Over the last few years, digital twins (DTs) are attracting growing attention and uptake in both industry and academia. While several definitions exist for a DT, most definitions of DTs focus on having an exact virtual replica (often called the virtual entity (VE)) of a real-world object or process, which typically consists of several models interacting with each other. Furthermore, due to the connection and synchronization with their real-world physical counterpart, DTs evolve continuously across their lifecycle. Often, however, details of construction and internal structure of DTs are left un- or underspecified. Over time, both these factors (un(der)specification and real-time changes due to synchronization) might lead to misuse, undesirable behavior, or runtime issues, like errors, and performance problems. This hinders the (re)use of DTs and/or its components for the intended purpose or any other future purposes. In this paper, we propose a new approach that helps to overcome the above sketched issues. We do so, in a case-driven way, by addressing a DT of an autonomously driving truck, developed by several researchers over a longer period of time, and with input of several MSc and PhD students. As it turns out, this DT lacks overall complete documentation. We demonstrate how logging can be used to learn about the actual observed runtime behavior of a DT and show how this behavior can differ from its intended behavior at design stage. We explore the different passive model learning techniques, such as Regular positive negative inference (RPNI), Flexfringe and Process mining, in order to (semi-)automate the process of obtaining behavioral models of DT. In addition, we showcase how the learned behavioral model of the DT, can be analyzed further to detect underlying causes of perceived runtime issues in DTs.