The acceleration response of a servo-hydraulic shaking table to a sinusoidal input motion is inevitably distorted by parasitic harmonic content caused by inherent non-linearities within the system. Herein, an algorithm is developed to characterize these parasitic motions in order to facilitate harmonic cancellation. The proposed algorithm is based on particle swarm optimization (PSO). Optimization is achieved by each particle’s movement, updated by its local best-known position and global best-known position according to a fitness function, which itself is a function of the estimation error between the identified acceleration and the original acceleration response. The estimation scheme is validated by experiments on a servo-hydraulic shaking table and results are compared with a more traditional harmonic analysis.