This study proposes to use the combination of gradient concept to enhance the learning capability of Deep Convolutional Networks (DCN), and four Partial Residual Networks-based (PRN-based) architectures are developed to verify above concept. The purpose of designing PRN is to provide as rich information as possible for each single layer. During the training phase, we propose to propagate gradient combinations rather than feature combinations. PRN can be easily applied in many existing network architectures, such as ResNet, feature pyramid network, etc., and can effectively improve their performance. Nowadays, more advanced DCNs are designed with the hierarchical semantic information of multiple layers, so the model will continue to deepen and expand. Due to the neat design of PRN, it can benefit all models, especially for lightweight models. In the MSCOCO object detection experiments, YOLO-v3-PRN maintains the same accuracy as YOLO-v3 with a 55% reduction of parameters and 35% reduction of computation, while increasing the speed of execution by twice. For lightweight models, YOLO-v3-tiny-PRN maintains the same accuracy under the condition of 37% less parameters and 38% less computation than YOLO-v3-tiny and increases the frame rate by up to 12 fps on the NVIDIA Jetson TX2 platform. The Pelee-PRN is 6.7% mAP@0.5 higher than Pelee, which achieves the state-of-the-art lightweight object detection. The proposed lightweight object detection model has been integrated with technologies such as multi-object tracking and license plate recognition, and it used in a commercial intelligent traffic flow analysis system as its edge computing equipment. There are already three countries and more than ten cities have deployed this technique into their traffic flow analysis systems.