Fisher discriminant analysis model and its application for prediction of classification of rockburst in deep-buried long tunnel

A Fisher discriminant analysis （FDA） model for the prediction of classification of rockburst in deep-buried long tunnel was established based on the Fisher discriminant theory and the actual characteristics of the project. First, the major factors of rockburst, such as the maximum tangential stress of the cavern wall σθ, uniaxial compressive strength σc, uniaxial tensile strength or, and the elastic energy index of rock Wet, were taken into account in the analysis. Three factors, Stress coefficient σθ/σc, rock brittleness coefficient σc/σt, and elastic energy index Wet, were defined as the criterion indices for rockburst prediction in the proposed model. After training and testing of 12 sets of measured data, the discriminant functions of FDA were solved, and the ratio of misdiscrimina- tion is zero. Moreover, the proposed model was used to predict rockbursts of Qinling tunnel along Xi＇an-Ankang railway. The results show that three forecast results are identical with the actual situation. Therefore, the prediction accuracy of the FDA model is acceptable.

A novel multimode process monitoring method integrating LCGMM with modified LFDA

Complex processes often work with multiple operation regions, it is critical to develop effective monitoring approaches to ensure the safety of chemical processes. In this work, a discriminant local consistency Gaussian mixture model(DLCGMM) for multimode process monitoring is proposed for multimode process monitoring by integrating LCGMM with modified local Fisher discriminant analysis(MLFDA). Different from Fisher discriminant analysis(FDA) that aims to discover the global optimal discriminant directions, MLFDA is capable of uncovering multimodality and local structure of the data by exploiting the posterior probabilities of observations within clusters calculated from the results of LCGMM. This may enable MLFDA to capture more meaningful discriminant information hidden in the high-dimensional multimode observations comparing to FDA. Contrary to most existing multimode process monitoring approaches, DLCGMM performs LCGMM and MFLDA iteratively, and the optimal subspaces with multi-Gaussianity and the optimal discriminant projection vectors are simultaneously achieved in the framework of supervised and unsupervised learning. Furthermore, monitoring statistics are established on each cluster that represents a specific operation condition and two global Bayesian inference-based fault monitoring indexes are established by combining with all the monitoring results of all clusters. The efficiency and effectiveness of the proposed method are evaluated through UCI datasets, a simulated multimode model and the Tennessee Eastman benchmark process.