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In this article, a new data-driven diagnosis method is proposed for mixed eccentricity (ME) in the external rotor permanent magnet motors (ERPMMs). Differently from the previous articles, the proposed method has the advantages of large sample size, high sample diversity, high efficiency, and strong generalization ability. First, the improved parametric analytical model (AM) of back electromotive force (EMF) of the ERPMMs is established. Then, the characteristics of the back EMF are analyzed. Accordingly, its amplitudes of fundamental waves and sideband harmonics are selected as the ME indexes. Afterwards, by using the proposed parametric AM, a database of ME signals is established efficiently, which contains tens of thousands of labeled samples. Furthermore, based on the back propagation neural network, a high-precision diagnosis model for ME in the ERPMM is established. Interference faults, such as unbalanced stator windings and uneven magnetization are also discussed. Finally, an experimental prototype for simulating the ME is manufactured and the effectiveness of the proposed method is verified. The maximum absolute diagnostic error is less than 4.0%. It provides a new idea for multiparameter diagnosis for ME.