kNN based on probability density for fault detection in multimodal processes

Recently, k-nearest neighbor rules (kNN) have drawn increasing attention for fault detection of multimodal industrial processes. However, the traditional kNN method performs poorly for weak faults in a dense mode when the dispersion degree of each mode is quite different. The reason is that the kNN statistics of weak faults are usually submerged by those of normal data in a mode with a high dispersion degree. To improve the fault detection performance of kNN in this case, this paper proposes a new multimodal fault detection method of kNN based on probability density. The proposed method does not need to consider the different degrees of dispersion between modes and avoids the problem of weak faults in a mode that has a low dispersion degree that is submerged by normal data in a mode with a high dispersion degree. A multimodal numerical example with different dispersion degrees of each mode and an industrial application in a semiconductor manufacturing process are used to verify the effectiveness of the proposed method. The simulation results demonstrate that the proposed method shows better fault detection performance than the kNN, local outlier factor, and weighted difference principal component analysis methods. The kNN method performs poorly for weak faults in a dense mode when the dispersion degree of modes is different. To solve this problem, the paper proposes a multimodal fault detection method of kNN based on probability density (PD-kNN). Use probability density (PD) to determine which mode test data belongs to. Detect the data by using established kNN model based on the training data of corresponding mode. Proposed method does not need to consider different degrees of dispersion between modes.