In order to diagnose faults effectively,capacity dimensions of real signals trispectral diagonal slices, 2 different definitions of 2 1/2 dimension of complex signals are calculated. 2 1/2 dimension spectrum have 16 different definitions, 2 definitions of which contain pre-coupling information or post-coupling information respectively. Corresponding to the different coupling features, their shapes show different self similarity characteristics. Based on the normal signals and fault signals acquired from a pressure relief valve′s vibration,different 2 1/2 dimension spectrum are obtained. Then these slices are used to calculate capacity dimension, and fault diagnosis is carried out on the calculated results. The experiment demonstrates that in fault diagnosis, the self-similarity of 2 1/2 dimension spectrum is more effective than that of real signals trispectral diagonal slices, thus an available method for fault diagnosis is providd.