A novel nonlinear second-order output spectrum (SOOS) approach for feature characterization and fault detection and location of bolt loosening in a satellite-like structure is proposed in this study using a simple sensor chain. The new method is developed based on a recently developed nonlinear decomposition method using the data measured from a chain of sensors for feature abstraction, together with the properties of transfer ratios of the SOOS of a multi-degree-of-freedom system with nonlinear components developed in this study. The new method is compared with other related vibration-based methods and validated with real experimental results. It is shown that the nonlinear SOOS of the satellite-like structure subject to a harmonic vibration excitation can be calculated efficiently, and it can be effectively and conveniently used as the fault indicator for detection and location of the bolt loosening problem of different severity in this complex structure.