Substations and transmission lines are inspected by unmanned aerial vehicle (UAV) on a large scale, and the captured images are usually delivered to the cloud to be detected by manual or convolutional neural network (CNN) intelligent algorithms for detecting foreign objects or defects, as these cannot be detected locally online by UAVs at this stage. In this paper, we propose a lightweight model based on improved wavelet scattering deep network, which can realize local online recognition of foreign objects on edge devices. The lightweight model contains an improved wavelet scattering network and a 3- layer small deep network. Among them, the wavelet scattering network is constructed considering the extraction of foreign object features and the computational complexity, using biorthogonal (bior) wavelets basis including bior1.1, bior2.2, and bior1.3 wavelets to construct a 3-layer scattering network and compute the modulus and scattering values of the nodes in each layer, replacing the functions of convolutional and pooling layers in the CNN. The small deep network contains 3 fully connected layers and 2 ReLU activation functions to recognize the extracted features. The experimental results show that the accuracy of this lightweight model is higher than 90% for all kinds of foreign object recognition; the accuracy of recognizing 1280*720 foreign object images on the Orange Pi 5B edge device is 94.9%, which is better than other models, and the processing speed is 149.3 frames per second (FPS), which enables local frame-by-frame online detection when the frame rate of the UAV captured video equal to or less than 60 FPS. The algorithm can also efficiently detect high-resolution images up to 1920*1080 with recognition speed of 67 FPS.