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For multimode processes, one generally establishes local monitoring models corresponding to local modes. However, the significant features of previous modes may be catastrophically forgotten when a monitoring model for the current mode is built. It would result in an abrupt performance decrease. It could be an effective manner to make local monitoring model remember the features of previous modes. Choosing the principal component analysis (PCA) as a basic monitoring model, we try to resolve this problem. A modified PCA algorithm is built with continual learning ability for monitoring multimode processes, which adopts elastic weight consolidation (EWC) to overcome catastrophic forgetting of PCA for successive modes. It is called PCA-EWC, where the significant features of previous modes are preserved when a PCA model is established for the current mode. The optimal parameters are acquired by differences of convex functions. Moreover, the proposed PCA-EWC is extended to general multimode processes and the procedure is presented. The computational complexity and key parameters are discussed to further understand the relationship between PCA and the proposed algorithm. Potential limitations and relevant solutions are pointed to understand the algorithm further. Numerical case study and a practical industrial system in China are employed to illustrate the effectiveness of the proposed algorithm.