Objective: Although digital twin technology has matured rapidly, prevailing transportation digital twins remain largely descriptive and reactive, focusing on static model replication and real-time data monitoring while lacking a closed-loop architecture capable of enabling end-to-end autonomous operation across the system's full lifecycle. Critically, current implementations omit persistent memory for experience retention and adaptive learning mechanisms for continuous evolution, leaving them fragile in complex, dynamic, or previously unseen operational contexts. Furthermore, dominant research paradigms optimize isolated components without cross-granularity coordination, thereby failing to realize system-level autonomy. To bridge these critical gaps, this study proposes a foundational design methodology for digital twins of autonomous transportation system (ATS), explicitly engineered to embed cognition, memory, and evolutionary intelligence into the core architecture. Methods: This study proposed a digital twin system design methodology for the autonomous operation of transportation systems by integrating autonomous operational mechanisms and digital twin technology with existing transportation systems, thereby providing support for realizing ATS. First, based on autonomous systems, a "perception, cognition, decision-making, control, execution, memory, and learning" autonomous operational mechanism was proposed to simulate human cognitive processes, which is then integrated into transportation systems to define the concept of ATS. Next, leveraging the concept of digital twin systems, a collaborative architecture comprising the physical, digital, and interactive spaces of transportation systems was constructed, highlighting the importance of digital space design in achieving ATS. To integrate autonomous mechanisms into transportation systems and address their inherent complexity, this study applied the autonomous operational framework to design digital twin systems in the digital space at multiple levels and scales, enabling autonomy. A multilevel architecture encompassing road networks, road segments, and transport equipment was designed to enable coordinated management across macroscopic, mesoscopic, and microscopic granularities. The study integrated multiscale modeling and simulation capabilities across spatial, temporal, data, and logical dimensions, supporting a complete decision-making process from system-level situation awareness to individual vehicle behavior prediction. By leveraging distributed computing across cloud, edge, and end devices, the system achieved distributed deployment and efficient execution of cognitive, decision-making, control, memory, and learning functions, enabling autonomous evolution and learning. Finally, the proposed system was validated through application scenarios including intelligent obstacle avoidance, intersection conflict coordination, and peak-hour route planning. Results: Based on the proposed design methodology for digital twin systems supporting autonomous transportation operations, three representative scenarios were evaluated. In intelligent obstacle avoidance scenarios, after detecting obstacles, vehicles rapidly evaluated multiple avoidance and driving options through coordinated decision-making among vehicle-, road segment-, and road network-level digital twins, generating optimal avoidance strategies, thereby improving decision accuracy and control responsiveness. In intersection scenarios, coordinated signal and vehicle control enabled by digital twins allowed the system to better adapt to changing traffic demands across different time periods, weather conditions, and unexpected events, enhancing both intersection throughput and vehicle efficiency. In peak-hour scenarios, collaborative path planning across these digital twins improved the autonomous operational capability and travel efficiency of transport systems during high-demand periods. Conclusions: The proposed methodology transcends conventional digital twin paradigms by embedding cognitive architecture, long-term memory, and self-improving learning capabilities directly into the system's design. It provides a theoretically grounded framework and an implementation-ready blueprint for building ATS that are not only safe and efficient at runtime but also resilient to uncertainty, capable of lifelong learning, and able to evolve system-level intelligence over time. This study lays essential groundwork for next-generation transportation systems that anticipate, adapt, and autonomously improve.