The invention discloses a method for detecting operation faults of an electro-fused magnesia furnace based on public subspace separation. According to the method, correlation processing is performed on a process variable and a quality variable which are obtained during operation of the electro-fused magnesia furnace by means of kernel partial least squares regression, extraction of public subspace is performed by means of processed quality correlative process data through a local tangent space alignment algorithm, original data space is further divided into quality correlative public subspace and quality correlative special subspace, and a corresponding kernel principal component analysis monitoring model is established. By means of combined monitoring of the quality correlative public subspace shared by a plurality of operation modes of the electro-fused magnesia furnace and the quality correlative special subspace of each operation mode, the false alarm rate of faults is reduced when the operation modes are switched, and sensitivity of fault detection is increased.