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

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