Complex Field Fault Modeling-Based Optimal Frequency Selection in Linear Analog Circuit Fault Diagnosis

Owing to the lack of feasible fault modeling method, hard (open and short) faults, and discretized parametric faults are still the mostly used fault models. These models cannot characterize all soft (parameter shifting) faults because that the parameter of analog element be of continuity character. To address this concern, a complex field fault modeling method is presented first. If fault happens to passive element xi in linear analog circuit, the real (U r ) and imaginary (U j ) parts of faulty voltage phasor U°(U°=U r +j U j ) must satisfy binary quadratic function F i (Ur,U j )=0, which is independent from the value of element xi and uniquely determined by its location and the nominal circuit under test. Hence, the binary quadratic function can model any continuous parameter shifting (soft) or hard fault. Second, to avoid calculating the explicit expression of binary quadratic function, a simulation-based method is given to obtain the locus of the change in the function F z in the complex plane. Besides, the nominal (fault-free) point, the loci determined by the binary quadratic functions might intersect with each other. It is referred to as aliasing problem in this paper. This problem can be solved by adjusting the frequency of the input signal. Therefore, a constraint optimization method is proposed to select optimal test frequencies. The proposed test generation and compression methods, when combined with the complex field modeling method, can pinpoint much more fault components with less test points and frequencies when compared with the other methods.