With the development of Industry 4.0 and smart manufacturing, improving production automation, intelligence, and digitalization has become a research trend in the Wire Arc Additive Manufacturing (WAAM) field. This study introduces a digital shadow that aims to improve the adaptiveness and dimensionality of monitoring systems in WAAM. Three sensors are used in the digital shadow: a welding electric signal sensor, a camera, and a laser profilometer to collect welding current and voltage data, image data, and point cloud data. The collected multi-scaled data are time and spatially synchronized by sampling multiple points along the welding path. Three ML algorithms are used for decision-making: Multi-layer Perceptron (MLP) classifier and YOLOv5 are used for time and spatial-scale detection, respectively, and a Variational Autoencoder (VAE) is used for the decision-level fusion. The system performance is then tested to detect defects and geometric errors in practical experiments and the res