Probabilistic fault diagnosis method based on the combination of nest-loop fisher discriminant analysis and analysis of relative changes

Bias of data location and increase in data variations are two typical disturbances, which in general, simultaneously exist in the fault process. Targeting their different characteristics, a nested-loop fisher discriminant analysis (NeLFDA) algorithm and relative changes (RC) algorithm are effectively combined for analyzing the fault characteristics. First, a prejudgment strategy is developed to evaluate the fault types and determine what changes are covered in the fault process. Two statistical indexes are defined, which conduct Monte Carlo based center fluctuation analysis and dissimilarity analysis respectively. Second, for the fault data containing those two faults simultaneously, a combined NeLFDA-RC algorithm is proposed for fault deviations modeling, which is termed as CNR-FD. Fault directions concerning bias of data location are extracted by the NeLFDA algorithm and then corresponding fault deviations are removed from the fault data. Then RC algorithm is performed on these fault data to extract directions concerning increase of data variations. These fault directions are used as reconstruction models to characterize each fault class. Particularly, the compromise between these two algorithms is determined by the Monte Carlo based center fluctuation analysis. For online applications, a probabilistic fault diagnosis strategy based on Bayes' rule is performed to identify fault cause by discovering the right reconstruction models that can make the reconstructed monitoring statistics have the largest probabilities of belonging to normal condition. The motivation of the proposed algorithm is illustrated by a numerical case and the performance of the reconstruction models and the probabilistic fault diagnosis strategy are illustrated using pre-programmed faults from the Tennessee Eastman benchmark process and the real industrial process data from the cut-made process of cigarettes in some cigarette factory.