A new input design method for online active fault diagnosis based on sum-of-ratios optimization

This paper proposes a new input design method for set-based active fault diagnosis (AFD) of discrete-time linear time-invariant (LTI) systems. The principle of set separation tendency-based AFD methods focuses on designing inputs to increase the separation tendency of output sets associated with different system modes and to discriminate inconsistent system modes step by step. Compared to existing works that aim to enlarge the separation tendency of output zonotopes, a new and enhanced characterization of the dispersity of a group of output zonotopes is introduced. Specifically, this dispersity is defined as the sum of ratios of the center distance to the total size of two different zonotopes in each pair, effectively describing the separation tendency of a group of output zonotopes. The objective of enlarging the separation tendency of output zonotopes is to maximize the newly introduced dispersity of output zonotopes at each time instant, achieved by formulating the design of one-step input as a sum-of-ratios problem. After a series of transformations, this problem is effectively solved using the 0$-$1 mixed integer quadratic programming framework. At the end of this paper, a numerical example is provided to illustrate the effectiveness of the proposed method.