Machine degradation is a complex, dynamic and irreversible process and its modeling is a leading-edge technology in prognostics and health management (PHM). In recent years, machine learning algorithms have been widely used to model machine degradation. However, these degradation models are not physically interpreted so that their extended uses are reduced and weakened. Aiming at solving this problem and visualizing informative features learned from degradation data, in this paper, a generalized machine degradation modeling methodology is proposed by integrating multiple-source fusion with genetic programming (GP). A composite fitness function of GP tailored for machine degradation modeling is innovatively designed. Afterward, multiple process sensor data, such as temperature, pressure, currents, etc., and non-process sensor data, such as vibration and acoustic signals, can be respectively modeled and fused into structurally interpreted health indicators from the time domain and the frequency domain. Moreover, the proposed methodology can automatically select informative frequency components and sensors, and provide transparent modeling architecture for early fault detection and subsequent monotonic degradation assessment. Another benefit of the proposed methodology is that complicated data preprocessing and manual feature extraction are not required anymore. Hence, the proposed methodology would have many potential applications and it is easy to implement for online machine degradation modeling. A gearbox run-to-failure dataset (non-process data) and an aircraft engine degradation dataset (process data) are studied to verify the effectiveness of the proposed methodology. Comparisons show that structurally interpreted health indicators constructed from the proposed methodology are superior to state-of-the-art works.