A Bayesian Optimization Method for Finding the Worst-Case Scenarios of Autonomous Vehicles

Scenario-based testing has become a crucial method for certifying the safety of autonomous vehicles amidst the rapid advancement of autonomous driving technology. The exploration of worst-case scenarios, which plays a vital role in safety assessments and accelerated improvements of autonomous driving systems, has posed challenges due to the high dimensionality of parameters and the uncertainty of the decisions of autonomous driving systems. To address these challenges, a Bayesian optimization framework was proposed herein as a solution. Surrogate models, including two Gaussian process-based and five non-Gaussian process-based models, are employed to replace part of the costly simulation models, to overcome the challenge of high dimensionality. The Jackknife and Bootstrap methods are used to estimate variance and calculate the acquisition function. Additionally, a differential evolutionary algorithm is employed to achieve efficient solutions while balancing exploration and exploitation, to overcome the challenge of output uncertainty. The proposed framework is validated through experimental results. It successfully identifies the worst-case scenarios in all three cases and the average number of tests for the optimal model in the most complex 9-dimensional scenario is less than 400. Notably, the approach using the Random Forest (RF) surrogate model achieves the highest search success rate in all three cases.