Structural Health Monitoring (SHM) is a modern approach for structure maintenance that can significantly enhance the safety and lifespan of civil infrastructure by continuously monitoring the condition of structures. The integration of autoencoder, a type of unsupervised learning neural network, into SHM systems offers the potential to significantly improve both the accuracy and efficiency of damage detection. Autoencoder can automatically identify anomalies in complex datasets, which is critical for early and precise detection of structural issues. This paper investigates the application of sparse autoencoder (SAE) for detecting damages of a model steel truss bridge. Acceleration signals are obtained from a high-fidelity finite element model of the bridge, both with and without damage. The performance of SAE in detecting these damages is assessed across different depths and locations, while also considering the effects of white Gaussian noise on detection accuracy. Monte Carlo simulations are used to evaluate the likelihood of correct damage detection, providing insights into the robustness of SAE in practical SHM applications. The findings demonstrate the effectiveness of SAE for damage detection across various damage depths and locations, emphasizing its potential for real-world SHM systems.