Abstract
This paper considers a fault diagnosis problem of linear systems and derives a fault diagnosis algorithm.
The motivation of this paper is as follows. Fault diagnosis methods are divided into two main classes, analytical method (which uses mathematical models of the system), and konw ledge-based method. This paper considers the problem after analytical method, because it will offer an efficient computerized automatic diagnosis technique if some difficulties which it has so far are settled. These difficulties are:
1) it requires highly nonlinear calculation if we exploit, for example, parameter identification method; and
2) it lacks a computer-oriented algorithm. To cope with these difficulties the algorithm presented here has two marked features:
1) it is based on linear algebraic consideration; and
2) graphical techniques are adoptable in part by introducing the system representation graph.
The former serves a simple calculation method, and the latter serves to introduce graphical algorithm techniques.
This paper considers the problem in the following manner. Firstly, it is shown that the observation vector lies in the subspace corresponding to the fault when the system is malfunctioning. Then this fact is used to distinguish faults under a certain condition which is made clear in this paper. Based upon these considerations, a fault diagnosis algorithm is proposed, and it is proved that the algorithm is justifiable. Finally, the algorithm is applied to a linear steady system to show
1) that a part of algorithm is replaced by a graphical algorithm which explains the relation between the fault diagnosibility and the system structure; and
2) that the quantities and the calculations in the algorithm are clarified through the concrete representation of the algorithm.
