In this work we propose proof-of-concept methods to detect malfunctions of the braking system in passenger vehicles. In particular, we investigate the problem of detecting deformations of the brake disc based on data recorded by acceleration sensors mounted on the suspension of the vehicle. Our core hypothesis is that these signals contain vibrations caused by brake disc deformation. Since faults of this kind are typically monitored by the driver of the vehicle, the development of automatic fault-detection systems becomes more important with the rise of autonomous driving. In addition, the new brake boosters separate the brake pedal from the hydraulic system which results in less significant effects on the brake pedal force. Our paper offers two important contributions. Firstly, we provide a detailed description of our novel measurement scheme, the type and placement of the used sensors, signal acquisition and data characteristics. Then, in the second part of our paper we detail mathematically justified signal representations and different algorithms to distinguish between deformed and normal brake discs. For the proper understanding of the phenomenon, different brake discs were used with measured runout values. Since, in addition to brake disc deformation, the vibrations recorded by our accelerometers are nonlinearly dependent on a number of factors (such as the velocity, suspension, tire pressure, etc.), data-driven models are considered. Through experiments, we show that the proposed methods can be used to recognize faults in the braking system caused by brake disc deformation.