Expandable Diffusion Map–Based Weighted <i>k</i>‐Nearest Neighbor Technique for Multimode Batch Process Monitoring

ABSTRACT The diffusion map–based k ‐nearest neighbor (DM‐kNN) rule faces two challenges in multimode batch process monitoring. Firstly, the DM method encounters difficulties in projecting new samples. The training samples are repeatedly feature extracted, resulting in a time‐consuming process. Faulty samples may be merged into normal samples and modeled together, which does not meet the requirements for fault detection. Secondly, DM‐kNN has poor monitoring performance for multimode processes with significant variance differences. This paper proposes a technique called the expandable DM–based weighted k ‐nearest neighbor (EDM‐WkNN) to solve these two issues. The expandable DM constructs a local projection matrix to attain the projecting of new samples. The effect of mode variance differences is eliminated by introducing weighted distances in statistic to overcome the difficulties caused by variance differences. We compare EDM‐WkNN with classical fault detection methods through numerical examples and the fed‐batch fermentation penicillin (FBFP) process. Our experiments confirm that the EDM‐WkNN method effectively monitors faults in multimode batch processes.