This work introduces a multi-output classification (MOC) framework designed for domain adaptation in fault diagnosis, particularly under partially labeled (PL) target domain scenarios and compound fault conditions in rotating machinery. Unlike traditional multi-class classification (MCC) methods that treat each fault combination as a distinct class, the proposed approach independently estimates the severity of each fault type, improving both interpretability and diagnostic accuracy. The model incorporates multi-kernel maximum mean discrepancy (MK-MMD) and entropy minimization (EM) losses to facilitate feature transfer from the source to the target domain. In addition, frequency layer normalization (FLN) is applied to preserve structural properties in the frequency domain, which are strongly influenced by system dynamics and are often stationary with respect to changes in rpm. Evaluations across six domain adaptation cases with PL data demonstrate that MOC outperforms baseline models in macro F1 score. Moreover, MOC consistently achieves better classification performance for individual fault types, and FLN shows superior adaptability compared to other normalization techniques.