Fault intensity diagnosis (FID) plays a pivotal role in intelligent manufacturing while neglecting dependencies among target classes hinders its practical deployment. This paper introduces a novel and general framework with deep hierarchical knowledge loss (DHK) to achieve hierarchical consistent representation and prediction. We develop a novel hierarchical tree loss to enable a holistic mapping of same-attribute classes, leveraging tree-based positive and negative hierarchical knowledge constraints. We further design a focal hierarchical tree loss to enhance its extensibility and devise two adaptive weighting schemes based on tree height. In addition, we propose a group tree triplet loss with hierarchical dynamic margin by incorporating hierarchical group concepts and tree distance to model boundary structural knowledge across classes. The joint two losses significantly improve the recognition of subtle faults. Extensive experiments are performed on four real-world datasets from various industrial domains (three cavitation datasets from SAMSON AG and one publicly available dataset) for FID, all showing superior results and outperforming recent state-of-the-art FID methods.