The main objective of this research is to diagnose single or multiple bolt loosening for a system exposed to environmental and operational uncertain conditions by implementing both vector auto regressive (VAR) model alone and VAR model coupled with singular value decomposition (SVD), Mahalanobis distance and principal component analysis (PCA). The research has been deployed on a three-storey system constructed with aluminum members in the laboratory medium. The damage simulation scenarios in system have been performed by loosening the frame bolts on each floor which cause the nonlinear effects. The system's ground storey has been excited with an electromagnetic shaker vibrating at band limited random frequencies. Accelerometers are attached to each edge of the floor to acquire the dynamic response of the structure and use their signals for damage diagnosis. The accelerometers' measurements were collected for eight loosening cases. Once these measurements have been processed and evaluated in statistical pattern recognition algorithms, their performance results have been compared and presented via tables and ROC curves. It is obtained from ROC curves that the VAR model coupled with PCA technique has the highest diagnosis performance score in terms of area under curve (AUC) and optimum true positive rate (TPR). The approach it has been followed here demonstrates that the individual sensor that is most affected by the loosening can be identified which could be implemented to detect the bolt loosening.