Approach to Fault Diagnosis in the Linear Systems by the Non-Parametric Method

Abstract

The topic of the article is the problem of fault diagnosis in the technical systems described by the linear dynamic models based on the non-parametric method. A feature of this method for the linear system models is that for the purpose of diagnosis the knowledge of the system's constant parameters is not required; it is sufficient to know only the dimensions of the input, state, and output vectors of the system. Thus, this method ensures an active robustness, which is concentrated at the stage of the residual generation and makes the residual insensitive to the uncertainties and, simultaneously, sensitive to the faults. The objective of the present paper is to extend the known non-parametric method to the linear discrete-time systems taking into account the specific features of the linear models. In order to isolate the faults, special decomposition and canonical form of each subsystem are used and then the redundancy relations based on these subsystems are obtained. A feature of the proposed solution is that in order to check the redundancy relations it is necessary to find a kernel of some matrix of the functional, which is constructed by on-line processing the system's inputs and outputs measured over a finite time window, i.e. without knowledge of the system's parameters. In order to decrease the computational complexity, it is suggested to calculate the time window on the basis of the structure of the matrices describing each subsystem. For decision making, the matrix of the syndromes is used. The theoretical results are illustrated by practical examples.