Drone Ground Impact Footprints with Importance Sampling: Estimation and Sensitivity Analysis

Morio, Jérôme; Levasseur, Baptiste; Bertrand, Sylvain · 2021 · OpenAlex-citations

DOI: 10.3390/app11093871

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Summary

This paper addresses the challenge of accurately estimating extreme ground impact footprints for fixed-wing unmanned aerial vehicles (UAVs) following a total loss of control due to main engine failure. The research is motivated by the need for precise probabilistic risk assessments to support regulatory authorization and mission planning. Standard Monte Carlo simulations often underestimate extreme impact zones (e.g., regions containing 95%, 99%, or 99.9% of impacts) due to insufficient sample sizes, leading to either overly conservative restrictions or uncontrolled risks. To resolve this, the authors propose using Multiple Importance Sampling (MIS) to estimate density minimum volume sets, which define these extreme quantiles more accurately than standard methods. The study employs a six-degrees-of-freedom (6DOF) dynamic model to simulate UAV descent trajectories, incorporating full flight mechanics and aerodynamic forces. The simulation assumes zero thrust and stuck control surfaces after failure, with initial conditions derived from a trim algorithm representing steady flight modes. Uncertainties are modeled using experimental data from real flights, specifically fitting a bivariate normal distribution to turn rate and flight path angle deviations, and adding Gaussian noise to control surface deflections. The core methodology involves generating initial samples via standard Monte Carlo simulation, estimating the output density, and then using MIS to target rare events. This process involves resampling from a modified density function focused on low-probability regions and combining these with original samples using weighted multivariate kernel density estimation to compute the threshold for the minimum volume sets. The results demonstrate that MIS significantly improves the accuracy of extreme ground impact footprint estimations compared to standard Monte Carlo approaches. By increasing the frequency of simulated impacts at high distances from the nominal aim without requiring excessive computational budgets, the method provides reliable probability maps for extreme quantiles. The analysis was applied to realistic scenarios, including cases with and without wind, showing that MIS effectively captures the tails of the impact distribution. Additionally, the paper performs a reliability-oriented sensitivity analysis to identify the most influential uncertain parameters affecting ground impact positions, providing insights into which variables contribute most to the dispersion of impact points. The significance of this work lies in its contribution to more robust and less conservative risk assessment frameworks for UAV operations. By enabling accurate computation of extreme fallout zones, the proposed method helps operators and regulators define safety levels at very low probability thresholds, which is critical for high-risk infrastructure. The sensitivity analysis further aids in understanding the dynamics of failure scenarios, allowing for better design and anticipation of hazard zones. This approach offers a computationally efficient alternative to massive Monte Carlo simulations, facilitating the generation of detailed probabilistic maps necessary for safe and feasible UAV mission planning.

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