Detecting construction equipment such as trucks, excavators, and mobile cranes from surveillance cameras is a vital part to provide robust and stable construction safety monitoring. A robust and real-time detection system is the key to success. In this paper, we investigate YOLOv3, a real-time object detector, for detecting common vehicle, i.e., car, bus, and truck as a preliminary study to gain insight on improving construction equipment detection. We prefer YOLOv3 for its superior accelerated inference speed, moderate model size, and efficient performance. Our major findings include (1) pretrained general-purpose YOLOv3 equipment detection model is adequate but often misses equipment at the far-end side of camera view; (2) we choose traffic scenes resembles construction sites, our best YOLOv3 model reaches 65.8% mean average precision (mAP) on test set; (3) YOLOv3-based equipment detection model has difficulty to transfer to novel scenes. When trained on 4 scenes and tested on 3 other scenes, test mAP drops to 31%; (4) Systematic confusion with background results in many vehicle detection false positives. We considerably improve overall detection mAP by learning a graph convolutional network (GCN) model to predict if detections are false positives. This GCN model improves equipment detection mAP from 65.8% to 69.3%.