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A hybrid fault diagnosis method is proposed in this paper which is based on the parity equations and neural networks. Analytical redundancy is employed by using parity equations. Neural networks then are used to maximise the signal- to- noise ratio of the residual and to isolate different faults. Effectiveness of the method is demonstrated by applying it to fault detection and isolation for a hydraulic test rig. Real data simulation shows that the sensitivity of the residual to the faults is maximised, whilst that to the unknown input is minimised. The simulated faults are successfully isolated by a bank of neural nets.