigid body dynamics, however engineers lack tools to determine the appropriate parameters to select for their analyses. Radar trackers, which have been successfully deployed to record the motion of rock fall events with high temporal and spatial resolution, present a great opportunity to characterize the in-situ behaviour of rock slopes. The numerical model parameters can be calibrated so that the modelled rock fall trajectory matches the measured trajectory, and the calibrated parameters can then be applied to nearby regions with similar geology. The present proposal outlines a methodology to conduct this calibration automatically and robustly, thereby allowing engineers to model rock fall hazards more accurately at their sites.The methodology is formulated as an optimization where the loss function is the summed distance between the modelled and measured bounce points. A Gaussian Process is employed to estimate the true form of the objective function, which allows us to minimize the number of function calls of the rock fall simulator. This additionally allows us to consider the error of the goodness-of-fit to provide practitioners with error bounds on the final solution.