This article presents a novel second-order output spectrum–based method for detecting and localizing multiple bolt loosening faults in complex structures with a sensor chain. This new method is developed based on a recently developed nth-order output spectrum estimation algorithm using only proper data obtained from a chain of sensors. The properties of the second-order output spectrum transmissibility of the sensor chain along physical structures with bolts are studied systematically. In the new method, the noise effect on accuracy of the estimation of fault indicators is investigated as well. The new method also considers more general nonlinear restoring forces not only due to faults but also due to inherent nonlinearity in structure when deriving the properties of the second-order output spectrum transmissibility. Extensive simulation and experimental results demonstrate that the second-order output spectrum of the studied structure can be estimated efficiently, and the second-order output spectrum transmissibility can be used as an effective and reliable damage indicator for the detection and localization of multiple bolt loosening faults in complex bolted structures.
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