Design of optimal structured residuals from partial 3 principal component models for fault diagnosis in linear systems 4

9 A new method to generate optimal structured residuals from partial principal component models is introduced. The models are 10 selected according to a pre-designed fault-to-residual structure matrix. The structures are so chosen that a certain degree of freedom 11 is left to allow optimization. The performance measure for optimization is the ratio of the fault-gain to the noise standard deviation 12 in the residual; a max–min solution is sought that maximizes the smallest of these measures within a given residual structure. In the 13 special framework of partial PC models, the solution is obtained as a linear combination of the eigenvectors spanning the residual 14 space of the partial model. For the basic case, a two-dimensional residual space, there is a single continuous-valued optimization 15 parameter; with higher dimensional residual spaces the dimension of the optimization problem is growing as well. The new para16 metric optimization is integrated with structural optimization, utilizing earlier results. Also, the basic static algorithm is extended 17 to discrete dynamic systems. In a simulation example, using data from an emulator of the Space-Shuttle main fuel tank, we dem18 onstrated one and two-dimensional searches (two and three-dimensional residual spaces) and compared them to the fixed, maxi19 mum-zero residual design. 2