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A novel fault detection method is proposed for detection process with nonlinearity and multimodal batches. Calculating the Mahalanobis distance of samples, the data with the similar characteristics are replaced by the mean of them; thus, the number of training data is reduced easily. Moreover, the super ball regions of mean and variance of training data are presented, which notonly retains the statistical properties of original training data but also avoids the reduction of data unlimitedly. To accurately identify faults, two control limits are determined during investigating the distributions of distances and angles between training samples to their nearest neighboring samples in the reduced database; thus, the traditional k-nearest neighbors (only considering distances) fault  detection (FD-kNN) method is developed. Another feature of the proposed detection method is that the control limits vary with updating database such that an adaptive fault detection technique is obtained. Finally, numerical examples and case study are given to illustrate the effectiveness and advantages of the proposed method

Adaptive Fault Detection with Two Time-Varying Control Limits for Nonlinear and Multimodal Processes