A generic framework is proposed for fault detection and recovery (FDR) in automated driving systems (ADSs) with inertial sensors, which is based on multitask one-dimensional convolutional neural networks (MONN). FDR plays an important role for safe and robust vehicle controls in driver-assistance and ADSs. Although model-based fault detection and recovery methods are well established in the literature, they need accurate model description and are often designed under ideal conditions. Data-driven fault diagnosis, however, might overlook apparent physical relations among sensors. In order to take advantage of both approaches, dynamic relations among measured physical quantities and temporal finite differences are introduced in a MONN as additional features. The proposed algorithm achieved more reliable performance and outperformed considered state-of-the-art methods under various testing conditions. Extensive experiments were conducted to empirically show the effectiveness of the proposed generic FDR framework.