Fault diagnosis of analog piecewise linear circuits based on homotopy

This paper deals with a verification method of diagnosis of analog piecewise linear circuits based on the homotopy approach. Homotopy maps one function f(x) into another g(x) by changing the homotopic parameter t∈[0, 1]. The homotopic path shows the passing way of some point x₀ from the function domain f(x) to an appropriate point x* of the function g(x). The idea of the method relies on the application of function f(x) to the description of a circuit under diagnosis in the nonfaulty state and of function g(x) to the description of a faulty circuit. The homotopic path is used for monitoring the change of some element parameter p_j from nominal to faulty value. In the presented method, the node homotopic paths are used for verification of fault hypotheses. The assumed hypothesis is true if different node homotopic paths hit the same end point. The essential feature of the method is the small number of hypothesis verifications. This method gives the possibility of fault localization as well as fault identification. The method is illustrated by the example of single-fault diagnosis of a one-stage transistor amplifier.