Fault isolation using analytical redundancy can be traced to aerospace applications , which utilizes information embodied in the mathematical model of the process for fault detection and isolation. An important related activity is due Gertler and coworkers , who try to diagnose faults by designing structured residuals that are insensitive to a particular subset of faults. Qin and Li  proposed an optimal structured residual approach with maximized sensitivity (SRAMS) which makes one structured residual insensitive to one subset faults while with maximized sensitivity to other faults. In our recent work , we analyze the SRAMS approach in detail and propose a new optimal structured residuals (OSR) approach for enhanced fault isolation.
In this work, we extend the OSR approach to multidimensional fault isolation in dynamic systems based on dynamic principal component models. To maximize fault isolation ability, a matrix of optimal structured residuals are designed. Each of them is insensitive to one subset of faults while being most sensitive to one of remaining ones. The maximum of all structured residuals in each row of the structured residual matrix is then selected as the optimal one for fault isolation. Through this approach, optimal structured residual directions with maximum fault isolation ability are obtained. The multidimensional fault isolabilty condition for deterministic and stochastic faults is investigated as well in this work. Simulation studies using data from a MIMO dynamic system and an industrial reactor are given to demonstrate the efficiency of the proposed algorithm.
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