Reliable operation and control of battery packs can lead to increasing applications of batteries as energy sources for mobile power systems such as electric/hybrid electric aircraft. If the operation of a battery pack is controlled and monitored thoroughly, the safety in the battery system of an electrified aircraft can be guaranteed. The battery model has many applications in battery management systems such as battery performance analysis and fault detection. To achieve an accurate fault diagnosis for electric aircraft, an intelligent fault detection scheme within an accurate battery cell model is required. In this study, an adaptive lithium-ion battery model is proposed in which models' parameters are estimated by a supervised machine learning paradigm. This adaptive battery model is developed based on a second order equivalent circuit model, which has a good representation of lithium-ion batteries dynamics. Comparative verification experiments show good accuracy and robustness of the machine learning-based parameter estimator lead to an accurate battery model with an average error less than 0.4%. Moreover, to see the effectiveness of this machine learning-based model in fault detection applications, a model-based fault diagnosis scheme is developed. Finally, the analysis of fault diagnosis tests under different test conditions proves that the proposed adaptive battery model can significantly improve the fault diagnosis accuracy of batteries.