Multivariate statistics based damage detection algorithms employed in conjunction with novel sensing technologies are attracting more attention for long term Structural Health Monitoring of civil infrastructure. In this study, two practical data driven methods are investigated utilizing strain data captured from a 4-span bridge model by Fiber Bragg Grating (FBG) sensors as part of a bridge health monitoring study. The most common and critical bridge damage scenarios were simulated on the representative bridge model equipped with FBG sensors. A high speed FBG interrogator system is developed by the authors to collect the strain responses under moving vehicle loads using FBG sensors. Two data driven methods, Moving Principal Component Analysis (MPCA) and Moving Cross Correlation Analysis (MCCA), are coded and implemented to handle and process the large amount of data. The efficiency of the SHM system with FBG sensors, MPCA and MCCA methods for detecting and localizing damage is explored with several experiments. Based on the findings presented in this paper, the MPCA and MCCA coupled with FBG sensors can be deemed to deliver promising results to detect both local and global damage implemented on the bridge structure.