Robust Mahalanobis distance-based lazy learning method for fault detection in high-dimensional processes

When using lazy learners based on the Mahalanobis distance (MD) function for process fault detection (FD), due to the curse of dimensionality, type I errors can increase significantly as the number of process variables increases. In high-dimensional data spaces, certain regions exist in which data samples are sparsely distributed. From the perspective of dense regions, the outlierness (i.e., degree of being statistical outliers) of samples in sparse regions increases as the data dimensions increase, leading to unstable estimations of classical covariance matrices for calculating MD function values. To solve this problem, a lazy learning method is proposed based on a robust MD function, where robust covariance matrices are estimated using a minimum covariance determinant method. Here, k-nearest neighbors and local outlier factor are employed as baseline learners. The proposed method can be applied to all types of lazy learning techniques. To verify FD performance, the proposed method is applied to two benchmark processes. The experimental results show that the proposed method can perform FD on very high-dimensional processes successfully without rapid increases in type I errors.