Different health-monitoring techniques were considered in the literature to enhance the safety and stability of Connected Autonomous Vehicle (CAV) platoons. Mitigating these faults is faster and more reliable if the fault structure is known. In this paper, we propose using transmissibility operators, which are relationships that relate a set of velocities with another in the platoon, to classify the faults. Transmissibility operators were shown to be exceptional in signal estimation. However, it is also shown to be noncausal and thus can only be used offline. To this end, we propose using Data Aggregation (DAgger), an extension to imitation learning, to transfer the classification experience from transmissibility operators to a novice machine learning agent to be used online. The integration of transmissibility-DAgger gives the ability to adapt to new fault classes without the need to re-train the diagnosis model from the beginning. A heterogeneous CAV platoon was modeled with three different faults separately. These faults are actuator disturbances, false data injection attacks, and communication time delays. The classification scheme depends on estimating the faulty signal in the case of each fault class. Next, the measured faulty signal is compared with the three estimations, and the closer fault estimation to the measured one is considered the actual fault on the platoon. The proposed algorithm is then tested on the platoon model and then applied to an experimental setup that consists of three autonomous robots. The proposed results are compared with six different machine learning classification models. The overall classification accuracy achieved was 95.8% for the experiment using the proposed approach.