Fault Diagnosis in Nonlinear Dynamic Systems by Non-Parametric Method

Abstract

The problem of fault diagnosis in technical systems described by nonlinear dynamic models based on non-parametric method is considered. The feature of this method for linear systems is that knowledge of the system parameter values is not required for purpose of diagnosis; it is sufficient to know only the dimensions of input, state, and output vectors of the system. Thus, this method provides active robustness which is concentrated on the stage of residual generation to make the residual insensitive to uncertainties and, simultaneously, sensitive to faults. The objective of the present paper is to extend the known non-parametric method to nonlinear discrete-time systems with non-smooth nonlinearities. A solution is based on so-called logic-dynamic approach using only linear methods to solve the problem for nonlinear systems. To isolate faults, special canonical form of the models which of them is invariant with respect to some fault and sensitive to other ones is used. The redundancy relations based on these models are obtained. The feature of the suggested solution is that to check the redundancy relations, it is necessary to find a kernel of some matrix of functionals which is constructed on-line by processing the system inputs and outputs measured over a finite time window, i.e. without knowledge of all system parameter values. To decrease computational complexity, it is suggested to calculate time window based on the structure of matrices describing each model. For decision making, matrix of syndromes is used. Theoretical results are demonstrated by illustrative and practical examples.