Comparison of various linear discriminant analysis techniques for fault diagnosis of Re-usable Launch Vehicle

In this paper, we use Linear Discriminant Analysis (LDA) techniques to diagnose Reaction Control System (RCS) thruster faults in a Re-usable Launch Vehicle (RLV) upon re-enrty. An RCS thruster operates in binary mode i.e. either ON or OFF. A mode is a particular combination of thruster ON/OFF values which is commanded by the controller. Different Linear Discriminant Analysis (LDA) techniques like CLDA (Classical LDA), FSLDA (Foley- Sammon LDA), ULDA (Uncorrelated LDA) are implemented in Matlab and used here to estimate the mode in which the vehicle lies based on the double derivative of pitch, roll and yaw angles. If the estimated mode is not same as the commanded mode then it implies a fault. Misclassification percentage of each of the LDA techniques with respect to percentage of training samples used, number of loading vectors, number of nearest modes and number of instances dropped after a mode change has occurred are evaluated and are compared to decide the one that suits the application. A thorough comparison of the three LDA techniques brings out a contrasting conclusion: unlike reported in LDA literature, CLDA performs better than FSLDA and ULDA for this RCS fault application, though FSLDA and ULDA are advanced variants of the CLDA.