Statistical learning for cyber physical system

Cyber-Physical Systems represent a critical intersection of physical infrastructure and digital technologies. Ensuring the safety and reliability of these interconnected systems is vital for mitigating risks and enhancing overall system safety. In recent decades, the transportation domain has seen significant adoption of cyber-physical systems, such as automated vehicles. This dissertation will focus on the application of cyber-physical systems in transportation. Statistical learning techniques offer a powerful approach to analyzing complex transportation data, providing insights that enhance safety measures and operational efficiencies. This dissertation underscores the pivotal role of statistical learning in advancing safety within cyber physical transportation systems. By harnessing the power of data-driven insights, predictive modeling, and advanced analytics, this research contributes to the development of smarter, safer, and more resilient transportation systems. Chapter 2 proposes a novel stochastic jump-based model to capture the driving dynamics of safety-critical events. The identification of such events is challenging due to their complex nature and the high frequency kinematic data generated by modern data acquisition systems. This chapter addresses these challenges by developing a model that effectively represents the stochastic nature of driving behaviors and assume the happening of a jump process will lead to safety-critical situations. To tackle the issue of rarity in crash data, Chapter 3 introduces a variational inference of extremes approach based on a generalized additive neural network. This method leverages statistical learning to infer the distribution of extreme events, allowing for better generalization ability to unseen data despite the limited availability of crash events. By focusing on extreme value theory, this chapter enhances statistical learning's ability to predict and understand rare but high-impact events. Chapter 4 shifts focus to the safety validation of cyber-physical transportation systems, requiring a unique approach due to their advanced and complex nature. This chapter proposes a kernel-based method that simultaneously satisfies representativeness and criticality for safety verification. This method ensures that the safety evaluation process covers a wide range of scenarios while focusing on those most likely to lead to critical outcomes. In Chapter 5, a deep generative model is proposed to identify the boundary of safety-critical events. This model uses the encoder component to reduce high-dimensional input data into lower-dimensional latent representations, which are then utilized to generate new driving scenarios and predict their associated risks. The decoder component reconstructs the original high-dimensional case parameters, allowing for a comprehensive understanding of the factors contributing to safety-critical events. The chapter also introduces an adversarial perturbation approach to efficiently determine the boundary of risk, significantly reducing computational time while maintaining precision. Overall, this dissertation demonstrates the potential of using advanced statistical learning methods to enhance the safety and reliability of cyber-physical transportation systems. By developing innovative models and methodologies, this dissertation provides valuable tools and theoretical foundations for risk prediction, safety validation, and proactive management of transportation systems in an increasingly digital and interconnected world.