In this work, we consider the problem of detecting the phenomenon of brake disc runout, which is usually caused by deformations of the brake disc in passenger vehicles. We introduce a novel measurement system that collects and processes information on the vibration profile of the vehicle, as well as the pressure of the brake fluid. Our novel processing method for the collected signals relies on model-driven adaptive wavelet neural networks. We demonstrate that the proposed signal processing methodology outperforms previous approaches to detect aberrations of the brake disc. In addition, the proposed neural network models are defined by interpretable parameters and have reduced complexity when compared to traditional and similar approaches. These characteristics make the proposed construction suitable for automotive applications.