Various monitoring systems have been implemented in civil infrastructure to ensure structural safety and integrity. In long-term monitoring, these systems generate a large amount of data, where anomalies are not unusual and can pose unique challenges for structural health monitoring applications, such as system identification and damage detection. Therefore, developing efficient techniques is quite essential to recognize the anomalies in monitoring data. In this study, several machine learning techniques are explored and implemented to detect and classify various types of data anomalies. A field dataset, which consists of one month long acceleration data obtained from a long-span cable-stayed bridge in China, is employed to examine the machine learning techniques for automated data anomaly detection. These techniques include the statistic-based pattern recognition network, spectrogram-based convolutional neural network, image-based time history convolutional neural network, image-based time-frequency hybrid convolution neural network (GoogLeNet), and proposed ensemble neural network model. The ensemble model deliberately combines different machine learning models to enhance anomaly classification performance. The results show that all these techniques can successfully detect and classify six types of data anomalies (i.e., missing, minor, outlier, square, trend, drift). Moreover, both image-based time history convolutional neural network and GoogLeNet are further investigated for the capability of autonomous online anomaly classification and found to effectively classify anomalies with decent performance. As seen in comparison with accuracy, the proposed ensemble neural network model outperforms the other three machine learning techniques. This study also evaluates the proposed ensemble neural network model to a blind test dataset. As found in the results, this ensemble model is effective for data anomaly detection and applicable for the signal characteristics changing over time.