Because of some advantages such as low cost, detachability and reusability, bolted joints are widely applied in various open beam-like engineering structures like steel beams and train rails and closed ring-type engineering structures like steel frames and oil pipelines to keep different structural components together. However, bolted engineering structures often encounter vibration-induced joint faults like self-loosening, crack, leakage and corrosion since they are generally subjected to external dynamic loads caused by vibration environments. Joint damages would seriously affect structures’ reliability and durability, and increase maintenance costs. Therefore, fault detection of bolted engineering structures is very important and necessary. For beam-like and ring-type engineering structures with single excitation and multiple damaged bolted joints, various methods monitoring changes in nonlinear structural features have been developed. To avoid the use of structural features from benchmark structures for reference during the derivation of damage indicators, a novel vibration-based fault detection approach utilizing features from damaged structures only is proposed in this study. In the new method, the dynamic model of bolted engineering structures is simplified as a general MDOF model with nonlinear elements simulating nonlinear bolt loosening faults. By changing the value of related mass, three similar equations from the damaged structure are used to form one matrix, and then the singularity of matrix is used to detect the existence and position of faults. Results from simulations on the beam-like and ring-type models with multiple damages demonstrate that the proposed approach could be an effective tool to estimate the state of bolted engineering structures.