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

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 not only 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 -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. 1. Introduction Fault detection has been one focus of recent efforts since there existed a growing need for the quality monitoring and safe operation in the practical process engineering [1–4]. The objective existences of dynamic change, multiple modes, and nonlinearity pose serious challenges for fault detection proceeding in most of the process engineering, such as semiconduction process [5–8]. Hence, an effective and adaptive fault detection technology is worth investigating in order to deal with these obstacles. Note that nonlinear PCA method [9] dynamic PCA [10] have been reported to be used for tackling dynamic and nonlinear process. Following them, [11] investigated the fault detection for nonlinear systems based on T-S fuzzy-modeling theory. Reference [12] investigated the nonlinear systems modeling and fault detection for electric power systems. However, the aforementioned methods fail to work well for the dynamic systems with nonlinearity together with multiple modes. Recently, [5, 6, 13–15] proposed some detection techniques to jointly address the nonlinear, multimodal, and dynamic behaviors of systems. References [5, 6] applied kNN rule and improved PCA-kNN to fault detection for semiconductor manufactory process with nonlinear and multimode behaviors. Reference [14] proposed an adaptive local model based on the monitoring approach for online monitoring of nonlinear and multiple mode processes with non-Gaussian information. Reference [15]