Structural health monitoring has been increasingly used due to the advances in sensing technology and data analysis, facilitating the shift from time-based to condition-based maintenance. This work is part of the efforts which have applied structural health monitoring to the Sydney Harbour Bridge – one of Australia’s iconic structures. It combines dimensionality reduction and pattern recognition techniques to accurately and efficiently distinguish faulty components from well-functioning ones. Specifically, random projection is used for dimensionality reduction on the vibration feature data. Then, healthy and damaged patterns of bridge components are learned in the lower dimensional projected space using supervised and unsupervised machine learning methods, namely, support vector machine and one-class support vector machine. The experimental results using data from a laboratory-based building structure and the Sydney Harbour Bridge showed high feasibility of applying machine learning techniques to dimensionality reduction and damage detection in structural health monitoring. Random projection combined with support vector machine significantly reduces the computational time while maintaining the detection accuracy. The proposed method also outperformed popular dimensionality reduction techniques. The computational time of the method using random projection can be more than 200 times faster than that without using dimensionality reduction while still achieving similar detection accuracy.